Ancient Music Adapted to Modern Practice 9780300146226

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Music Theory Translation Series CLAUDE V. PALISCA, EDITOR

OTHER PUBLISHED VOLUMES IN THE MUSIC THEORY TRANSLATION SERIES:

The Practical Harmonist at the Harpsichord By Francesco Gasparini, translated by Frank S. Stillings, edited by David L. Burrows. The Art of Counterpoint, Part Three of Le Istitutioni harmoniche By Gioseffo Zarlino, translated by Guy A. Marco and Claude V. Palisca. Hucbald, Guido, and John on Music: Three Medieval Treatises Translated by Warren Babb, edited with introductions by Claude V. Palisca. The Art of Strict Musical Composition By Johann Philipp Kirnberger, translated by David Beach and Jurgen Thym. Introductory Essay on Composition By Heinrich Christoph Koch, translated by Nancy Kovaleff Baker. On Music, in Three Books ByAristides Quintilianus, translated with introduction, commentary, and annotations by Thomas J. Mathiesen. On the Modes, Part Four of Le istitutioni harmoniche By Gioseffo Zarlino, translated by Vered Cohen, edited with an introduction by Claude V. Palisca. The Florentine Camerata: Documentary Studies and Translations By Claude V. Palisca. Fundamentals of Music By Anicius Manlius Severinus Boethius, translated with introduction and notes by Calvin M. Bower. Musical Poetics By Joachim Burmeister, translated with introduction and notes by Benito V. Rivera. The Theory of Music By Franchino Gaffurio, translated with introduction and notes by Walter Kurt Kreyszig. Musica enchiriadis and Scolica enchiriadis Translated with introduction and notes by Raymond Erickson.

Ancient Music Adapted to Modern Practice NICOLA VICENTINO

Translated, with Introduction and Notes, by Maria Rika Maniates

Edited by

Claude V. Palisca

Yale University Press New Haven and London

For Timothy

aiev apiarevsiv KOI vneipo%ov s^svai aMcov. —Homer, Iliad, 6.208 The preparation of this work was made possible in part by a grant from the National Endowment for the Humanities, an independent federal agency. Copyright © 1996 by Yale University. All rights reserved. This book may not be reproduced, in whole or in part, including illustrations, in any form (beyond that copying permitted by Sections 107 and 108 of the U.S. Copyright Law and except by reviewers for the public press), without written permission from the publishers. Set in Garamond and Coda Petrucci™ types by Igor and Linda Popovic. Printed in the United States of America by BookCrafters, Inc. Chelsea, Michigan. Library of Congress Cataloging-in-Publication Data Vicentino, Nicola, 1511-ca. 1576. [Antica musica ridotta alia moderna prattica. English] Ancient music adapted to modern practice / Nicola Vicentino; translated with introduction and notes by Maria Rika Maniates; edited by Claude V. Palisca. p. cm. — (Music translation series) Includes bibliographical references (p. ) and index. ISBN 0-300-06601-5 (alk. paper) 1. Music—Theory—16th century. 2. Musical intervals and scales—Early works to 1800. 3. Archicembalo. I. Maniates, Maria Rika, 1937- . II. Palisca, Claude V. III. Title. IV. Series. MT5.5.V5313 1996 780.1—dc20 95_49843 CIP MN A catalogue record for this book is available from the British Library. The paper in this book meets the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources. 10 9 8 7 6 5 4 3 2 1

Contents Foreword by the Series Editor Translator's Acknowledgments

vii ix

Introduction

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Errata in the Musical Examples

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Ancient Music Adapted to Modern Practice [Preface] Book on Music Theory Book I on Music Practice Book II on Music Practice Book III on Music Practice Book IV on Music Practice Book V on Music Practice About the Instrument Called the Archicembalo Appendix I: Vicentino's Petition to Venice for a Printing Privilege Appendix II: Diagram of the Keys in One Octave on the Archicembalo Appendix III: Chart of the Steps from the Comma to the Proximate Major Third Appendix IV: Copy of the Original Warrant Made on the Debate Appendix V: Table of the Names of the Keys on the Archicembalo in Descending Order Appendix VI: Table of String Lengths Based on Lemme Rossi Appendix VII: Table of Cents Values for the First Tuning System of the Archicembalo Appendix VIII: Table of Cents Values for the Second Tuning System on the Archicembalo Appendix IX: Table of the Major and Minor Triads in the Second Tuning of the Archicembalo Bibliography Index

3 6 21 86 136 229 315

445 446 447 448 450 451 452 453 454 457 475

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Foreword by the Series Editor

Vicentino's L'antica musica ridotta alia moderna prattica is one of the most famous books in the history of music theory and one of the least read. When the International Musicological Society began its series Documenta musicologica, Uantica musica was among the first treatises issued in facsimile by Barenreiter-Verlag in 1959. The original is relatively rare. At the last count forty-three copies of the 1555 printing have survived in public libraries, only six of them in the United States. Thanks to the facsimile, however, Vicentino is cited frequently in the literature. The book holds a unique place in mid-sixteenth-century music. Unlike most early theorists, Vicentino did not simply synthesize and transmit the practice of his time. He aimed to change how composers wrote and how musicians thought about music. While Gioseffo Zarlino's Le Istitutioni harmoniche of 1558 stood for the status quo, Vicentino led the avant garde. His best-known contribution is, to be sure, the adaptation of the ancient Greek chromatic and enharmonic genera to modern polyphonic practice. But he also campaigned for a closer rapport between music and the subject matter and feelings of the texts composers set, both sacred and poetic. He challenged the view that part-writing always had to conform to the rules of counterpoint, which had reached ultimate refinement. He admitted exceptions for the sake of expressing the feelings of a verbal text. In this he anticipated the manifestos of Vincenzo Galilei and Claudio Monteverdi. Like Zarlino, two of whose books were published in our Music Theory Translation Series, Nicola Vicentino was a composer, choir director, and teacher. Unlike Zarlino, he never obtained an important post as a conductor or singer. This may explain his tireless campaign to promote himself, his theories, and his special kind of music. Although not educated in Greek or ancient literature, he probably did more for the cause of reviving an ancient Greek musical practice than any of the m'ore learned humanists. He was convinced—and persuaded many around him—that one path to the recovery of the legendary power that music had in antiquity was through the revival of the ancient chromatic and enharmonic genera. In the book translated here, Vicentino set out to adapt these genera to the polyphonic music practiced in the mid-sixteenth century. The special VIiI

Vlll

harpsichord and organ he designed helped to propagate these non-diatonic scales, until then little used. Besides Vicentino himself, Luzzasco Luzzasch and Carlo Gesualdo, his colleagues in Ferrara, experimented with the chromatic-enharmonic instruments, which helped them master resources that changed the music of their time. Echoes of this music may be heard in that of Orlando di Lasso, Luca Marenzio, and numerous others. Maria Rika Maniates has been associated with Vicentino for a long time. Her first article on Vicentino appeared in the Journal of the American Musicological Society in 1975, and he is a central figure in her book Mannerism in Italian Musical Culture, 1530-1630 (1979). She has converted Vicentino's convoluted prose into plain modern English without blunting the vigor or vitiating the complexity of his thought. Only small parts of L'antica musica have been previously published in translation into any language. The obscurity of the original Italian and the inscrutability of its musical examples, using new symbols that Vicentino invented to notate his chromatic and enharmonic music, have been obstacles to editors and translators. Maniates and our computerautographer—who is also a music theorist—Igor Popovic, have worked out a system for representing and electronically printing the notation. Their success in making this work accessible will permit a wider understanding of Vicentino's theories. The preparation and publication of this work could not have been realized without the assistance from the National Endowment for the Humanities, to which we are ever grateful. CLAUDE V. PALISCA

Translator's Acknowledgments

Work on this book was supported by different grants at different stages. I am extremely grateful for the generosity of the institutions named here: the National Endowment for the Humanities of the United States of America; the Social Sciences and Humanities Research Council of Canada (SSHRC); and the Connaught Committee, the Humanities and Social Science Committee of the Research Board, and the School of Graduate Studies, all of the University of Toronto. Funding from these agencies allowed me to take two research leaves, one in 1982-83 as Connaught Senior Fellow and one in 1985-86 on a SSHRC leave grant. It also made possible the research assistance of two doctoral students in musicology, Terry Brown and Brian Power, who were meticulous in the performance of their duties; the encoding of the first draft on computer by William Bowen, who was intrepid in deciphering my manuscript; the music autography and encoding of the camera-ready copy by Igor Popovic, who remained tranquil when dealing with the complexities of Vicentino's text; and last, yet first, the editorial stewardship of Claude Palisca. Acknowledgements are due to the graduate students of two seminars who worked with the translation: Larry Beckwith, Alison Bell, Durrell Bowman, Terry Brown, Stephanie Conn, Kara Elash, Maureen Epp, Michelle Garon, Rebecca Green, Mark Kerr, and Brian Power. I am greatly indebted to colleagues whose advice on matters related to their expertise helped to make rough places plain: Richard Agee on Venetian printing privileges; William Bowen on mathematics and harmonic science; the late Henry Kaufmann on the archicembalo and the genera; Art Levine on solmization; Johannes Seeker on sixteenth-century keyboard instruments and their tuning; Alexander Silbiger on enharmonic compositions; and Diane Ota on the measurements in the drawings of the archicembalo. Claude Paliscas expertise is catholic in range and depth. I thank him for his unflagging support, his wise counsel, and his many cogent suggestions, large and small, as this project evolved to a state of readiness for publication. Special thanks go to the staff of Yale University Press, especially to Susan Laity for her careful editing and to Harry Haskell for his support and advice.

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INTRODUCTION. Nicola Vicentino dei Vicentini was born in Vicenza in 1511 and died around 1576-77 in Milan. His name and birthplace are recorded in a document concerning his appointment as chapel master in Vicenza in 1563.1 His date of birth can be assumed from two references in his treatise Ancient Music Adapted to Modern Practice (Rome, 1555): the woodcut giving his age as forty-four and his assertion that he was thirty-nine in 1550. The year of his death, shortly after the plague that ravaged northern Italy in 1575 and again in 1576, is given by Ercole Bottrigari in // Desiderio (Venice, 1599).2 Vicentino studied in Venice under Adrian Willaert sometime during the 1530s. His first book of five-voice madrigals (Venice, 1546) proudly announces his indebtedness to his "unique" and "divine" master.3 Given the unexceptional music in this collection, Vicentino's comments about his new or rediscovered styles of composing, allegedly influenced by Willaert, amount to little more than the customary platitudes. Vicentino styled himself "Don" on the title-page, indicating that he should be considered a distinguished priest. Several other documents corroborate his vocation.4 Possibly this title of respect was accorded to Vicentino when he entered the service of Ippolito II d'Este, cardinal of Ferrara. Just as we cannot ascertain when Vicentino began and ended his studies with Willaert, so we cannot say when he joined and quit the retinue of the cardinal. It is possible, however, to suggest some reasonable hypotheses. For the years of study under Willaert, the mid- to late 1530s are plausible. The somewhat younger Gioseffo Zarlino began his studies under Willaert at the age of twenty-four in 1541. Vicentino was 1. Giovanni Mantese, Storia musicale vicentina (Vicenza, 1956), p. 47, note 36, and Henry W. Kaufmann, The Life and Works of Nicola Vicentino (American Institute of Musicology, 1966), p. 16, note 8. An advertisement of the arciorgano gives a similar form of his name. [Descrizione deWarciorgano] (Venice, 1561), section 1. Kaufmann, Life and Works, facing p. 172. For a description of this broadsheet, see note 41, below. A letter dated 1570 implies that Vicentino was then fifty-nine years of age (see note 44, below). 2. The circumstances of Vicentino s death are given by Bottrigari in the text and marginalia on p. 41 (MacClintock translation, [American Institute of Musicology, 1962], p. 52). 3. Emil Vogel, Alfred Einstein, Francois Lesure, and Claudio Sartori, eds., Bibliografia delta musica italiana vocale e profana pubblicata dal 1500 al 1700 (Pomezia, 1977). 4. The Vicentine record of 1563 lists him as clericus, and Ghiselin Danckerts calls Vicentino capellano to the cardinal of Ferrara in his Sopra una differentia musicale (Rome: Biblioteca Vallicelliana, Ms. R 56A, no. 15b (ca. 1555-56) Bk. I, chaps. 1 and 2. For more information on this manuscript, see note 9, below. Another set of documents (Venice, 1549) alludes to Vicentino as the Reverend Father Nicola (see App. I).

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twenty-three in 1534 when, he claimed, he began research into the theory and practice of ancient Greek music. In order to understand Vicentino's association with the cardinal of Ferrara, we should review briefly the career of this prince of the church.5 According to the custom of the day, Ippolito II, the second son of Duke Alfonso I and Lucrezia Borgia, was destined to serve the church, and his elder brother, Ercole II, inherited the duchy of Ferrara. Ippolito was named archbishop of Milan at the age of ten and succeeded to the see a year later upon the sudden death of the incumbent, his uncle Ippolito I.6 In 1538 Ippolito II was sent by his brother, now the duke, to France to gather support for the Estense claim to the duchy of Milan after the death of Duke Francesco II Sforza in 1535.7 Nothing came of these intrigues except that Franfois I persuaded Pope Paul III to name Ippolito, now royal counselor to the house of Valois, a cardinal in pectore. When the duke of Ferrara signed a peace treaty with the pope in 1539, Ippolito's status was announced in a public consistory in March of the same year. He arrived in Ferrara on 6 August 1539 and, after appropriate celebrations, went on to Rome on 18 October to receive his red hat from the pope. These events mark the start of the cardinal's lavish public career. Ippolito II began to gather a retinue of Italian men of letters, artists, and musicians in the late 1530s and early 1540s.8 Perhaps this is when he heard about Nicola Vicentino, the priest who claimed that with proper support and encouragement he could revive the fabled secrets of ancient Greek music. Although the exact timing of Vicentino's enlistment in the cardinal's service is not known, the early to mid-1540s are probable years. Several documents indicate that Vicentino was with the cardinal in Rome 5. After 1561 it was customary to call Ippolito II "cardinal of Ferrara" to distinguish him from his nephew Luigi d'Este, known as Cardinal d'Este. Luigi s elevation to the cardinalate in 1561 was arranged by his uncle with Pope Pius IV, who needed Ippolito s services at the time. Like his uncle, Luigi Cardinal d'Este was a cultivated man; he patronized Torquato Tasso between 1565 and 1572, before Tasso was appointed court poet by Duke Alfonso II, Luigi s elder brother. 6. Lodovico Ariosto dedicated an early version of Orlando furioso (1516) to Ippolito I d'Este, his patron until 1517. The young Adrian Willaert also worked for Ippolito I at around the same time. 7. The ties between the Estensi and the French royal family were close. Duke Ercole's wife was Princess Rene'e of France. 8. Among those who enjoyed the cardinal s patronage were Celio Calcagnini, humanist writer, professor of Greek and Latin, and co-founder of the Accademia degli Elevati in Ferrara; Marc-Antoine Muret, humanist, poet, and commentator; Pirro Ligorio, antiquarian and architect, designer of the Casino, a retreat in the gardens of the Vatican, for Pope Pius IV, as well as of the Villa d'Este for the cardinal; Pierre Sandrin, choir master at the cardinal's court between 1552 and 1561; and the composer Giovanni Pierluigi da Palestrina.

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in the fall of 1549, the year Ippolito replaced Jean Cardinal du Bellay as the official envoy of the king of France to the Holy See. On 10 November 1549 Pope Paul III died. During the ensuing threemonth conclave Ippolito II made a strong bid for the papal tiara. He failed because the pro-French electors were outnumbered by a coalition of reformers and pro-Imperial electors. Pope Julius III emerged as a compromise candidate on 8 February 1550 and pacified Ippolito with a gift, the governorship of Tivoli. There the cardinal passed many summers at the sumptuous Villa d'Este. In 1551, in spite of Ercole's attempt to remain neutral, the Este family was embroiled in Italian territorial wars. Spanish and Florentine forces besieged Siena, a strategic city under French protection. Because Henri II of France considered the Sienese an unruly and duplicitous lot, he found it necessary to appoint a series of lieutenants-governor in an effort to hold on to the city. One of these was Ippolito, who tried to defend Siena in the French king's name from 1 November 1552 to 5 June 1554. Vicentino went to Siena with his patron, and he later used the stay in this city to excuse the delayed publication of his treatise. After Ippolito's discharge, the cardinal returned first to Ferrara and then to Rome. On 13 March 1555 Pope Julius III died. In the short conclave that followed, the pro-French faction once again tried to have Ippolito II elected, and the pro-Imperial faction once again opposed him. A reform-minded group backed the eventual winner, Marcellus II, whose pontificate lasted barely a month (9 April-1 May). Ippolito seems not to have made a bid for the papacy at the next conclave, at which the severe and ascetic Pope Paul IV was elected. During Paul's pontificate, the cardinal of Ferrara kept a low profile. But when Paul IV died on 18 August 1559, a four-month conclave once more thrust the cardinal into prominence as the pro-French candidate. He was blocked, as usual, by the proImperial faction. A third group organized the election of Pope Pius IV on 25 December. While Ippolito was sequestered in conclave, Duke Ercole II died. Ippolito devoted the early part of 1560 to the festivities and practicalities of crowning a new duke of Ferrara, his nephew Alfonso II d'Este. Unlike Paul IV, the affable Pius IV liked the cardinal of Ferrara and decided to put to use Ippolito's diplomatic expertise and intimate knowledge of the French court. The upsurge of Calvinism in France was particularly troubling to the papacy at this time, when the Council of Trent was being reconvened. To settle the religious turmoil, the pope in 1561 appointed Ippolito confidential envoy to the court of the queen mother, Catherine de Medicis. The cardinal went to Ferrara on 22 July,

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and he left Italy on 7 August 1561 with a large entourage that included Jacopo Laynez, general of the Jesuits and chief theologian of the Council of Trent. Ippolito did not return to Italy until 1563. The period 1564-65 was spent mainly in Rome. In 1566 Duke Alfonso II went to fight the Turks in Hungary and named his uncle governor of the Ferrarese duchy in his absence. The remaining years of Ippolito's life were uneventful, as he gravitated to the peripheries of secular and religious politics. He continued to enjoy his leisure at the Villa d'Este, where he died on 2 December 1572. He was buried at the Church of San Francesco in Tivoli. The evidence shows that, especially from 1549 to 1563, the cardinal of Ferrara was an important figure not only on the French and Italian political scene but also at the papal court. He undertook diplomatic and military commissions in Italy and France on behalf of both religious and secular authorities. He was papabile no fewer than three times. Retainers of prominent persons have been known to assume postures they consider commensurate with the exalted rank and destiny of their patrons. Thus, some of the high drama described by participants in the musical events between 1549 and 1555 can be ascribed to Ippolito's pride—and to Vicentino's. The first document linking Vicentino to the cardinal of Ferrara is an unpublished treatise by the musician and theorist Ghiselin Danckerts. The manuscript exists in three versions: the first draft was written sometime in or shortly after June 1551, the second after May 1555 (two copies), and the third around 1559-60.9 Danckerts, a member of the Sistine Chapel since 1538,10 was elected one of two judges on 2 June 1551 to preside over a public debate on the ancient musical genera between Don 9. Sopra una differentia musicale (Rome: Biblioteca Vallicelliana, Ms. R 56A), nos. 15a, 15b, and 33, respectively. The first two are autographs: no. 15a is a rough draft dated "in questo anno 1551"; no. 15b, the only version to contain copies of the documents on the debate, must have been written after Vicentino's treatise appeared on 22 May 1555 because Danckerts makes insulting remarks about Vicentino's copies of the documents. This version exists in another copy, Ms. R 56B, which opens with a letter "To the Readers" ("UAutore alii Lettori,"in Maria Augusta Alves Barbosa, Vincentivs Lvsitanvs: Ein portugiesischer Komponist und Musiktheoretiker des 16. Jahrhunderts [Lisbon, 1977], pp. 187-89). The third, no. 33 (ca. 1559-60), is a revised clean copy by another hand; less virulent and more erudite in tone, it was probably intended for publication. Unless otherwise indicated, all subsequent references are to no. 15b. 10. Danckerts was dismissed in 1565 during the post-tridentine reform of the papal choir. Of him the record states: "He has no voice, is exceedingly rich, given to women, useless." Lewis Lockwood, "Danckerts, Ghiselin." The New Grove Dictionary of Music and Musicians (London and New York, 1980), 5: 220.

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Vicente Lusitano and Vicentino.11 Vicentino lost the debate. From what Danckerts and Vicentino wrote about the aftermath, it seems that the cardinal and his chaplain were upset and outspoken about the unfavorable verdict.12 For this reason Danckerts hastened to defend his opinion in writing soon after the debate (first version of 1551). He set this matter aside until Vicentino published his treatise (which contained his side of the story), then made extensive revisions of the first draft, adding personal invective and malicious gossip, as well as his own version of the events and the documents they engendered. These circumstances warn us that Danckerts is no more trustworthy a source of information than Vicentino. In the second version Danckerts slyly recounts an episode designed to depict Vicentino as a charlatan who inveigled the gullible.13 Apparently, in the fall of 1549 some retainers of Niccol6 Cardinal Ridolfi14 approached Vicentino with a request that he teach them to sing his "new" chromatic and enharmonic music. He refused, it was reported, because he sought the proper reward for his fifteen years of hard work (a job in the papal choir, surmised Danckerts)15 and also because he feared that the fruits of his labors would be stolen. The singers must have persevered, however, for a notarized contract was drawn up on 25 October 1549 by Felice de Romaulis, notary of the Apostolic Chapel.16 The contract stipulated that Vicentino would instruct five or six singers, provided that, on penalty of the considerable sum of 200 to 300 scudi,17 no one would reveal the secret of the genera for a period of ten years. No one was tempted to 11. The other judge was Bartolome' de Escobedo. Lusitano, a Portuguese theorist and composer, may have been a singer in the papal choir. He became a Protestant around 1561 and left Rome for Strassbourg. 12. Danckerts, Sopra una differentia* Bk. I, preface; Ms. R 56B, "To the Readers" (see note 9, above); and Vicentino, Lantica musica, Bk. IV, chap. 43. 13. Sopra una differentia, Bk. I, preface. 14. Niccol6 Ridolfi, nephew of the sister of Pope Leo X, was made a cardinal in 1517. He was bishop of Vicenza and Urbino and archbishop of Florence. 15. This statement places the beginning of Vicentino s studies in 1534, when he was twenty-three years old. As will be seen shortly, it is an accurate report. 16. Felice de Romaulis, a highly respected notary in Rome, opened an independent practice in 1552, the date of his first business register. 17. It is difficult to ascertain the buying power of sixteenth-century currency. A few relative statistics, however, indicate that the penalty was severe. The Roman scudo in 1551 was worth slightly more than the Florentine scudo and the Venetian ducat. The latter coins were equivalent to seven lire (20 soldi made up one lira, and 12 denari made up a soldo) whereas the Roman scudo was equivalent to 7.5 lire (seven lire, ten soldi). A skilled craftsman in Venice could make up to 20 soldi a day, a less skilled one about 10 soldi. In the early sixteenth century, the complete maintenance of a schoolboy cost on average 15 scudi a year.

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breach the contract because, according to Danckerts, the secret proved worthless. However low Danckerts' assessment of Vicentino's secret may have been, there can be no doubt as to its value for Vicentino. Moreover, Vicentino's fear of intellectual espionage was not entirely unfounded. Such things did happen—as in the scandalous case of Niccolo Tartaglia and Girolamo Cardano.18 Tartaglia had become famous after winning a public challenge in algebra in 1535. He refused to divulge his weapon— a solution to cubic equations—in order to use it to make money by tak ing on all comers in open mathematical combat. Through persistent flattery and vows of silence, Cardano wormed the secret out of him and then published it in theArs magna (Nuremberg, 1545), giving due credit to Tartaglia. Tartaglia was furious. He resorted to such vile slander that he lost the respect of the scientific community, even though he was the injured party. But Cardano's story, like Vicentino's, is an instance of human frailty, not quackery. In view of Vicentino's plans in the fall of 1549, his insistence on the protective contract was quite reasonable; at that time he had pending, or so he thought, the publication of his book in Venice. There are two documents related to this event: first, the formal petition to the doge and the Seignory of Venice for a printing license and privilege as well as a tenyear monopoly; second, the granting of that printing privilege by the Council of Ten (see Appendix I).19 The wording of the documents, for all its legalism, is vague as to the precise nature of the material for which Vicentino requested privilege and monopoly. We know that a petitioner had to submit a copy of his work to be assessed by two readers appointed by a committee of the University of Padua. After a vote by the members of the Senate, the Council of Ten either granted or denied the petition.20 Neither the reports nor the names of the readers in Vicentino's case have come down to us. The minute of the Council of Ten refers simply to "works" on the practice of the chromatic and enharmonic genera. But Palestrinas salary in 1551 as director of the Julian Choir was six scudi per month. 18. A prolific writer on the sciences, Cardano pronounced on musical matters, including Vicentino's archicembalo. See Opera omnia (Lyons, 1663), Bk. Ill, chap. 602; Writings on Music, edited by Clement A. Miller (American Institute of Musicology, 1973), p. 220. 19. Richard J. Agee, "The Privilege and Venetian Music Printing in the Sixteenth Century" (Ph.D. diss., Princeton University, 1982), pp. 8-14 and 101-2; the documents are transliterated by Agee on pp. 222-23 (nos. 26 and 27). My translations appear in App. I below. 20. The Senate, about 120 members in all, was responsible for day-to-day legislation. On 30 October 1549, 112 senators were present.

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the petition suggests that Vicentino had in mind two types of material— the treatise, to which he (or the notary) alludes with the generic title "The Practice of the Chromatic and Enharmonic Genera," and collections of vocal music composed in the two genera. The existence of such collections (now lost) is proved by information in the tracts of Bottrigari and Gandolfo Sigonio.21 Vicentino certainly would not have considered publishing compositions in the genera before the appearance of his treatise had established him as an authority on the subject. The Roman and Venetian documents of 1549 indicate that Vicentino was planning to publish, and soon: most likely a version of the treatise. Why nothing appeared in Venice in the years immediately following 1549 is not known. Negotiations with a printing firm may have been stalled for any number of reasons, probably financial, given the complex notation required for the chromatic and enharmonic genera. Even after the publication of his treatise (Rome, 1555) Vicentino did not rush into press with his radical chromatic and enharmonic music. Instead, he traveled around the centers of northern Italy with a group of singers who under his direction, performed this strange music—not always with success, it seems. Vincenzo Galilei reports that at a concert before notables in Ravenna (probably in the early to mid-1560s) the a cappella performance of an enharmonic madrigal by Vicentino ended in a shambles when one of the singers lost his place and could not be set aright.22 In June 1551, about a year and a half after Ippolito's first and most promising bid for the papacy, Vicentino and Lusitano engaged for the better part of a week in their public disputation on the genera. The narrative given here attempts to amalgamate, where possible, the two ver sions of the events given by Danckerts and Vicentino.23 21. Bottrigari, IIMelone secondo (Ferrara, 1602), pp. 4 and 7, and Sigonio, Discorso intorno amadrigali eta'libri... da D. Nicola Vicentino (Ferrara, 1602), pp. 32-35. The internal and external evidence suggests that Vicentino's first and second books of four-voice madrigals, which included chromatic and enharmonic compositions, appeared in the late 1560s or early 1570s. Maria Rika Maniates, "The Cavaliere Ercole Bottrigari and His Brickbats: Prolegomena to the Defense of Don Nicola Vicentino Against Messer Gandolfo Sigonio," in Music Theory and the Exploration of the Past: Essays in Honor of Patricia Carpenter•, edited by David Bernstein and Christopher Hatch (Chicago, 1993), p. 160. 22. Discorso intorno alluso deWenharmonio (1587-91), fols. 9r-9v, edited by Frieder Rempp in Die Kontrapunkttraktate Vincenzo Galileis (Cologne, 1980), p. 166. Galilei also reports that in Venice in 1560 one Giacomo Finetti, a disciple of Vicentino's, admitted that he had to abandon his masters enharmonic music in order to make a proper living. Aside from Galilei's praise of Finetti s keyboard skill and fine contralto voice, nothing is known about this musician. 23. Sopra una differentia, Bk. I, preface and chaps. 1-5, and Vicentino, below, Bk. IV, chap. 43.

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Because it is impossible to reconstruct the oral confrontation between the two protagonists, we cannot assess accurately the justice of the verdict against Vicentino. The extant written documents show that both men based their arguments on passages from De institutione musica, by Boethius, and that they read antithetical meanings into the same citations. Mostly they talked at cross-purposes and fought, in Bottrigari's words, like two blind pugilists flailing the air.24 The precipitating cause of the debate was a polyphonic setting of the plainchant Regina coeli, performed at a private concert given by Bernardo Acciaiuoli-Rucellai at his palace on the Tiber.25 In the presence of many guests, Lusitano and Vicentino began arguing about whether the composition belonged to the diatonic genus, Lusitano taking the positive side and Vicentino the negative. So heated did the altercation become that Vicentino challenged Lusitano to a formal debate in public, staking two gold scudi on the outcome.26 Since the proceedings began in early June, we can assume that the concert probably took place at the end of May.27 We can also assume that besides Lusitano there were present other members of the papal choir, Danckerts included. Did this group sing the Regina r0£//? Was the motet composed by Lusitano?28 Did the presence of the cardinal of Ferrara spur Vicentino to make his flamboyant and quixotic gesture? On the morning of Tuesday, 2 June, the papal choir sang the Solemn Mass of the Most Blessed Sacrament at Ippolito's titular church in Rome, Santa Maria in Aquiro degli Orfanelli alia Capranica.29 Then, before the choir members and many prelates, the debate was inaugurated. The two contestants affirmed the gist of their previous argument, the wager between them, and the selection of two judges from the papal choir, 24. II Melone discorso armonico (Ferrara, 1602), p. 17. 25. Danckerts Sopra una differentia, Bk. I, chap. 2. Bernardo Acciaiuoli-Rucellai, who was related to an eminent Florentine banking family, took over the Roman banking firm and the name of another Florentine, Luigi Rucellai, on Luigis death in 1549. See Bk. IV, note 79, for the concert. 26. See note 17, above. The reference to scudi d'oro might have been made to distinguish the well-known Roman gold coins from a special mintage of silver scudi in 1551. 27. The different drafts of the preface to Danckerts' treatise give slightly different starting dates. See Barbosa, Vincentivs Lvsitanvs, p. 204, note 3. 28. Robert Stevenson, "Vicente Lusitano: New Light on His Career," Journal of the American Musicological Society 15 (1962): 74-75. 29. Danckerts, Sopra una differentia, Bk. I, chap. 2, and this edition App. IV. The warrant signed by the two contestants on 7 June 1551 is reproduced only by Danckerts. Its authenticity was witnessed by four persons: [Giovanni] Battista Preccarese (Procarese) 1'Aspra on 24 November 1555, [Don] lacopo Martelli on 14 April 1555, Stefano Bettini on 29

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Danckerts and Escobedo. Vicentino and Lusitano also agreed to accept the verdict without recourse to appeal. It seems to have occurred to someone at that point that so abstruse a debate could lead to a split verdict. For this reason, it was decided to elect a third judge, Giulio da Reggio (Julio da Rezzo), who was supposed to cast a deciding vote if the other two judges could not agree.30 The proceedings were then adjourned. The events of 2 June were the preliminaries. The debate proper began on 4 June in the presence of the cardinal of Ferrara at the Palazzo Monte Giordano, his magnificent residence in Rome. When it was over, Ippolito asked for a verdict and encountered an obstacle. Danckerts had been called away from Rome on personal business. In Danckerts' absence, Escobedo maintained that he and da Reggio did not constitute a valid jury. The cardinal commanded the two men to consult with Danckerts and to bring down a verdict no later than 7 June. Danckerts returned to Rome on the morning of 5 June. As he recalled, his two colleagues told him what had transpired the day before. Because their accounts were contradictory, Danckerts refused to accept their evidence and requested instead written abstracts from the debaters. The same day, Vicentino wrote him a short deposition and Lusitano a longer one. Vicentino's recollection of the circumstances is slightly different. He gives the impression that only he was asked to provide Danckerts with a short memorandum, as it were, and that on learning of this circumstance, Lusitano hastened to write a much longer letter. This imputation of furtive and unsportsmanlike behavior was obviously conditioned by later events, in particular—if Vicentino is to be believed—Lusitano's humiliation at the hands of the cardinal and his subsequent attempt to stave off further public embarrassment. After Mass on Sunday morning, 7 June, a final session was held at the Apostolic Chapel in the Vatican at Ippolitp's request. This was a formal event, conducted in public before the judges, the papal choir, a group of ecclesiastical dignitaries, and an assembly of learned persons. The dignitaries included leronimo Maccabeo, bishop of Castro and director of the chapel, Monsignor Marcantonio Falcone, bishop of Cariati and a close friend of the cardinal of Ferraras, Annibale Spadafora, archimandrite of Messina, and Giovan Francesco Caracciolo, abbot of Sant'Angelo April 1556, and Antonio Barre on 1 May 1556. For information on the last three, who also witnessed Vicentino's copy of the sentence, see below, Bk. IV, note 107. The first signatory, a young man, later joined the papal choir. 30. Sopra una differentia, Bk. I, chap. 2. Other than his alleged expertise in music, no information about Giulio da Reggio is available.

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a Fasanella.31 Since Ippolito was unable to attend, one of these prelates, most likely Monsignor Falcone, acted as his official representative. First the warrant was read aloud, and then it was signed by the contestants to confirm its accuracy. Vicentino and Lusitano then embarked on a lengthy dispute. They argued their respective positions well, reinforcing their assertions with many references to musical authority. It seems that the judges found it difficult to keep track of the score. They therefore suggested that the contestants renounce their oral combat in favor of the letters they had sent to Danckerts two days earlier. Vicentino and Lusitano apparently agreed to this more dispassionate manner of ending the debate, for neither would cede ground to the other in the heat of personal combat. The depositions were produced, and each contestant read his aloud to the audience. The judges, having already studied the documents in detail, came to their decision shortly after the readings. The sentence, against Vicentino, was drawn up and signed that day. In the preface to his treatise, Danckerts admits that he was angered by the reports brought to him by Falcone of Vicentino's clamorous slandering of the judges, the judgment, and the members of the papal choir. It was such insolent behavior, aggravated by the subsequent appearance of Vicentino's treatise, that prompted him to write down the events as he remembered them. Danckerts denounces Vicentino for propagating lies and falsifying documents and signatures. This accusation of lying cannot be proved, however, since discrepancies in the accounts of the debate may have arisen from faulty memory of past events. The second accusation, a serious one, can be assessed from the two sets of documents.32 A comparison shows that, minor variants aside, there are two issues of substance: the signatures and the nomenclature of the diatonic genus. In Danckerts' version of the documents, the disputed genus is always called "diatonic," whereas Vicentino three times cites his own usage as "purely 31. leronimo Maccabeo de Toscanello, canon of St. Peter's basilica and bishop of Castro, was director of the pontifical chapel from 1550 to 1564. Marcantonio Falcone was elected bishop in 1545. The aristocratic Spadafora family had been a political force in Messina since the fifteenth century; in the mid-sixteenth century, several of its members held the rank of senator. Giovan Francesco Caracciolo, the second son of the lord of Salvia, was a member of a wealthy and powerful Neapolitan family. Following a long-standing family tradition, he took over the Abbey of Sant'Angelo a Fasanella from his uncle, Marino Cardinal Caracciolo, governor of Milan. The names of these persons, as well as the sequence of events on 7 June, are given in Danckerts, Sopra una differentia, Bk. I, chap. 1. 32. Three of the four documents were published by Danckerts and by Vicentino: the sentence and the letters to Danckerts from Vicentino and Lusitano, respectively. The warrant was printed only by Danckerts (see note 29, above).

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diatonic."33 The phrase "purely diatonic" also appears three times in the text surrounding the documents. Early in the chapter, these words refer twice to Vicentino's alleged remarks during various phases of the confrontation. The third time the words appear during an explanation of a passage from Boethius and encapsulate Vicentino's contention that the presence of melodic major and minor thirds adulterate the pure diatonic genus, transforming it into the mixed diatonic common to the music of his day. Danckerts condemned Vicentino for adding the word semplice to the original documents, as well as for telling the story in such a way that the verdict seemed unjust and inapposite. To use Danckerts' sarcastic words, the dispute was never "about such purely diatonic music as against diatonic music doubled with a lining."34 Intriguing is Danckerts' implicit suggestion that had Vicentino argued at the outset about the "pure diatonic," the outcome of the debate might have been different. Vicentino certainly clarified his definition of pure and mixed diatonic music in 1555.35 And shortly after the debate, even Lusitano moved closer to Vicentino's position on the subject of the genera.36 At the end of the sentence Vicentino indicates that four persons signed and testified to the effect that the sentence and the two depositions were faithful copies of the originals: Don lacopo Martelli, Vincenzo Ferro, Stefano Bettini (called II Fornarino), and Antonio Barrfe. Three of these signatories (Martelli, Bettini, and Barrfc) are identical with the ones listed by Danckerts. After reading the names listed by Vicentino, Danckerts summoned the men to his house, where, he claims, they professed astonishment when confronted with the offending page and insisted on repudiating their signatures. Danckerts recounts this story. Apparently he was concerned only that three of his signatories also signed for Vicentino, although Vicentino (according to Danckerts) had doctored the documents by adding semplice^ "pure," to the word diatonic. Did Vicentino 33. These self-references occur twice in his letter to Danckerts and once in Lusitano s letter. See Bk. IV, notes 87 and 92. 34. "Da la qual Musica Diatonica semplice, o, Diatonica foderata, o doppia." 35. In the treatise, the word semplice appears many times: for instance, to refer to the pure diatonic, chromatic, and enharmonic modes (Bk. Ill, chaps. 1, 5, 6,7, 8, 9,10, 11,12, and 48) and to the pure genera (Bk. I, chap. 4). 36. Introdutione facilissima drnovissima di canto fermo, figurato, contraponto semplice dr in concerto, con regole generali perfarfughe differenti sopr'il canto fermo ... (Rome, 1553), "De tre generi della musica," fols. F2v-F3r. In the facsimile of the 1561 edition by Giuliana Gialdroni (Lucca, 1989), this section is on pp. 22v-24v. See Gialdroni, "Introduzione," p.

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fabricate his witnesses? It seems unlikely, especially since one of them (Barre) later published the treatise in which his ostensibly unauthorized signature appears. Did Danckerts fabricate this incident? More likely, he exaggerated the reaction of the group. It is impossible to decide who, if anyone, is telling untruths. Certainly Barre's name appears below the sentence, both in the first (1555) and in the second (1557) printing of Vicentino's treatise. The sentence must have been delivered to Ippolito within a few days, if not directly on Monday, 8 June. A copy of it, recalls Vicentino, was presented in person by Lusitano, so anxious was he to collect his reward. The cardinal read the sentence aloud and enjoined Vicentino to pay up, which he did on the spot. Lusitano received his two gold scudi. He also received an unwelcome reward, a tongue-lashing from the cardinal before the assembled throng. Much has been made of a statement by Vicentino about the timing of the verdict and the writing of the sentence.37 Vicentino was often a careless writer. In this case he discusses at length the written depositions of 5 June and then says that the decision was made and pronounced four or six days later—that is, 9 or 11 June. These dates correspond roughly to the time Ippolito was apprised of the verdict. They do not, however, correspond to the date of the sentence, 7 June, which came four or six days after the start of the debate, depending on whether one considers it to have begun on 1 or 3 June. Between these dates comes the first formal gathering of the disputants, five days before the signing of the sentence. Vicentino's phrase "four or six days later" may refer not to the immediately preceding events of 5 June but rather to the beginning of the story. Such logical and syntactical interstices are not unusual in his writing. In the event, Vicentino tells us that a few days after learning of the decision, the cardinal and his retinue left for Ferrara. After that they went on to the besieged city of Siena. In 1555 they were again in Rome. Two conclaves took place that year, one on the death of Julius III, and one on the death of Marcellus II. Toward the end of the second conclave, Vicentino's treatise made its appearance in Rome, on 22 May. By late 1555 Vicentino must have been back in Ferrara, for on 15 December of that year he wrote a letter from that city to Guglielmo Gonzaga, duke of Mantua. In it he refers to a published work (probably the treatise) and ten five-voice madrigals which had been sent to the 37. Giuseppe Baini, Memorie storico-critiche delta vita e delle opere di Giovanni Pierluigi da Palestrina (Rome, 1828), Bk. I, note 424, and Kaufmann, Life and Works, pp. 30-31.

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Mantuan court.38 Vicentino inquires humbly whether the madrigals had been performed and admits that since they belong to a new practice, they might appear strange to the uninitiated. From this comment we may infer that these madrigals were composed in the chromatic and enharmonic genera. Sensing that they had not been well received, Vicentino closes his letter with an offer to send others in the common style, recommending them as easy to sing. In the treatise the phrase musica communa alludes to the ordinary "diatonic" music of his day—that is to say, music that in his opinion used not only the major semitone and whole tone of the diatonic genus but also the minor third of the chromatic and the major third of the enharmonic. The distinction between a novel, hence demanding and reserved, practice as opposed to a common, hence simple and popular, one is announced as an aesthetic and social principle in the treatise. Every normative and prescriptive rule given by Vicentino follows from this distinction. The next documented event in Vicentino's life is the second printing of the treatise by Barr£ in Rome in 1557. Except for the date on the title page and feeble attempts by a house editor to correct some errors in pagination, the two versions are identical.39 Ippolito left for France on 23 July 1561. Since little is known about Vicentino's activities between 1561 and 1563, it is tempting to surmise that he accompanied his patron.40 It seems more likely that Vicentino was giving concerts of his chromatic and enharmonic music in Italy during the 1560s. He was at that time searching for a post. This is made clear in the closing paragraphs of a handbill about the arciorgano, an organ built along the lines of the archicembalo, that appeared in Venice on 25 October 1561.41 On 9 January 1563 he received the appointment 38. Franz X. Haberl, "Das Archiv der Gonzaga in Mantua," KirchenmusikalischesJahrbuch 1 (1886): 33, and Kaufmann, Life and Works, p. 34, note 90. 39.1 compared the 1555 edition to the 1557 edition located in the Euing Music Collection, University of Glasgow Library, Scotland. 40. There are some documented French connections, but these date from the 1570s. Vicentino's Passa la nave mia appeared in Adrien Le Roy and Robert Ballard's Mellange de chansons (Paris, 1572). In a letter to Orlando di Lasso dated 14 January 1574, Le Roy says that the French king, Charles IX, was fond of chromatic music, especially Vicentino's. In the preface to the Premier livre des amours de Pierre de Ronsard (Paris, 1578), Antoine de Bertrand affirms Vicentino's belief that the subtle intervals of the enharmonic genus are singable. Kaufmann, Life and Works, pp. 42-44. 41. See note 1, above. The handbill has sixteen sections, clearly marked by overhanging paragraphs. Vicentino's interest in an appointment is stated in sections 15 and 16. In section 2, Vicentino gives the name of the builder of the arciorgano, Vincenzo Colombo, a renowned organ maker at San Marco and other Venetian churches between 1558 and 1588.

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of chapel master at the Cathedral of Vicenza. He stayed there until 19 January 1565.42 The period between 1565 and 1570 is a blank. Vicentino may have enjoyed a pension from the cardinal of Ferrara that enabled him to continue his peregrinations around northern Italy, supplementing his income with gifts from patrons before whom he performed his music. But he may also have been based in Milan as early as 1565. This possibility is suggested by a letter of 31 March 1565 sent to Milan by the bishop, Carlo Cardinal Borromeo, during his work to reform the papal choir in Rome. The cardinal writes that he is gathering Masses to supplement the one ordered from his choir master at the Duomo, Vincenzo Ruffo, and asks his subordinate to commission a chromatic Mass from Vicentino, if the latter is in Milan.43 The last three extant documents from Vicentino's lifetime are connected with Milan. In a letter of 25 March 1570 to Prince Wilhelm, later duke of Bavaria, Vicentino refers to himself as the rector of San Tommaso in Milan.44 Intended as a prelude to a request for a position, the letter is filled largely with self-congratulations, although it records the sending to Munich of compositions in the three genera. This music may account for a record of payment to Vicentino made by the Milanese agents of the Bavarian court on 14 December 1570.45 The other documents are collections of vocal music for five voices: the fourth book of motets and the fifth book of madrigals, published in 1571 and 1572, respectively, by the Milanese printer Paolo Gottardo Ponzio.46 Both publications refer to Vicentino as "arch-musician," a title given him in the lost books of fourvoice madrigals discussed by Sigonio and Bottrigari. Like the extant fifth book of madrigals, the lost books were prepared by pupils, admirers, and friends of the arch-musician.

42. See note 1, above, and Kaufmann, Life and Works, p. 36. 43. Lewis Lockwood, "Vincenzo Ruffo and Musical Reform after the Council of Trent," Musical Quarterly* 43 (1957): 149-50. 44. For a translation and reproduction of the original, see Kaufmann, Life and Works, pp. 40—41 and facing p. 40, respectively. 45. Giuseppe Caimo, also of Milan, received the same payment as Vicentino. Kaufmann Life and Works, pp. 42 and 45-46. 46. There survives only the quintus part-book of the motets, discovered in 1957 by H. Colin Slim in the archives of the Duomo of Piacenza. Kaufmann, Life and Works, pp. 42 and 86, notes 123 and 108. The madrigals were edited by a disciple, Ottavio Resino, about whom nothing else is known.

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Vicentino's Sources Whether Vicentino can be called a humanist depends on how the term is defined. Most historians of the Renaissance would consider a humanist of the period to be a scholar engaged in the recovery of ancient Greek and Roman culture and in editing, translating and interpreting the original documents. By this definition Vicentino was not a humanist, for there is no evidence that he dealt with original documents or artifacts or that he even read much of the ancient literature on music available in translation.47 However, he undoubtedly was affected by and participated in the humanist movement, since he was trying to revive a practice that had been neglected since ancient times. Some scholars have called those who, like Vicentino, aimed at recapturing the legendary powers of ancient music "musical humanists."48 Vicentino surely fits into this category. It is evident that he had read or heard about the ability of ancient Greek music to sway human passions, to attract and tame animals, and to cure physical and mental ailments. Such stories were widely disseminated. Vicentinos main source was Boethius. Although Boethius compiled his work in the middle of the sixth century and wrote in Latin, he based his treatise on ancient Greek sources. Vicentino and his contemporaries did not realize how dependent Boethius was on his Greek models and how faithfully he followed them, but he showed good instincts in trusting Boethius' authority. Vicentino cited Boethius frequently—118 times by name, usually with precise references to chapter and book of De institutione musica libri quinque. Although we cannot identify the edition or manuscript Vicentino used, the citations in the text are consistent with both the editio princeps of the complete writings of Boethius published in Venice by Giovanni and Gregorio de Gregori in 1492 and the reprint of it by the same printers in 1499. This is especially evident in the references to chapters from Books IV and V of Boethius, which follow the chapter numbering of these editions rather than that of the manuscripts, as do later editions and translations.49 47. Among those who take this position are Karol Berger, Theories of Chromatic and Enharmonic Music in Late I6th-Century Italy > p. 41 and pp. 39-40, and Claude V. Palisca, Humanism in Italian Renaissance Musical Thought (New Haven, 1985), p. 253. 48. For example, Carl Dahlhaus, "Musikalisches Humanismus als Manierismus," Die Musikforschung 35 (1982): 122-24 and 128; Paul Oskar Kristeller, "Music and Learning in the Early Italian Renaissance," in his Renaissance Thought II (New York, 1965), p. 156; and Edward E. Lewinsky, "The Musical Avant-Garde of the Renaissance," in Art, Science and History in the Renaissance (Baltimore, 1967), p. 135. 49. The Latin edition by Gottfried Friedlein (Leipzig, 1867) and the English translatio

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Counting the references to Boethius does not by itself tell us much unless we evaluate them in the context of references to other authors, the preponderance of which are allusions rather than explicit citations. With respect to Boethius, Vicentino admits that the "Book on Music Theory" relies on the Fundamentals of Music, and this regardless of whether the source is acknowledged in a formal manner. Thus, the 36 references to Boethius in this section of Vicentino's treatise are acknowledged by inference, if not by citation. Boethius is also a source in the five "Books on Music Practice," where 19 of the 82 references are tacit. Thus, we can say that of the 118 references to Boethius, 99 are acknowledged. The number of modern sources is quite high: 26 persons (equally split between musical and nonmusical authors) receive 241 references. Although the references in this category outnumber those to Boethius, those to no single author do so. The two highest numbers of citations, 50 for Lusitano and 40 for Vicentino himself, must be adjusted to exclude references to the story of the public debate. This done, the self-references to Vicentino virtually disappear, leaving the field to Franchino Gaffurio (33 references) and Lusitano (now reduced to 25), the latter citations having to do with material in his treatise. Among these, the references to improvised counterpoint (about half of the total) are tacit whereas the rest, concerning Lusitano's poor grasp of the genera, are cited for all the world to see. Of the 30 references to Danckerts, only one, a sardonic allusion to chessboard canons, is tacit (for the sake of decorum?). In contrast, all 14 allusions to Lodovico Fogliano are tacit, even though Fogliano was probably Vicentino's source on matters of ancient tuning and modern temperament. One might suspect Vicentino of deliberate subterfuge, but he also relied heavily on Gaffurio s Practica musicae (Milan, 1496)—and remembered to acknowledge this authority only once out of 33 allusions. Other references could be classified as explicit if we accept that pronouns such as they&nd. many qualify as references to specific people. This is true of six of the 11 references to Heinrich Glarean, except that in this case such vague phrases as "some people," "some authors," and "others" function as circumlocutions about modal theories of which Vicentino disapproves. Although it is not clear that sixteenth-century musicians distinguished medieval from ancient sources, I shall separate the two categories for the sake of clarity. Vicentino's medieval sources receive 92 references within by Calvin M. Bower (New Haven and London, 1989) rely on the manuscripts. The German translation by Oscar Paul (Leipzig, 1872) uses printed sources and hence contains the chapter numbering used by Vicentino.

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a relatively small group of 13 authors. The sources fall into two groups: biblical, religious, and specifically patristic literature on the one hand and music theory on the other. The references to Boethius outnumber all other medieval references. Among the fathers and doctors of the Church, St. Thomas Aquinas stands first, with six references, all of them tacit. At the other end of the scale is St. Athanasius, with two references, one explicit and one tacit. Aquinas is overshadowed by two music theorists: Guido of Arezzo, with 33 explicit references, and Jehan de Murs, with 17, of which only two are unacknowledged. Among the ancient sources apparently used by Vicentino are 23 authors, who receive 62 references. The most frequently cited is Aristotle, with 22 references (including citations to the Physical Problems, which at that time was included in his canon, as well as to Porphyry's introduction to the Categories^ in accordance with tradition Vicentino does not name Porphyry and accepts this book into the canon). Seven of these references identify Aristotle simply as "the Philosopher/' The next most frequently cited are Cicero, Quintilian, and Vitruvius, with four references apiece; only Vitruvius is named (once). Euclid has a single, explicit reference in the text. The significant omission in this category is Ptolemy, whose diatonic syntonon tuning lies at the heart of Vicentino's theory of the genera. How did Vicentino come to know what was said in sources he may not have bothered to identify? Opinion has it that Vicentino heard about these works from learned friends and reported their evidence as best as he remembered it.50 This mustering of humanist opinions gives a qualified response to the question of Vicentino's learning. It helps us address the problem of evaluating his erudition, though few scholars concede that it explains the presence of remarks on ancient music that are not taken from Boethius. When proposing associations between Vicentino and specific humanists, scholars most frequently list the following men: Gian Giorgio Trissino, Giambattista Giraldi Cintio, Francesco Patrizi, and Lilio Gregorio Giraldi. Giraldi, an erudite humanist, was born in Ferrara but spent his life elsewhere. His sojourn in Rome as papal secretary ended in 1527, long before Vicentino arrived in the entourage of the cardinal of Ferrara. In De deis gentium (Leyden, 1545) Giraldi dedicated the sixth book, on the 50. Kaufmann, Life and Works, pp. 20-21; Claude V. Paliscas comment, reported in Studi Musicali 3 (1974): 97; Giulio Cattin, "Nel quarto centenario di Nicola Vicentino teorico e compositore," Studi Musicali 5 (1976): 36; and Berger, Theories of Chromatic and Enharmonic Music, p. 41.

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gods of the underworld, to one Nicolaus Vicentius whose brother Benedictus had died recently.51 Many years later, in 1570, Vicentino seems to allude to "family,"52 in a document that gives his name in Latin as "Nicolas Vicentinus." The vagaries of sixteenth-century spelling make it impossible to ascertain the identities of the Nicolaus and Benedictus Vicentii known to Giraldi. Patrizi would seem to be a likely member of the Ferrarese humanist circles in which Vicentino moved.53 But although Patrizi maintained close connections with members of the court of Ferrara throughout his life, he himself did not reside in that city until 1578, when he became professor of Platonic philosophy at the University of Ferrara. He occupied this chair, created for him by Duke Alfonso II, until 1593. Vicentino had left the service of Ippolito II in 1563, however, and by 1570 was situated in Milan. Nor did the timing of their earlier stays in Venice coincide.54 It would seem that opportunities for personal contact between the two men were limited. Nonetheless, because Patrizi had a prestigious position in Ferrara when he published the first two "decades" of his famous Neoplatonic work, Delia poetica (Ferrara, 1586),55 it is customary to call him a Ferrarese humanist. Vicentino's writing, by contrast, betrays a Neo-Aristotelian and scholastic mode of thought. Patrizi's discussions of ancient music in La deca istoriale (Books I and IV, but especially VI and VII) and to a lesser extent in La deca disputata (Book IX) have nothing to do with Vicentino's theories. The moderns mentioned by Patrizi are both Florentines: Galilei, whose Dialogo della musica antica e delta moderna (Florence, 1581) he had read, and Giovanni de' Bardi, with whom he had apparently consulted.56 That Patrizi should mention the Estense encouragement of Vicentino's chromatic and enharmonic music does not prove that he had any personal 51. Kaufmann, Life and Works, p. 20, and Cattin, "Nel quarto centenario," p. 36. According to Giraldi, Benedictus was a learned man who studied with Calcagnini (see note 8, above). No mention is made of Nicolaus' profession. 52. "Turn amicis turn parentibus." See notes 1 and 44, above. 53. Claude V. Palisca, "A Clarification of 'Musica Reservata in Jean Taisnier s Astrologiae, 1559," Acta Musicologica 31 (1959): 152, and Kaufmann, Life and Works, pp. 19 and 112, notes 28 and 44. 54. Vicentino was there in the mid- to late 1530s; Patrizi in the mid-1550s to the late 1560s, between trips to Cyprus. 55. The other five of the ten planned decades, in order of completion between 1587 and 1588, are La deca ammirabile, La decaplastica, La deca dogmatica universal*, La deca sacra, and La deca semisacra. The seven decades are available in a modern edition by Danilo Aguzzi Barbagli. 3 vols. (Florence, 1969-71). 56. La deca istoriale, Bk. VI (Barbagli, 1: 329 and 330).

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knowledge of the music or the man. In the dedication to Lucrezia d'Este, duchess of Urbino, the name of Don Nicola Vicentino appears as the last of the illustrious musicians patronized by her family. The preceding names in this decidedly retrospective list are: Guido, Fogliano, Josquin Desprez, Willaert, and Cipriano de Rore.57 Telling is the absence of Luzzasco Luzzaschi, who dominated music at the court of Ferrara between 1570 and 1596. If Patrizi's knowledge was firsthand, then Vicentino did not exaggerate the ducal family's interest in his experimental music. If secondhand, then Patrizi's source may have colored his perception of Vicentino's importance. Who could that source have been? Bottrigari's close friendship with Patrizi during his self-imposed exile in Ferrara (1576-87), his ardent championship of Vicentino, his touting of Vicentino's book to others, and the names on the list suggest that the learned Bolognese humanist gave Patrizi this information.58 Giambattista Giraldi Cintio—poet, dramatist, and literary critic— spent much of his productive life in Ferrara, the city of his birth. After holding the chair of philosophy at the University of Ferrara for about a decade, he succeeded his teacher, Celio Calcagnini, as professor of rhetoric. When Cintio's patron Duke Ercole II died in 1559, the wily Giovanni Battista Nicolucci (called "II Pigna") managed to engineer Cintio's departure from court.59 After a few years of steadily declining health, Cintio returned to Ferrara, where he died in poverty. During his heyday, however, the highly esteemed Cintio was court secretary and tutor to the future Duke Alfonso II. If Vicentino taught his experimental music to the ducal heir, it is probable that the two men knew each other. Moreover, all Cintio's dramatic works were produced at court. The staging of these works must have put Cintio into contact with musicians. Aside from incidental music, which need not have concerned the playwright, the tragic choruses that closed each act were intended for polyphonic vocal setting. Unfortunately, most of the music written for these performances is lost.60 57. Barbagli, 1:4. 58. Maniates, "The Cavaliere Bottrigari and His Brickbats," pp. 138 and 140. 59. In his Discorsi intorno alcomporre de i romanzi, delle comedie, e delle tragedie (Venice, 1554), Cintio printed a preliminary poem to II Pigna, "his pupil." Pigna then published I romanzi (Venice, 1554): in his dedication to Luigi Cardinal d'Este, Pigna not only denied having studied with Cintio but also accused the older man of appropriating a youthful essay of his. There ensued an acrimonious public argument, in which Pigna emerges as a clever but unsavory character. The letters of self-defense written by Cintio are available in Camillo Guerrieri Crocetti's edition, Scritti critici (Milan, 1978), pp. 289-302. 60. There survive two choruses composed by Rore for a production of Selene in 1548.

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Because no documents connect Vicentino with any productions of Cintio's dramas at court, the argument for linking the two men rests on a passage in the dramatists Discomofl554.61 This passage, the sole sub stantial allusion to music, seems to anticipate Vicentino's assertions about the proper social setting of ordinary and extraordinary music.62 But in context it has little to do with Vicentino's premise. To explain the derivation of the word canto, Cintio contrasts the modern gibberish sung by strolling minstrels in city squares with the praise of virtuous men customarily sung at aristocratic banquets in ancient Greece and Rome. Although both writers are dealing with decorum, Cintio's statement cannot be construed as an apology for extravagance and novelty. Rather, Cintio sought to emphasize the ancient precedent for the inherent nobility of the romance as a genre. More tantalizing is the putative connection between Vicentino and Trissino, an important humanist active in Vicenza. The conjectures are as follows: first, Vicentino benefited from the learned discussions at Trissino's sumptuous Villa Cricoli near Vicenza; second, he was influenced either by Trissino's writings or collections of books; and third, he obtained his post at Ferrara through the good offices of Trissino.63 Vicentino nowhere acknowledges Trissino's patronage, even in passing, however. Nor is the musician mentioned in any of the known documents on Trissino and his circle of friends and associates, even though music was a part of the daily regimen of members of the "AccademiaTrissiniana." Any circumstantial evidence must be examined apart from the web of conjectures outlined above. The idea that Trissino's definition of the epic in La poetica (Vicenza, 1529 and Venice, 1562) influenced Vicentino's definition of the extraordinary music reserved for the nobility must be rejected. For one thing, this definition was not published until 1562.64 For another, it is but a paraphrase of Aristotle's Poetics, like everything else in Parts V and VI. Trissino implies that the heroic poem, like the ancient epic, ought to have heroic subject matter. As in the case of Cintio's work, the themes of La poetica are genre and decorum. Trissino's studies at the University of Ferrara (ca. 1512-13) and his Ferrarese sojourn in exile (1538-40) were dominated by his mentor and Wolfgang Osthoff, Theatergesang und darstellende Musik in der italienischen Renaissance (Tutzing, 1969), 1:321-23. 61. Kaufmann, Life and Works, p. 210. 62. "Discorso sopra i romanzi," in Discorsi, pp. 6-7. 63. Kaufmann, Life and Works, pp. 17-18; Milton Kirchman, Mannerism and Imagination (Salzburg, 1979), p. 50; and Cattin, "Nel quarto centenario," pp. 32-37. 64. La poetica, La quinta e sesta divisioney pp. 6v and 24v. Facsimile. Munich, 1969.

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friend, the illustrious Vicentine humanist Nicolo Leoniceno. Today Leoniceno is remembered chiefly for his pioneering scholarship in medicine and related fields, work that included translations (notably, of Galen of Pergamum) and critical writings on scientific method. In 1499 Leoniceno completed a Latin translation of Ptolemy's Harmonics for Gaffurio.65 A manuscript copy came into the hands of Trissino when Leoniceno died. Apparently, Leoniceno had wished to give the translation to Pope Leo X, and Trissino fulfilled this intention by giving it to Pope Paul III. Among the subjects that drewTrissino's interest, Vitruvius and classical architecture were particularly prominent. Vicentino names Vitruvius in a passage that presents some of his most important comments on stylistics. Since Vicentino had access to any one of a dozen editions of Vitruvius printed in Italy after the editio princeps (Rome, 1492), however, it cannot be established that Trissino drew his attention to this well-known source. Trissino's veneration of Vitruvius is reflected in the work of his prot£g£, Andrea di Pietro da Gondola, to whom Trissino gave the name Palladio. Just as the patron transformed a stonecutter into a humanist architect, could it be that he sparked the humanist aspirations of a music-maker? Trissino made several trips to Rome with Palladio, and on one he pre sented the pope with a copy of Leoniceno's translation of Ptolemy. Relevant to this investigation is Trissino's letter of presentation, dated 13 August 1541,66 According to Trissino, Leoniceno believed that the music of his day kept alive scarcely one-third of the dignity of ancient music, and this third, the diatonic, lacked the accuracy and perfection of the ancient genus. To explain why Ptolemy, Manuel Bryennius, and other Greek writers should be made available to musicians, Trissino points out that the proper divisions of the tetrachords recommended by Ptolemy have been lost. Even Boethius, the Latin authority for all theorists from Guido to the present, failed to elucidate the generic system as laid down by Ptolemy, as he might have intended to do in the incomplete fifth book of De institutione musica. Given the circumscribed context of the letter, it is difficult to arrive at 65. For an assessment of Leoniceno as a translator of Ptolemy, see Palisca, Humanism, pp. 117-23. 66. The complete original Latin text is printed in F. Alberto Gallo, and Giovanni Mantese "Nuove notizie sulla famiglia e sull'opere di Nicolo Leoniceno," Archivio veneto 72 (1963): 21-22. The central portion of the letter is also available in Latin in Bernardo Morsolin, Giangiorgio Trissino (Vicenza, 1878), pp. 500-501, and Gallo, "Musici scriptores Graeci," Catalogues translationum et commentarium (Washington. 1976), 3: 71-72; in Latin and English in Palisca, Humanism, p. 120; and in Italian in Mantese, Storia musica, p. 28.

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an authoritative interpretation. Trissino seems to echo the main thesis of Vicentino's treatise as well as, with respect to the diatonic genus in modern music, the debate between Vicentino and Lusitano. This can be read into the Trissino's assertions, which match Vicentino's, about the two abandoned genera and the deficiency of the genus currently in use. These parallels, however, may be fortuitous. Trissino's talk of Ptolemaic genera is purely antiquarian and speculative in tone. There is no compelling reason to suppose that Trissino would have supported radical proposals to adapt the genera to modern practice. Against a connection between the two men is the evidence that Vicentino seems not to have read Ptolemy's Harmonics. Surely Trissino would have allowed Vicentino to look at the manuscript had the musician been a member of his group. Even if Vicentino had only skimmed Leoniceno's translation, he could have pretended a thorough knowledge in order to lend weight to his argument. Vicentino refers repeatedly to the diatonic syntonon tuning, otherwise known as just intonation, but without giving it a name or citing a source—inconceivable omissions unless he had culled his facts from an unspecified secondary source. In all likelihood this source was the Musica theorica (Venice, 1529), by Fogliano. The evidence in the text points to a haphazard and inaccurate conflation of propositions and opinions taken from Fogliano's treatise, including the unattributed references to the tuning first named diatonic syntonon by Ptolemy. This hypothesis rests on bits and pieces of textual evidence scattered throughout Vicentino's treatise, oddments that produce traces of a hidden source. Against the hypothesis stands the unequivocal reference to Ptolemy in Vicentino's 1549 application for a Venetian printing license. In that document, Ptolemy's name is associated with two neglected genera, the chromatic and enharmonic. These genera cannot be adapted to modern practice without the diatonic syntonon tuning. But the tuning of vocal music accompanied by a keyboard instrument is a complicated matter, aggravated by Vicentino's confusion between the premises of pure harmonic science and applied temperament. This situation seems to me the result partly of Vicentino's undisciplined temperament and partly of his faulty understanding of Fogliano's tunings for keyboard instruments. What classical sources did Vicentino read? Like the learned Gaffurio and Zarlino, he did not read Greek.67 But unlike them, Vicentino nei67. Few musicians could boast of this humanist skill. Palisca names Fogliano, a Modenese theorist patronized by the Este family, Bottrigari, and Francisco de Salinas (Humanism, p. 111). Gioseffo Zarlino, the great theorist and contemporary critic of Vicentino, commis-

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ther commissioned translations of Greek works on music nor scrounged in libraries to find such manuscripts. We may therefore conclude that he used only material published in Latin or Italian. To understand the range of ancient sources that may have been used by Vicentino, we must ascertain which Greek texts on this subject had been translated and published before 1555. The works of Plato, Aristotle, and Plutarch were available, and they included the spurious Physical Problems and On Music, attributed to Aristotle and Plutarch, respectively. Other Greek authors on music theory, in rough chronological sequence, are: Euclid, Aristoxenus, Ptolemy, Cleonides, Porphyry, Gaudentius, Aristides Quintilianus, Michael Psellus, and Bryennius. Only Cleonides' Introduction to Harmonics was published, usually under the name of Euclid. This epitome of the Harmonic Elements of Aristoxenus duplicated information in the fifth book ofVitruvius' De architectura, which Vicentino knew. Compendia on ancient lore contained sparse technical information, although their remarks on legend and performance practice were copious: these sources include two dictionaries (one by Julius Pollux and the lexicon ascribed to Suidas) and the Deipnosophists, by Athenaeus. None was available in translation. Under these circumstances, Boethius' De institutione musica became Vicentino's authoritative text. Vicentino did not bother with such humanist regurgitations of Greek sources as De expetendis et fugiendis rebus (Venice, 1501), by Giorgio Valla or De harmonia musicorum instrumentorum opus (Milan, 1518), by Gaffurio. Indeed, he had little patience with speculative ruminations and scholarly pretensions. Assessing Vicentino's erudition is not easy, given his careless identification of sources. As we have seen, the only precise references are to Boethius' De institutione musica. For the rest, the editor must rely on repetition or paraphrase of facts, concepts, terms, and phrases. Although I identify probable sources in the notes to this edition, a few problems merit comment here. Vicentino makes two statements that are so general as to defy source specificity. The first is an allusion to the miraculous powers of ancient music described by many "authors." The legends about the prodigious effects of music were transmitted by innumerable ancient Greek and Roman as well as medieval writings. The four main themes of these writsioned the physician and classicist Antonio Ermanno Gogava to translate Aristoxenus' Harmonic Elements. Gogava responded by first giving Zarlino a copy of his translation of Ptolemy's Harmonics, a source used by Zarlino in his Le istitutioni harmoniche (Venice, 1558).

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ings that I discuss here appear in the better-known stories, although I do not imply that Vicentino knew all the sources in which they occur. Two themes concern nature—inanimate, as in the legend of Amphion and the stones of Thebes, and animate, as in the tale of Arion and the dolphin.68 In the third, music is reputed to be a cure for all manner of physical ailments, from pestilence to snakebite and sciatica.69 The legend of Orpheus contains all three themes and produces a fourth, the power of music to move the human passions and affections.70 It is to the affective power of music that Vicentino alludes. This power was exemplified in three standard stories: Pythagoras and the Taorminian youth, Timotheus the Aulete and Alexander, and David and Saul.71 Ancient physicians, philosophers, mystics, and musicians were credited with the therapeutic use of music to heal mental disorders.72 Timotheus the Aulete, whose music moved Alexander so profoundly, was often confused with Timotheus of Miletus, who added strings to the kithara in order to perform chromatic melodies. This Timotheus was punished by the Spartans for his audacious subversion of musical and moral standards.73 Vicentino's second statement classifies music according to genus and potential audience: diatonic music is fit for public venues and plebeian ears, as opposed to chromatic and enharmonic music, which is appropriate for private venues and aristocratic ears. This well-known passage is a conflation and reinterpretation of several ancient sources. Concepts of 68. Herodotus, History, 1.23-24; Strabo, Geography, 13.24; Pliny, Naturalis historia, 9.8.25; Dio Chrysostom, Discourses, 32.61 and 37.2-4; Pausanias, Description of Greece, 9.5.7 and 30.2-4; Gellius, Noctes atticae, 16.19.1-23; Clement of Alexandria, An Exhortation to the Greeks, 1.1.1; St. Augustine, De civitate Dei contra paganos, 1.14; Macrobius, In somnium Scipionis ex Ciceronis VI libro de rep. eruditissima explanatio, 2.3.8; Capella, De nuptiis Philologiae etMercurii libri II, 9.908; and Cassiodorus, Varia, 2.40. 69. Gellius, Noctes, 3.10.13 and 4.13.1-4; Capella, De nuptiis, 9.926; and Boethius, De inst. mus., 1.1. 70. Ovid, Metamorphoses, 10.1-77; Dio Chrysostom, Discourses, 32.63-65; Clement of Alexandria, Exhortation, 1.1.1; Macrobius, In somnium Scipionis, 2.3.8; Capella, De nuptiis, 9.927; Boethius, Consolatio philosophiae, 3.12; and Cassiodorus, Institutiones divinarum et saecularum litterarum, 2.5.9, and Varia, 2.40. 71. Quintilian, Institutio oratoria, 1.10.32; Dio Chrysostom, Discourses, 1.1—8; Clement of Alexandria, Exhortation, 1.5.2; St. Basil, To Young Men on How They Might Derive Profit from Pagan Literature, 9.8-10; Boethius, Deinst. mus., 1.1; Cassiodorus, Institutiones, 2.5.9 and Varia, 2.40; Isidore, Etymologiarum sive originum libri XX, 4.13; and Euthymius, Commentarius in psalterium, "prologus" and 10. 72. Diodorus of Sicily, Library of History, 8.28.1; Gellius, Noctes, 4.13.1-4; Capella, De nuptiis, 9.926; Boethius, De inst. mus., 1.1; and Cassiodorus, Institutiones, 2.5.9. 73. Dio Chrysostom, Discourses, 32.67 and 33.57; Pausanias, Description, 3.12.10-22; and Boethius, De inst. mus. ,1.1.

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classes of music (nomoi), regulated by the decorum of subject matter and associated with venerable and lofty music, appear in Plato and PseudoPlutarch, who also contrast the implied nobility of bygone practice to the coarseness and venality of the music popular in their day.74 But neither associates the degeneration of music with the predominance of the diatonic genus, although Pseudo-Plutarch implies something of the sort. Plato and Pseudo-Plutarch lament the defunct customs of honoring the gods and praising good men and Homeric heroes. More pertinent is Cicero's approval of the ancient patrician custom of singing the praises of virtuous men at private Roman banquets.75 In Cicero we find a connection between edifying topics and social circumstances, namely, private lordly entertainment. Of course, Pseudo-Plutarch praised the music played in the ancient temple over the music performed in the theater of his own time. A similar distinction is implied in Aristotle's often-cited comparison of the theatrical music beloved by the vulgar class of mechanics and laborers with the ethical melodies sung to the lyre for the appreciation of freemen and educated persons.76 None of these authors associates any of the genera with social distinctions. There are, however, some remarks by Pseudo-Plutarch on the enharmonic genus that seem to have had a profound influence on Vicentino: in particular, the description of the history and practice of music among the very ancient Greeks before the degradation of the art.77 Of special interest is the legend of the younger Olympus, who founded a new and lofty style by introducing the enharmonic genus, the only genus studied in the olden days, according to this source. This state of affairs was completely reversed by the debased practice of PseudoPlutarch's time. Lazy, incompetent musicians banished the noble and majestic enharmonic genus of the ancients, claiming that no one could hear its subtle intervals. They used instead the diatonic and chromatic genera.78 The last remark provided Vicentino with evidence for his definition of "tempered and mixed music" and for the conclusion that in his own day the "pure diatonic" (as the ancient Greeks knew it) was neither 74. Plato, Laws 3.700a-b and 7.800c-e, and Republic, 10.607a, and Pseudo-Plutarch, On Music, 6.1133c, 27.1140d, 12.1135c2-f, and 40.1145e. 75. Cicero, Tusculanae disputationes, 1.2.3 and 4.2.3-4. See also Isidore, Etymologiarum, 3.16.3 and Cicero, Brutus, 18.71. 76. Aristotle, Politics, 8.7.1342a. 77. Vicentino may have known the translation of De musica by Carlo Valgulio (Brescia, 1507). Palisca, Humanism, pp. 88-100, and The Florentine Camerata: Documentary Studies and Translations (New Haven, 1989), pp. 13-44. 78. Pseudo-Plutarch, On Music, 7.1133e, 11.1135B, 34.1l43e, and 38.1l45a-c.

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understood nor practiced. This, of course, was the crux of the 1551 debate with Lusitano. The references to Vitruvius present problems with respect to terminology and interpretation. Vicentino uses modo/modito refer to the classical orders of architecture whereas Vitruvius used genus/generum.™ The first Italian version (Como, 1521), brought out by Cesare Cesariano, Buono Mauro, and Benedetto Govio, used the rather infelicitous term generatione. The Venetian humanist Daniele Barbaro chose maniera/ manierefor his Italian edition (Venice, 1556). In his translation of Leone Battista Alberti's De re aedificatoria (Florence, 1550), Cosimo Bartoli used ordine/ordini. Vicentino misread his source on the matter of the mixing of the orders. Vitruvius was a purist, although he did suggest the possibility of combining some pairs of orders.80 This misinterpretation may have been prompted by the commonplace notion that the Romans used a "composite" order, one emulated by the moderns.81 Another source problem concerns Vicentino's division of the whole tone into five minor dieses. Tantalizing though it is to suggest that he took this division from Marchetto of Padua,82 the evidence does not support this conjecture. The parallel is striking, but it is more likely that Vicentino encountered the idea in an intermediary source, such as Fogliano, Gaffurio, or Pietro Aaron. I have already discussed the evidence for Fogliano's influence, and he is not the only "modern" hidden in the text.

79. Vitruvius, De architecture 4.1.1-3, 4.3.1, 4.6.1 and 6, and 4.8.4-5. 80. De architecture 4.6.6, 4.1.2-3, and 4.8.5. Isidore twice mentions the five genera of columns given by Vitruvius: Doric, Ionic, Tuscan, Corinthian, and Attic, in his Etymologiarum, 15.8 and 19.10. 81. For example, Giorgio Vasari, Le vite depiu eccellenti architetti, pittori, etscultori italiani (Florence, 1550), "Introduzione alle tre arti del disegno ... e prima dell'architettura," chap. 3. A letter of 1519 to Pope Leo X, written by Raphael and probably Baldassare Castiglione, alludes to Roman buildings with several manners (dipiu maniere). See Raffaelo nei document^ edited by Vincenzo Golzio (Vatican City, 1936), pp. 91-92. 82. Lucidarium in arte musice plane (1317-18), edited by Jan W. Herlinger (Chicago, 1985), pp. 231-68. See Herlinger, Lucidarium, p. xx, and Karol Berger, Musicaficta (Cambridge, 1987), pp. 24-25 and 29.

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The Treatise For the most part, the organization of the treatise is logical. But as is often the case with large works of this period, the sequence of ideas from book to book or from chapter to chapter does not always form a coherent pattern. Certain chapters were added later, and the degree of integration depends on their placement and on the nature of the book into which they were inserted. Two additions occur in "Book IV on Music Practice." Chapter 43, the last in the book, gives Vicentino's account of the public debate, even though this subject is more apposite to Book III, where the genera are explained. Still, there can be no doubt that chapter 43 was appended to Book IV some time after 1551. The other addition, adapted from Lusitano, is chapter 23, on improvised counterpoint. It appears in the midst of a set of chapters on written counterpoint, and its ostensible link to the preceding chapter is extremely weak. It might be argued that the similarity to Lusitano was a coincidence, were it not for the categories described. Lusitano's treatise was published in 1553. Either this chapter was inserted between 1553and 1555 or Vicentino saw a manuscript copy of Lusitano's work between 1549 and 1553. Vicentino writes in an unself-conscious style that moves easily from the pedestrian didactic to the partisan militant. The exception is the chapter on the public debate, where he mimics the legalistic tenor of the proceedings while betraying the depth of his anger and resentment. Vicentino often digresses within chapters to matters that are tangential to the topic at hand. These digressions—on style, decorum, genre, singing, performance practice, and theology—are often more interesting than the topics they interrupt. To read Vicentino's prose is to follow the natural flow of his ideas as they occurred to him. Given Vicentino's casualness, it is not possible to determine exactly the order in which books were written. The outer books seem disconnected from the central section on music practice. "Book V on Music Practice" (on the archicembalo, actually) could stand on its own. The link between the "Book on Music Theory" and the books on music practice is more ambiguous. Certainly, the music theory section provides a background for the music practice. But the omission of the music theory would not impede the reader's understanding of the material in the music practice. These discontinuities are to some degree reflected in the prose and organization of the three parts distinguished here: "Book on Music Theory," books I-IV on music practice, and book V on the archicembalo.

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Vicentino was less a learned antiquarian than a practical theorist, a bias frequently cited by scholars to account for the uneven quality of the writing. Although it is true that readers find themselves alternating between admiration and exasperation, the flaws result not from Vicentino's lack of erudition but rather from his lack of concentration, especially with respect to technical subjects that require sustained systematization. For instance, egregious errors mar his method for solmizing the genera, his lists of intervals on the archicembalo, and his dismissal of Glarean's four extra modes—all practical topics. His instructions for tempering the archicembalo, a subject on which harmonic science and practical mechanics should reach a workable compromise, raise more problems than they solve. Where humanist erudition is seminal—for unaccompanied vocal tuning in the genera—Vicentino confounds two incompatible premises: the Ptolemaic, based on the mathematics of superparticular whole-number ratios, and the Aristoxenian, based on the geometry of irrational partitions of interval sizes. The result is a hopeless muddle. In contrast, his knowledge of ancient sources helped shape a singularly astute, though controversial, concept of decorum that places his ideas in the vanguard of musical rhetoric, especially stylistics. Vicentino had no models in the field of music theory. The originality of the treatise, then, lies in its philosophy of music, no matter how poorly argued it may be. Vicentino talks about three levels of style: high, middle, and low. He dismisses low subjects because they are frivolous and stresses the gravity of church music, warning composers against debasing it with popular material. He repeatedly enjoins musicians to use their judgment in differentiating chamber from church music, solo ensembles from large choral forces, and so on. His postulate for vocal chamber music—that its purpose is to express the text—pertains to ordinary and extraordinary vocal music alike. Both styles have in common a set of rules for increasing the intelligibility of the words. These rules represent what we now recognize as standard techniques for observing the prosody of language. They do not, however, suffice for depicting passions and poetic imagery. Vicentino makes it clear that the latter goal requires the deployment of various interval sizes, from the tiniest to the largest, each assigned a gradation of tenseness or slackness, depending on its size, speed, and melodic direction. In a highly expressive style, these interval sizes include a range of enharmonic inflections, from the minor diesis (one-fifth of a whole tone) to the major octave (a perfect octave enlarged by one minor diesis). In common music for untutored ears, the recommended techniques are limited to those that impart a modicum of stylish flair and textual

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clarity without disrupting the docile conventions expected by the public. Vicentino specifies these techniques and their logical disposition in three chapters devoted to the beginning, middle, and end of a composition. This is probably the first systematic application of rhetorical tools to musical structure, here described in such terms as good and bad, modern and outdated. And yet Vicentino makes it clear that the criteria of logic and coherence severely hamper the potential for high style and expressiveness. For Vicentino, the structural elements of music are comparable to the columnar scaffolding of buildings and to the linear design of paintings. Such elements as generically inflected intervals correspond to architectural or visual ornaments. In extraordinary music for cultivated ears, the eloquent portrayal of the words allows—indeed demands—an incredible variety of ornaments. Even structural elements can be bent out of shape, as it were, so long as these aberrations depict the text. Vicentino flaunts the chaotic effect of the genera by elevating it to an aesthetic dictate for stylized style. The cadence of the human voice is the main vehicle of emotive resonance. And the minute steps of the genera provide the most flexible means of imitating vocal inflection. Singers, he says, must overcome their innate laziness and learn to vary their technique, following the model of orators. All irrational and unruly techniques are acceptable when they produce "marvelous effects." These effects do more than compensate for any lack of logical coherence; the more graphic and surprising they are, maintains Vicentino, the more moved the listeners. He presents a meticulous list of words and images, each with its own representation by means of melodic, harmonic, and rhythmic figures. These are the precious ancient secrets wrested from oblivion, which the brutish ears of common folk cannot appreciate. This sort of stylization is reserved for the refined ears of discerning patrons of music. Vicentino does not deny the artificial, contrived, and affected qualities of this style. On the contrary, he makes a virtue of them. The implication is clear. Receptive listeners will understand that his adaptation of ancient music to modern practice enables them to participate in the lofty exercise of music described by so many ancient authors. He wrote what he thought were reasonably progressive works for large choirs, for example, but he reserved his truly radical works for the solo ensembles of aristocratic chamber music. The sincerity of Vicentino's humanist aspiration cannot be doubted. His belief in the value of resurrecting the secrets of ancient music was genuine in that he tried to realize a vision of the sublimity of Greek

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music. Because this revival was to take place in modern polyphony, Vicentino assessed the modern adaptation as superior to its model—a sort of emulation. The feasibility of his technical precepts is another matter, however. To attribute their deficiencies to his meager knowledge of classical sources is to misconstrue the problem. Simply put, he failed to grasp the inconsistencies between what he read and what he wrote. Scientific enquiry was not his strong suit, and no amount of reading would have corrected this weakness. The best way to introduce the subject of the genera is first to consider the sizes of the intervals relative to each other and then to discuss their tuning. If we take the tetrachord hypaton, B-E, the division of the fourth would yield the intervals seen in example 1.

Example 1 Intervals in the Genera Example 1 shows that the smallest interval is the minor diesis, even though in theory any minor diesis could be split into two commas. The major diesis (equal to two minor dieses) is the same size as the minor semitone. Which name is used will depend on the spelling of the interval: for example, B-C, is a minor diesis whereas C-O is a minor semitone. Three minor dieses make up the major semitone. Thus, a whole tone contains five minor dieses: B-B, B-B#, B*-C, C-C, and C-O, for instance. The fourth division in example 1 shows one way to write a major third enlarged by a minor diesis (B#-E), an interval Vicentino calls "proximate major third." (The major third from B* is E*.) Another way would be to

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keep the intervals as shown in Division 3, the enharmonic genus, but to inflect the last pitch, E, up one minor diesis, changing it toE. This alteration also creates the outline of an inflected fourth (a proximate fourth in Vicentino's terms) between B-E. Vicentino's rules for composing in the genera, either pure or mixed, are easy to understand. How they work out in practice is more difficult to unravel. The inconsistency of Vicentino's description of tuning systems need not trouble us here, because the verification of intervals does not depend on choosing between the two tunings he confuses in his text. One may verify the admissibility of intervals by using the integer ratios of Ptolemy's diatonic syntonon tuning, espoused by Vicentino's critic Zarlino and known today as just intonation. In many places in his treatise Vicentino seems to have in mind the diatonic syntonon, for he names its ratios for the whole tone (10:9 and 9:8), minor third (6:5), major third (5:4), minor sixth (8:5), major sixth (5:3), as well as for the perfect fourth (4:3), perfect fifth (3:2), and octave (2:1). A ratio for the major semitone is not specified; however, it (16:15) can be extrapolated by subtracting the "sum" of the 10:9 and 9:8 whole tones from the fourth.83 As I pointed out earlier, Vicentino does not elucidate this tuning in a systematic manner, nor does he name it or its ancient expositor. When Vicentino describes the species of intervals belonging to each genus, he speaks of a single melodic line. In this respect he seems to follow the practice of ancient musicians, as understood by the humanists of his day. He departs from this view when he insists that generically inflected melodies can be combined in a contrapuntal texture written according to the procedures of received practice in the mid-sixteenth century: that is, polyphony featuring imitative points, homophonic passages, and canon (though he dislikes canon because its abstract technical nature causes composers to disregard the projection of the text). Within this practice, composers may bend the rules of treatment of dissonance by introducing unruly and irrational interval species in order to express the affective nature of the words. The extent to which this should be done will depend on the social circumstances of the composition—the nature of the text, the performers available, the venue, and the audience. These are matters of decorum. Pertinent here is the technique of using the genera in polyphonic composition. The intervals of the fourth, fifth, and octave are common to all genera. Because these intervals define the structure and limits of the eight 83. There are also some approximate and some erroneous ratios given in Bk. V. The latter include 21:20 for the minor semitone and 14:13 for the major semitone.

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modes, their size may be inflected chromatically or enharmonically in linear sequence but never in simultaneous alignment.84 Intervals larger than the fifth, being compound, do not affect the genus. Hence, large and compound intervals may be used in any of the genera. Each genus, however, has a set of steps proper to it alone, and any member of this set suffices to define the genus. It follows therefore that a melody in, say, the chromatic genus cannot retain its purity when adulterated by steps proper to either the diatonic or the enharmonic, except when such offending intervals are separated by rests. Mixing the genera is certainly permitted, but the composer must understand how and when to do so. Music in the pure diatonic genus is restricted to the linear intervals of the diatonic major semitone and the diatonic whole tone. The intervals proper to the pure chromatic genus are major semitone, minor semitone, and minor third. Microtonal inflection is included in the following steps of the pure enharmonic genus: minor diesis (half of a minor semitone), major diesis (the same as a minor semitone), and major third. From this description it is evident that each pair of genera has one interval in common: the diatonic and chromatic share the major semitone, whereas the chromatic and enharmonic share the minor semitone. Therefore, the major semitone is foreign only to the enharmonic genus, just as the minor semitone is foreign only to the diatonic genus. Each of the other intervals—the minor diesis, whole tone, minor third, and major third—is exclusive to one genus. Vicentino maintains that inasmuch as modern composers deploy major and minor thirds and, to a lesser extent, minor or accidental semitones in the polyphony of his day, such music is not purely diatonic but rather a mixture of the genera. This was the issue he debated with Lusitano. Even if Vicentino had made it clear at the beginning that he was differentiating "pure diatonic" from "mixed diatonic" music, the debate would probably have shifted ground to become a wrangle about the status of thirds: were thirds simple or compound intervals? If they were classified as simple, Vicentino would have won. But if they were considered compound, Lusitano could have argued that they were made up of whole tones and semitones, intervals already present in the diatonic genus. In the event, Vicentino in his treatise doggedly refers to ordinary practice as "tempered and mixed music." Any compositions with minor semitones or thirds in their melodic contours must be classified as tempered and mixed diatonic music. 84. Vicentino writes proximate fourths, fifths, and octaves only in secular chamber music: proximate fourths and fifths appear often whereas proximate octaves are rare, though not unknown.

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Of course, one could write polyphony in the pure diatonic genus, a very limiting choice, according to Vicentino. Much more striking are compositions in the pure chromatic and pure enharmonic genera. In his treatise Vicentino provides examples of the three pure genera. He also recommends mixing the genera by means of various performance options, all of which entail selecting various combinations of written accidentals.85 The above excursus is clear as far as it goes. It explains the use of the adjective mixed by Vicentino with respect to ordinary or common practice. It does not, however, explain his use of tempered. The assumption behind example 1 is that there is a geometric (visual) division of intervals, an assumption characteristic of Aristoxenian tuning. Vicentino, of course, knew nothing about Aristoxenus' method except the allegation that it was "irrational," an allegation made by Boethius and later writers on the basis of remarks attributed to Ptolemy and other ancient theorists. Because Vicentino himself recommends using the instrument to help singers master the subtle intonation of the genera, it is best to abandon the diatonic syntonon in favor of the thirty-one-note tuning system on the archicembalo. In this tuning Vicentino combines temperament (in order to approximate the just thirds and sixths of the diatonic syntonon) and enharmonic inflection (in order to divide the whole tone into five dieses). The use of temperament explains the adjective tempered with respect to ordinary practice, insofar as thirds in this tuning are almost completely just or pure. And thirds, according to Vicentino, come from the chromatic and enharmonic genera. The division of the whole tone into five dieses, coupled with tempered thirds, allows the composer to deploy minor semitones, major dieses, minor dieses, and proximate steps and leaps of all sizes in the extraordinary and refined music that features the chromatic and enharmonic genera.

Book on Music Theory This little book lays out the theoretical basis in the abstract for the ensuing five books on music practice. Although, as Vicentino avers, its contents are derived mostly from Boethius, some material comes from other authors. In terse, unimaginative prose Vicentino surveys in rapid succession and in more-or-less logical sequence the Pythagorean ratios, the ancient tetrachords, the monochord, the three genera, the fourth-, fifth-, and octave-species, the eight modes, the range of stationary and movable steps, and the division of the whole tone into two semitones, 85. The way these options work in Vicentino's compositions in the treatise is explained in "Mixing the Genera," below.

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five dieses, and ten commas. The concluding chapter is a tedious apologetic list of omissions from the Boethian canon. The material is usually straightforward, except for a few oddities. For instance, the chapter on how to find the harmonic mean (according to Isidore of Seville) has no bearing on anything else in the book. More troubling is Vicentino's statement that the eight modes are derived from the octave-species. The modal structure he describes, based on Gaffurio's system of the eight church modes, does not correspond to that of the ancient octave-species copied from Boethius, even with the addition of the eighth mode, attributed to Ptolemy. Many music theorists in this period made facile assumptions about the octave-species and the modes similar to that put forward by Vicentino. Most of them glossed over the discrepancies and did not try to tell their readers how the ancient octavespecies changed into the species they knew. Few went so far as to describe both systems in such minute detail, and none would have done so while asserting that the two were matching sets.

Book I on Music Practice The main burden of Book I is to explain the linear intervals available in melodies composed in the diatonic, chromatic, and enharmonic genera. Before laying out this pitch repertory, Vicentino indulges in historical speculation, some of it fairly accurate and some highly fanciful. From the achievements of Guido of Arezzo, especially in solmization, he goes on to the notational inventions of Jehan des Murs. Here Vicentino inserts a digression on the social usage of the genera according to propriety; we are to understand that as an innovator Vicentino belongs to an august tradition. He next presents his solmization system, designed to accommodate the inflections produced by the three genera. But the gamuts in chapter 5 are theoretical constructs with little, if any, practical benefits. In order to arrive at a closed system Vicentino had to devise solutions that deviated from standard solmization patterns. This is confusing in a system that is so complex it requires a set of five syllables to pass from one diatonic whole tone to the next—actually, two different sets of five, one going up and one down. To add to the confusion, the hapless reader encounters unexplained applications of "mutatio mentalis et vocalis"86 and many errors and omissions in the music examples. 86. On "mutatio vocalis et mentalis," see Aaron, Libri tres de institutione harmonica (Bologna, 1516), Bk. I, chap. 13, and Stefano Vanneo, Recanetum de musicaaurea (Rome, 1533), Bk. I, chap. 21.

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All patterns, regular and irregular, are deployed so as to make it possible for a singer to go through the gamut twice, once in the soft and once in the hard hexachord. The natural hexachord is affiliated with the other two and may be used whenever necessary or convenient. It should noted that the bifurcated system of hexachords is relatively new in the mid-sixteenth century. The bulk of Book I is devoted to detailed descriptions, illustrations, and characterizations of each interval, beginning with the comma, continuing through the minor enharmonic diesis and the major enharmonic diesis (or minor semitone), and finishing with the proximate imperfect fifth, the natural fifth, and the accidental fifth. Perhaps tired of his own pedantry, Vicentino lumps the rest (the larger intervals) into a single chapter and quickly closes the book with a Tree of the Division in an attempt to schematize the intervals within the octave. The characterization of each interval according to its direction and speed calls forth a battery of adjectives, the most frequent of which are tense (coupled with cheerful) and slack (coupled with sad). Such adverbs as very and somewhat indicate degrees of intensity, as do stronger adjectives like sweet, gentle, vivacious, and imperious.

Book II on Music Practice Having described linear intervals, Vicentino turns to progressions in two or more steps and for two or more voices. Book II deals essentially with matters of voice-leading in part music that is limited to the ordinary vocabulary of the tempered and mixed diatonic genus. The polyphonic handling of the pure chromatic and enharmonic as well as the hybrid genera is put off to Book III. Hence, Book II can be categorized as a section on the rudiments of composition. For the most part, the chapters follow in logical sequence, starting with the unison and ending with the fifteenth and twenty-second. The introductory chapter, on the principles of composition, is redundant and needlessly complex, but it nonetheless introduces some intriguing criteria of aesthetic value. Noteworthy in this book are the chapters on the tritone, the imperfect fifth, hidden parallel octaves, free dissonances, syncopation of various kinds, leaps, and rates of motion. The music examples usually bear such prescriptive captions as "for two voices," "for eight voices," and "for four or more voices." These are clear but by no means consistently applied. The reader will also find descriptive captions: "good," "not too good," "bad," "better," "old-fashioned," "not too modern," and "doubtful."

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Vicentino does not expand the detailed characterization of melodic intervals to include intervals in simultaneous alignment, despite his emphasis in the introductory chapter on the importance of matching linear and simultaneous intervals in counterpoint—that is, on taking care not to negate the character of a linear sequence with inappropriate simultaneous progressions. Only imperfect simultaneous intervals—thirds and sixths, both major and minor—are accorded characterization. Even so, it is not clear how their deployment would affect the character of a composition. In the last chapter Vicentino makes some helpful comments on tempo, thus picking up one of the threads in his opening on compositional goals. In addition to several digressions on the sins committed by singers, this book contains commentaries of differing length and cogency on such subjects as natural number, mathematical unity, and Trinitarian doctrine. Although the thrust of the book is eminently practical, Vicentino injects some passing remarks on harmonic science, chiefly with respect to the mathematical definition of imperfect consonances.

Book III on Music Practice The intriguing feature of Book III is the music illustrating the genera, pure or mixed, in modern polyphony. Vicentino's exposition of the genera follows a set pattern. He first describes the species of fourths, fifths, octaves, and modes in each genus. He then goes on to discuss cadences and closes with an example. Near the end of the book he prints three compositions, each of which mixes the genera in a different way. The book ends with a rambling and confused account of stationary and movable steps. The closing chapters on the mixed genera are balanced by the opening ones on the pure genera. The pure diatonic genus, according to Vicentino, is to be distinguished from the tempered and mixed diatonic used in the music of his day. The structure of the eight pure diatonic modes, as in the "Book on Music Theory," is derived not from the seven octave-species of ancient music but rather from the church modes. Nonetheless, the names (Dorian and Hypodorian through Mixolydian and Hypermixolydian) and, by inference, the ethical qualities imputed to these allegedly ancient modes are ascribed by Vicentino to the ancient Greeks. Transposition with one flat ("on the soft hexachord") or with several flats ("feigned music") introduces the eight modes as they appear in the tempered and mixed diatonic. A digression at the start of this excursus brings together the subjects of Vitruvius and architecture, painting and

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perspective, the importance of the text, and the decorum of modal stability and modal anarchy. The description of the ordinary modes concludes with a snarled misconstruction of Glarean's extra modes, which Vicentino dismisses out of hand. After describing pure diatonic cadences using only diatonic major semitones, Vicentino demonstrates the pure diatonic mode in a four-voice composition without a text (see example 26). The next eight chapters, on cadences in ordinary practice, concentrate mainly on commonplace techniques. However, Vicentino's comments on diminished cadences, avoiding the cadence, and voice function (soprano and bass in particular) are generally perceptive and occasionally innovative. A single chapter on composing for five parts closes off this section. The next section concerns composition in the pure chromatic genus. The description of species, modes, and cadences is condensed into eight chapters. This section ends with the illustration of a cheerful chromatic motet for four voices, Alleluia. Haec dies. In the final section, five chapters suffice to deal with enharmonic species, modes, and cadences. Vicentino inserts one chapter on mixing the species of the genera. It should be noted that his treatment of genus and species, here and elsewhere, is less than a model a clarity. The music example is a fragment of a pure enharmonic madrigal for four voices, Soav'e dolcardore. Each of the next three chapters demonstrates how to mix the genera in a composition. Two partial four-voice madrigals, Dolce mio ben and Madonna, ilpoco dolce, can be performed in five different ways. In the fourvoice secular Latin work, Musica prisca caput, in honor of his patron Ippolito II, the genera are presented in succession: diatonic, chromatic, and enharmonic. Vicentino concludes with a somber five-voice liturgical motet in the pure chromatic genus, Hierusalem, Hierusalem.

Book IV on Music Practice Book IV has been called musica poetica, an apt term insofar as the book covers compositional techniques from rudimentary to advanced levels.87 The first thirteen chapters present routine lessons on notation, for the benefit of composers and performers. The next three chapters— on how to begin, continue, and end a composition—raise the level of the discourse. From this point on, technical rules are always qualified with respect to genre, style, and decorum. Before embarking on the rules of counterpoint, Vicentino gives the 87. Kaufmann, Life and Works, p. 147.

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reader recommendations on spacing and texture, on avoiding barbarisms in pronunciation, on varying the tempo, and on deploying major and minor thirds to achieve happy and sad moods, respectively, along with a warning to singers not to inflect thirds without considering the text. The next seven chapters proceed from a discussion of two-voice counterpoint to one about composing for two and three choirs. As noted earlier, this pedagogical sequence is interrupted by a chapter on improvised counterpoint based on Lusitano. Chapters 29 and 30, on prosody and the representation of moods and images of a text, are central to Vicentino's aesthetic. They lead naturally to an exposition of more sophisticated techniques. But only after an oddly placed chapter on proportions does Vicentino deal with such advanced compositional procedures as fugue (syntactic imitation), canon, and double and invertible counterpoint. The final chapters have a practical goal: they tell the reader how to find unwritten canons, how to check for errors, and how to conduct. In the latter, Vicentino advises singers to project the spirit of the music, taking as their model the art of the orator. Book IV ends with the story of the debate.

Book V on Music Practice About the Instrument Called the Archicembalo Book V is replete with repetitive lists, examples, and exercises geared to teaching and to learning by rote. The usefulness of this material must be questioned, especially in view of the high incidence of typographical and/or authorial errors and omissions. The archicembalo, with its two manuals and six ranks of keys (three on each manual), was legendary.88 In the opening chapters of Book V, Vicentino describes the dimensions of the instrument: it is about 194 centimeters long, 77.6 centimeters deep, and 21.4 centimeters high. The keyboard spanned three and a half octaves from IF to Id Vicentino had drawings made of the two manuals of the keyboard, which are reproduced here as figures 1-3.89 As an aid to the discussion of the two manuals and their tuning, Appendix II presents a schematic drawing of the keys in one octave for each manual. The first manual has 19 keys per octave: 7 diatonic white keys in the first rank, 5 black keys in the second rank, and 7 shorter black keys in the third rank. The second manual has 17 keys per octave: 7 88. Luzzaschis prowess on the archicembalo is mentioned by Bottrigari in IlDesiderio, p. 41 (MacClintock translation, p. 51). 89. See also App. II. The names of the keys on the archicembalo are prefaced by Arabic numbers to indicate the ranks from 1 to 6.

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white keys in the fourth rank, 5 black keys in the sixth, and 5 shorter black keys in the sixth. Thus, each octave has 36 keys in all, and the entire keyboard encompasses 130 keys from IF to lcf. Appendix II and figures 2-3 will confirm that the highest rank in each manual contains "split" black keys except for the short keys in the third rank that split the diatonic semitones of the first rank. When referring to keys of the archicembalo, the translation includes first the rank on which the key appears and then the modern spelling of the note. Vicentino describes two different tuning systems for the archicembalo. The first of these produces a thirty-one-note octave. As near as can be determined, the first two ranks of keys on the first manual are tuned in meantone. The third rank of 7 keys splits the 5 black keys of the second rank and adds 2 half-size upper black keys between the diatonic semitones. These 12 black keys divide the major semitone, whether diatonic or chromatic, into one major and one minor diesis. Thus, the first manual produces a nineteen-note octave. The fourth rank, first on the second manual, is one diesis higher than the first rank on the first manual. The 7 keys on the fourth rank divide the minor semitones between white and black keys on the first manual into two minor dieses. The 5 keys on the fifth rank divide the minor semitones between black and white keys on the first manual into two minor dieses. As a result, the thirty-one notes in the octave are one diesis apart. This sort of "equal temperament" is audible only when the instrument is played in the three genera mixed together. In the diatonic genus, or in the diatonic and chromatic genera combined, the tempering reverts to meantone. Indeed, the first tuning system of the archicembalo is meant to substantiate Vicentino's contention that the music of his day was in the tempered and mixed diatonic. It must be said that the role of the sixth rank of keys in the first tuning system is not at all clear. Vicentino intended to have 7 split black keys in this rank but could only fit in 5. These 5 keys divide the minor diesis between the white keys of the first rank and fourth ranks into two commas. In some circumstances, not always accurately described or illustrated, the comma keys are supposed to produce consonances closer to pure sizes than the other inflections possible on the instrument. But this rank is incomplete and hence limited in function. The sixth rank, however, is indispensable to the second tuning system. The 17 keys of the second manual are tuned by perfect fifths from the appropriate keys on the first manual, which is still in meantone. By following Vicentino's careful instruction for fingering, a performer can play

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thirty almost-pure major and minor three-note or four-note vertical sonorities, out of a possible thirty-four. Intriguing though this second system may be, it is clear that everything Vicentino has to say in the rest of the fifth book takes the first tuning system as a point of departure. Five chapters are devoted to illustrating the seven octaves from 1A to 5G1* on each of the 5 keys (minus the comma rank) that divide the whole tone into five minor dieses. Chapter 59, double the length of the chapters just mentioned, is an interminable lesson in clef reading. Vicentino shows the player what each of the seven octaves looks like in the clefs that house its natural diatonic notation, as well as in eight other clefs that use chromatic and enharmonic accidentals to reproduce the natural diatonic pattern. Discounting the comma keys in the sixth rank (about which more below), the keys on the other five ranks of the archicembalo produce a thirty-one-note octave. In chapters 8-38 Vicentino attempts to list and illustrate, chapter by meticulous chapter, every single perfect and imperfect consonance, together with all the available inflections above and below each of the 31 keys. This attempt, though valiant, fails. He forgets 4F altogether. With regard to the other keys, it is rare that Vicentino's long verbal lists of consonances tally with the music examples. His description of major and minor semitones, whole tones, and minor dieses is less pedantic and more instructive. But here as elsewhere, problems arise from Vicentino's use of such directional terms as ascending and descending. In the act of playing, the placement of fingers and hands may contradict the direction of linear intervals. For instance, a "downward" movement—that is, to the left on the keyboard—from 1A to 6 A produces the step of an ascending comma; a backward shift by the hand away from the body from 2G& to 3A& produces an ascending minor diesis, whereas the same motion from 2B17 to 3A* on a split key produces a descending minor diesis. Clearly, players of the archicembalo had their work cut out for them. And it is not surprising that Vicentino, too, should have been confused from time to time. Notation also adds to the confusion. There are no enharmonic equivalents, in the modern sense of the term, in the thirty-one-note octave: for instance, 2G* is not the same as 3A1'. But the system needs to be a closed one. Thus, pitches described occasionally as "C#" and "F#" are the enharmonic equivalents of 5D and 5G , respectively, and pitches notated occasionally as O and F^ are the enharmonic equivalents of 4B and 4E, respectively. The only extant keyboard instrument that resembles Vicentino's archicembalo is the one-manual harpsichord built by Guido Trasuntino

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of Venice in 1606 for Camillo Gonzaga, count of Novellara.90 This instrument has a thirty-one-note octave and lacks the sixth rank, a feature that supports the hypothesis that this rank is not required for the first tuning system. Instead of putting the fourth and fifth ranks on a separate manual, Trasuntino hit on the more practical solution of splitting the "accidental" keys (his are white whereas Vicentino's are black) into two sets of two split keys, making a total of four for each, and inserting a narrow split key instead of a single half-key between the diatonic semitones. This arrangement makes the instrument easier to play.

The Diatonic, Chromatic, and Enharmonic Compositions I should like now to discuss the compositions written by Vicentino according to the rules of the genera: first a purely diatonic work; then two purely chromatic works; and finally a purely enharmonic work. After considering the problems inherent in Vicentino's methods of mixing the genera, I shall discuss the three works in the mixed genera. Finally, I shall analyze the example in the genera reprinted by Vicentino from Lusitano's treatise.

A Diatonic Composition Without Words Pure diatonic music is harsh. It cannot express the words because of its paucity of consonances; particularly noticeable is the absence of major and minor melodic thirds. Of course, Vicentino overlooks the presence of simultaneous major and minor thirds produced by contrapuntal voiceleading. To show what such counterpoint would be like, he creates a four-voice example without a text. When he later recapitulates the compositions in the genera, he excludes this work, since it is merely an academic exercise, not a composition. The exercise is strict.91 90. Pictures of this instrument, now in the Museo Civico of Bologna, are available in John Henry van der Meer, "Trasuntino," Die Musik in Geschichte und Gegenwart, 13: 626; Raymond Russell, The Harpsichord and Clavichord (London, 1959), Plates 13A-B; Wilhelm Dupont, Geschichte der musikalischen Temperatur (Nordlingen, 1935), p. 53.Thearchicembalo attributed to Vicentino by Cardano (see note 18, above) bears little resemblance to the instruments described here. Bottrigari mentions the existence of three instruments—the archicembalo kept in Ferrara and an arciorgano made in Rome for the late cardinal of Ferrara and another made in Milan under the supervision of Vicentino. Just before he died, Vicentino was apparently working on the construction of yet another archicembalo. See Ildesiderio, p. 41 (MacClintock translation, pp. 51-52); also note 88, above. 91. The eight melodic thirds all have intervening rests. Because all the semitones must be diatonic, not even the penultimate note in the soprano should be raised.

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Alleluia. Haec dies This pure chromatic motet for four voices shows that if it is not too outrageous, chromatic music can be sung in church by any ordinary choir. Since Alleluia. Haec dies is an Easter text, the motet must project a joyous rather than a sad mood. For this reason, notes Vicentino, he has introduced a few major thirds from the enharmonic genus on significant words. The words are "and rejoice," and Vicentino uses for them the ascending major third, an interval with a markedly cheerful character.92 The motet has a relatively stable harmonic design.

Hierusalem, Hierusalem More somber, in keeping with its liturgical function, is the pure chromatic motet for five voices. The text is the refrain for the three lessons in the first nocturne for matins on Maundy Thursday, Good Friday, and Holy Saturday. Vicentino singles out the opening fugue because it presents the chromatic tetrachord, and he alternates the order of the two semitones and the minor third. This contrapuntal deployment of the tetrachord produces constant semitonal inflection and fluctuation between minor and major sonorities. With small circles of fifths and thirdrelated vertical sonorities, the fluctuation results in mildly unstable harmony.

Soave dok'ardore Vicentino demonstrates pure enharmonic music with the first fourteen measures of a four-voice madrigal. Though fragmentary, Soav'e dolcardore indicates some of the problems endemic in writing enharmonic counterpoint. Discounting note repetitions, the piece has seventy melodic intervals. Of these, fifteen (about 22 percent) do not belong to the enharmonic genus: four minor thirds, eight major semitones, and three whole tones.93 Only the bass is a pure enharmonic melody. One could excuse the three descending minor thirds (mm. 5 and 7 and three of the major semitones (mm. 11-14) as text-oriented exceptions, since the first group sets the words "sweet passion" and the second 92. Vicentino's count of major thirds is not accurate. There are, as he says, two in the soprano (mm. 17—18 and m. 19), one in the alto (m. 15), and one in the bass (m. 18). Bu the tenor has only one major third (mm. 15-16); the part also features two ascending whole tones (m. 17 and mm. 17—18), which Vicentino neglects to mention. 93. Minor thirds: soprano, m. 7; tenor, mm. 5 and 11; bass, m. 7. Major semitones: soprano, mm. 13-14; alto, m. 5, mm. 1-12, and m. 12; tenor, mm. 4, 5, 13, and 13-14. Whole tones: alto, m. 5; tenor, mm. 5 and 12.

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the word sighs. Minor semitones and minor dieses would have projected the words just as effectively, however. One suspects that these lapses, like others noted below, result from Vicentino's grappling with the exigencies of harmony and counterpoint. Enharmonic inflection creates "proximate" intervals, that is, intervals enlarged or reduced by one minor diesis. When writing in the enharmonic genus, the composer must alter many legitimate melodic intervals into proximate size—including fourths, fifths, and sometimes octaves. But in Soave dolc'ardoreVicent'mo uses this devise to camouflage seven extraneous melodic steps (10 percent of the total): two major semitones, two whole tones, and three minor thirds.94 Scrutiny of the simultaneous sonorities in this excerpt shows that each of them, regardless of how eccentric the spelling may seem, is a perfectly aligned major or minor vertical sonority. These sonorities take precedence over, and indeed are the reason for, the melodic anomalies noted above. The strangeness of the harmony arises from the constant shifts between the diatonic and the enharmonic vertical sonorities formed by the linear contours of the four voices.

Mixing the Genera Dolce mio ben and Madonna, il poco dolce are the first halves of two four-voice madrigals that exemplify ways of mixing the genera by means of various performance options. According to Vicentino each work can be sung in five ways: diatonic, chromatic, chromatic and enharmonic, diatonic and chromatic, and diatonic, chromatic, and enharmonic. He gives details of only the first three options, however. In the diatonic, the singers ignore all accidentals. In the chromatic, they sing the flats, sharps, and naturals, but not the superscript dots. In the enharmonic, they sing all the accidentals, including superscript dots. From these instructions, we may extrapolate the procedures of the fourth and fifth options. To combine the diatonic and chromatic, the singers would ignore all superscript dots and sing some, but not all, of the other accidentals. To mix the three genera, they would sing all the superscript dots and omit some of the other accidentals. These strategies are logical in the context of Vicentino's rules for defining the melodic content of each genus in its 94. Enlarged major semitones: soprano and alto, mm. 3-4. Reduced whole tones: soprano, mm. 4-5 and 9. Enlarged minor third: tenor, mm. 4-5. Reduced minor thirds: bass, mm. 5-6 and 13. Four extraneous intervals have intervening rests, two of them enharmonically inflected: minor third (soprano, mm. 5-6 and 8-9); proximate minor third (alto, m. 13); and proximate whole tone (tenor, mm. 10-11).

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Introduction

pristine state. But the applicability of the five options in the two compositions seems capricious at best. Each madrigal is based on a distinct premise, which in turn raises several different problems, some apparently irremediable. Vicentino was either hasty or lazy. He seems not to be aware, on the one hand, that each madrigal exhibits only one unproblematic option or, on the other hand, that neither can be performed in all five ways.

Dolce mio ben The only option for performing Dolce mio ben that poses no difficulties is the third, using all the accidentals for the chromatic and enharmonic genera. The madrigal exhibits neither melodic nor harmonic irregularities. That this was the original version of the composition is corroborated by Vicentino's description of the work as a completely chromatic madrigal with a few enharmonic intervals. Because of the prominence of melodic thirds, both major and minor, there can be no purely diatonic version of this work. The first option, therefore, works only if the key signature is observed as a means of transposing the mode. Omitting the key signature, which Vicentino associates with modes five and six in modern polyphony, produces far too many diminished and augmented intervals between B and R The omission of the accidentals does away with minor semitones (or major dieses) and minor dieses, but does not eliminate the forty melodic thirds; it can only change their species.95 Dolce mio ben is in the tempered and mixed diatonic, so to speak. Even so, there are three dissonant vertical sonorities and one dubious simultaneous alignment. The latter (first half of m. 17) occurs on the second note of a melodic tritone in the bass. The former (first half of mm. 5, 9, and 21) are the products of carelessness, inasmuch as Vicentino failed to realize that omitting the flats on the thirds of these sonorities would not harmonize the now naturalized notes with their uninflected fifths and octaves. Leaving the flats in does not solve the problem, for all the intervals formed by the flattened notes would become proximate, producing enharmonically inflected vertical sonorities. The alternative— lowering the flattened notes (gf|? and d'1') to f and c' respectively—breaks the rules by introducing melodic minor semitones. 95. Six thirds in the soprano: mm. 2-3, 4, 12-13, 17, 20, and 22; fourteen in the alto: mm. 1-2, 2, 6, 7-8, 9-10, 10, 11-12, 12 (two), 14, 17-18, 19, 21, and 21-22; twelve in the tenor: mm. 3, 5, 8, 10, 12 (two), 14-15, 17, 22, 23, 24, and 24-25; and eight in the bass: mm. 3, 3-4, 5-6, 10, 13, 15, 17-18, and 19-20.

Introduction

Iv

In the "sweet chromatic" version, we encounter the same set of problems in a slightly different guise. The second notes of three prohibited melodic intervals—all minor enharmonic dieses—form enharmonically inflected vertical sonorities that are foreign to a chromatic work.96 Omitting the flats produces the melodic interval of the major semitone, a species permitted in the chromatic genus; however, the resulting simultaneous sonorities would then be same as the dissonant ones in the diatonic version. Changing the flattened notes (g^ and d'1*) to the natural pitch below (f and c1) not only "corrects" the simultaneous sonorities in question but also follows the rules of the pure chromatic genus. All in all, the second option works better than the first, though not as well as the third. Although the fourth option, a combination of the diatonic and chromatic genus, permits the singers some discretion in the use of accidentals, it does not of itself solve the problem of the three dissonant sonorities (mm. 5, 9, and 21). It is necessary to correct these in the same way they are fixed in the purely chromatic option. The final option, which combines all three genera, is workable only if the intervals of the enharmonic genus are never omitted. Their presence ensures that the problematic sonorities discussed above are consonant major sonorities. In choosing which other accidentals to keep, the singers must take care to sing all the flats on the first half of m. 17 in order to avoid the problem noted above with respect to the first diatonic option. Madonna, ilpoco dolce There is only one faultless and hence unproblematic way to perform Madonna, ilpoco dolce\ by means of the fifth option, which combines the three genera. Again, the key signature and all enharmonic inflections must be observed, whereas discretion may be exercised in the use of other accidentals. A passing-note on the second beat of m. 31, on the words "to weep," produces the sole enharmonically inflected "major triad" in the composition. This sonority must be sung as written: otherwise, there will occur intolerable dissonances like those noted in Dolce mio ben. The other four performance options entail problems of varying degrees of complexity. To perform the diatonic option, the singers must omit not only all the accidentals written in their parts but also the key signature. Since the 96. First half of mm. 5 and 21: d, a, d', g*. First half of m. 9: A, e, d'1*, a and A, a, d?t, e'. The major thirds in these sonorities are enharmonically enlarged and the minor thirds correspondingly reduced.

Ivi

Introduction

madrigal is in G Dorian, retaining the key signature would produce a number of diminished and augmented intervals between B^ and E. This is exactly the opposite solution to the one suggested for the diatonic option of Dolce mio ben. Nonetheless, Madonna, il poco dolce, with its forty-five melodic thirds, is also in the tempered and mixed diatonic genus.97 Harmonic problems akin to those found in the diatonic version of Dolce mio ben appear in greater numbers in this madrigal. Because the diatonic option of Madonna, il poco dolce lacks a B1*, a total of nine diminished vertical sonorities result, involving the pitches B, D, and F in a variety of simultaneous alignments.98 One cannot avoid these awkward alignments by keeping the key signature intact, because doing so would produce another thirteen diminished sonorities, some lasting an entire measure.99 Moreover, the lowering of G1' and D1* to G and D, respectively, as required for major sonorities in the enharmonic genus, results in ten dissonant sonorities.100 For possible solutions, see the discussion of the diatonic option of Dolce mio ben. The chromatic option for Madonna, ilpoco ^/^necessitates the singers observing the key signature and all accidentals except for the superscript dots. Even with the application of these flats, sharps, and naturals, the incidence of linear intervals that are extraneous to the chromatic genus is so high as to nullify its purity: sixty-one whole tones, nine major thirds, and four minor dieses—about 25 percent of the total (discounting repeated notes).101 The harmony features the same enharmonically 97. Eight thirds in the soprano: mm. 9-10, 12, 21, 25, 28, 32, 32-33, and 42-43; fourteen in the alto: mm. 2-3, 3, 12, 12-13, 14, 16, 28, 29, 30-31, 31, 32, 34-35, 39-40, and 41-42; nine in the tenor: mm. 2-3, 12-13, 13, 15, 16, 26, 27, 34, and 40-41; and fourteen in the bass: mm. 2,4, 7-8, 8, 8-9, 13 (two), 17-18, 22-23, 25, 31-32, 32-33, 33, and 38-39. 98. First beat of mm. 22 and 31; second beat of mm. 24 and 31 (the latter with a dissonant e' in the soprano); third beat of mm. 30 and 41; last half of mm. 21, 33, and 34. 99. First and fourth beat of m. 37; second beat of m. 31, with a dissonant fin the tenor; third beat of m. 24; fourth beat of m. 29; first half of mm. 6, 8, 10, 25, and 41; all of mm. 15, 18, and 39. 100. First half of mm. 2, 5, 23, 27, 28, and 29; beat 3 of m. 36; last half of mm. 4, 20, and 40. 101. Thirteen whole tones in the soprano: mm. 2-3, 3 (two), 3-4,9, 10, 11-12, 12, 1213,31-32, 34, 35-36, and 39-40; twelve in the alto: mm. 2, 3, 9 (two), 13, 15,15-16,1920, 24, 31-32, 37, and 37-38; twenty-five in the tenor: mm. 3, 3-4, 4, 7-8, 8, 11 (two), 14-15, 15-16, 17-18, 22-23, 25, 29, 30, 32-33, 33-34, 34-35, 36-37, 38, 38-39, 41 (two), 41-42, 42, and 42-43; and eleven in the bass: mm. 3, 3-4, 9, 10, 11 (two), 13, 1415, 18-19, 33-34, and 38. Four major thirds in the alto: mm. 2-3, 12-13, 31, and 39-40; four in the tenor: mm. 15, 16, 21-22 (proximate), and 40-41; and one in the bass: m. 33.

Introduction

Ivii

inflected sonorities as Dolce mio ben, but they occur more frequently in spite of the small number of melodic minor dieses.102 The way to eliminate these sonorities, which are foreign to the chromatic genus, is the same as in Dolce mio ben. The third option calls for the singing of all accidentals, including superscript dots. Since the enharmonic genus joins with the chromatic, all the melodic major thirds and minor dieses are acceptable; however, the melodic whole tones are not. Of course, all the erstwhile major vertical sonorities, which featured disallowed proximate thirds in the purely chromatic option, now become consonant. Harmonic problems have been resolved, although the melodic contours still exhibit impurities. The result of the fourth option is the opposite, for the mixing of the diatonic and chromatic genera ensures that the ratio of foreign melodic intervals is sharply reduced (only nine thirds and four dieses). But the harmony retains the eleven problematic sonorities associated with the chromatic version. Musicaprisca caput A secular Latin motet for four voices that sets a prose text in honor of Vicentino's patron, Ippolito II Cardinal d'Este, Musicaprisca caput is the most successful composition in the treatise. There are no signs of negligence or indolence. A few slips, perhaps, in the linear genera, but these could be forgiven for the sake of faultless harmony and hints of theoretical justification. The composition is divided into three continuous sections, one in each genus—diatonic, chromatic, and enharmonic—that match the meaning of the text. The first (mm. 1-15) consists of whole tones and major semitones in linear sequence. This section shows the pure diatonic genus. The harshness attributed to this genus by Vicentino, one surmises, is intended to portray the "darkness" in which ancient music has languished. Extraordinary, even radical, chromatic vocabulary in the second section (mm. 15-30) represents the "antique and sweet numbers," now rediscovered and rejuvenated. The appearance of enharmonic harmony in the last section (mm. 31-48) builds to a climax. The name Ippolito is always accompanied by enharmonic vertical sonorities. At the end, the Two minor dieses in the soprano: mm. 26-27 and 43-44; one in the alto: m. 40; and one in the tenor: m. 36. 102. First half of mm. 2, 5, 23, 27, 28, and 29; beat 2 of m. 31; beat 3 of m. 36; last half of mm. 4, 20, and 40.

Iviii

Introduction

notion of "high" is depicted by an enharmonic octave leap surrounded by diatonic notes and the sending of Ippolito's deeds "above the heavens" by two proximate octaves in succession. The rhetorical gesture is unmistakable. The fact that the first section of this motet, while unremarkable, has neither melodic nor harmonic errors shows that it is possible to compose a relatively short piece of vocal music in the pure diatonic genus. Therefore any dissonant and awkward moments in the first option of either Dolce mio ben or Madonna, ilpoco dolce cannot be excused as the inevitable outcome of pure diatonic counterpoint. For some reason, the purity of the genus in the diatonic section of Musica prisca caput is not matched by the chromatic and enharmonic sections. The pure chromatic genus is adulterated by ten extraneous intervals.103 Most occur near the end and hence might be excused as cadential ornaments. Be that as it may, these foreign intervals make up almost 9 percent of the melodic steps in a homophonic and homorhythmic section. There are four intervals that are foreign to the pure enharmonic genus.104 Seven disallowed intervals are masked by enharmonic inflection.105 These eleven extraneous intervals account for 12 percent of the melodic steps. Not all the melodic errors in genus are explicable in terms of voiceleading between consonant simultaneous sonorities, although some do fit this category. Vicentino suggests another justification in his description of the tripartite division of the text, each verse of which is set in turn to the species of the diatonic, the chromatic, and the enharmonic genus. The key word here is species, for species refer to a specific size and type of interval, genus to a specific sequence of species. It is possible, then, to have a chromatic enharmonic species in the pure enharmonic genus, if the species in question entails a spelling normally associated with the chromatic. It is also possible to compose music consisting of the species of a genus, thereby indicating that the genus need not be pure. Although Vicentino is by no means consistent in his technical terms, the wording used to describe the application of the genera in Musica prisca caput seems not to be accidental. 103. One whole tone in the soprano: m. 19; two whole tones in the alto: mm. 28-29 and 29; four in the tenor: mm. 28 (three) and 28-29; two in the bass: mm. 29-30 and 30. One proximate major third in the alto: mm. 26-27. 104. One major semitone in the soprano: m. 39. Three minor thirds in the bass: mm. 38, 41-42, and 42. 105. One proximate major semitone: alto (mm. 39-40). Two proximate whole tones alto (m. 43) and tenor (mm. 45-46). Four proximate minor thirds: alto (mm. 31-32), tenor (m. 38), and bass (mm. 34 and 45-46).

Introduction

lix

Lusitano s Polyphonic Example of the Genera In the last chapter of Book IV, Vicentino rehashes the debate with Lusitano, agonizes over the unfavorable verdict, and attempts to vindicate himself by mustering additional arguments for his cause and by excoriating the judges and his adversary for their manifest stupidity. He ends with a fusillade against a bit of counterpoint in the mixed genera that was composed by Lusitano, which he inaccurately reprints toward the end of this chapter.106 Before examining Lusitano's example and Vicentino's blistering comments, we should consider what Lusitano had to say about the genera.107 His remarks, though concise, are not models of clarity. An adherent of Pythagorean tuning (the diatonic ditoniaion), Lusitano defines the steps of the diatonic genus as tone, tone, and minor semitone; the steps of chromatic genus as minor semitone, major semitone or apotome, and minor third; and the steps of the enharmonic genus as diesis, diesis, and major third. A diesis has two commas, a minor semitone four commas, and a major semitone five commas. His notation is intended to depict graphically the size of these intervals—two crossed lines for the diesis, four for the minor semitone, and five for the major semitone.108 From the text and music example, it is evident that Lusitano needs three kinds of "sharps"—two-stroke (x), four-stroke (j|), and five-stroke (^)—to indicate the number of commas by which an ascending step is raised above any given pitch. He does not describe the notation of descending steps, except for a passing reference to the flat for the downward major semitone: this means simply that a flattened note forms a minor semitone above a natural note and a major semitone below a natural note. Lusitano does not explain when one should use the four-stroke sharp as opposed to the flat for an ascending minor semitone. In Lusitano's example, there is only one integral minor semitone—at the end of the alto voice. Its spelling is discussed below. In melodies, the diesis may split the minor semitone of the diatonic and chromatic genera. The major semitone, Lusitano states, is not divided in any of the genera, although in his opinion one may break it up into a diesis and another unspecified interval of three commas. He justi106. From Introdutione facilissima dr novissima, fols. F2v-F3r (Galdrone facsimile edition, pp. 22v-23r). The original bears the caption "Esempio come si metteno in consonantie" (Example of how they [the Genera] are harmonized). 107. Vicentino quotes part of the relevant passage in Bk. IV, chap. 43. 108. In Vicentino s text these distinctions are not observed, either because of his own or the printer s negligence. This is why example 43 in the introduction is taken from Lusitano s treatise.

be

Introduction

fies this unequal division by comparing it to the division of the whole tone (made up of nine commas)109 into a minor and major semitone. The major semitone, we are to understand, is sung only in the chromatic genus. Under ordinary diatonic circumstances, the whole tone is made up of two minor semitones (four commas apiece) and one comma. It is not clear why Lusitano bothers with the hypothetical division of the major semitone. All major semitones in Lusitano's example are undivided, though at first glance the notation might suggest otherwise. Vicentino makes no attempt to deal with the linear sequence of intervals in the individual voices, probably because he did not understand it. In the top three voices, the intervals are collocated in such a way as to demonstrate the mixture of the genera. But Lusitano's idea of the function of accidentals is singular. It seems that some, but not all, of the accidentals are cumulative—that is to say, certain signs must be read only with respect to the preceding pitch, and hence the system works only in one direction: in this case, in ascending order. At any given point, the performers are supposed to look at the next note in order to discover how many commas higher they should sing. For instance, Cx would indicate different pitches, depending on whether it came between C and 0 or between 0 and D. This distinction between notation and pitch may seem easy enough to master once singers become accustomed to it, but it cannot be and indeed is not consistent. Unless natural notes, regardless of their placement, correspond to stable pitches, mayhem will ensue. And confusion reigns when natural notes are spelled with accidentals, as at the end of the alto voice, where B^ (indicating five commas above the preceding B1*) is to be read as equivalent to B^. This pitch forms a major semitone above the preceding & and a minor semitone below the succeeding C. The B^ itself is meant to signal the minor semitone above A. Why did Lusitano not use A* for this pitch? He had to write a B^, inasmuch as the minor semitone above A has been mediated by a diesis; therefore, a fourstroke sharp after a two-stroke sharp would raise the pitch in question six commas above A instead of four. So, like natural notes, flattened notes must be read as equivalent to stable pitches. Only sharps are cumulative. The splitting of the diatonic minor semitone is easy to find. In the alto, A goes to B^ via A1*; the latter forms a diesis with the pitches before and after it. A similar sequence occurs in the tenor where E goes to F via E^ Also easy to locate are two undivided major semitones: one in the soprano (C to Cx) and one in the tenor (F to Fx). Another integral major 109. Introdutione facilissima drnovissima, fol. A4r (Galdrone facsimile edition, p. 4v).

Introduction

Ixi

semitone— the one with the odd spelling (B^ to B^) — occurs in the alto. The cumulative effect of the "sharps" is best seen in the splitting of two minor semitones in the chromatic genus, both of which follow upon major semitones formed by a five-stroke sharp after a natural note. Thus, in the soprano, the minor semitone C^ to D is divided into two dieses by Cx, and likewise in the tenor, F^ to G is split into two dieses by Fx. Example 2 shows all the divisions. It corroborates Lusitano's assertion that the whole tone contains nine commas. Soprano Number o f commas

c

c% 5

c* 2

d' 2

e' 9

Alto Number o f commas

a

ax 2

b1' 2

b* 5

c' 4

Tenor Number o f commas

e

ex 2

f 2

fi* 5

f 2

g 2

Example 2 Lusitano's Chromatic-Enharmonic Melodies in the Soprano, Alto, and Tenor Parts Vicentino's sole remark on the melodic contours is to insist, as he does everywhere in the treatise, that the semitone in the diatonic genus must be major, not minor. As for harmony, Vicentino erupts in mock horror at the numerous false fifths, fourths, and thirds exhibited by the example. In order to corroborate these criticisms, it is best to translate Lusitano's pitches into their counterparts in the thirty-one-note tuning system of the archicembalo. Just how Lusitano imagined his chromatic and enharmonic inflections would work in Pythagorean tuning is a moot point. Example 3 reproduces in diagram format the nine vertical sonorities made by the four voices in Lusitano's example. Soprano Alto Tenor Bass Sonorities

c' a e A 1

d'b a e A

2

2

d'b a e A 3

d1 a f d 4

d? a g^ d 5

d' a g^ d 6

d' b^ g g 7

d1 b g g 8

e' c' g c 9

Example 3 Lusitano's Example with Vicentino's Spellings In example 3, sonorities 1, 4, 8, and 9 present no problems, provided the alto voice sings the correct pitch for the penultimate note. False fourths and fifths are seen in sonorities 2, 3, and 6. False major thirds appear in

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Introduction

sonorities 2 and 5. In sonority 5, the size of the major third produces a false minor third as well. The reverse occurs in sonority 7. In addition, sonorities 3 and 6 substitute a false fourth for the major third. In tandem with other voices, this false fourth produces a false sixth in sonority 3, and a false minor third in sonority 6. Certainly, in terms of the tuning for chromatic and enharmonic inflections put forward by Vicentino, Lusitano's example is nonsense. Had Vicentino taken the time to correct Lusitano's errors, the result would have been something like what is shown in example 4.

Bass

c" a e A

c'1 a e A

d lb a e A

d' a f d

d1 a f* d

d1 a g^ d

d' b g g

d1 b g g

e1 c' g c

Sonorities

1

2

3

4

5

6

7

8

9

Soprano Alto Tenor

Example 4 Lusitano's Counterpoint Corrected after Vicentino

A Note on the Translation The translation is based on L'antica musica ridotta alia modernaprattica printed in Rome in 1555 by Antonio Barre. The second printing in 1557, also by Barre in Rome, does not offer variant readings because it was made from the 1555 plates. No attempt has been made to record the countless typographical errors found in the text, but editorial alterations of substance are recorded either in the text or the notes, as appropriate. The page numbers of the original are given in brackets throughout the text, as, for example, [3r] for recto page 3. Every effort has been made to produce a fluent and natural English translation without altering the original textual meaning. At the same time, the different modes of writing—Vicentino's voices, as it were— have been allowed to speak from the translated pages. Thus, the reader can discern Vicentino the theorist, Vicentino the theologian, Vicentino the pedagogue, Vicentino the pedant, Vicentino the polemicist, and so on. The sole major alteration of Vicentino's text occurs in Book V, chapters 9-39, where the prose lists of consonances available above and below the various keys on the archicembalo are reduced to tables. The reader may compare this method of presentation with Vicentino's in Book V, chapter 8, where the translation follows the prose of the original.

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Ixiii

In the notes I differentiate between two kinds of in-text references: unequivocal sources and probable or likely identifications assayed by author, quotation, or paraphrase. Clear-cut sources are simply cited. Uncertain sources are either prefaced by a word like probably or placed in the context of a specific discussion of source problems. In a few complex instances the reader is referred to the discussion in the introduction. In all cases, definite and likely sources are limited to those available in printed editions in Latin and/or Italian. All ancient Greek sources (names and titles) in the bibliography and index are given in English and Latin. The latter forms show how the sources would have appeared to readers of Latin, like Vicentino. The reading of musical notation requires exactitude in even the simplest examples, let alone in Vicentino's more radical experiments. For this reason, all editorial changes in the transcriptions have been recorded. Additions appear in square brackets. In keeping with Vicentino's notation for enharmonically inflected notes, the music examples feature superscript dots above all such notes. Again, editorial additions are enclosed in square brackets. Where notes, rests, or accidentals have been altered in any way, the original notation is given in the list of errata below.

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Errata in the Music Examples Bookl Example 5.2 Error: the order under C sol fa ut is incorrectly given as N. S. H. Compare ex. 5.1. Example 5.5 Misprints: segment 3, note 4 isB; segment 7, syllable 1 in line 2 is fa. Example 5.6 Misprints: segment 4, directive H. is on line 1; segment 8, syllable 2 is mi; directive H. is on the left, incorrectly indicating a descending rather than an ascending pattern. Example 5.7 Misprint: segment 8, note 2 is A. Example 5.8 Misprints: segment 4, directive H. is on line 1; segment 6, hexachord directive is N. Example 11.3 Errors: segment 1, hexachord directive is H. and syllables are la sol fa re mi. Example 15.2 Misprints: all segments, dot over note 2. Example 20.2 Misprints: segment 3 has magg\ segments 1 and 4 have incomp\ segment 4, note 3 has a flat. Example 23 Error: caption has et semitoni. Example 38.1 Misprints: segments 1 and 2 are marked nat. Example 42 Errors: in the top half of the tree (the divisions in the natural fourth), after major diesis, comp. di due Di. mi; after Accid. minor semitone, incomp\ Accid. minimal third is Terza manco di min. acrid. In the bottom half of the tree (the divisions in the octave), the natural and accidental tritones are missing. These tritones should also have corresponding proximate intervals; see exx. 37.1 and 37.2, segments 5 and 3. Bookll Example 4 Error: segment 1, upper voice is f g e. Example 5 Misprints: segment 5, tenor has semibreve, minim, semibreve. Example 9 Error: the layout is jumbled. The two alto parts for ex. 9.la follow one another on one staff. In ex. 9.2, the alto and tenor appear on the same upper staff with the bass notated below at the end of the lower staff. This leaves three parts (tenor, tenor, bass) on the lower staff to make up ex. 9.3. Example 14 Misprint: segment 1, voice-parts are reversed. Example 19.4 Misprint: top voice, note 3 is a semibreve.

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Errata in the Music Examples

Example 25.1 Misprints: soprano and alto are e' and c1, respectively. Example 25.4 Misprint: tenor has b. Example 28.1 Misprint: segments 7-16, the staves are reversed. Example 28.2 Misprint: segments 1-12, the staves are reversed. Example 29 Misprints: last segment, upper voice, notes are e and g.

BookUI Example 8 Misprint: note 25 is a semibreve. Example 16.2 Misprint: redundant flat before note 26. Example 18.3 Misprint: note 3 is a semibreve. Example 21.2 Misprint: note 7 is a breve. Example 24.3 Misprint: segment 3, note 2 is a dotted croma. Example 34.3 Misprint: segment 3, soprano, note 4 is a. Example 41.2 Misprint: note 5 is a breve. Example 44 Misprint: tenor, m. 17, note 3 has a flat. Example 50 Misprints: segment 1, bass, superfluous c breve at the end; segments 2 and 5, soprano, alto, and bass, note 3 is a breve; tenor, notes 3 and 4 are breves; segment 4, soprano, tenor, and bass, note 3 is a breve; alto, notes 3 and 4 are breves. Example 51 Misprint: m. 4, soprano, the dot should be centered over the breve; m. 13, soprano, note 4 is a semibreve. Example 52 Misprints: m. 16, alto, note 1 has a superscript dot; m. 18, soprano, note 2 has a superscript dot; m. 21, alto, note 2 is a semibreve; m. 25, soprano and bass, note 1 is a breve. Example 53 Misprints: m. 8, alto, note 1 has a superscript dot; m. 43, tenor and bass, note 1 is a long. Example 54 Misprints: m. 36, alto, note 1 has a superscript dot; m. 38, alto, note 1, tenor, note 2, and bass, note 1 lack a superscript dot; m. 39, soprano, note 3 is C"; m. 40, soprano and tenor, note 1 has a superscript dot; m. 42, soprano, note 1 has a superscript dot; m. 47, soprano, note 3 has a superscript dot. Example 55 Misprint: m. 25, soprano, note 1 is a long. BookJV Example 2.2 Misprints: fourth series, second set, key signature of four flats, on f, on a, on a', and on e1. Example 31.4 Misprint: tenor has bass clef. Example 31.5 Misprint: bass, note 8 is a white breve. Example 34.4 Misprint: caption reads "A tre voci alia decima sopra."

Errata in the Music Examples

bcvii

The alignment of the voices in these examples is a muddle. Because the counterpointing voices are more-or-less simultaneously aligned with their common plainchant, the caption reads "for three voices" and incorrectly repeats the interval "at the tenth." The copyist mistakenly took exx. 34.3 and 34.4 to be a single three-voice counterpoint, as is the case with the ex. 34.5, which is adjacent to exx. 34.3 and 34.4. Example 34.7 Error: the four voices of exx. 34.6 and 34.7 are strung out consecutively on a single staff, leading to a confused set of captions. Hence, around the first pair of voices (ex. 34.6) one finds above, "II medesimo procedere, & i gradi medesimi," and below, "A duo voci Tenore & Tenore." And around the second pair (ex. 34.7) one finds above, "A duo voci, con un sospiro, per terza sopra," and below, "parte ch'era di sopra and parte ch'era di sotto." Example 35.2 Error: tenor, last note is a long. Example 36 Misprint: soprano, m. 8, note 1 is a minim. Example 43 Misprint: bass, last note is a breve. BookV Example 11.2 Misprint: segment 2, caption has 3 min. Example 12.2 Misprint: segment 2, caption has 3 min. Example 13.2 Misprints: segment 4, upper note has a superscript dot; segment 8, upper note is 4.E. Example 14.1 Misprints: segment 2, note 2 is 3e*; segment 5, note 2 is 4.A. Example 14.2 Misprint: segment 5, note 2 is 6e'. Example 15.1 Misprints: segment 1, lower part has 3e# and 5^. Example 16.1 Misprint: segment 1, lower part, note 2 is 3e*. Example 18.1 Misprints: segment 4, lower part has 5A1' and 3A1*. Example 18.2 Misprints: segment 1, upper part, note 1 is 3b#; segment 5, upper part, note 2 is 3e f *. Example 19.2 Misprints: segment 2, lower part, note 1 is C^ segment 5, lower part, note 2 is 3A*. Example 20.1 Misprint: segment 5, lower part, note 2 is 5G1*. Example 20.2 Misprints: segment 5, upper part has 4d' and 3d'K. Example 24.1 Misprint: segment 4, lower part, note 1 is 3$. Example 29.2 Misprints: segment 5, upper part has 4d' and 3d'*; segment 6, upper voice has 4f. Example 32.1 Misprints: segment 1, lower part has 5$ and 3$. Example 32.2 Misprints: segment 4, upper part, note 2 is 3$', segment

Ixviii

Errata in the Music Examples

5, upper part has 5g^ and Ig. Example 33.1 Misprints: segment 1, lower part, note 3 is 4.a; segment 2, lower part has 5^ and 3^. Example 35.1 Misprint: segment 2, lower part, note 2 is 2g*. Example 36.1 Misprints: segment 4, lower part has 5& and 4c. Example 36.2 Misprints: segment 4, upper part has 2g* and 3^; segment 5, upper part has 5^, 6a, and 4a. Example 37.1 Misprint: segment 1, lower part, note 1 is 3gf.gb Example 40.1 Misprints: segment 17, note 1 is cl|?; and both notes are copied an octave too high. Example 45.1 Misprint: caption has "in terzo & quarto ordine." Example 47.1 Misprints: segments 2 and 3 are labeled "tone" and "semitone," respectively, as are segments 5 and 6. Example 48.2 Misprints: segment 10, notes 2 and 3 are 4E and 3E*; segment 13, notes 2 and 3 are 5B and 3B*; segments 10 and 13, first interval is labeled "major diesis"; segment 13 labeled "natural tone." Example 49.2 Misprint: segment 12, note 4 is B#. Example 50.1 Misprint: segments 5 and 10, an extra "minor diesis" label. Example 50.2 Misprint: segments 10 and 13, an extra "minor diesis" label. Example 51.1 Misprints: segment 2, note 3 is B; segments 1, 5, extra "minor diesis" label. Example 51.2 Misprints: segments 2, 3, 5, 10, 11, and 13, extra "minor diesis" label. Example 52.1 Misprints: segments 9 and 13, extra "major diesis" label. Example 52.2 Misprints: segment 2, extra "minor diesis" label; segments 10 and 13, extra "major diesis" label. Example 53.2 Misprint: octave-species 3, note 8 is 3b*. Example 53.5 Misprint: octave-species 4, note 4 is 3a#. Example 53.6 Misprint: octave-species 4, note 6 is 3df|?. Example 53.7 Misprint: octave-species 4, note 6 is 2ell>. Example 55.1 Misprint: octave-species 3, note 7 is 2R Example 56.1 Misprints: octave 3, note 7 is 3g4 octave 7, note 3 is 4B. Example 57.4 Misprint: octave 4, note 6 is 3d1*. Example 59.1 Misprints: series 2, set 3, second flat of key signature is on d'; series 3, set 3, note 2 is 3a'# and note 10 is 3b'*; series 5, set 6, note 2 is 3B&; series 6, set 4, C clef is on the first line; series 7, sets 2, 4, 6, 7, and 8, note 11 has a sharp; series 7, set 8, note 9 is 2f #. Example 59.2 Misprints: series 6, set 2, note 2 has a redundant flat; series 7, set 8, note 2 is 5&.

Errata in the Music Examples

Ixix

Example 59.3 Misprints: series 1, set 2, note 10 is d"*; series 3, set 6, note 10 is 2c'*; series 4, set 2, note 9 is 3d"1'; sets 5 and 6, note 9 has a sharp sign; series 6, set 5, notes 7-10 are 3b*, 3d'1', 5e!l>, and 3e'*; set 7, notes 4-11 are 3B», 5d l?t , 3d», 3d, 5g"^, 5a^, 3a«, and 3b«; series 7, model set, notes 1-10 have sharp signs; set 7, note 11 is 3b*. Example 59.4 Misprints: series 1, set 3, note 12 is superfluous; series 3, set 5, note 11 is 4F and the note before it is superfluous; series 4, set 8, note 10 is 5^. Example 59.5 Misprints: series 1, set 3, note 1 isg^; series 2, set 5, note 8 isc'1'; series 5, set 8, notes 7 and 10 are & and f*; series 6, set 4, note 11 is 5^; series 7, set 7, note 11 is 5B17. Example 62.1 Misprint: segment 11, note 2 is Sa1*. Example 62.3 Misprints: segment 4, note 1 is 51^; segment 5, notes are 3a* and c*; segment 6, note 2 is gK Example 62.4 Misprints: segment 11, note 1 is 4e; segment 12, note 2 is 2e ft . Example 62.5 Misprints: segment 8, note 2 is lc f ; segment 9, note 2 is 2c'*; segment 10, note 2 is lc f ; segment 12, note 2 is If. Example 62.6 Misprint: segment 4, C clef is on the third instead of the fourth line. Example 64.1 Misprint: segment 8, note 2 is 5gf|>. Example 64.3 Misprint: segment 8, note 1 is 4b.

Ancient Music Adapted to Modern Practice, Including the Explanation and Examples of the Three Genera with Their Species, and Including the Invention of a New Instrument That Incorporates All Perfect Music Along with Many Musical Secrets Newly Published by the Reverend Master Don Nicola Vicentino in Rome by Antonio Barr£, 1555

Overleaf: Portrait of Nicola Vicentino at the age of forty-four. Outer border: Reveal to me the obscure and secret things of thy science. Inner border: Inventor of the archicembalo and also of the practical division of the chromatic and enharmonic genera; Title page, L'antica musica ridotta aUa moderna prattica (Rome: Antonio Barre, 1555). By permission of the British Library (Hirsch I,591and785,m.33).

[Preface] To the Most Illustrious and Very Reverend Cardinal of Ferrara [Ippolito II d'Este], Honored Lord and Patron Having been encouraged for many years by Your Most Illustrious and Very Reverend Highness to complete my labors on ancient music and wishing to make them known finally to the world, I decided to publish them under your protection and benevolence. Thus, those persons who like perhaps to sting others at first sight will have little respect until, having seen my arguments, they recognize the truth. Once the truth is known I do not doubt that, setting envy aside, they will praise this work and thank you, Illustrious Lord, for having been the cause of my undertaking so great an enterprise and presenting it to them with your help and favor. This work will reveal definitively many secrets that have neither been put into practice nor perused in theory from the time of Pythagoras, the discoverer of musical ratios, up to the present. It will also demonstrate how this kind of music can be accommodated in church and in private chambers, and with what instruments we can exalt Almighty God as well as soothe and appease our souls through such music. Just how useful and delightful this can be to mankind is shown in the words of Boethius and of all those who have made mention of this science.1 By this I do not mean that I have spoken so comprehensively that nothing can be added but rather that I have said enough for others to bring this science gradually to its maturity by means of these beginnings. And so I deserve praise only for having added material that will awaken others to bring it to perfection. This prospect, however, originated almost entirely from your goodness and generosity, Illustrious Lord, for you deigned to receive me among so many of your brilliant men and to aid me so ardently. It therefore remains for me to recommend myself to you with this work (more your harvest than mine), humbly kissing your hand. The very humble servant of Your Most Illustrious and Very Reverend Lordship, Don Nicola Vicentino.

To doe Readers Learned and prudent readers, I am not certain which has been my greater task: to disinter the practice of ancient music from dark obscurity and bring it to light as if with a new birth, or to comply with the 1. Deinst. mus., 1.1 and 1.2. 3

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[Preface]

usage of the vernacular language and accordingly disclose to you my mind on this subject. Even though the material itself is obscure and difficult— for we use elements from past ages that now differ in ratios2 and in practice—we are nonetheless devoted to a science that has its own principles. And through these principles this science can attain the clarity of truth by means of demonstrations and effective arguments.3 As for language, we have as many rules as there are writers. Reading now one, now another for my amusement, I find that the language we use today is just like Proteus, who purposely changed himself into diverse shapes.4 Consequently, by clinging in subservience first to this writer and then to that writer, I almost became a new Vertumnus5 myself. I have taken some care in this matter after diligently reading over my work many times. Yet I do not doubt that detractors and calumniators of good works who aim at nothing but malice will contradict me on this issue, being unable (so I believe) to lay any other blame on me. And so to obviate all this, I declare at the outset that I did not feel obliged to write in the style of Boccaccio and that I scarcely had time to worry over every insignificant little word because of the great scope of my work. Moreover, I wished to follow the usage of many Tuscan cities. Whoever observes them closely will see that in the variety of their pronunciation and spelling these cities almost duplicate the characteristics of the five dialects so diligently observed by the ancient Greeks.6 You will therefore find in my work now odire, now udire, here cantante^ there cantore, sometimes deve, other times dee or de; also anchora and ancora, instrumento, stormento and stromento, consonanze and consonantie, b and overo, la and quella, debbono and devono, avviene and adviene, cadentie and cadenze, ritrovi and ritruovi, tono and tuono, domando and dimando, veggono and vedeno, avertirh and avvertirh> satisfatto and 2. That is, in the mathematical tenets of harmonic science. 3. Demonstrations and arguments are tools of Aristotelian logic, as in Aristotle, Metaphysics, 2.2.996B, Posterior Analytics, 1.2.71b, and Prior Analytics, 2.16.64B. 4. The old man of the sea in Greek mythology is mentioned in Homer, Odyssey, 4.363570; Virgil, Georgics, 4.385-529, znAAeneid, 11.26-63; and Ovid, Met., 2.9 and 8.730-31, and Ars amatoria, 1.769-70. 5. The Roman god of gardens and orchards, who used his power to change shape to woo Pomona, goddess of fruit trees, is mentioned in Ovid, Met., 14.623-771, and Fasti, 6.409. 6. The five Greek dialects (Attic, Doric, Aeolic, Ionic, and Common) are listed in De dialectis (Venice 1557), fols. 297v-300v, by Johannes Philoponus (John the Grammarian), an Alexandrine philosopher and scholiast of the sixth century A.D. Many editions of this work were published in the first half of the sixteenth century. But see also Isidore, Etymologiarum sive originum libriXX, 9.1.

[Preface]

5

sodisfatto, as well as many other such niggling details. But do not censure me, for in imitation of the Greeks I wished to follow the varied usage of our language. Nothing else occurs to me, dearest readers, except to say that those of you who wish to learn from me the practice and science of music and not of language should pay close attention to the heart of my subject matter rather than to idle chatter and trifles. If you do so, I believe you will reap a not indifferent harvest. Love me, then, and defend me against calumniators just as I, loving you, did not shrink from all this hard work. Farewell.

Book on Music Theory

Chapter 1 Proem [3r] Very diverse, guileless readers, are the opinions of philosophers concerning the origin and goals of music. It is well known that many philosophers discovered many things; however, by searching, calculating, disputing, and likewise opposing each other's opinion, they have bequeathed uncertainty instead of theory or practice to mankind. Aristoxenus, who depended solely on sense, denied reason, whereas the Pythagoreans, in contrast, governed themselves solely by reason, not sense. Ptolemy more sanely embraced both sense and reason,1 and his opinion has satisfied many people up to now. In this work, however, you will recognize many cases in which reason is not a friend to sense, and sense is not receptive to reason.2 And I shall give you detailed information as to how compatible sense and reason can be, thus enabling you to assess the dearth of sweet musical concords in the past. Therefore, with experience as the mistress of things,3 it will be easy to judge the difference between ancient and modern music by considering examples of both. I shall not prolong this chapter by telling you about the antiquity, the excellence, the many musical effects, or even all of the first inventions of music. However small they were, these inventions seemed quite substantial to men for a little while; but when they were later developed by posterity, the inventions became insignificant. Many people laughed at the work of their predecessors. But they should not have done so, because nothing can reach its perfection without a beginning. Such first inventions deserve a great deal of praise, since it is an easy matter to add to them afterward.4 So that contemporaries and posterity may judge what is good and what is more in keeping with the diversity of the times, I have published my work to the glory of the Holy Trinity, and to be used by those who have 1. The comments on Aristoxenus, the Pythagoreans, and Ptolemy are taken from Boethius, De inst. mus., 5.3. 2. This warning echoes a sharp statement made by the Modenese theorist Lodovico Fogliano on the legitimacy of the sensory apprehension as opposed to the rational definition of consonances. Musica theorica (Venice, 1529), Bk. II, chap. 1. 3. See, for instance, Aristotle, Posterior Analytics, 1.30.46a. 4. This idea may have been borrowed from St. Thomas Aquinas, In decem libros ethicorum Aristotelis adNicomachum expositio, 1.50.11 :cl33.

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not read on this subject in the Tuscan or the Latin language. For those who do not understand this sort of discourse, I have tried to make it easier by joining practice with theory and by providing examples—something that has never been done by anyone up to now—so they may grasp what the ancients abstrusely wrote about music. Therefore, as regards the discussion of theory in this book, I explain briefly the musical ratios as well as some of the indispensable chapters in Boethius. Whoever wishes to see a more extensive treatment may read the latter. Inasmuch as many things have been said many times by many people, I shall not resort to repetition. Rather I shall explain to you only the most difficult matters, setting aside the discussion of all topics pertinent to practice for the ensuing books.

Chapter 2 How Pythagoras Discovered the Musical Ratios [3v] The first principles of the sciences merely show us how people make doors to houses. The first discoverer of musical ratios was Pythagoras (as Boethius affirms in Book I, chapter 10, of his work). By experimenting with the weight of certain hammers he had previously heard being hit sonorously by some blacksmiths, Pythagoras discovered that the sesquitertial ratio [4:3] between two such hammers formed the harmony of the diatessaron. He also found the ratios of the diapente, the diapason-plus-diapente, and the double diapason by means of these hammers. In addition, he recognized that the whole tone was present in the sesquioctaval ratio [9:8]. After first explaining all these ratios theoretically, I shall show you how they are adapted to practice according to their distinctive musical characters. To return to the philosopher [Pythagoras], I must point out that he was not content with the above-mentioned discoveries. He also wanted to find, by means of numbers, the way to climb by step to the consonance of the diatessaron, which practitioners call the fourth. Having noticed that two sesquioctaval ratios did not reach the sesquitertial ratio and that three sesquioctaves greatly exceeded it, Pythagoras realized that the number providing the third part would also complete the sesquitertial ratio exactly. Thus, by tripling two sesquioctaval ratios and adding them to the third part, he made the sesquitertial ratio, which produces the consonance of the diatessaron.5 5. The third part of the diatessaron is the minor semitone of 256:243. One does not, however, triple two sesquioctaves. Apart from the attribution to Pythagoras, this passage corresponds roughly to Boethius, De inst. mus., 1.17. Elsewhere Vicentino ascribes other

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He called the first interval between the first and second ratios a whole tone, and likewise the interval between the second and third ratios; however, the remainder he called the minor semitone because it was a number that, when doubled, failed to reach either of the sesquioctaval ratios. Thus the diatessaron was composed of two sesquioctaval whole tones and one minor semitone. Not satisfied with this experiment, Pythagoras wished to compound many pitches and tetrachords. I shall explain the method he followed in the next chapter.

Chapter 3 On the Method Pythagoras Followed to Compound Five Tetrachords Together, Along with Their Names After discovering the ratio and the measurement of the harmony produced by the weight of the hammers when struck, Pythagoras conducted many other experiments to see whether such a ratio always produced the same consonance in various materials.6 Setting aside these many experiments, I shall describe to you only the method he followed to compound the five tetrachords together and to climb by step up to fourteen pitches. The method was this. He began by taking a number that he thought would serve the sesquioctaval ratio throughout the tetrachords.7 Proceeding through them by the steps of a whole tone, a whole tone, and a semitone, he was able to climb continuously up to the required number of pitches. The first tetrachord proceeded through semitone, whole tone, and whole tone; the second did likewise, but in such a way that the end of one tetrachord was the beginning of the next. When he tried to add another tetrachord with the same sequence of pitches, he discovered that neither the ratio of the diapason nor that of the diapente was accurate. He therefore added, between the two lower and the two upper tetrachords, yet another tetrachord, in the middle. This tetrachord joined the two lower tetrachords to the two upper at a juncture where it was necessary to insert a whole tone, for each tetrachord had to begin with a semitone and end with a whole tone. But the fifth discoveries to Pythagoras without the authority of Boethius; for instance, the definition of the genera ("Music Theory," chap. 4) and the construction of the five tetrachords (chap. 5). The reference to Pythagoras' discontent may have come from Jehan des Murs, Notitia artis musicae (also known as Ars nova musice), edited by Ulrich Michels (American Institute of Musicology, 1972), Bk. I, chap. 3. 6. Boethius, De inst. mus., 1.11. 7. Ibid., 1.17. The number is 192, and it provides the sequence 192, 216, 243, 256 for the intervals in the diatessaron.

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tetrachord began on the end of the fourth, just as the second did in relation to the first.8 To this sequence of tetrachords, or [4r] pitches, Ptolemy added another pitch, called acquired9—that is, the diapente against the main string of the middle notes, the diapason against the middle note, and the double diapason against the last note of the highest notes.10 And to clarify matters, he called the first tetrachord below this the principal of the principal notes and the second the principal of the middle notes. The third tetrachord, placed between the two lower and the two upper tetrachords, was called tetrachord of the conjunct notes, and the fourth, tetrachord of the divided notes (because they were already divided), and the fifth, highest, because it was the highest of all.11 I have not used the Greek names so as not to befuddle the wits of the auditor with obscure words. Whoever wishes to know them may read Boethius.12 Indeed, I find it a strange idea to write a work in the vernacular tongue and then sometimes to use Greek or other foreign words if I can do without them. Anyone who wishes to delve into this matter in more detail may read Boethius. I have spoken about the terms in a succinct fashion, since they are not essential to my purpose. You will receive clarification on this matter in the chapters on music practice [Book I, chapters 6-11 and 14-24], where the difference in the ancient whole tones and semitones will be described and clear examples also given. 8. This is a brief description of the standard version of the Greater and Lesser Perfect Systems combined. Their tetrachords are enumerated in the next paragraph. Vicentinos brevity leads to some confusion here. The tetrachord listed as the one added after the insertion of a whole tone above the first two (hypaton and meson) is of course the disjunct tetrachord (diezeugmenon) of the Greater Perfect System. It is linked conjunctly to the fourth tetrachord (hyperboleon). The tetrachord described as situated between two lower and two upper tetrachords can only be the third (synemmenon), which is conjunctly linked to the meson below it in the Lesser Perfect System. Only with the schematic combination of both systems do we arrive at a total of five tetrachords. 9. Nowhere in the classical or medieval literature is the addition of an "acquired" (proslambanomenos) pitch ascribed to Ptolemy. The proslambanomenos is called adquisitus by Boethius in De inst. mus., 4.3, and by Capella in De nuptiis Philologiae etMercurii libri II, 9.931. 10. The intervals above the proslambanomenos, only the second of which is given by Boethius (De inst. mus., 1.20), are as follows: A-e (hypate meson), A-a (mese), and A-a (nete hyperboleon). 11. In De inst. mus., 1.26, Boethius ascribes a shorter version of the Latin equivalents for the Greek terms to Albinus, a writer on metrics and music. But Vicentino's terminology comes directly from Capella (De nuptiis, 9.931): principalis principalium, principalis medium, coniunctarum, divisarum, and excellentium. 12. De inst. mus., 1.20. Vicentino may be recalling here the criticism of Cicero's use of Greek terms by Macrobius (In somnium Scipionis, 4.11—12).

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After compounding the five tetrachords, the philosopher conducted a substantial experiment to discover which steps belonged to the tetrachord as well as how many ways he could descend and ascend with various pitches. I shall describe all this to you in the next chapter.

Chapter 4 The Method Pythagoras Followed to Distinguish the Steps of the Pitches in the Tetrachords While planning to begin the division of the pitches in the tetrachords, Pythagoras realized that he could do so in three ways, but lacking confidence in the sense of hearing, he wished to proceed securely with reason.13 He therefore had a box constructed, one palm wide and five palms long.14 At both ends of its length he placed a small stationary bridge, one finger in height. Over one bridge he stretched a sonorous string of gut or brass and fastened it below by passing it over another movable bridge of the same height as the fixed ones. By pressing this string with his finger, he could shorten and lengthen it at will. Then, by means of these measurements, he found the true distance of the pitches of the tetrachord: the whole tone, the semitone, and the diesis. He called this box the monochord, because it measured every pitch with a single string. Thus, by means of the sesquitertial ratio, Pythagoras discovered the true size and distance of the tetrachord or diatessaron. This ratio established, he started at one end and found the true distance of the first whole tone by means of the sesquioctaval ratio, and then in the same way the distance of the second whole tone. The remainder was the distance of the minor semitone. And this was the [diatonic] division of the diatessaron: into two sesquioctaval steps of equal length and one short step. Finding the second division of the tetrachord entailed taking the distance of the first sesquioctaval step plus the exact half of the second, even though they [the Pythagoreans] did not concede that a whole tone 13. Boethius, De inst. mus., 1.10. 14. The invention of the monochord (also called regula) is credited to Pythagoras by Boethius (De inst. mus., 1.11), who mentions its wooden construction as well as its fixed and movable bridges (4.18) but gives no dimensions. One possible but highly unlikely source for this information was the monumental compendium De expetendis etfugiendis rebus opus (Venice, 1501), by the Venetian humanist Giorgio Valla. Valla describes the chordotone, a rectangular polychord ten palms long and two palms wide ("De musica libri V," Bk. V, chap. 6). More likely, Vicentino recalled these measurements from Heinrich Glareans reference to Vallas chordotone. Dodekachordon (Basel, 1547), Bk. I, chap. 17. Unpalmo denotes a measure ranging from 7.62 to 10.16 cm., the average length of the palm of the hand.

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could be divided into two equal semitones. Pythagoras called this step, which was made up of one and a half whole tones, the trihemitone. He placed the remainder of the second whole tone in sequence before the minor semitone. And this was another division of the tetrachord: into one large step the size of one and a half whole tones (called the trihemitone), a second step the size of an exact semitone, and a third one the size of a minor semitone. All the above steps were considered incomposite, that is, without any division of the intervals. Making the third and last division entailed combining the distance of two sesquioctaves, a step he called the incomposite ditone. Pythagoras divided the remaining minor semitone into two equal parts, each of which he called diesis. And this was the final division of the [4v] diatessaron: into one large step the size of two whole tones and two tiny steps the size of one-half a semitone.15 The second division was called chromatic, which means transformed into steps unlike those of the first division. The third and last was called enharmonic, which means composed of small parts. The latter is very sweet and smooth, as you will hear in practice.

Chapter 5 On the Diatonic Genus Since I have spoken in general about the three sequences of steps in the tetrachord, it seems appropriate now to discuss each of them individually. Because they are divided into several species, I call them genera.16 I shall illustrate them with diagrams so that they may be better understood. Imagine having in hand the neck of a lute whose fingerboard will be divided into each genus. Thus the length of the two horizontal lines represents the distance of the diatessaron, whereas the vertical lines, representing the finger spaces, show the distance of the whole tones or sesquioctaval ratios as well as of the small part of the major semitone.

Example 5 Division of the Diatonic Genus

15. Boethius, «De inst. mus., 1.21. 16. See "Music Practice," Bk. I, chap. 6.

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Book on Music Theory.

Chapter 6 On the Chromatic Genus The chromatic genus is sweeter than the diatonic,17 and it proceeds to its fourth through different steps from those taken by the diatonic. For the diatonic goes through whole tone, whole tone, and semitone—all incomposite intervals—whereas the chromatic proceeds through trihemitone, semitone, and semitone. Although the trihemitone is made up of the distance of one and half whole tones, this entire distance or step is called an incomposite trihemitone.18 The remainder of the second whole tone forms a step called a semitone,19 and the third step is the same as the minor semitone of the diatonic genus.

Example 6 Division of the Chromatic Genus

Chapter 7 On the Enharmonic Genus The enharmonic genus is more sweet and smooth than the other two genera, and it differs in its steps as much from the chromatic as from the diatonic. The first step is equal to the distance encompassed by two whole tones, and it is called an incomposite ditone by Boethius.20 The second step, called a diesis, is one-half of the minor semitone.21 The third step, likewise called a diesis, is the other half [5r] of the semitone, as is evident in example 7.

Example 7 Division of the Enharmonic Genus 17. Although the sweetness of the chromatic genus was a widely accepted notion, it is probable that Vicentino s description of this genus and of the enharmonic in "Music Theory," chap. 7, as well as the etymology given at the end of chapter 4 are based on statements made by Franchino Gaffurio in Practica musicae (Milan, 1496), Bk. I, chap. 4. 18. Boethius, De inst. mus.y 1.23. 19. This interval turns out to be a major semitone. See "Music Practice," Bk. I, chap. 7. 20. De inst. mus., 1.23. 21. Ibid., 1.21.

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Chapter 8 On the Utility of the Partitions of the Tetrachord Because all the other consonances were derived from the diatessaron, this interval was so highly esteemed by the ancients that they were content to divide it by the genera and to derive from it the tetrachords, thereby expanding their system to many pitches. Thus, adding to the diatessaron they formed the diapente, and then adding the diatessaron to the diapente they formed the diapason. By adding a diapente to the diapason they formed the diapason-plus-diapente, and, again, by adding a diatessaron to the latter consonance they formed the double diapason. If we leap to these consonances solely by fourths or fifths, they are called incomposite; if we proceed by whole tones and semitones, they are called composite. The diatessaron, then, is composed of two whole tones and one semitone, the diapente of three whole tones and one semitone, the diapason of five whole tones and two semitones, the diapason-plusdiapente of eight whole tones and three semitones, and the double diapason of ten whole tones and four minor semitones. Moreover, all the above-mentioned semitones, according to Boethius,22 are to be considered minor semitones.

Chapter 9 On the Three Species of the Diatessaron The consonances themselves acquire a variety of species by changing the sequence of tones they contain. Insofar as the sequence of tones in the diatessaron can be altered in three ways, the species are likewise three in number: one species through semitone, whole tone, and whole tone; another through whole tone, semitone, and whole tone; and the last

Example 9 [The Species of the Diatessaron] 22. Ibid., 1.33.

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through whole tone, whole tone, and semitone, as is evident in example 9. These are the species of the diatessaron according to Boethius in chapter 13,23 although they are used differently in practice.

Chapter 10 On the Four Species of the Diapente By the same token, there are four species of the diapente because it is varied in four ways. One species occurs when the diapente proceeds through whole tone, whole tone, whole tone, and semitone; another through whole tone, whole tone, semitone, and whole tone; the next through whole tone, semitone, whole tone, and whole tone; and the last through semitone, whole tone, whole tone, and whole tone.24

Example 10 [The Species of the Diapente]

Chapter 11 On the Seven Species of the Diapason [5v] The species of the diapason are seven in number, of which three are formed by the three species of the diatessaron and four by the four species of the diapente described above. According to Boethius in Book IV, chapter 13, of his Fundamentals of Music,2* the first in the series is composed of the first diatessaron placed under the last diapente; the sec23. Ibid., 4.14. The sequence is correct but the direction of the steps is reversed here and in "Music Theory," chap. 10. 24. Boethius De inst. mus., 4.14. 25. Bower translation (New Haven 1989), Bk. 4, chap. 14.

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ond one, of the second diatessaron placed under the penultimate diapente; and the third, of the last diatessaron placed under the antepenultimate diapente. Thus are generated three species of the diapason. The other four, made up of the four species of fifth placed under the diatessaron, are also formed in this way. The first diapente placed under the last diatessaron forms the fourth species of the diapason; the second diapente under the penultimate diatessaron forms the fifth species; the third diapente under the first diatessaron forms the sixth species; and the fourth diapente under the first diatessaron forms the seventh and last species of the diapason.26 From these are formed the modes, as will be seen in the next chapter.27

Chapter 12 On the Eight Modes Different countries had various customs with regard to combining the diatessaron with the diapente. And by singing with these combinations, people have generated several modes, commonly called tones—such as Lydian, Phrygian, Dorian, and others.28 In this chapter I shall describe to you the true formation of these modes. Up to the time of Ptolemy there were only seven modes (the same number as the species of the octave), and to these seven he added another.29 For since there were four species of fifth, he discovered that he could vary the octave in eight ways, four of which put the diatessaron above the fifth and four below. The first mode, called Dorian, is formed by the first diapente below and the first diatessaron above. The second, Hypodorian, is formed by the first diatessaron and the first diapente placed above it because the diatessaron must be underneath. The third, the Phrygian, is composed 26. Up to this point Vicentino's treatment of the species is internally consistent. If "S" and "T" are taken as abbreviations for the semitone and whole tone, respectively, the three species of the diatessaron in chapter 9 are: S T T (4a), T S T (4b), T T S (4c); and the four species of the diapente in chapter 10 are: T T T S (5a), T T S T (5b), T S T T (5c), S T T T (5d). The seven species of the diapason described here are: S T T & S T T T (4a & 5d), T S T&TSTT(4b&5c),TTS&TTST(4c&5b),TTTS&TTS(5a&4c),TTST &TST(5b&4b),TSTT&STT(5c&4a),STTT&STT(5d&4a). 27. Like many other theorists, Vicentino misunderstood the ancient octave-species and the Boethian modes. Moreover, what follows has nothing to do with the structure and order of the seven octave-species here described. 28. Boethius, De inst. mus., 4.16. 29. Ibid., 4.17 and 18. Like Gaffurio (Practica musicae, Bk. I, chap. 7) and Glarean (Dodekachordon, preface), Vicentino followed Boethius in incorrectly assigning an eighth mode to Ptolemy, even though the latter rejected it (Harmonics, 2.9 and 10).

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of the second diapente and the second diatessaron. The fourth, called Hypophrygian, is made up of the second diatessaron and the second diapente above it.30 The fifth mode is composed of the third diapente and the third diatessaron, and it is called Lydian. The sixth, called Hypolydian, is composed of the third diatessaron and the third diapente placed above it. The seventh is composed of the fourth diapente and the first diatessaron, and it is called Mixolydian. The eighth and last, called Hypermixolydian, is made up of the first diatessaron and the fourth diapente.31 This description suffices to explain the modes. I have omitted many other matters that are not crucial here, for they can be found in Boethius,32 who discusses them at length, and also in my "Music Practice" [Book III, chapters 4-23 and 47-49].

Chapter 13 On Movable and Stationary Steps and on Those That Are Neither Completely Movable Nor Completely Stationary Since the custom of writing the pitches of the musical notes on lines and spaces is not a very old one, it was certainly not discussed by the ancients. Yet Boethius does show in Book IV, chapter 12, of his Fundamentals of Music53 how in his day each of the three genera was written in Greek and Latin characters, including the acquired note,34 and all the pitches of the five tetrachords were divided into three parts. Some of these pitches he called stationary, others movable, and still others neither completely stationary nor completely movable. The stationary pitches were eight in number: that is to say, they included the first acquired note as well as all the initial and final notes of the five tetrachords. Boethius called them stationary because they were written with the same letters in each of the three genera. Those that were 30. An error in the case of the Hypophrygian, and also of the Hypolydian described below, gives sotto (below) instead ofsopra (above) for the placement of the diapente. 31. The analysis of the species in the modes does not follow the enumeration of the octave-species in the previous chapter, but rather conforms to that of the church modes as given by Gafrurio, except for a few minor discrepancies (Practica musicae, Bk. I, chaps. 815). The modes are as follows: Dorian, T S T T & T S T (5a & 4a); Hypodorian, T S T & T S T T (4a & 5a); Phrygian, S T T T& S T T (5b & 4b); Hypophrygian, S T T& S T T T (4b & 5b); Lydian, T T T S & T T S ( 5 c & 4c); Hypolydian, T T S & T T T S (4c & 5c); Mixolydian, T T S T & T S T ( 5 d & 4a); Hypomixolydian, T S T & T T S T (4a & 5d). 32. De inst. mus., 4.15 and 17. 33. Bower translation, Bk. 4, chap. 13. 34. See "Music Theory," chap. 3, above.

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neither completely movable nor completely stationary were the steps that, retaining the identical height or depth, were written with the same characters in the diatonic and chromatic genera; in the enharmonic, however, they were written with different ones. These included all the intervals of the minor semitone [6r] as they were supposed to be used in the time of Boethius35 because they were identical in the diatonic and chromatic genera but altered in the enharmonic. The movable ones, then, were all the rest. They were called completely movable because they changed in every genus. I have taken this information solely from Boethius.36 But because we do not use this way of writing music today, it is utterly useless, as will be seen in my section on music practice.

Chapter 14 How to Calculate the Harmonic Mean Between Two Numbers of Consonant Ratios To determine the harmonic mean between two musical ratios is the same as discovering a middle ratio that agrees with the two extreme numbers, as in the example of the duple ratio [2:1]—called the octave in practice—whose harmonic mean is the diapente or fifth. In order to deduce this harmonic mean, we use the following set of calculations. To make it easy, I shall pick a ratio with small numbers, such as 6 to 12, which form a duple ratio in relation to each other. First, you subtract the smaller from the larger number, that is, 6 subtracted from 12 to leave 6. You then multiply this remainder by the given smaller number, which is 6. And you say "6 times 6 makes 36." The result of this multiplication, 36, is divided by the sum of the two given numbers, that is, 6 plus 12 to make 18. It is therefore proper that you should divide 36 by 18. And as many times as your divider will go in, so much greater will be the unity with the given smaller number, which is 6. Because 18 goes into 36 two times, you add 2 to 6, making 8. And the latter number, 8, is the harmonic mean between the two related numbers, 6 and 12.37 The truth is that 8 related to 12 is the sesquialter ratio [3:2], which is called the fifth in practice, whereas 8 related to 6 is the sesquitertial ratio, which means the fourth in practice. And 6 and 12 is the duple ratio, called the octave in practice. 35. De inst. mus., 1.17 and 33; 2.22 and 28; 3.6, 9, 13, and 16; and 5.16. 36. Ibid., 4.13. 37. Vicentino's ratios, 6:8:12, are double those given by Boethius (De inst. mus., 2.12). Elsewhere Boethius chose the numbers 10 and 40 in order to find all three means—the arithmetic, geometric, and harmonic (De inst. mus., 2.17, and De institutione arithmetica

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Thus, with this method of subtracting, multiplying, dividing, and adding, you discover the harmonic mean of the duple ratio. The same set of calculations will work for any other harmonic mean.

Chapter 15 On the Whole Tone, Semitone, Diesis, and Comma I stated earlier that the whole tone has the ratio of 8 to 9 [see chapters 2, 4, and 5]. Therefore, when it is divided, the smaller part is called the major semitone, and the larger part the minor semitone. In terms of numbers, let us say the ratio of 16 to 18 is the whole tone.38 Since 17 is the middle term, the ratio of 17 to 18 is the minor semitone and 16 to 17 the major semitone. The difference between 16 and 18 is the comma, which is equivalent to the pitch difference between the minor and major semitones according to Boethius39 but not according to our practice. If you wish to understand this matter perfectly, you may proceed thus. Take the number of the major semitone and subtract the minor semitone. The remainder is the difference between them. It is called the comma, that is, the smallest pitch difference that can be discerned by the sense of hearing,40 as I shall exemplify in the section on music practice [Book I, chapter 14]. The diesis is exactly one-half of the minor semitone, as I explained with respect to the enharmonic genus.

Chapter 16 Epilogue on the Topics Included as well as Omitted from the Five Books of the "Fundamentals of Music," by Boethius In this book on theory, I spoke mainly about the following topics: the method Pythagoras used to discover the musical ratios; the system he followed to compound five tetrachords in each of the three genera with the construction of the monochord; the three species of the diatessaron, the four species of the diapente, and the seven species of the diapason; the eight modes; the movable and stationary steps as well as those that libri duo, 2.50). Even though Vicentino s calculations for arriving at the harmonic mean are the same as those of Boethius, why did Vicentino chose 6 and 12 instead of 10 and 40? He copied the method from Isidore, Etymologiarum sive originum libri XX, 3.23. 38. Boethius, De inst. mus., 1.16. 39. Ibid., 3.9. 40. Ibid., 3.10 and 13.

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are neither completely movable nor completely stationary; the way to [6v] find the harmonic mean; and finally the whole tone, semitone, diesis, and comma. All of the above were presented in accordance with Boethius' views, setting aside, so to speak, the following topics:41 the antiquity, excellence, and effects of music, whether cosmic, human, or instrumental; the pitches and elements of music; the species of inequality and the five kinds of ratios contained in them; and the definitions of sound, interval, and consonance. Because such matters are revealed better through proof than arguments, I also did not state that one should not base one's judgment entirely on the senses on account of their fallacious nature but should rather put one's faith in reason.42 Nor did I describe the many ways Pythagoras conducted experiments with musical ratios, nor what constitutes a continuous and a diastematic voice, nor the process of hearing; neither did I mention any of the classifications of the theorem [Boethius' method], nor those people who added strings; nor did I name those who studied the stars—because these topics are completely useless today.431 omitted the discussion of the consonances, for I shall describe their nature in the section on music practice [Book I, chapters 25-34 and 37-41].44 And I left out the innumerable disputes among Plato, Nicomachus, Ptolemy, Aristoxenus, and many others.45 Nor did I define musician and singer because such definitions abound in many writings.46 Even less was included from Boethius' second book; for instance, nothing about how Pythagoras established philosophy, about the differences in quantity, about why the multiple genus precedes the other genera, about square numbers, and about numbers that generate consonances or how they are derived.47 I described the harmonic mean but not the geometric and arithmetic means, nor continuous and discontinuous means, nor how consonances were derived by Nicomachus, Eubolides, and others.48 41. The omissions alluded to in this and the next paragraph pertain to the first book of Boethius' treatise. They here appear in the following order: De inst. mus., 1.1 and 2; 1.3; 1.4; and 1.8. 42. This belief, with which Vicentino takes issue, is stated in De inst. mus., 1.9. 43. Ibid., 1.11, 12, and 14; 1.15, 20, and 27. 44. Ibid., 1.28 and 29. 45. Ibid., 1.31 and 5.17. 46. Ibid., 1.34. 47. Ibid., 2.2, 3, 4, 6, and 7-11. 48. Ibid., 2.12-16, and 18 and 19.

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From Boethius' third book I did not repeat the statement that a superparticular ratio, Aristoxenus notwithstanding, cannot be divided equally, nor many other disagreements with Aristoxenus.49 Neither did I state how Philolaus divided the whole tone, nor that the whole tone is more than 8 and less than 9, nor that the apotome means the major semitone.50 And from the fourth book I omitted what differences exist among the pitches, and speculations on discrete quantity, the chapter on the musical names and letters in Greek and Latin, and the partition of the regular monochord in the diatonic genus and with the ratios of the five tetrachords divided into the three genera.51 I left out Ptolemy's verdict on differences among sounds because I shall make them audible in the section on music practice.52 Also omitted are the discussions of the unison, of equisonant, consonant, and discordant pitches, of the divisions of whole tones and the genera according to Aristoxenus, and of which steps in the genera are called dense or non-dense, tense or slack.53 I passed over these topics because none of them has any value whatsoever for our practice, as will become clear from the experience of our ratios. For compared to the ancient ratios, ours are not only more numerous but also more sonorous. But why, then, in our times do we not observe musicians producing those effects that authors claim were made in antiquity?54 The cause, I maintain, is the overabundance and profusion of music today. However good an impression these effects may make, they no longer move people as they did when they were first discovered.55 For novelty, insignificant though it may be, earns much more admiration than what is commonplace and later magnified, as is evident from old-fashioned compositions. Even performances of such compositions can move people to laughter, although in their day they were considered very good. Thus, it cannot be disputed that now people are much more knowledgeable about music than they were in the past. However, the present-day profusion of music garners little esteem for the art. End of the Book on Music Theory 49. Ibid., 3.1-3. 50. Ibid., 3.5 and 6. 51. Ibid., 4.1,2, 3, and 4-12. 52. Ibid., 5.5. Vicentino does not mention that this last group of omissions pertains to material in the fifth book. 53. Ibid., 5.5, 6, 11, 12, and 16. 54. The probable sources that Vicentino read on the effects of ancient music are discussed in the Introduction, "Vicentino's Sources." 55. On the element of surprise or the unusual in music, see Pseudo-Aristotle, Physical Problems, 19.6.918a.

Book I on Music Practice

Chapter 1 Proem [7r] Just as the goal of speculative science is the truth of science itself, so the goals of practice are the actions and demonstrations of art.1 This is why it is now necessary to come to the principles of practice. In view of what I found recorded in the collected ancient chronicles, my readers should know that men have always performed music naturally and in various ways.2 For as we see and hear with respect to all peoples of the world, each nation has its own accents and distinctive pitch steps. When people sing together they find instinctively a certain accord of consonances according to their region, language, and nationality. And even though their singing disagrees with those ratios of practice approved by science, such discords nonetheless seem like consonances to them. For just as a practitioner forms good habits from reason and custom, so the contrary is true of him who is guided solely by nature (as are brute animals without reason).3To such a man, everything he performs in singing is good—even dissonances—for he lacks "a good ear." This defect is heard every day in certain folk singers and others who not only make discord when singing but also rejoice and delight in such discord. But others, who sing by mere custom and without reason, cannot hear dissonances because nature and a well-habituated ear have accustomed them to good and bad harmony alike.4 Still others, though they sing according to reason and custom, nevertheless have some sort of aural defect. The cause of their failure lies in a natural deficiency, although they make a considerable effort in the performance of music. There are certain others who hear music accurately. These are the people who have developed a deep proficiency in music practice through nature and art. 1. See for example, Aristotle, Nicomachean Ethics, 6.6.1140a-b and 1.1.1094a. 2. It is impossible to ascertain precise sources for so general a statement. Observations on national and regional practices appear in the following: Herodotus, History, 2.79; Strabo, Geography, 5.2.C 220, 9.3.C 421, 10.3.C 467-88 and C 470-71, and 10.4.C 480; Pliny, Naturalis historia, 7.56.204; Gellius, Noctes atticae, 1.11.1-16; Apuleius, Metamorphoses, 8.30 and 10.31-32. 3. See, for instance, Aristotle, "Art" of Rhetoric, 1.10.7 (1369b), and Nic. Eth., 7.7.1149b. 4. Possibly Aristotle, Nic. Eth., 7.11.1152a.

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Because of the great diversity between the hearing of one person and that of another, composers must create as much diversity in their compositions as there are listeners' opinions if they want to satisfy all judgments based on the sense of hearing. For it happens that some listeners praise a discordant composition and censure a harmonious one. In contrast to these extremes, some want to hear bland compositions. Others prefer simultaneous accord and discord. Some take pleasure in accord without discord, whereas others loathe harmony altogether. Some want harmony with slow motion, some with fast, and some with motion that is neither slow nor fast. From this variety in nature we recognize the difference between the learned and the ignorant, the expert and the inexpert. But whenever the adjudication of a composition is at issue, it is mandatory to bow to the judgment of the most experienced people in the profession of that sort of music. For it cannot be denied that all musical compositions that please listeners will always be praised by them, whether these works are good or not.

Chapter 2 On the Inventor of the Syllables Ut Re Mi Fa Sol La and of the Hand; On the Dots We Formerly Used to Sing From, Instead of the Notes in Use Today Although comparisons are tiresome, it is nevertheless necessary to point out differences so they will be understood by practitioners and speculative thinkers alike. In this way we may distinguish the good, the worse, and the better on the basis of reason and practice. To begin the discussion of music practice, I shall respond point by point to chapters in Boethius that pertain to [7v] practice. As for the discovery of music found by chance from the hammers,5 I reply as follows. In a similar way, the syllables of our practice were discovered by chance by the reverend father, Brother Guido the Monk, while he was singing the hymn of St. John. According to what this same Guido wrote,6 it was customary many years ago to record the characters of music with seven letters of the Latin alphabet. As it happens, the Greeks wrote music with notes and signs in their own way. But I shall not discuss them now because Boethius demonstrates in Book IV, chapter 3 [of Fundamentals of Music], the signs and characters as they should be written in 5. The legend of Pythagoras and the smithy. See "Music Theory," chap. 2. 6. Epistola de ignoto cantu (Scriptores ecclesiastici de musica sacra potissimum, 2: 43-45, edited by Martin Gerbert. [St. Blasien, 1784]. Guides Epistola is dated around 1028-29.

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all three genera and in the modes of music. Because the latter are useless for our practice, I shall set them aside and tell you about the seven letters: A B C D E F G. These letters were used by the predecessors of Father Guido in the following way: for singing from A to B a whole tone; from B to C a semitone; and from C to D they made the step of a whole tone; from D to E a whole tone; from E to F a semitone; and from F to G a whole tone. And so, ascending and descending invariably with these seven letters as written, they produced steps and leaps in such a manner that it was very difficult to learn them. Indeed, before learning plainchant, they wasted ten years on this. The revered father, who was himself trained in the practice, searched diligently for an easy method for learning the musical characters and their names, so that pupils could derive the maximum profit in the least time. Thus, as I already mentioned, it occurred to him by chance while singing the hymn of St. John to select the first syllable of the lines from the first stanza of the hymn. From Ut queant laxis he took the first syllable, "ut"; then from Resonare fibris he took "re"; and he put them together as ut re. Then from Mira gestorum he said "ut re mi." From Famuli tuorum he added "fa" and wrote "ut re mi fa." He then followed with Solvepolluti, making "ut re mi fa sol." And from the last line, Labij reatum sancte loannes, he wrote "ut re mi fa sol la." And because these syllables were easy to pronounce, he began to teach them. Those who learned them became proficient in one month. Guido was not satisfied with this invention. He set out to discover characters and an easy way to write down these vocalized syllables in practice. For brevity's sake he wrote down a dot instead of the semibreve we use and placed it on four lines and spaces, as in example 2.

Example 2 [Guides Dots] Having realized that this was easier than the preceding practice, Guido searched assiduously for an arrangement and rule that pupils would find easy. Thus he sought to form a hand. And on the lines of its joints he wrote the six syllables, ut re mi fa sol la. To make things easier he took the left hand and combined these syllables with the seven letters that people had sung before. Since the letters were already in use, this combination did not seem strange to pupils. Because the original sequence of the letters began with a whole tone and then led to a semitone, it seemed preferable to him to put the semitone in the middle of the four whole tones. Thus Guido could accommodate

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the semitone without disturbing the order of the hymn, for the semitone, being the high vowel / in pronunciation, fell between mi and fa. He caused the distance of a whole tone to be sung from ut to re, from re to me another whole tone, from mi to fa the semitone, and then in sequence from fa to sol a whole tone, and from sol to la another whole tone. Consequently, if readers measure accurately the difference between the syllables, they will find that the semitone has two whole tones below and two above and that it is therefore exactly in the middle. This ordering resulted from the pronunciation of whole tones and semitones by means of these syllables. Guido then added the letters A B C D E F G t o the syllables ut re mi fa sol la. In paying homage to previous inventors, he decided to honor the Greeks first. He thus began by writing the first letter in the order of the hand as a Greek gamma; adding to it the syllable ut, he wrote down "Gamma ut." Thereupon followed the order of the hand in which he also honored the Latins.7 Guido took the first letter of the [8r] Latin alphabet and, adding A to the syllable re, he wrote "A re." And next, adding mi to B, he said "B mi." With C added to fa he pronounced "C fa." D joined to sol he called "D sol." And with the letter E connected to la, he concluded the set with "E la." As a result, the first combination of the letters and syllables was: Gamma ut, A re, B mi, C fa, D sol, E la. Now, because there were seven letters and six syllables, there was an odd letter left. Therefore Guido came to the realization that the seven letters yielded the composition of two tetrachords, and that in proceeding in sequence to the third tetrachord, the first letter repeated itself, followed by the others in the same sequence.8 Because the same letters repeated themselves, Guido did not consider it inappropriate to begin again with the identical syllables, doubling and tripling them so that they could serve on a line or a space to make a mutation. The mutation not only changed the name of the note character but also transformed whole tones into semitones or semitones into whole tones by means of signs. Moreover, in order to be able to construct more tetrachords or fourths, it was necessary for Guido to add as many syllables as were required for practical convenience, even two or three together. And if more had been needed for his practice Guido would 7. Dodekachordon (Basel, 1547), Bk. I, chap. 1, by Heinrich Glarean. 8. Vicentino's use of tetrachord may seem an odd substitute for hexachord. He is thinking in terms of two four-interval sets between A and G, beginning with re-mi in the hard hexachord and ending with fa-sol in the natural hexachord. Like all writers before him, Vicentino attributes the invention of the hand, or the hexachord system, to Guido, even though there is no documentary evidence that Guido ever used it.

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have added more syllables, as is evident in the arrangement of the hand, with its doubled or tripled syllables, such as F fa ut or G sol re ut. So Guido augmented and diminished the order of the hand to facilitate the composition of many fourths in keeping with the opportunities for making mutation. In those times the hand was made for plainchant. It was thus possible to sing with ease and orderliness in church all those matters pertaining to obligatory sacred observance.

Chapter 3 On the Invention of the Natural and Flat Signs and the Signs Called Clefs by Practitioners The arrangement of the hand was effected by Guido the Monk in the way I informed you, although some people think that the natural and flat were invented by others. From what I can gather, it seems clear to me that these two signs could not have been invented by anyone but Guido the Monk for the following reason: he could not otherwise have formed the fourth from B fa B mi to the low F fa ut [descending b-f], the fifth from B fa B mi to the high F fa ut [ascending b-f], and the fifth from the low F fa ut to B mi [descending f-B], on account of the octave equivalence between B fa B mi and B mi with a flat [descending b-B]. In the days when plainchant flourished, B mi was put in the third order of the hand.9 It was therefore necessary to write B fa B mi on B mi in order to have all the consonances we use in these days as well as the conjunction and disjunction of the third and fourth tetrachords, as I said earlier ["Music Theory," chapter 3]. I am quite certain that Guido the Monk did not put a flat on low, high, or very high E la mi. I shall prove this assertion with two arguments. First, when Guido discovered that the semitone did not follow in sequence from the beginning of the third order, he placed there the flat sign so that on leaving A la mi re and ascending to B fa—mi, you would sing the step of a semitone with the syllable fa. To prevent disciples from getting mixed up at that very point, Guido put a natural sign because he realized that when a flat was written, a semitone was formed, whereas when a natural was written, a whole tone would be formed between A la mi re and B fa B mi with the syllable mi. For the flat he wrote the syllable fa. Therefore, if it is true that the syllable fa is not written on E la mi in Guide's hand, we can be certain that he did not put a flat on E la mi, which is proved by his hand. For just as he had written fa on B fa B mi, 9. That is, the hexachord on F.

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he might have written a flat with the syllable fa on E la mi, saying [8v], "E la mi fa." Such a thing, however, does not appear in his hand. The other argument is as follows. In Guide's work only plainchant is discussed,10 and in plainchant only a few flats are used. It is true, however, that the flat was added to E la mi by his successors—that is, by our predecessors—to accommodate measured music more than plainchant, as you can understand from what I said above. It is undoubtedly true that in Guido's time the singing of plainchant at first required great labor on account of its scanty practice. For this reason, one had to have infinite patience in teaching it and in suffering those in the profession who hated it.11 According to a letter in Guide's work addressed to him by one of his students, a monk who found himself far away from his master, Guido was informed that in those parts all the singing teachers refused absolutely to renounce the primordial rules of singing with the letters A B C D E F G.12 Even so nowadays. I spoke with some Venetian merchants who affirmed that in certain parts of Hungary it is still customary today to sing with the letters A B C D E F G. Returning to Father Guido, I declare that, armed with great patience and restraint, he taught many how to sing, and besides this, he composed the Gradual and began to use it for effortless singing in churches. Even though he came to be hated by music practitioners, Guido nonetheless refused to discontinue his pursuit of so fine an enterprise. And so, by persevering and singing his invention every day, he came to the attention of Pope John XX of Rome,13 who desired not only to see the new way of notating the Gradual but also to hear the singing of the syllables ut re mi fa sol la. The pope sent two nuncios, who escorted 10. As the following citations show, Vicentino did not know the Micrologus, in which Guido discusses polyphony. 11. Although this information can be found in Guide's Epistola (Scriptores ecclesiastic^ 2: 43), Vicentino may have encountered it in the Aliae regulae, also called Prologus in antiphonarium (Scriptores ecclesiastici, 2: 34-35, and Tres tractaculi Guidonis Aretini, edited by Joseph Smits van Waesberghe [Buren, 1975], pp. 61-62). Along with the commentary known as Regulae rhythmicae, the Epistola and Aliae regulae (the latter written about 102025) formed part of collection known in the sixteenth century as the Introductorium. 12. Guido, Epistola (Scriptores ecclesiastici, 2: 44). Somehow Vicentino has confounded the sender, Guido, with the recipient, Brother Michael. 13. Vicentino s numbering follows the normal practice for his time, based on the dubious evidence that there were two popes rather than one named John after Boniface VII in 985. The first was said to have reigned for about four months as John XV; hence the true John XV received the number XVI, and John XIX became John XX. In the sixteenth century the standard source of papal biographies was the none-too-accurate work by the Roman hu-

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Guido to His Holiness, to whom he showed the Gradual. His Holiness venerated Guido as an oracle, for he was overjoyed that under his blessed reign such new inventions should be shown to the world. Moreover, after he heard the revered father sing these syllables, His Holiness rose from his seat and embraced the brother with so many gracious words that it seemed to the onlookers that Father Guido was esteemed and venerated by His Holiness like a god on earth. He was asked to stay at the papal court. But the Reverend Guido declined for legitimate reasons: not only did the climate not agree with him but also he was accustomed to the monastic life and dedicated to the study of music. Thus, with the pope's gracious permission, he returned to live at Pomposa, the seat and abbey of my lord and patron, the Most Illustrious and Very Reverend Cardinal of Ferrara, Ippolito II d'Este, under the happy reign of His Excellency the Duke of Ferrara [Ercole II] of the house of Este. Father Guido stayed at Pomposa, the place where, after much study, he first came upon the discovery of the syllables, ut re mi fa sol la, and the characters of the points and also constructed the arrangement of the hand, as you have learned. And every day Guido expanded this practice by means of study. He placed certain signs at the beginning of the lines so that the dots written on lines or spaces could be easily understood. At the start of the four lines he wrote three different letters placed in various locations, writing now one and now another according to the high or low range of the plainchant. The three letters—F, G, and C—designated the names of the points by means of the syllables ut re mi fa sol la.14 These letters—F, G, and C—were later called clefs, although their written form is corrupt in these times. In plainchant they have been quite common for some time now. But in measured polyphony there remains only the letter G, because instead of C this sign is written It; and instead of F this other sign, ^Y , or this one,3^.15 It seems to me that in the very beginning two letters needed to be drawn in one stroke, C and F for the natural and soft manist and papal librarian Bartolomeo Platina. Both the Latin printing and the Italian edition, translated and emended by Michele Bonelli, list the pontiff in question here as John XX. De vitis acgestis summorumpontificum (Cologne, 1540), fols. 189v-190r, and Delle vite depontefeci (Venice, 1552), p. 140. Except for reducing the number of nuncios from three to two, Vicentino otherwise embroiders Guide's account in the Epistola (Scriptores ecclesiastici, 2: 43-45) with a few extravagant touches of his own. 14. Guido describes the lines, the spaces, and the letters, of which there are only two (C and F), in theAliae regulae (Scriptores ecclesiastici, 2: 36-35, and Tres tractaculi, pp. 66-70). 15. Probably Lodovico Fogliano, Musica theorica (Venice, 1529), Bk. Ill, chap. 7. See also note 48, below.

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hexachords, and C and G for the natural and hard hexachords,16 so that singers would know through practice how to transform the names of the syllables from one tetrachord to another, as example 3 amply illustrates.

Example 3 [Solmization]

[9r] In plainchant, more than four lines were never used, and this is still true today because the melody neither ascends nor descends more than eight to nine pitches. More-modern musicians added a fifth line to accommodate measured polyphony. Thus, with the favor of Pope John XX of Rome, the Reverend Guido imparted the principles and knowledge of music to his pupils by means of these signs. The practice of these signs and syllables was put into use in 1024, judging from what was written in the fascicles of the ancient chronicles.17

Chapter 4 On the Inventor of the Eight Note-Values of Measured Music and How They Were Constructed, and on the Addition of Signs Made by Many at Various Times The invention of the syllables ut re mi fa sol la along with the hand, and the lines, dots, and clef signs have been described. As it happens, dots or points were used in plainchant. Nevertheless, when works for two voices began to be composed, the writing of points continued for a time. When a composer made a duo, the listeners said it was a fine counterpoint because he wrote one point against the other. From this custom of composing one point against another we have inherited an improper way of referring to our compositions. For in truth we should no longer say counterpoint today, since it is not the custom to write points but rather it is the custom to write the notes and characters discovered by the very great philosopher Jehan des Murs, who worked in France at the 16. The text contains an error that compounds the problem of ambiguous terminology at this point. "G & F per b rotondo, & per natura, & C et G per natura & per \ quadro refers to the soft, natural, and hard hexachords, respectively. Bk. I, ex. 3, shows that the first two letters should be C and F and that "per natura" should precede "per b rotondo." Earlier in the chapter "b rotondo" and "^ quadro" denote simply the flat and natural signs. Similar double duty occurs in Bk. I, chap. 4, and elsewhere. This sort of ambiguity was commonplace in treatises of the time. 17. Precisely which chronicles remains unclear. However Vicentino arrived at 1024, the date is not implausible, since Guido fled to Arezzo around 1025-26 and visited Rome in 1027-28.

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University of Paris.18 This man discovered how to write the eight shapes or signs for the notes we today are accustomed to using on the lines and spaces. He also discovered the circle and the semicircle, cut and uncut, with numbers as well as circles and semicircles that have dots written in many ways, as well as rests,19 as you will see later on [Book IV, chapters 3-8]. All these signs were added after the invention of the eight musical shapes. Others added to their compositions the flat on E la mi as well as a sign of four little lines written thus, fl. In this way people added gradually here one thing and there another. Indeed, a short time ago there was added to the keyboard of the organ a semitone on the third A la mi re [3A1*]20 above G sol re ut; this was done in order to be able to couple the semitone with the fifth above on E la mi with a flat. And so many people have discovered many things, always for the better and for increasing the availability of consonances on various pitches by the application of the natural, flat, and sharp signs. In my opinion, the natural and the flat signs were the beginnings on which the eight musical shapes were founded, as follows. Wishing to form eight musical note-values—that is, the maxim, long, breve, semibreve, minim, semiminim, croma, and semicroma,21—Jehan des Murs had to base his thinking on certain preexistent shapes of music practice and out of them to carve other shapes. It therefore seems to me that the process could only have happened thus: he carved the eight note-values from the 1? and the \\ in a way I shall describe to you below. Indeed, the creation and formation of these note-values has convinced me that everything I wrote above is true. Let us first consider the breve. Its form (if you examine it well) is a \\ with stems, and it then becomes the breve, seen in the form M, because it is carved from the t|. Together with the long and the maxim, the breve at that time must have been associated with singing in the hard hexachord because all three shapes are somewhat similar. It is clear that the long is a 18. Colophon to the Musica speculativa (Scriptores ecclesiastici, 3: 283). 19. Notitia artis musices (also known asArs nova musice), edited by Ulrich Michels (American Institute of Musicology, 1972), Bk. II, chap. 6. See also Scriptores ecclesiastic!, 3: 296. 20. The phrase A la mi re terzo refers to the key that produces Ak above G on the third rank of the keyboard of the archicembalo (Bk. V, chap. 4, and App. V). 21. This list is wrong. Des Murs gives five note-values from the maxim to the minim (Notitia, Bk. II, chap. 6, and Scriptores ecclesiastic^ 3: 295). However, Vicentino's fanciful account of the genesis of note-shapes is based to some extent on observations made by des Murs on rectangles, tails, dots, positions, and directions (Notitia^ Bk. II, chap. 4, and Scriptores ecclesiastic!, 3: 294-95). But see also Stefano Vanneo, Recanetum in aurea (Rome, 1533), Bk. II, chap. 2.

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tj with a stem, that is, ^j; the maxim has a similar shape but [9v] is different in size, as shown here: |. Then, from the I? was carved the semibreve which is a 1? without a stem, as you see here: O. Having formed the two notes, that is, the breve, H> and the semibreve, O, the philosopher [des Murs] realized that the square and round shapes were connected to the hard and soft hexachords, respectively, and, moreover, that the natural hexachord was associated with both of these hexachords. Therefore, he did not have to find any note-value associated with the natural hexachord, for nothing but the letter C was its clef sign. The truth is that whenever a composition is written in the hard hexachord, this hexachord is always accompanied by the natural hexachord; the same thing happens with the soft hexachord.22 After forming the notes associated with the hard and soft hexachords, the philosopher gave them names. The square he called breve, for it was originally a t) with two long stems; having cut off the two stems, he called it an abbreviated note-value—a breve, that is, for it was no longer elongated with two stems. Now the \> has only one stem in contrast to the two stems of the l|. Because des Murs cut off the single stem of the k it occurred to him to call the I? without its stem a semibreve, for he had re moved from it one less stem than from the t|. The removal of one stem from the 1? amounted to one-half of the two stems of the ^ and for this reason he was correct to call this note-value a semibreve. And to identify it as half of a breve by a name associated with the notion of halving the breve, he added semi, which means half in this case, to the word breve. By combining semi and breve he formed the word semibreve, which was and is associated with one-half of a breve. Then the philosopher had to consider that the accents of pronunciation were varied, as were its speeds, and that the two note-values, breve and semibreve, could not serve the various rates of motion required in the delivery of the singing voice. It was therefore necessary to augment and diminish the two durations of the breve and the semibreve, using their two shapes as a basis. So as not to raise difficulties for those who already had some experience with these two shapes he used the same ones. Moreover, because it was easy to recognize their value, he put back the stems on these notes, restoring them somewhat to their original written form. So that it would be possible to recognize which were formed from the t] and which from the t, and also to distinguish them from the shapes 22. The suggestion of a bifurcated system of hexachords (hard and soft) places Vicentino among the progressive thinkers on solmization.

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already added to these two signs, he put a stem on the right side of the breve: ^. And since this shape had a longer stem than the I], he called it a long, after the stamina of the stem. This note was twice the value of the breve. Then, to make the long a longer value—twice as long in fact—he added half the body to its length. Because it was twice as long, as shown here, |, you can see that it is as big as two longs combined together. He called it a maxim, that is to say, the longest of all the note-values found in music. After all, the shape called maxim originated first from the tj (which was converted into a breve without two stems), and then from the breve with a stem on the right side (which became the long), and finally from the long with an elongated body, to become the maxim. Afterward, more-modern musicians arranged parts of these notes together and made various bindings out of these shapes. These varied bindings were called ligatures. Many people have written about these shapes, describing the many ways they are bound together, their values, and also certain oblique and square shapes. I shall not explain these ligatures because, as I have already told you, many people have done so. It seems to me that I have said enough about the origin and purpose of the breve, the long, and the maxim. There remains to describe the birth of the minim, semiminim, croma, and semicroma. As I said earlier, the beginning of all these note-values was of necessity in the I? and the t|. After removing the stem from the there remained the body of the semibreve. Inasmuch as the delivery of a motion faster than a semibreve happened in compositions, the philosopher had to add a stem to the semibreve. So that it should look like a I and yet show a difference [lOr] in value equal to one-half of a semibreve, he applied the stem to the middle of its body, in this way: ^. Thus you can recognize the difference between the 1? and this shape, called mini by the philosopher to signify a value smaller by half of a semibreve. From the same shape he formed others, each a different shape with a different value, diminishing the value of the minim by blackening it and adding flags to the stem. The first of these was the minim itself, but made black, as seen here: J; it was called semiminim because its value was one-half that of the minim. Then he added to the latter shape a little flag on top of the stem in this way: 4 • It was called a croma, for it was transformed, as it were, by the subtraction of the value of one-half of the semiminim. This shape, with another little flag added above it in this way, R, became the semicroma, for its value was one-half that of the croma. This was how the philosopher carved these note-values out of the I?, even though in these days we avail ourselves of them for songs in both

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the hard and soft hexachords. Indeed, the ascent and descent of the fourths, fifths, and octaves that constitute the modes can be changed as much by the hard as by the soft hexachord. For this reason (coming back to the topic), we do not distinguish the use of those note-values generated solely by the t{ from those generated by the k segregating the former for the hard and the latter for the soft hexachord. Thus we have a greater abundance of various rates of motion in performance. These comments suffice as to the invention of the eight musical notevalues discovered by their inventor, a man who lived 329 years after Guido the Monk. Judging from compositions today, we can be sure that such polyphony has been completely lost. But as far as the work of Jehan des Murs is concerned, he has greatly helped the world despite the 250 years that have intervened between his time and the present.23 The enlightened state of mind between those times and ours is shown by the examples of those who have added one thing and others who have added something else. Therefore, to show the world that I have not wasted many years of labor either in teaching or helping others, I now publish in this treatise the practice of all three genera, both pure and mixed (whether genera mixed with genera, species with species, and even genera with species), other discoveries never before described by anyone else, and the various ways you can compose in tense and slack manners. There exist today a number of professionals in music who condemn any effort to learn, and who even disparage the exertions made by so many celebrated philosophers in their quest to understand the ultimate division of music. But persons such as these will not deter me from learning and investigating new things, for knowledge is a characteristic of man.24 This is why I have never ceased trying to adapt these genera and species more easily to practice by means of voices as well as to create an instrument [archicembalo] whose construction and design my kind readers may observe in "Book V on Music Practice." Even if I am unable to make much profit from this practice, at least I shall provide an incentive to fine talents, who will bring it gradually to a better state. How great can be the reward in seeing and hearing compo23. Any attempts to reconcile Vicentino's dates are doomed to fail; however, 200 years, unlike 250, gives us a range of probable chronologies. First, using the date of publication (1555) we arrive at 1355 for des Murs, and then, deducting 329, at 1036 for Guido of Arezzo, the latter a date too far away from 1024. Second, the date of the first draft (1549) puts des Murs at 1349 and Guido at 1020. And finally, by taking 1553 as the likely date for revisions, we find des Murs placed in 1353 and Guido in 1024. 24. See, for example, Aristotle, Metaphysics, 1.1.98 Ib, and St. Thomas Aquinas, In decent libros ethicorum Aristotelis adNicomachum expositio, 1.50.10:cl26.

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sitions as they developed in the past is demonstrated by a comparison of the music of our times with that practiced a hundred years ago, even fifty, twenty-five, or ten years ago. The same goes for my work in the future, for in ten, twenty-five, fifty, or a hundred years and more, it will be possible to see and hear how maladroit are my compositions and those of my contemporaries compared to the compositions of our successors. The reason is that it is easy to supplement things already discovered, whereas inventions and beginnings are extremely difficult. I therefore rejoice in God's grace whereby, for His honor and glory, I may bear honorable comparison with music professionals in these times. I have truly labored for many years. At the pleasure of Divine Goodness, I was enlightened to begin this treatise in my fortieth year, the Holy Year 1550 [lOv], during the most blessed pontificate of Pope Julius III.25 Persevering with unremitting study, I was able to amplify this treatise as much from the benefit of composing it as of teaching it to many persons who have profited rather well from it up to now, especially in the glorious city of Ferrara, where I dwell at present. By providing others with a knowledge of the theory of this art and by adapting it to practice in my compositions, I have induced many lords and gentlemen to appreciate the sweetness of this harmony. And they in turn, enchanted exceedingly by it, have striven to learn it with the most exceptional diligence. For in effect they understand that (as ancient writers show) chromatic and enharmonic music was reserved appropriately for another purpose than was diatonic music: the latter was sung at public festivals in communal places for the benefit of coarse ears, whereas the former was used to praise great personages and heroes for the benefit of refined ears amid the private diversions of lords and princes.26 On account of the miraculous sweetness of chromatic and enharmonic music, and so as not to fall short in any way from the virtue of ancient princes, His Excellency Alfonso d'Este, Lord Prince of Ferrara27—aside 25. Here, as elsewhere, Vicentino hammers at the idea of hard work. Ghiselin Danckerts reports that by 1549 Vicentino had been studying the genera for fifteen years, giving us a starting date of around 1534. Sopra una differentia musicale (Rome: Biblioteca Vallicelliana, Ms. R 56A, no.!5b, ca. 1555-56), Bk. I, preface. Certainly, the year 1550 (Vicentino was then thirty-nine years old) conflicts with the dating of Vicentino's application for a Venetian printing privilege and a ten-year monopoly in 1549. See App. I. Perhaps Vicentino settled on 1550 in order to pay homage to the reigning pontiff, who was elected that year. Guido, it will be recalled, put his system into practice in 1024, the year of the election of John XIX [XX]. 26. See the introduction, above. 27. The future duke of Ferrara, Alfonso II (reigned 1559-97).

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from the favor he bestowed on me—has learned this music with such consummate alacrity and grace that the world recognizes in him the image of the perfect prince. Just as he deserves eternal glory for feats of arms, so he bears an immortal name also in the sciences. As for the virtues of his soul, whoever does not know how prudent, just, magnanimous, and liberal is this prince can never know the true model of these virtues. And the Most Illustrious Lady, his aunt Sister Leonora d'Este, is a lady of the holiest life who, stripped of the snares of this world, has completely dedicated her present life to God. This lady no less admirably combines the study of the theory and practice of the three genera with that of instruments and of fine literature. What shall I say about the Most Illustrious Ladies, the Lady Princess Lucrezia and the Lady Leonora, her sister? These ladies, to whom nature has been more prodigal than liberal, are not content to surpass the world in nobility, grace, and beauty. Rather they wish to couple it with so much virtue that they surpass every marvel imaginable. They too have derived so much benefit from this science that they are most worthy of eternal praise.28 It gives me pleasure to remind readers that, as everyone knows, the illustrious house of Este has of its own volition learned those sciences that it supported and maintained for others by its singular generosity. For this reason it long ago became a haven for brilliant men. And today His Excellency, the Lord Duke Ercole II, is as much the meritorious father of his country as he is the upholder and protector of all the virtues. Thus, just as the initiation of the syllables ut re mi fa sol la took place in Pomposa under the happy auspices of this house (as I said), so under the aegis of the duke's brother, my lord and patron, the Most Illustrious and Very Reverend Cardinal Ippolito II, I have established the goal and ultimate division of practicable music with these syllables and with my instrument. In spite of the weakness of the beginnings of every science, it is nevertheless to be hoped that the science of music, advancing now on one, now on another front, will shortly succeed in attaining perfection, and moreover that posterity will become aware of the grandeur and 28. The list of the progeny of Duke Ercole II omits two of his legitimate children: Anna, the eldest, and Luigi, the youngest. Anna, perhaps the most talented of all, was married in 1548 to Francis d'Aumale, due de Guise. Luigi, a future cardinal, rebelled against an imposed clerical career by running away to France, where he led a dissolute life despite his early elevation to the bishopric of Florence in 1550. Also missing from this list is the illegitimate youngest daughter, Lucrezia, who like her aunt Leonora joined the religious order of Corpo di Cristo.

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nobility of this art and strive to discover by diligent examination the infinite secrets hidden in it. And just as music practice in the world today has, in the hands of very learned musicians, made such marvelous progress from its beginning up to the present, so may the same happen (with God's help) to this, my weak beginning. I hope that my successors will greatly exalt this music practice, which, even with my inferior understanding, I find extremely profound.

Chapter 5 Explanation of the Hand Marked with Signs Denoting the Species of the Three Genera, with Seven Rules of the Hand or Seven Hands29 [1 lr] Perhaps my readers may think I have discussed many superfluous matters in the previous chapters, such as the invention of the syllables and the note-shapes, as well as the present and future times in which the labors of men appear gradually to the world. But insofar as some people added one thing and others added many, it seems proper to me to commemorate these innovations not only to please those who enjoy reading the stories of our predecessors—who always amplified and clarified their science and practice,—but also to warn my contemporaries and successors not to be amazed if I augment and enrich the knowledge of the practice and science of music more than is customary. Truly, it is an uncontested fact to learned men that whoever is astounded by something must be ignorant of its practice and theory alike. Those who understand these matters never betray astonishment to others. All the same, I notice that nowadays some singers and musicians, who believe themselves knowledgeable, show their amazement to everyone whenever they encounter a novelty in musical signs that has been introduced for the sake of some sort of consonance. Straightway they begin by saying, "It is not good, it is not easy to sing," and conclude that "it will not endure," citing the example of past composers to prove that if the practice in question were good those composers would have used it. Thus do these singers and musicians betray to all that they have forgotten how to study their profession. But these poor devils, devoid of such knowledge, fail to realize that if what they allege were true—that is, if music practice from its first invention had had a fixed goal—it would 29. The eight music examples in this chapter, each connected to one rule of the hand, do not contradict the count of seven hands given twice in the title and thrice in the text. The seven hands are additions (Bk. I, exx. 5.2 to 5.8) to the so-called Guidonian hand (Bk. I, ex. 5.1), even though the latter has a B^ in the lowest octave.

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have been impossible to augment or diminish that practice in any respect. Yet many gradual changes and improvements in this practice have occurred in the works produced by composers of the past. And no proof is required for things that have actually happened. Consequently, readers should not be astonished if I show them several rules of the hand with new practical arrangements and also explain the written signs in the following way. In the diatonic order the signs are written according to the arrangement of Guido the Monk, except for the beginning of the hand. Instead of A re, B mi, and C fa ut, I write A la mi re, B fa B mi, and C sol fa ut, as you see in example 5.1. Beginning this way is indispensable because it allows the mutations of B^ and B1" that appear in the descending melodies of the measured music associated with the second mode [Hypodorian] in the soft hexachord and with the fourth mode [Hypophrygian] in the hard hexachord.30 Guide's hand does not accommodate these tones. Other orders are written with the signs of the chromatic species. The ascending flats are all major semitones [example 5.3], whereas the descending ones are minor semitones. I shall notate two orders, one with flats and one with chromatic dieses, or sharps, that, contrary to flats, are minor semitones when ascending [example 5.2] and major semitones when descending. Still other orders are written with dots over the notes [example 5.4]. The dots denote one-half of the minor semitone. When the dot is located between the interval of a minor semitone it is called a minor enharmonic diesis, since this semitone comprises two minor enharmonic dieses. But when the dot divides the major semitone, then the first enharmonic diesis is minor and the remainder, which fills out the major semitone, is a major enharmonic diesis. The latter is the same size as a minor semitone.31 Here is the rule for dividing the major semitone: if the division occurs in an ascending direction the first diesis is minor and the second major, and the reverse obtains for dividing [llv] the descending major semitone, for in this case you will always find the first diesis to be major and the second minor. Lest this practice seem strange to you at the outset, let me assure you that you will understand these divisions better in the fifth book because of the many examples contained in it [chapters 40—58]. Moreover, your 30. In the lowest A-a octave of the gamut, the Hypodorian tends toward B1" (B fa) whereas the Hypophrygian retains B (B mi). 31. See Bk. I, chaps. 8, 11, 15, 18, and 19. The combining of two sets of solmization patterns (Bk. I, exx. 5.5 and 5.7) produces a whole tone that contains five dieses (e.g., A, A, A», Bk, Bk, andB).

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skill will be improved by my instrument, called the archicembalo, since practical examples are more convincing than notatec! examples accompanied by words. Although this instrument is depicted [Book V, chapters 1-4 and figures 1-3], students will go beyond merely learning about its design. True, the drawing itself is incapable of reproducing any pitch intonations. Yet students will derive so much benefit from the experience of working with it that once the instrument is constructed, it will not seem as difficult to produce these intonations as it would have been had they not seen or worked with the drawing of the instrument beforehand. Let us now proceed to the explanation of the seven hands. I shall first discuss the conventional hand of Guido the Monk and then enumerate the seven hands I have added to it. Since Guide's hand was made known to the world many years ago, no one should be surprised that I now notate it with seven ascending pitches. Indeed, this description is crucial because it can introduce students to the way they should learn all the other unstable pitches.32 If a student grasps all the seven letters in example 5.1, he will understand the entire hand. So I begin with the lowest A la mi re instead of A re and then describe all the natural pitches in ascending order with the seven letters up to G sol re ut, that is, A B C D E F G. I shall then write the chromatic and enharmonic pitches with the names and directions underneath so that you may learn to read them either ascending or descending with major and minor semitones. Examples of these pitches can be seen in examples 5.2 to 5.8.

Example 5.1 Demonstration of the Diatonic Hand

Readers will note that I offer no explanation of these exiguous pitches, that is, I do not say that this pitch is sung in the natural hexachord, the other in the soft, and the third in the hard. It suffices to place under the notes the signs by which they are to be sung. Students will thus notice the following signs below the notes: ^ t, and nat.331 presume to illustrate 32. Vicentino means the movable steps that shift position in the genera. See "Music Theory," chap. 13. 33. In the examples, the letters H., S., and N. stand for the hard, soft, and natural hexachords, respectively.

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these seven letters to professionals so that they may understand me well. As for students, I placed the example of these pitches first not to instruct them in Guide's hand, already expounded by so many, but rather so that they can use it to apprehend more easily the chromatic and enharmonic pitches along with their names in the following examples.

Example 5.2 Demonstration and Example of the Chromatic Hand Ascending by Minor Semitones

[12r] The seven letters written in example 5.2 help you to understand the entire chromatic hand with ascending and descending minor and major semitones, for when the prescribed notes have a sharp attached to them they show the division of the minor semitone when ascending and that of the major semitone when descending. These notes are read like the natural ones, with the first note having two names. For instance, if on A la mi re there are two notes, one natural and one chromatic, you say "la mi" on the natural note and "re" on the accidental chromatic note, as marked by the signs of the three hexachords.34 This little rule is brief and easy to understand.

Explanation and Example of the Chromatic Hand Ascending by Major Semitones There now follows the chromatic hand written with ascending major semitones through the seven letters of the diatonic hand [example 5.3]. The notes signed with a flat show the division of the major semitone when ascending and that of the minor semitone when descending. Students should observe that whereas sharps are always written on the location of the natural note, whether on a line or a space, the reverse happens with the sign of the flat. If composers wish to ascend a major semitone from the low F fa ut on a line, they put a flat on the low G sol re ut, which is on a space. And if a player is on G sol re ut and must go up a major semitone, a flat should be written on the line of A la mi re. Carelessness in writing such flat signs may result in mistakes in their placement, so that what appear to be semitones on a line really belong to a space. 34. The notes B* and EP appear on the third rank of keys of the archicembalo. See Bk. V, chap. 4, and App. VI.

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The notes signed with a flat should be read in the same way you read natural notes. Although some people find these notes difficult to perform, they must nevertheless persevere in practicing, just as they did with the natural notes. They should practice the flats with the division of the archicembalo, supplying two names for the natural notes according to the rule I gave above for the sharps of the ascending minor semitones. The ascending flats are shown with seven letters sung on the natural, soft, and hard hexachords in example 5.3

Example 5.3 Demonstration of the Chromatic Hand with Ascending Major Semitones35

When these flats jump a third, fourth, fifth, or more, singers should apply the mutations of the natural semitones to the steps making up the leap and call the leap of the minor and major third "fa-re" and "mi-ut," that of the fourth "fa-ut," and that of the fifth "fa-fa." Both in ascent and descent, these leaps resemble natural leaps. Therefore, it does not transgress the chromatic rule to say "ut re mi fa sol la" on every line and space whenever singers find mutations to be convenient. These mutations will be confirmed by my archicembalo, for it shows that on every location of the keys you can say "ut re mi fa sol la" to the written signs of the semitones and the enharmonic dieses.

35. The function of the second line of syllables is to supply the ones missing in the top line, which supports Vicentino's contention that any or all of the syllables can be sung on any pitch. The same is true of the extra syllables, fa and re, in the first line under E la mi and F fa ut. This claim relates to his advice concerning leaps involving flattened notes, for if these are solmized as he suggests, each of the extra syllables will occur at least once in each segment. In segment 2, B is one diesis higher than B, forming a major semitone above B1".

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Explanation of the Ascending Enharmonic Diatonic Hand with the Seven Letters of the Hand In the fourth rank of keys on my instrument there occurs a diatonic order that makes the same use of whole tones and natural semitones as does the natural diatonic order.36 Now I shall give it a name. As a start, [12v] I call it the enharmonic order because it uses the enharmonic division when mixed with all the other divisions of whole tones and semitones that may occur in my music practice. The notes written in this enharmonic order are to be read as if they were natural diatonic notes. Second, I call it the natural enharmonic when it ascends by whole tone and semitone in its fixed sequence, to distinguish it from the natural diatonic. And third, when it yields the division of the whole tones by major and minor semitones, I call it the enharmonic chromatic order to differentiate it from the chromatic that I have already divided out of the diatonic order.37 In example 5.4 I show the ascending enharmonic diatonic hand, starting on the lowest A la mi re and rising through the seven letters. It should be absolutely clear that the notes are written according to the diatonic order and are to be read with the same syllables. The dots above the notes show the enharmonic diesis, which merely signifies that these notes are sung one-half of a minor semitone higher [than those in example 5.1].

Example 5.4 Demonstration of the Ascending Enharmonic Diatonic Hand with the Seven Letters of the Hand

36. The natural diatonic provides the white keys of the first rank on the lower manual. The enharmonic diatonic of the fourth rank, the first set of keys on the upper manual, duplicates the former, one minor diesis higher. See Bk. V, chap. 3, and App. VI. 37. The third distinction refers to the enharmonically raised chromatic pitches supplied by the fifth rank, the second set of keys on the upper manual. The second name denotes the internal and self-sufficient ordering of pitches on the fourth rank. The first name alludes to the microtonal inflections produced by the fourth rank in contrast to any of the pitches produced by the three ranks of the lower manual. See Bk. V, chap. 3, and App. VI.

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Explanation of the Enharmonic Hand with the Seven Ascending and Descending Letters and with the Names of the Noie$T)ividing the Whole Tone and Semitone, Starting on the Lower A La Mi Re and Ending on the Low A La Mi Re The enharmonic division will be illustrated by two pairs of ascending and descending examples, the first dividing the minor semitone and the second dividing the major semitone. When reading the notes readers are advised to do as follows. Begin [each segment] with the natural note, giving this note its proper name. Do this not only at the beginning but also at the end, on the subsequent natural note. Taking advantage of the closest possible mutations, move effortlessly, as the practice of mutation enjoins, and find each natural note, as shown by examples 5.5 to 5.8, with their divided whole tones and semitones.38

Example 5.5 A Hand with Minor Semitones Dividing the Whole Tone into Four Ascending Enharmonic Dieses39

38. Vicentino's solmization is discussed in the Introduction. 39. The pattern of the dieses (D) in the whole tone is: mD, mD, MD, mD. The dieses in the semitone are: mD, MD. Segment 2 demonstrates the solmization of a major semitone by mutatio vocalis, the only way to accommodate five syllables in an interval made up of four pitches, inasmuch as B* and & are two spellings for the same pitch. The spelling B* (like E*) is assigned to a key in the third rank of the archicembalo (see Bk. V, chap. 4), although C7 occurs in some examples in Bk. V.

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Example 5.6 An Enharmonic Hand with Minor Semitones Descending to the Beginning of the Mode Through the Seven Letters of the Hand, Each Whole Tone Divided into Four Parts and Showing How It Should Be Read40

Example 5.7 An Ascending Enharmonic Hand with Major Semitones Dividing the Whole Tone into Four Parts and Showing How to Read the Seven Letters of the Hand41 40. The pattern of the dieses in the whole tone is: mD, mD, MD, mD. The dieses in the semitone are: MD, mD. 41. The pattern of the dieses in the whole tone is: mD, MD, mD, mD. The dieses in the semitone are: mD, MD.

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Example 5.8 An Enharmonic Hand with Major Semitones Descending to the Beginning of the Mode Through the Seven Letters of the Hand with the Whole Tone Divided into Four Parts42

[13r] Singers may use the archicembalo to sing the major diesis in the same way as the minor semitone. There is no difference whatsoever in size between the name of one note and the next. [13v] In other words, the difference between mi and fa is the same as the one between fa and sol, barring the major diesis. With these rules everyone will sing the syllables easily in a short time.43

Chapter 6 Explanation of the Practice of the Diatonic Genus, with an Example From the preceding discussion you have learned about the invention and the way of making rules or hands so as to put into practice the species of the three genera, both together and separately. All the same, it is essential for the information of the readers to explain these genera and species so that you will know not only how to implement the signs in compositions but also how to recognize the distance of the pitches with 42. The pattern of the dieses in the whole tone is: mD, MD, mD, mD. The dieses in the semitone are: MD, mD. 43. Contrary to conventional practice, where mi-fa is always smaller than fa-sol, in Vicentino's gamuts these syllables are the same size, except when they encompass the major diesis. For instance, in Bk. I, ex. 5.5, mi-fa in line 2 of segment 1 is an mD, whereas in segment 6 it is an MD; similarly, fa-sol in segment 3 is an mD and in segment 5 an MD.

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signs and to determine whether the pitches belong to genera or to species. But first everyone must understand what genus and species are, in order to grasp the explanation of those hands containing the three genera and their species. Genus, then, according to philosophers,44 is that which subsumes diverse species under it. It is divided into the primary genus and the subordinate genus. Philosophers call primary the genus that has no genus above it and subordinate the genus that has genera above and species below it. And they call species that which is below genus. It too is divided into two types: the subordinate and the particular. The subordinate species is the same as the subordinate genus, but the particular species does not have under it other species but merely individual things. I have gone over this material so that you may better understand everything I shall say about the three genera and their species. As Boethius writes,45 there are three musical genera: the first is called diatonic, the second chromatic, and the third enharmonic. The diatonic is the genus that organizes its species—two whole tones and a semitone— in a consecutive sequence within the fourth. The species thus generate the composite fourth without a gap, as is shown in example 6, whose semibreves are called, in practice, "mi fa sol la."

Example 6 [Diatonic Fourth]

Students are advised that the diatonic genus we use is not exactly the same as the one of which Boethius wrote, for Boethius' diatonic genus is composed of a minor semitone and two sesquioctaval [9:8] whole tones.46 You must realize that in contemporary practice we form the diatonic genus out of one major semitone, one sesquinonal [10:9] whole tone, and one sesquioctaval whole tone. This inequality of tones affords us the advantage of being able to use the consonances of the third and sixth, both major and minor. Readers should know that in Boethius' division, 44. This lesson on genus and species is based on the first two chapters of the Introductio in Aristoteli categorias a Boethio translata (also known as Isagoge), by Porphyry, a Phoenician Neoplatonist who also wrote a commentary on Ptolemy's Harmonics. His introduction, which simplifies the material in Aristotle's Topics and Categories (also known as Depraedicabilibus) became an integral part of the Aristotelian canon, and in Boethius' translation, the standard textbook on logic. The five predicables are: genus, difference, species, property, and accident. 45. De inst. mus., 1.21. 46. De inst. mus., 4.6.

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no third or sixth can be accommodated in practice.47 Moreover, the fourths and fifths of Boethius are perfect, whereas ours are a little blunted and shortened in the tuning of instruments. The difference between our practice and the one discussed by Boethius is this: Ancient musicians used the genera individually in their practice and consequently the minor semitone with two sesquioctaval whole tones were satisfactory for the genera. But in our times, both the sound of practical music and the tuning of instruments are unlike those of ancient musicians, for we use the genera and the species together and with more consonances than they had—namely, thirds and sixths. To be able to have more consonances as well as to make many steps, we do not find it inconvenient to blunt a fifth and enlarge a fourth, as I said. This blunting, as you will learn in the proper place [Book V, chapter 5], does not shock the sense of hearing because the quantity removed is so tiny in itself and because these particles are distributed here and there wherever they are needed. Practitioners of this tuning describe such fifths and fourths as [I4r] tempered.48 For this reason, the music we practice is called tempered music mixed with the larger parts of the three genera and some chromatic species. And the diatonic we used is called the tempered diatonic, that is to say, a genus composed of the species of the whole tone divided by the major semitone.49 Some people might argue that inasmuch as this genus is not composed of two sesquioctaval whole tones and a minor semitone, it cannot properly be called diatonic. My rebuttal rests on the etymology 47. The connection to two sizes of whole tone with consonant thirds (5:4 and 6:5) and sixths (5:3 and 8:5) suggests the diatonic syntonon tuning of the Alexandrine mathematician and philosopher Ptolemy (Harmonics, 1.15), a tuning later advocated by Gioseffo Zarlino for modern vocal practice in Le istitutioni harmoniche (Venice, 1558), Bk. II, chaps. 39 and 40. Although Vicentino does not identify the Ptolemaic system here, he elsewhere betrays an awareness of it in connection with his archicembalo. See Bk. V, chaps. 6 and 62, and Bk. II, chaps. 17 and 21. This connection suggests the influence of Fogliano. 48. The gist of this paragraph suggests that Vicentino here, as elsewhere, put together an inaccurate and rather haphazard conflation of propositions and opinions culled from the Musica theorica, by Fogliano, an organist and choirmaster who served the Este family in Modena. Fogliano's text, then, may explain the anomalies in Vicentino s arguments. See notes 15 and 47, above, and notes 66, 72, and 85, below. 49. This is the crucial issue in the debate between Vicentino and Lusitano. Vicentino argued that the music of his day mixed the whole tones and semitones proper to the diatonic genus not only with the minor semitone of the chromatic but also with the "larger parts" of the chromatic and enharmonic genera, namely, the minor and major third. Such music could not be defined as purely diatonic in genus. Moreover, he confounded the utility of "non-diatonic" intervals with some sort of temperament. See also Bk. IV, chap. 43.

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of the word diatonic. The name of the diatonic genus refers to its course through two consecutive whole tones followed by a semitone without a single gap; it does not refer to the ratios of these steps. Boethius himself, when discussing the meaning of all three genera in Book I, chapter 21, says that the diatonic genus is so called because it proceeds through whole tone, whole tone, and minor semitone within its fourth. He does not attribute the name to the two sesquioctaval whole tones contained in it. On the contrary, he calls it diatonic because it moves through two consecutive steps of a tone and then through a semitone. Therefore, every time you see a fourth made up of two sesquioctaval whole tones [and a minor semitone], or of one sesquioctaval and one sesquinonal whole tone plus a major semitone, or of two tones and a semitone of whatever ratios proceeding through the consecutive steps of two whole tones and a semitone, then this fourth is called diatonic on account of the whole tones and semitones, not on account of their ratios. The species of this genus are the natural whole tones and the natural semitone. I designate them as such on the authority of Boethius, who discusses all three genera in Book I, chapter 21.50 There he says that the diatonic genus is somewhat harsher and more natural than the others. The chromatic and enharmonic are subtle. To conclude, it is possible with my hands to form all three genera with their species on both the stationary and movable pitches, as you will see in the following chapters.

Chapter 7 Explanation of the Practice of the Chromatic GenuSy with an Example In the chromatic genus the fourth has two consecutive semitones, one major and one minor, and a remainder that forms the distance of an incomposite trihemitone without any interruption, as seen in example 7.

Example 7 [Chromatic Fourth]

You should know that the same thing happens in the chromatic genus as in the diatonic, for none of the genera I use are similar to the genera described by Boethius. Boethius' chromatic proceeds through a minor semitone and another semitone, which turns out to be larger than the 50. Misprint: "capitulo XXII." See also De inst. mus., 1.1.

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former semitone.51 Let me warn you that Boethius divides the tone into equal parts, a calculation that contravenes the conviction of many philosophers.52 And yet in this case he made the aforesaid division, leaving a remainder that suggests the trihemitone. But the latter interval is not like our trihemitone, which is called composite, because its size is such that anyone spanning the distance from one extreme to the other would pass through three semitones. This genus, on the contrary, produces a step of three semitones without interruption, 53 and the step is therefore called an incomposite trihemitone. The chromatic genus I use in my practice, as you see in example 7, begins first with the major semitone and then has the minor (the opposite arrangement from that of Boethius). These two semitones generate a whole tone. And what remains is the rest of the perfect fourth, in practice called a step or a leap of a minor third. The distance of one whole tone plus one major semitone is spanned by [I4v] the trihemitone. When put together, the two semitones and the step of the minor third make up a fourth. For the reasons mentioned above, this genus is constructed neither with ratios similar to those described by Boethius, nor with the identical steps of semitones and trihemitone. It is nonetheless a chromatic genus insofar as the difference between Boethius' division and mine is a small one. 51. De inst. mus., 4.6. See also "Music Theory," chap. 6. This semitone is neither the apotome (2,187:2,048) nor the syntonic major semitone (16:15). Perhaps this is why Vicentino refuses to be specific. The chromatic genus given by Boethius is: minor semitone (256:243), "major" semitone (81:76), and minor third (19:16). The three intervals add up to a 4:3 fourth. However, the two semitones produce a tone of 64:57 rather than the Pythagorean tone of 9:8, thus leaving a minor third that is a little larger than the received Pythagorean minor third of 32:27. 52. De inst. mus., 4.6. Even though this rebuke misses the mark, Vicentino has uncovered an anomaly in the canon of classical harmonic science, one repeated by Franchino Gaffurio in his De harmonia musicorum instrumentorum opus (Milan, 1518), Bk. I, chaps. 5 and 6, and Bk. II, chaps. 2 and 9. In his calculations involving string lengths, Boethius confuses the difference between two lengths with the intervals formed by the ratios represented by these lengths, thus contravening his statement that the tone cannot be divided into two equal parts (3.1 and 11). The diatonic tetrachord is 3,072, 2,916, 2,592, 2,304. For the chromatic tetrachord, Boethius takes the distance between 2,592 and 2,304, and divides this distance (288) into two equal halves. He then adds one-half of 288 to 2,592 to get 2,736. The numbers 3,072, 2,916, 2,736, and 2,304 produce the chromatic genus described in note 51, above. Clearly, Boethius does not divide the tone into two equal parts, though his allusion to semitonal segments seems to imply this action. In reality, he uses an equally incompatible visual or mechanical method to shift the location of pitches. 53. Corrupt text: "fa il grado di semitono senza intervallo." A step of one semitone makes no sense in the context.

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Boethius says that chromatic means nothing more than the changing or the transforming of the diatonic sequence.54 So first we have the fourth containing the diatonic genus proceeding through whole tone, whole tone, and semitone; now the fourth advances through two semitones and a step of a minor third. Boethius calls it chromatic not only because of the difference of the ratios but also because of the transformed steps: transformed from one system into another. In calling this genus "colored" he did not mean to speak of color in similitudes rather than in literal terms, as some people believe.55 For just as mixed colors present diverse effects to the eyes, so transformed musical steps mixed in ascent and descent provide the ear with a variety of sounds.56 We come now to the method to be used to read the notes of the semitones. To ensure the utmost facility, read them according to the natural diatonic usage. For there exists on every note, whether on a line or a space, the suitable opportunity of saying the syllables ut re mi fa sol la throughout, as readers deem it more convenient. Readers will make the mutations from one to the other syllable at the sign of the natural, flat, or sharp. They will do the same for my invention of writing dots over the notes that, according to the circumstances, may be accompanied by naturals or flats. This will be clarified in the chapters on the species of these genera, that is, the diatonic, chromatic, and enharmonic [chapters 9-13].

Chapter 8 Explanation of the Practice of the Enharmonic Genus, with an Example Two of the three genera have been explained. It now remains to discuss the enharmonic genus. Let it be known that the fourth in the enharmonic genus described by Boethius57 proceeds with two steps that are enharmonic dieses and then with a step of a ditone or incomposite leap of a major third without interruption. Together with the ditone the two dieses produce a fourth and thus comprise the enharmonic genus. The fourth is divided in this way. First, the semitone is divided into two equal parts, each of which Boethius calls a diesis.58 Remember that 54. De inst. mus., 1.21. 55. The notion that Boethius used figurative language is hardly singular. Perhaps Vicentino had in mind the etymological cavil raised by Capella about the derivation of the Latin colorabile from the Greek chromatike in De nuptiis Philologiae etMercurii libri II, 9.942. 56. See Bk. Ill, chap. 15; also, perhaps, Pseudo-Aristotle, On the Cosmos, 5.396b. 57. De inst. mus., 1.21 and 4.6. 58. Again it must be noted that Boethius does not divide the major semitone but rather

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up to now the word diesis has been used in music practice to refer to the division of the whole tone into two unequal parts. For this reason, it is necessary to add to the term a specification drawn from the species of the genus, so as not to confuse pupils. Thus, whenever a sharp sign occurs, it will be called chromatic diesis to indicate major or minor semitones, and whenever a dot is written over a note, it will be called a [minor] enharmonic diesis, which means one-half of a minor semitone or the first part of the major semitone, the rest being the major diesis. The major diesis is not notated because, as the remainder of the major semitone, it is the same size as the minor semitone. This I explained in the description of the hands. Let us return to the division of the genus that is made up of two dieses and a ditone, in order to fill in [15r] the fourth. According to Boethius, the ditone encompasses two sesquioctaval whole tones, and it is called an incomposite ditone. And Boethius calls this genus enharmonic in reference to the greatly condensed space occupied by the small parts. But the enharmonic I use is not divided like that of Boethius. For I divide not only the minor semitone but also the major semitone so that, according to the circumstances in composition, I can use various steps and consonances as well as the genus with the divisions of unequal semitones. Our ditone is an interval of two whole tones, one sesquioctaval and one sesquinonal, on account not of the actual variety and divergence arising among the steps of different whole tones but of the need for several ratios.59 The reason the division given by Boethius is not the same as the one we use is as follows. We have a greater abundance of steps, consonances, and harmony than did the ancients. This is proven by comparing their division to ours, for we have many divisions that generate a harmony that is more varied than the one described by Boethius. Whoever does not believe this statement need only make an experiment to discover much more than I can remember to put down in writing. So that students may begin using this theory in a secure way, I offer example 8.1 to show the genus signed in the way I notate it. I shall disthe distance between 3,072 and 2,916, into two equal parts (3,072 - 2,916 = 156 -5- 2 = 78). He then adds 78 to 2,916 to produce 2,994. The sequence of 3,072, 2,994, and 2,916 yields a minor diesis of 512:499 and a major diesis of 499:486. The rest of the tetrachord is the regular Pythagorean ditone of 81:64. De inst. mus., 4.6. 59. The two tones add up to the major third (5:4) in Ptolemy's diatonic syntonon tuning. Vicentino here seems to subordinate the audible distinction between the two sizes of whole tone to the mathematical procedure required to produce the pure consonances of the third and sixth. See Bk. I, chaps. 22 and 25.

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cuss its species in the appropriate chapter [11]. Meanwhile, pupils will find example 8.1 illuminating.

Example 8.1 [Enharmonic Fourth]

And I present it in a simple way, to demonstrate its division. Thus, in moving from the first to the second note with the voice, the practitioner will raise his voice by the amount of one-half of a minor semitone. For the remainder of the major semitone—that is, from the second to the third note—he will sing the distance equivalent to a minor semitone. Then, from the third to the fourth note, he will make a step or a leap of a major third (called an incomposite ditone), that is the same as the utmi sung in practice. If you are singing the notes, do not be startled that you must call the first note mi and second note mi again, for thus you avoid mutating the natural name to the fa belonging to C fa ut. If you consider this matter for a time, you will see that by chance we often sing the same name for two notes in our practice. I show this with example 8.2, in which you will say "fa" naturally for the second note, and on the third note repeat "fa" accidentally.

Example 8.2 [Repeated Solmization Syllables]

Such repetitions do not annoy practitioners, save for the usual trifles. But you are advised to learn well the intonation of the pitches, either by repeating the syllables or else by some other exercise. You cannot then fail to put the words to the notes. For at that stage, the most important thing is to produce the steps and leaps of the pitches accurately because when words are sung, one does not choose one syllable over another, nor does one fret over the repetition of syllables. One is concerned rather to deliver and sing the steps and leaps in tune. I wished to make this small digression so that some people would not be amazed by such repetitions. They are unimportant. And should anyone suggest that repetition is a great disruption in music, you may judge the issue by the argument given here.

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Chapter 9 Explanation of the Practice of the Species of the Diatonic Genus, with an Example In chapter 6 I stated that species is what is placed under genus and that it is divided into the subordinate and the particular species. Not to be unduly redundant, the species of the diatonic genus is that part which with other parts makes up the body called genus—that is, mi fa sol la, which in our practice [15v] we call a fourth composed of the species of semitone and whole tone. These divisions, a major semitone and two consecutive whole tones, are the species of this genus. They appear in the consecutive steps of example 9, both ascending and descending: from the first to the second note there is a major semitone, from the second to the third a whole tone, and from the third to the fourth a whole tone.

Example 9 [Diatonic Species]

Chapter 10 Explanation of the Practice of the Species of the Chromatic Genus, with an Example The species of the chromatic genus are those divisions that fall under this genus. The steps appear in example 10.1, from the first to the second note, the second to the third, and the third to the fourth, moving from one note to the next. These segments of steps Boethius calls species of the chromatic genus.60 Example 10.1 [Chromatic Species]

It should be said that the species of the chromatic genus is one thing and the chromatic species quite another. The chromatic species occurs anywhere you find the species of any genus transformed into steps other than the ones proper to that genus. For instance, when the step of a whole tone occurs instead of the natural semitone of the diatonic genus or sequence, that step is a chromatic species placed diatonically.61 The 60. Boethius does not use the predicable species. However, his nomenclature of the degrees of the Greater and Lesser Perfect Systems in the three genera implies this term. De inst. mus., 1.22 and 4.8; also note 61, below. 61. As in Boethius, De inst. mus., 1.22, where he says, for instance, that when the "diatonic lichanos hypaton" is altered in the chromatic genus, it is called either chromatic diatonic or chromatic lichanos hypaton.

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same thing happens when the step of a natural whole tone becomes the step of an accidental semitone, for the latter is called a chromatic species or the natural transformed from a whole tone into the step of a semitone. Therefore, whenever the steps of the species of each genus do not obey the sequence of their genus, it is necessary to name them according to their transformation. Depending on their notation, these steps are called chromatic diatonic or enharmonic diatonic. The accidental chromatic species in question here may arise in every genus, and the transformation of the steps also arises in every genus, not only to execute consonances but also to create the variety of steps needed for the melodic lines that create tenseness and slackness in every genus. Because of their structure, these steps either excite or weaken the souls of the listeners. Which steps in each genus are tense and which slack will be understood at the proper place [chapters 14-42]. To return to the chromatic species, Boethius (as was said above) called chromatic species or chromatic order any species that was altered from its original placement to another in any genus, whether diatonic, chromatic, or enharmonic.

Example 10.2 Chromatic Species

Example 10.2 shows these species, and the hands previously discussed demonstrate the names of the species, with examples to accommodate the naming of every species. When a melody is completely chromatic, it is sung with the same pronunciation of syllables as is a natural melody, that is, by approaching the nearest mutations for convenient leaping and descending. It is possible to use the sequence of the natural mutations for the accidental ones, even though this practice may seem a little strange at first. Nevertheless, habituation in such mutations will alleviate any mental vexation.

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Chapter 11 Explanation of the Practice of the Species of the Enharmonic Genus, with Examples62 [I6r] The species of the enharmonic genus are arranged in the order of the hand; and the examples in this chapter divide the whole tone into four singable parts—that is, into four enharmonic dieses. The names of the notes are easy to use, for a singer has to adjust to the melody, be it in the natural, the hard, or the soft hexachord, according to the position of the signs. He will thus give the proper name of the syllable to the first natural note, advance through the second, third, and fourth notes, and reach the fifth note, which is the limit of the first whole tone and the start of the second whole tone. Thus singers will always say the name of the natural notes, proceeding with suitable mutations through the middle notes, which notes arrive at the limit of the whole tone (as I said) as if they were natural notes. A small illustration [example 11.1] will clarify how easy it is to sing all kinds of dieses in the enharmonic order.

Example 11.1 Whole Tone Divided into Four Ascending Parts As you can see, you climb from G sol re ut to A la mi re by means of four enharmonic dieses, dividing the whole tone into the following pitches: First you must make a minor diesis from the first to the second note. From the second to the third you make a major diesis because the semitone between the first G sol re ut and the first A is major, causing the second diesis to be major. But when there is a minor semitone at the start, be warned that the division produces two minor dieses. The subsequent semitone will be divided into two dieses, one major and one minor, as in example 11.2.

Example 11.2 Whole Tone Divided into Four Ascending Parts 62. For solmization, compare Bk. I, ex. 11.1, with ex. 5.7, segment 8; Bk. I, ex. 11.2, with ex. 5.5, segment 8; and Bk. I, ex. 11.3, with ex. 5.8, segment 1, and ex. 5.6, segments 1,2, and 3.

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The same rule applies as did in example 11.1 but in reverse— that is to say, the rule that when the major semitone occurs in the first division of the whole tone, the first diesis is minor and the second major and that the subsequent minor semitone contains two equal minor dieses. The immutable rule is as follows. When you are moving away from the natural note and about to make an enharmonic diesis, the first diesis will always be minor, whether the semitone happens to be major or minor. This will be the first diesis both in ascent and in descent. Just as you always make a minor diesis at the start when leaving the natural note by means of a diesis, so at the end of this tone you always make a minor diesis with the last diesis on the penultimate note— that is, from the fourth to the fifth note. Moreover, as I said, you end on another natural pitch after the last diesis, and consequently this diesis will always be a minor one both in ascent and in descent, as shown in example 1 1.3.

Example 11.3 [Whole Tone Divided into Four Descending Parts]63

[I6v] It is possible to make a major diesis at the beginning and ending of a whole tone; this step, however, is also a minor semitone.64 In order to distinguish the enharmonic division from the chromatic, it is necessary always to put a minor diesis at the start and at the finish, for the reason given above. It is now clear which method is required to read the species of the enharmonic order that divides the whole tone into four parts and which are the major and minor dieses of the whole tone in the chromatic species. It will be seen from the examples found in the disquisition of Book V on the instrument I call the archicembalo, the preeminent and most perfect of all instruments, that this instrument does not lack any consonance. Do not fear that you cannot learn to sing and play such divisions, because I sing and play them quite easily. The practitioner who wishes to learn to sing these divisions should avail himself of instruments having such divisions, such as the archicembalo, the violone, with its divisions into semitones, or the lute, with the same division.65 It should not come as a surprise that I enlist the help of instruments for learning the method of singing such minute divisions. The reason is 63. In segment 3, the natural hexachord goes beyond the whole tone to include the major semitone below. 64. See chap. 8, above. 65. Vicentino alludes to the frets on the violone and lute. See Bk. V, chap. 66.

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that this novel method has not yet been put into practice. For anyone wishing to practice without a master, the instrument acts as the guide, which leads to practical results in a short time. It is probable that the first person to discover the way to sing the distance of the steps of the whole tone and semitone (which were and are natural) could not have done so without the expedient of an instrument. How much more, then, should one work with instruments when learning those steps which are not natural, as are the diatonic steps everyone instinctively knows how to sing? So much the more must students apply themselves with instruments, for these steps are subtle and smooth.

Chapter 12 Explanation of the Ligatures of the Chromatic Species, with an Example The notational ligatures of the species of tempered music66 that have been used up to now are many and varied. Since they have been described by many people, I shall set them aside and instead discuss in this chapter the ligatures of the chromatic species. I must caution you that, even though they are written in the same way in compositions, the ligatures are differentiated by the signs. On the one hand, the note-shapes of tempered music proceed by accidental and natural whole tones and semitones that have the value of the entire body of the ligature. On the other, in the chromatic species the note-value of a maxim, long, breve, semibreve, and so on, is written with signs, so that a note is changed by a major or minor semitone as composers may require for the sake of the words. When the natural, flat, or sharp sign is placed before the note-shape on the same line or space, the entire duration will be sung under that sign, which may be the sign of either a minor or a major semitone. For every note-shape having any semitonal sign in front of it, a little below but nearby, the first half of that note-value will be sung under the semitonal sign that precedes the note somewhat below it; the other half will be sung naturally. Now comes the reverse. When the note-shape has any sign after it, nearby and a little below, the first half will be sung naturally and the other half according to the sign that has been placed after the note. Whenever composers need to put a flat after a note, they should write it turned toward the back of the note, so that singers will understand that the flat sign applies to the second half of the note-value. There is no need to reverse the natural sign because its body has two 66. See chap. 6 and note 48, above.

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stems that look the same on either side. However, the natural should be written closely enough to the note so that every practitioner will recognize that [17r] it belongs to this note and not to the one preceding it. Written in this way, these signs may also apply to one-half of the minim and semiminim.

Example 12 [Chromatic Ligatures]

Example 12 covers all the chromatic ligatures with the signs of the minor and major semitone. To help pupils understand more easily which are the major and which the minor semitones, I offer this brief rule. Singers should know that both natural and sharp signs apply to ascending minor semitones. So that all signs may operate in their proper places, composers must never write the sharp instead of the natural, as in B fa B mi. In this location it is absolutely obligatory to sing according to one of two signs, either the natural or the flat. Consequently, if the sharp sign is written in the location of B fa B mi, all those who see it will decide at once that the composer did not mean the signs of the hand,67 and they will sing now with a natural, now with a flat, and now with a sharp sign. It seems to me that I have said enough about the ascending natural and sharp. It is not necessary to remember anything else about the two signs, except to say that they have diverse effects: in ascent they indicate minor semitones and major semitones in descent. The flat has the opposite effect, for when it ascends it forms the major semitone, and descending it becomes a minor semitone. All these signs apply to every order and species, in both the chromatic and enharmonic orders. It so happens that in the enharmonic, all the ascending semitones are signed with the flat and with a dot over the note next to the flat. I shall not prolong this explanation here because I shall write in great detail about all the ranks of the archicembalo in Book V. 67. The hexachord system.

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Chapter 13 Explanation of the Ligatures of the Enharmonic Species, with an Example The same disposition occurs in the enharmonic ligatures as in the binding of notes in the chromatic species. For just as sharps, naturals, and flats were signed to show how either the entire duration of the notevalue, its first half, or its second half is to be sung, so also is the sign of the dot applied in the enharmonic species. Whenever composers wish to make a ligature in the enharmonic order, they must follow this rule. Every time the dot is written over a note— that is, in the center over a note—that note will be sung and played entirely in the enharmonic order. This dot signifies the raising of the pitch one-half of a minor semitone higher than the natural order. And when you encounter any note, either by step or by leap, with the dot written over its center (as I said), then that note is always raised above the usual intonation—the one sung by everyone in general—by the equivalent of one-half of a minor semitone. But when this dot is written over the front part of a note, that first part is sung higher by one-half of a minor semitone, whereas the second part is sung according to the natural order. And when the dot is placed over the rear part of a note, the second part is sung higher by one-half of a minor semitone [17v], whereas the first part is sung according to the natural order. I shall not extend this discourse on the dot because the matter will be discussed amply in the fifth book on my instrument. Example 13 supplies sufficient guidelines concerning the ligatures of the enharmonic species.

Example 13 [Enharmonic Ligatures]

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Chapter 14 Explanation of the Step of the Comma and Its Nature, with an Example68 In my music and performance, I have discovered nineteen steps among the natural and accidental notes in the division of the fourth.69 Their differences and divisions will be discussed in the chapters to come. As it happens, among these steps there are four accidental steps, each of which is identical to a natural step: the natural major semitone, the natural whole tone, the natural minor semitone, or the natural major third. All the rest form dissimilar steps. And among these is a step that is smaller than the others. Philosophers call it a comma, and it is the smallest of all the parts of the enharmonic diesis.70 These particles occur between blunted and perfect fifths; you will hear all the differences on the archicembalo.71 Boethius, therefore, while reasoning out the difference between the major and minor semitone in Book III, chapter 13, of the Fundamentals of Music, said that Ptolemy called the comma the very smallest part perceptible to the sense of hearing.72 Anyone wishing to try an experiment should choose a string of brass or gut that makes a sound when struck and then divide the whole tone into ten parts, as on my archicembalo.73 He will then hear the tenth part very clearly, just as I have described it here. 68. There is no example in this chapter. Elsewhere this interval is indicated by a superscript comma. See Bk. I, chaps. 31 and 34, and Bk. V, passim. 69. See Bk. I, ex. 42. 70. Whoever the philosophers might be, the definition is an extrapolation from Boethius, De inst. mus., 2.31. 71. These differences depend on which tempering was applied to the archicembalo. Vicentino alludes merely to standard practice. See Bk. V, chap. 5. The most likely system is the meantone tuning described by Pietro Aaron in the Toscanello in musica (Venice, 1529), Bk. II, chap. 41. This hypothesis is confirmed by Lemme Rossi, an astronomer and mathematician, in his Sistema musico overo musica speculativa (Perugia, 1666), pp. 83 and 86. See App. VI. The difference between the pure or perfect fifth (3:2) of 702 cents and the tempered fifth on the archicembalo of 697 cents is 5 cents. Vicentino's claim notwithstanding, 5 cents is not a full comma on the archicembalo but rather about one-quarter of the comma of 19 cents. This value is not equivalent to either the ditonic or syntonic comma. 72. The ditonic or Pythagorean comma, the difference between the apotome and the minor semitone, is 531,441:524,288. The syntonic or Ptolemaic comma, the difference between the major and minor whole tone, is 81:80. Boethius discusses the ditonic comma in De inst. mus., 3.12 and 13. There is no reference to Ptolemy in either chapter. Possibly Vicentino associated Ptolemy with theories of temperament because of a passing reference to him in Fogliano's Musica theorica. See note 48, above. 73. But a tenth part of which whole tone? One-tenth of the Pythagorean tone and the major tone of the diatonic syntonon (9:8) is 20.4 cents. One tenth of the syntonic minor tone (10:9) is 18.3 cents. One tenth of the tempered whole tone on the archicembalo is 19.4

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Chapter 15 Explanation of the Step of the Minor Enharmonic Diesis and Its Nature, with an Example The discourse on musical steps in the preceding chapter may seem to have disrupted the proper order of the chapters in which I considered other material, more to educate the listener than to demonstrate the ligatures. In order, therefore, to avoid prolixity I decided to make a bit of an introduction beforehand to describe how the ligatures are used in chromatic and enharmonic melodies: in short, to talk about their species. Indeed, it is extremely important to know how to arrange in compositions all the musical steps of which I spoke previously, for out of them is unearthed a harmony that can be harsh, sweet, smooth, or very smooth, according to the [18r] accompaniment of consonances and motion.74 The step of the minor enharmonic diesis is almost small enough to be called a comma, for it is the same size as the comma found between the minor and major semitones—not according to Boethius but rather according to my instrument.75 But even though the minor diesis is this size, you must call it a minor enharmonic diesis because it corresponds to that part of the division that is one-half of the minor semitone. This step is by nature sweet and very smooth, as is shown in example 15.

Example 15 The Step of the Minor Enharmonic Diesis, Ascending and Descending

The minor enharmonic dieses written in example 15 are often used to help a consonance.76 This step is slack and smooth, both ascending and descending. cents. See App. VII. Not only does Vicentino ignore the incompatibility of any form of tempering with the diatonic syntonon tuning but he also compounds the problem by deciding that his natural whole tone will be the syntonic minor tone. See Bk. I, chap. 23. The latter is not the same size as the tempered whole tone on the archicembalo. 74. See Bk. II, chap, 1. 75. Again, Vicentino obfuscates the issue. The Pythagorean, or ditonic, comma is 24 cents, whereas the difference between the major and minor semitone in Ptolemy's diatonic syntonon is 41 cents, an amount closer to the tempered minor enharmonic diesis of 39 cents. See App. VII. Thus, five dieses or ten commas are contained within the whole tone. See chap. 14 and note 31, above. 76. See Bk. V, chaps. 8-38.

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Chapter 16 Explanation of the Step of the Major Enharmonic Diesis or Minor Semitone and Its Nature, with an Example The nature of the step of the major enharmonic diesis is tense in ascent and slack in descent. Readers are advised that the major diesis is often used instead of the minor semitone, for the two steps are identical in size. But because the former constitutes the larger part of the major semitone, it must named after its division. The term major diesis, which means a segment or division of what has been divided, is derived from a Greek word. For this reason, every segmented or divided pitch yields a part called diesis. To distinguish among the divisions, however, it is necessary to connect the word diesis to the divided parts, either big or small, as I said above. Example 16 demonstrates the steps of the major diesis.

Example 16 The Steps of the Major Enharmonic Diesis, Ascending and Descending

Chapter 17 Explanation of Several Consecutive Steps of the Major and the Minor Diesis and Their Nature, with an Example The step of the diesis, both major and minor, is smooth and very sweet, as was said above.77 Whenever composers or players compose any theme with these steps in fugues or imitations, they may make as many of them as they please. However, even when set to a fast rate of motion, these steps will be melancholy. Several consecutive steps of the major and minor dieses are given in example 17.

77. But Vicentino also says the ascending major diesis is tense (see chaps. 16 and 18).

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Example 17 [Major and Minor Dieses]

Chapter 18 Explanation of the Minor Semitone and Its Nature, with Examples of Its Composite and Incomposite Forms [18v] Sometimes minor semitones favor the consonances of the enharmonic order and become similar to major enharmonic dieses. As I indicated earlier, these intervals are the same size. And they both are cheerful when ascending and sad when descending. In short, minor semitones and major enharmonic dieses share the same qualities. Example 18 will help students to recognize which semitones ascend or descend and which are composite or incomposite. All minor semitones are accidental, for there exist no minor semitones in music practice that are notated without accidentals. In example 18.3 I chose the major diesis for the minor semitone for the sake of convenience in composing.78

Examples 18.1 and 18.2 [Major and Minor Semitones] 78. A matter of notational spelling. See Bk. I, ex. 16.2, segment 3.

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Examples 18.3 and 18.4 [Major and Minor Semitones]

Chapter 19 Explanation of the Major Semitone and Its Naturey with Examples of Its Composite and Incomposite, Natural, and Accidental Forms Natural music produces both major and minor natural semitones within the fourth. And it is just as natural to hear the singing of the minor semitone in place of the major semitone whenever it is not practicable for novice students to sing the pitch of the major semitone I use. The minor semitone is described by Boethius in his diatonic division.79 But in my practice, I use the major semitone to suit the tuning of the imperfect consonances, as I said before. While singing a composition, it is frequently necessary for singers to lower a semitone or a whole tone as they proceed from the beginning to the conclusion. This explains why some persons wish to use the semitone to display an excessive delicacy in their singing; they therefore make the semitone smaller than the major, reducing it to a minor semitone. Not wanting to clash with these singers, their colleagues (fine experts) consequently lower the step or leap in their part in order to accord with them. Thus proceeding in this way, the singers collectively continue to lower the pitch until they reach the end of the composition. This dislocation intrudes not only in unaccompanied singing but also in singing with instruments. Some rather inexperienced singers, whenever they sing to the accompaniment of instruments, [do not] usually realize by the end that they have lowered the pitch by a whole tone, more or less. The instruments, of course, will convince them of this fact; if they are wind instruments, singers will realize how much they have lowered the pitch; and if they are keyboard instruments, singers will hear a discordance. Similarly [19r], many singers do the opposite. Whenever they come across an ascending sharp denoting a minor semitone, these singers raise it so much that the other singers are forced to comply in concert. The more minor semitones they encounter, the higher they raise the pitch at 79. De inst. mus., 4.5 and 4.6 and 4.8-11.

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the end of the composition. Still others raise or lower the whole tone and change the major semitone, called mi-fa in practice, into a whole tone. The results are the same as what I described above. I made this small digression to alert singers that they should not only understand the formation of major and minor semitones but also avoid discord with others when singing together both with and without instruments. Singing frequently with instruments is very beneficial to singers. Few singers, in my opinion, accord well with others unless they first practice with keyboard instruments. Wind instruments are less stable because of the greater flexibility of the player's breath. Returning to the explanation of the major semitone, let me say that its nature is such that when it ascends it generates slackness and sadness, and when it descends it produces tenseness and cheerfulness. This is true of both the natural and the accidental major semitone. Be warned that I did not distinguish between natural and accidental minor semitones because in the divisions of my practice I use only accidental minor semitones, as I said before. To demonstrate major semitones, I present them in example 19, both ascending and descending, [incomposite] and composed of one minor and one major diesis. When the semitones are composite and ascending, the minor enharmonic diesis is first and the major diesis second.

Example 19 [Major Semitones]

Chapter 20 Explanation of Several Minor and Major Semitones and Their Nature, with Examples of Their Ascending and Descending, Composite and Incomposite, Natural and Accidental Forms Sometimes composers or players decide to create various themes in order to write a fugue and to make diverse answers, now with minor, now with major semitones. This technique provides ample opportunity to delight the listeners with plenteous variety and to integrate easily vari-

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ous consonances with various steps. These steps have the qualities explained above. When listeners hear now a major and now a minor semitone, their ears find these steps pleasant if they are suitably combined, either for the instrument or for the words, in such a way that the singing of these different semitones corresponds to the nature of either one. Example 20 shows the different semitones: single minor and major and several minor and major, both ascending and descending, accidental and natural, composite and incomposite.

Example 20 Several Major and Minor Semitones, Ascending and Descending, Composite and Incomposite, Natural and Accidental80

Chapter 21 Explanation of the Step of the Minor Whole Tone and Its Nature, with Examples of Its Composite and Incomposite Forms [19v] The step of the minor whole tone is always accidental and comprises either two minor semitones or one major semitone and one minor enharmonic diesis. Because it is larger than the major semitone and smaller than the natural whole tone by one minor diesis, the minor whole tone has an innate tendency to participate in the nature of both the major 80. Segment 11 has two overlapping composite semitones, a major one between & and g, and a minor one between g and g^.

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semitone and the natural whole tone. Hence, the ascending minor whole tone is slack yet somewhat tense, and when descending it makes the same effect, depending on the accompanying consonances. Example 21 shows these steps with their notes and signs in ascending and descending motion. The nature of the composite form is like that of the incomposite, both in ascent and descent.

Example 21 The Composite and Incomposite Step of the Minor Whole Tone

Chapter 22 Explanation of the Step of the Natural Whole Tone and Its Nature, with Examples of Its Composite and Incomposite Forms It transpires in our practice that we have two sorts of whole tone within the diatonic fourth, one in the sesquioctaval and one in the sesquinonal ratio. Nevertheless, we do not stop calling these whole tones diatonic when they follow each other because such a small discrepancy does not impede the succession of tonal steps.81 Perhaps some people may be surprised that, insofar as my intention was to discuss the many ways of dividing the fourth, I did not start by dividing the whole tone into two unequal parts and then four unequal parts and afterward construct other steps from the whole tones, as will be done in later chapters. I began according to the [20r] usual Greek musical division, which always starts with the smallest parts. Then, following the proper order, I formed a tree of ratios and divisions growing from the roots of the fourth and fifth, included and conjoined in the octave, as you will see in the tree of the octave that has been divided into all the segments pertinent to music both for singing and playing [chapter 42]. 81. See chap. 8, above.

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To return to the step of the natural whole tone, let me say that when this tone ascends it creates an intensifying effect, and when it descends it is slack, as is evident in the ascending and descending whole tones in example 22. In their written form these whole tones can be composed of two divisions of semitones, one major and one minor, and also of four divisions of enharmonic dieses.

Example 22 Natural Whole Tones and Semitones

Chapter 23 Explanation of the Step of the Chromatic Whole Tone of the Same Ratio as the Natural Whole Tone and Its Nature9 with Examples of Its Composite and Incomposite Forms According to philosophers, accident is defined in two ways.82 In the first, the accident is that which is present or absent without corrupting the subject. The second definition says that the accident is that which may or may not belong to something, yet is always present in the subject. It can be divided into two parts: an inseparable and a separable accident. We are now dealing with a separable accident, the step of the accidental whole tone. The accidental whole tone arises from the conjunction of various semitones and dieses in order to integrate the consonances. And from these reinforcements some accidental whole tones are produced by means of various signs, which I have already explained. It is such whole tones as these that are called accidental, if I make myself clear. Minor and major whole tones are named and recognized from the difference in their smaller or larger sizes, the latter being called accidental major or accidental minor. Since the accidental whole tone has the same ratio as the natural whole tone, it is tense when ascending and slack when descending. Example 23 demonstrates how to write these steps ascending or descend82. Like the previous discussion of genus and species, this digression on the accident comes from Porphyry's Introduction this time from the fifth chapter. See Bk. I, chap. 6, above. In Vicentinos turgid explanation, it is not clear that the definitions are merely two ways of saying the same thing.

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ing, and composite or incomposite. All of them share the qualities of the natural whole tone.

Example 23 Some Accidental Whole Tones

Chapter 24 Explanation of the Major Whole Tone and Its Nature, with Examples of Its Composite and Incomposite Forms [20v] Five kinds of whole tone steps are found in music. As I said before, the first is the step of the minor whole tone, and the second is the natural whole tone, which has both the sesquioctaval and the sesquinonal ratios. The third is the sesquinonal ratio itself. Because it cannot be distinguished from the sesquioctaval in the practice of singing on account of the small difference between the two, we accept its recognition as the natural whole tone. The fourth is the accidental whole tone, made up of various semitones and dieses. Thus composed, this species of whole tone is called chromatic whole tone, or whole tone transformed from the nature of a major semitone by the addition of another minor83 semitone to become a whole tone. To make a fine and varied composition, composers should change the musical steps often, not only the whole tones and semitones but also the major and minor thirds. In this continual shifting (appropriate only to playing or singing when words are to be set), composers would do well to heed the following extremely important observation. Consider the case of a player or composer who, having sung or played a little, makes a modulation that enters the chromatic species and then, having embarked on this way of playing or composing, persists in this system for a while. The method offers no variety to the listener except for the very first note heard upon entering the chromatic species, when he is moved by the transformation of the step involved.84 Indeed, after entering this species, 83. Error: maggiore. It is the major whole tone, not the accidental whole tone, that contains two major semitones. 84. On the element of surprise, see "Music Theory," chap. 16.

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the modulation will eventually seem no different from what preceded it, on account of its undue prolongation and lack of variety in steps. Indeed, varying the steps of music delights more than always keeping to one way of regulating them. Experience in this matter will make it clear and unequivocal to everyone. I make this brief comment so composers will always keep in mind this kind of variety. Thus, when they use these methods and steps to enter the chromatic species in their compositions, they will realize how important variety is and how unsatisfactory is a composition that continuously repeats the above-mentioned steps and leaps that, so to speak, seem to return an infinite number of times. I shall now discuss the fifth kind of whole tone, the major whole tone. By nature it is more tense than the other whole tones when it ascends because it is composed of two major semitones or of one whole tone and one minor diesis. When the major whole tone descends, it is more slack than the other whole tones. Example 24 illustrates how signs should be applied to these composite and incomposite steps, which are always accidental whole tones.

Example 24 The Composite and Incomposite Major Whole Tone

Chapter 25 Explanation of the Composite and Incomposite Step or Leap of the Minor Third Smaller Than the Natural Minor, Which I Call Minimal Third, and Its Nature, with Examples [21r] In the preceding chapter I said that in my practice there are five kinds of whole tone in different divisions, except for the accidental tones. I did not mean minor and major accidental whole tones but rather those whole tones I call simply accidental, without the adjective major or minor. The latter are to be understood always as those whole tones that occur by accident from the same ratios as those of the two natural whole tones—that is, the sesquioctaval and the sesquinonal, whose difference

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is not discernible in singing.85 But in the tuning of instruments this division or difference is indispensable. Now that the five kinds of whole tone have been understood, I should tell you that I find in music six kinds of leaps of the third. The first is called the step of the accidental minimal third, the second the natural minor third, the third the accidental minor third; the fourth is formed by a third that is larger than the minor but smaller than the accidental major third, the fifth is the natural major third, and the sixth and last is the accidental major third.86 So that readers may thoroughly understand my discourse, I use the terms as follows. Natural I call those steps most frequently used without too much effort and skill. The other steps, which disrupt the conventional order, I call accidental. Such accidental steps can be major or minor. The reader should know that the step of the minimal third (meaning less than the natural minor third) has a value such that in ascent it is slack and in descent somewhat tense. This is because it is formed by a whole tone and a minor semitone, as is shown in example 25, which presents several ascending and descending steps.87 Although it is possible to illustrate many kinds, a few of these incomposite and composite steps will suffice for now.

Example 25 The Step of the Third Smaller Than the Minor Third, or the Composite and Incomposite Minimal Third

85. See chaps. 8 and 22, above. The ensuing remark on the necessity of the two whole tones found in Ptolemy's diatonic syntonon for the tuning of instruments suggests that Vicentino had read Fogliano's treatise, Musica theorica, Bk. Ill, chap. 1. See also note 48, above. 86. This listing is incorrect. Of the seven thirds, Vicentino has forgotten the last, the third larger than the natural major third by one enharmonic diesis. See chap. 31, below. 87. Bk. I, ex. 25, bears out Vicentino's definition of the minimal third. All the intervals are one diesis smaller than the natural minor third. See App. VII.

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Chapter 26 Explanation of the Composite and Incomposite Step of the Natural Minor Third and Its Nature, with Examples When the step of the natural minor third ascends it is slack, and when it descends it is somewhat tense. This step is found in two locations and has two names in music practice. Boethius calls both them incomposite because they have no interruptions,88 just as in practice we say "re-fa" and "mi-sol." The composite steps, as re mi fa and fa mi re, share slackness and tenseness both descending and ascending. Example 26 shows both incomposite and composite minor thirds.

Example 26 The Composite and Incomposite Step of the Minor Third

Chapter 27 Explanation of the Step of the Accidental Minor Third and Its Nature, with Examples of Its Composite and Incomposite Forms [21v] In the preceding chapter I discussed the steps of the two natural minor thirds or leaps of the semiditone, which are composed of one whole tone and one major semitone without interruption. In this chapter, therefore, I should explain what sort of thing is the step of the accidental minor third, a step that arises accidentally. This interval is indicated by the sign of a flat, a natural, or a sharp or by a superscript dot, now in one order and now in another, according to the composer's need to vary the steps and to integrate the consonances. The subtraction of a minor semitone from the step of the major third leaves the accidental minor third, a step that is the same size as the natural minor third. The nature of this accidental step is that when it ascends it is slack, and it is somewhat tense when it descends. Composers should be aware of all kinds of steps and leaps. Some make a good effect and some a bad effect, depending on the way they are well or badly matched with consonances. I shall instruct you on the good and SS.Deinst. mus., 1.23.

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bad effects of these consonances in the appropriate chapters [Book II, chapters 1-30]. Example 27 includes the incomposite and composite forms of the minor accidental third. These intervals have the same ratios and qualities as their natural counterparts.

Example 27 The Composite and Incomposite Step of the Accidental Minor Third

Chapter 28 Demonstration of the Step of the Third Larger Than the Minor Third and Its Nature, with Examples of Its Incomposite and Composite Forms Many times, a composer may need to make a step larger than the minor third but at the same time smaller than the major third by one minor diesis. To demonstrate its notation and nature, I advise you that in ascent this interval shares the nature of the major third because it is proximate to the latter. It is therefore somewhat [22r] tense. When it descends, of course, it is somewhat sad and slack because it is so proximate to the major third. You should know that in my usage the terms proximate third, proximate fourth, and proximate fifth always refer to those steps or leaps that are a little larger than natural steps or accidental steps but that have the same ratio as natural ones. As to the third larger than the minor third, example 28 demonstrates how to write both incomposite and composite forms. Their nature is the same as that of the natural steps, even though they are always accidental. Now everyone can compose them on his own.

Example 28 The Composite and Incomposite Third Larger Than the Minor Third

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Chapter 29 Explanation of the Step of the Natural Major Third and Its Nature, with Examples of Its Composite and Incomposite Forms To help readers understand the explanation of the two steps of the major third, I shall elucidate them as follows. In practice the steps of the third have two names, ut-mi and fa-la. Boethius calls the third an incomposite ditone.89 In our practice we do not use the same ratio because our incomposite ditone is ut re mi and fa sol la [chapters 6 and 8].90 I shall now discuss the incomposite natural major third. This leap has a nature different from that of the natural minor third: in ascent the minor third is slack, whereas the major is tense and imperious; and when the minor third descends it is very slack and sad, whereas the descending major third is somewhat tense. Thus the two intervals have diverse effects, as I said. Example 29 shows the incomposite and composite forms of this interval, forms that by nature are tense in ascent and slack in descent.

Example 29 The Incomposite and Composite Natural Major Third

Chapter 30 Explanation of the Step of the Accidental Major Third and Its Nature, with Examples of Its Composite and Incomposite Forms Wherever nature is deficient in any respect, many of its defects may be redressed by an accident, as is evident in sundry natural orders. Moreover, with his natural talent, the artificer adorns these defects so well 89. Ibid., 1.23. 90. This cryptic remark refers to the minor [10:9] and the major [9:8] whole tone present in the composite ditone, a combination characteristic of diatonic syntonon tuning. The natural minor whole tone of the diatonic syntonon should not be confused with Vicentinos accidental minor whole tone, which is one diesis smaller than the natural whole tone. See Bk. I, chaps. 21 and 42.

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that they seem very good and beautiful.91 So it happens in music practice that the natural order is seen [22v] to be defective in many respects. And with the accidental augmenting and diminishing of natural steps, nature acquires the enormous advantage of being able to use every sort of consonance in every location, as can be gauged by the great richness of steps regained on my archicembalo. Furthermore, the practical experience of singing as well as reading my book will convince everyone as to the usefulness of such an abundance of steps. I therefore turn now to the incomposite and composite steps of the accidental major third, whose nature resembles that of the natural major thirds. When ascending they are very tense, but when descending they produce sad and slack effects. These steps may be seen in their notated forms in example 30. The nature of the composite accidental major thirds is like that of their natural counterparts. In all the previous examples and in the ones to come, I give only a sampling in comparison to the many examples for the archicembalo [Book V, chapters 8-38].

Example 30 The Incomposite and Composite Step of the Accidental Major Third

Chapter 31 Explanation of the Third Larger Than the Major Third and Its Nature, with Examples of Its Composite and Incomposite Forms The step that is larger than the major third is always accidental and contains the particle of a minor enharmonic diesis or a comma added to the major third. Its nature is as follows: ascending it is extremely tense and descending extremely sad and slack. The notation of the step, as seen in example 31, conforms to the incomposite order. The [in] composite has the same nature as the composite step, both ascending and descending. 91. For the accident as a logical category, see chap. 23, above. Aristotle does not say that accidents can correct defects in nature. But in the treatise on architecture, De re aedificatoria, Bk. II, chap. 6, by the famous theorist and architect Leone Battista Alberti, there are statements to the effect that nature seldom produces anything that is absolutely perfect and that the function of ornaments is to conceal the flaws in the artists model.

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Example 31 The Incomposite and Composite Step Larger Than the Major Third92

Chapter 32 Explanation of the Leap of the Natural Fourth, Its Steps, and Its Nature, with Examples of Its Composite and Incomposite Forms Enough has been said about all the steps and leaps generated by the fourth. I shall now discuss the natural fourth itself. Its tenseness and slackness appear in the ascent and descent of the pitches, respectively, both in steps and in leaps. Among the leaps the smallest is the fourth (according to philosophers).93 However, following practical usage, I sometimes in my practice call the step of the third [23r] a leap, even though I also adopt the term step from the ancients. Let us now return to the leap of the fourth. It is of such a nature that in ascent it is tense and in descent slack. Ancient philosophers venerated the fourth so much that they praised its goodness and simplicity,94 not only because it was the interval that formed the basis for all the arrangements of the tetrachords but also because on it was built the fifth. For 92. All the major thirds in Bk. I, ex. 31, are one diesis larger than the quasi-pure thirds (426 - 387 = 39 cents), except for those with superscript commas. The latter (406 cents) are only one comma (19 cents) larger. See App. VII. Evidently, there was insufficient room on the archicembalo to include jacks for the comma keys on C and E See Bk. V, chaps. 17 and 58, and App. II and VI. 93. Boethius calls the diatessaron the smallest consonance (De inst. mus., 1.10). The only ancient writer to approximate Vicentino s distinction between the fourth as the smallest leap and the third as the largest step was Pseudo-Euclid, properly Cleonides, in Harmonic Introduction, 5. It is unlikely that Vicentino knew this source, even in Valla's 1497 Latin translation. According to Boethius' De inst. mus., 1.21, the tetrachord was the smallest stable framework for the movable steps making up the genera, of which the major third was the largest. 94. For example, De inst. mus., 1.20, where Boethius attributes this statement to Nicomachus, as well as Gafrurio, Theorica musice, Bk. V, chap. 1, and Glarean, Dodekachordon, Bk. I, chap. 5.

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the philosophers added a whole tone to the fourth to form the fifth, and then they joined the fourth and the fifth to make the octave.95 This is how the cardinal dignity of the perfect consonances ensued from the fourth, which is here shown in its composite and incomposite forms. When this leap is an ascending composite fourth, it is tense, especially if the semitone is placed after the two whole tones. If the semitone is placed first, then the leap is partly tense and partly slack, both in ascent and in descent, on account of the semitone below. If the semitone is in the middle of the ascending or descending fourth, the steps have the same effect as in the latter case. In practice there are three kinds of leaps or incomposite fourths; this is also true of the fourths composed of steps, as you see in example 32.96

Example 32 The Incomposite and Composite Leap of the Natural Fourth and Its Steps

Chapter 33 Explanation of the Leap and the Step of the Accidental Fourth and Its Nature, with Examples of Its Incomposite and Composite Forms The accidental fourth can be formed in many locations, of which I shall discuss but a few. The rest are set aside for the demonstration of the archicembalo, for in discussing it I shall have plenty to say on this matter.97 Both the nature and the ratio of these leaps are the same as the natural fourth. They are tense in ascent and slack in descent. The sampling in example 33 shows the incomposite leaps and the composite steps of this fourth, whose nature is identical to the aforesaid natural fourth. 95. As in Boethius, De inst. mus., 1.16 and 18. 96. The order of the fourths in the text and in Bk. I, ex. 32, follows the order given by Gaffurio in his Practica musicae, Bk. I, chap. 5, rather than the Boethian order reproduced earlier in "Music Theory," chap. 9. See also note 102, below. 97. The fourth, accidental, natural, or otherwise, is not discussed in Bk. V.

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Example 33 The Incomposite Leap and the Composite Steps of the Accidental Fourth

Chapter 34 Explanation of the Leap Larger Than the Fourth, Its Steps, and Its Nature, with Examples of Its Composite and Incomposite Forms [23v] In compositions it is often necessary to sing and play some leaps larger than the fourth. The nature of such intervals is lively when ascending but sad and slack when descending. The part marking the excess over the fourth is either a minor enharmonic diesis of many different kinds or a comma. I shall write about these leaps when I get to the keyboard of the archicembalo. It suffices merely to touch on the topic here, for the fullest possible discussion is deferred until the explanation of the archicembalo.98 All the same, some examples of such leaps are given in example 34.

Example 34 The Incomposite and Composite Leap Larger Than the Fourth and Its Steps

98. See note 97, above.

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Chapter 35 Explanation of the Incomposite and Composite Leap of the Natural Tritone, Its Steps, and Its Nature, with Examples It is admissible to count the leap of the tritone among the leaps of the fourth, even though practicing singers and composers accept it solely in its composite form, for they cannot bear the harshness of its incomposite form. Although the tritone contains four pitches, singers and composers do not include it among the leaps of the fourth. The reason is that it has no semitone anywhere. Yet this leap occurs occasionally in compositions. Although troublesome to sing, this interval is indispensable whenever the words require a marvelous effect," for by nature it is vivacious and shows great force when ascending, and when descending it makes a very funereal and sad effect. The leap is found between F fa ut and B fa B mi in the hard hexachord, both in the low and high registers, as shown in example 35. Some singers do not hesitate to practice it. After all, with continual usage every difficult thing becomes easy in all professions; if the tritone is sung composite, why cannot one—with practice—sing it incomposite?

Example 35 The Incomposite and Composite Natural Tritone

Chapter 36 Explanation of the Leap of the Accidental Tritone and Its Nature, with Examples of Its Incomposite and Composite Forms [24r] The leap of the accidental tritone can be formed on any location of the musical steps. It has the same nature as the natural tritone. Ascending, it is extremely tense and descending, extremely slack. This is 99. The effect of the marvelous is one of surprise and astonishment. Vicentino cites the element of surprise as an agent for moving the passions at the end of chap. 16 of the book on music theory. One ancient source that contains a comment on the affective power of music is Pseudo-Aristotle's Physical Problems. See "Music Theory," note 55. The author of this tract also comments on the emotional impact of irregular elements in music, as opposed to unrelieved uniformity (Problems, 19.9.918a).

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evident in example 36, which presents some of its incomposite and composite forms.

Example 36 The Incomposite and Composite Accidental Tritone

Chapter 37 Explanation of the Natural and Accidental Leap of the Imperfect Fifth and Its Nature, with Examples of Its Incomposite and Composite Forms Every time composers need to make a leap larger than the tritone— that is, to make a natural imperfect fifth—they will touch the B mi string in the hard hexachord and leap up to the low F fa ut. The same procedure is followed one octave higher. The leap of the accidental fifth can be created accidentally on any location by means of both chromatic and enharmonic signs. This is done at the convenience of the composer. The nature of both leaps, that is, the natural and the accidental imperfect fifth, is as follows. When they are incomposite they are slack in ascent, but in descent they share slackness and tenseness. When they are composite, these imperfect fifths create the effects of tense and slack steps both ascending and descending, as explained in the sections on those steps. A few natural and accidental leaps of the imperfect fifth are shown in example 37.

Example 37.1 The Incomposite Leap of the Imperfect Fifth, Both Natural and Accidental

Example 37.2

The Steps in Some Imperfect Fifths, Both Natural and Accidental

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Chapter 38 Explanation of the Leap Larger Than the Accidental Imperfect Fifth, with Examples of Its Composite and Incomposite Forms100 [24v] The accidental leap larger than the imperfect fifth has a nature such that in ascent and descent it shares slackness and tenseness, for it lies between the imperfect fifth and the natural perfect and accidental perfect fifth. This is evident in example 38, which gives the incomposite form as well as the composite form along with its steps. These steps have the effects noted above.

Example 38 The Accidental Leap Larger Than the Imperfect Fifth in Its Composite and Incomposite Forms101

Chapter 39 Explanation of the Leap of the Natural Fifth and Its Nature, with Examples of Its Composite and Incomposite Forms The number of steps and leaps generated by the fourth has been discussed in the preceding chapters. Every time composers use a leap that is neither longer nor shorter than the natural leap they name it after the natural one. This universal rule apples to all such leaps. We come now to the leap of the perfect or natural fifth, a leap that is by nature very tense when ascending and very slack when descending. This leap is so familiar that almost everyone sings it naturally without laboring to learn it from a master. The same is true of the fourth and the octave, moderately speaking of course, for there are certain people who possess neither an ear nor a nature that is receptive to any consonance. I do not refer to such people. The composite and incomposite leaps of the fifth occur in four locations in the arrangement of the fifth. When the leaps are composite, their steps constitute the difference between them. 100. Misprint: title has "naturale, & accidentale." 101. The imperfect fifths in Bk. I, ex. 38.1, are one diesis larger than the natural tritone. Those in Bk. I, ex. 38.2, are one diesis larger than the ones in ex. 38.1 and one diesis smaller than perfect fifths. See App. VII.

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In other words, the leaps reveal by their steps what sort of fifths they are, either tenser or slacker.102 The first species of fifth has the semitone after the whole tone and immediately before two consecutive whole tones. These combined steps of the fifth share slackness and tenseness when ascending, and when they descend they are slack. Even though the descending major semitone is tense, it nevertheless yields to the majority. Since there are three slack descending whole tones and only one semitone, the more numerous steps overpower the single one. The combined steps of the second species of the second fifth are lively and tense when ascending, whereas descending they are slack and sad. The steps of the third species of the third fifth are very tense when ascending because of the placement of the semitone above the three whole tones. In descent these steps are very sad. At the start of their ascent the steps of the fourth species of the fourth fifth are tense until the semitone, but from the semitone until the end of [25r] this fifth they are somewhat slack. When descending they are somewhat tense until the first whole tone after the semitone, but the subsequent two descending whole tones are slack until the end of the fifth. This is because the nature of every descending whole tone is slack, whereas every ascending one is lively and tense, as was explained with respect to the nature of whole tones. Example 39 illustrates the qualities of the leaps and steps of the natural fifth.

Example 39.1 The Incomposite Natural Fifth

Examlple 39.2 The Steps of the Natural Fifth

102. As was the case with the fourths, the order in the text and in Bk. I, ex. 39.2, follows what is given by Gaffurio in his Practica musicae, Bk. I, chap. 6. In "Music Theory," chap. 10, Vicentino presents the Boethian order (De inst. mus., 4.14).

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Chapter 40 Explanation of the Leap of the Accidental Fifth and Its Nature, with Examples of Its Incomposite and Composite Forms In musical compositions you may write leaps of the accidental perfect fifth on every location, whereas in the natural order this convenience is restricted because of the disjunction between the second and third tetrachords that ascend from B fa \ mi to the high F fa ut in the hard hexachord; the same occurs at the octave. This disruption also appears in the fourth in the hard hexachord between the low F fa ut and B fa \ mi as well as at the octave. No one should be taken aback if within a chapter I delve somewhat into the reasons behind some matter to which I should dedicate its own chapter. This is so because some things should be put together when I am explaining any problems they may raise. Whatever is omitted in one chapter will be supplied in another. The explanation of the leap of the accidental fifth must be made here with demonstrative examples. You should know that the leap of the accidental perfect fifth has the same ratio and nature as the natural fifth. Readers may take it as a firm rule that whenever I say "natural fifth" I always mean the perfect fifth. The accidental fifth, then, is tense when ascending and slack when descending, as I said in the preceding chapter. Its steps have the same nature as the natural ones, as is shown in example 40.

Example 40.1 The Incomposite Leap of the Accidental Fifth

Example 40.2 The Steps of the Accidental Fifth

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[25v] In example 40.2 I have notated four series103 of steps in the accidental fifth. The first series ascends through a minor semitone, whereas the second ascends through a major semitone. Both of these are arrangements of steps in the first fifth, written with two signs, one for the minor and one for the major semitone. The third series, showing the second fifth, is to be read according to the order of this fifth. The fourth and fifth series show the third fifth, and the sixth series shows the fourth fifth. These series of the fifth are also illustrated by the signs for the minor and major semitones. They should be read according to the order of the four fifths: the first and second series are read with the syllables re mi fa sol la; the third with mi fa sol re mi; the fourth and fifth with fa sol re mi fa; and the sixth with ut re mi fa sol. All the composite series are tense when ascending and slack when descending, like the natural fifths.104 The accidental leaps are also similar to the leaps of the natural fifths, as example 40.1 demonstrates.

Chapter 41 Explanations of the Incomposite and Composite Leap Larger Than the Fifth and Its Steps, of All Sorts of Major and Minor, Natural and Accidental Sixths and Sevenths and Their Proximate Intervals, and of the Octave with Its Proximate Interval, and Their Nature When composers decide to make a leap larger than the fifth by one enharmonic diesis, which is half of a minor semitone, or by a comma, then that leap will be lively and tense when ascending and slack when descending. The composite steps have the same nature as those of the natural fifth. The same holds true for all the following leaps: the minor sixth, the leap larger than the minor sixth, the major sixth, the leap larger than the major sixth, [26r] the minor seventh, the leap larger than the minor seventh, the major seventh, the leap larger than the major seventh, the octave, and the leap larger than the octave. The steps within all these leaps are similar to the leaps themselves, both ascending and descending. By remembering the steps of the fourth and fifth discussed earlier, everyone should be able to compose any leap and step on their own. When the steps or the leaps have an extra enharmonic diesis, for in103. Vicentino here confuses the four kinds of diatonic fifth with the six successions of steps in the accidental fifth given in Bk. I, ex. 40.2, and described in this paragraph. 104. But see chap. 39, above.

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stance, that extra increment is called proximate. When the natural fifth leaps or ascends by step, I refer to it as the natural leap of a fifth or the steps of the natural fifth. And when it has that extra increment, I call it a proximate fifth, that is to say, a part closer to the fifth than any other. In the Tree of the Division of All the Steps and Leaps(below), I call proximate the increment that exceeds any step or leap by a minor enharmonic diesis. And I call most proximate the increment that exceeds any step or leap by a comma, an amount indicated by a comma sign over the note.105 However, if you consult the Tree of the Division you will discover that to simplify matters for the readers I have omitted the most proximate size in every case. I decided not to provide examples in this chapter because everyone can now form the steps and leaps listed above by means of the increment of the comma or the minor and major enharmonic diesis and with the addition of the minor or major semitone. Everyone can also form all kinds of leaps by attaching steps to the leaps I have discussed, like adding a whole tone to the fourth to compose a fifth, a major semitone to the fifth to get a minor sixth, or a whole tone to the fifth or a ditone to the fourth to get a major sixth. Adding and subtracting in this way, each person will familiarize himself with all the steps and leaps that occur in my practice, be they natural or accidental, as well as with the proximate and most proximate steps above the natural and accidental intervals alike.

Chapter 42 The Tree of Division of the Natural and Accidental Steps and Leaps That Can Arise in the Octave Divided by the Fourth For the information of students of my practice, I decided to assemble all the steps and leaps that arise from the divisions of my music practice and my archicembalo, in order to facilitate performance on the instrument and also to ensure that the steps and leaps in my practice are understood by singers. The shape of this tree can be found at the end of this chapter [example 42].106 Experienced singers and players are advised that they will not understand the first book unless they read the entire work. In particular, they must understand the fifth book, wherein the construction of my instru105. See chaps. 14, 31, and 34, above. 106. Whereas the top half of the tree is fairly straightforward, the bottom half is rather jumbled. Consult App. Ill for a graph of the twelve distinct steps with their sizes and the chapters in which they are discussed.

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ment is described and illustrated. For it is with the archicembalo that you come to know every conceivable step and leap in my practice, as well as how to compose and notate them. My readers should not be troubled if I resort occasionally to repeating some of the divisions, explaining them yet another time, or if I jump from one chapter to the next. I have espoused this style to give a better understanding of the explanations of the examples, because for students all new things are difficult at first. [26v] Whenever any step or leap requires the addition of a minor diesis, that step or leap is called proximate. Whenever the increment is a comma, it is then called a most proximate step or leap, as I said above.107 End of Book I on Music Practice

107. But most of the proximate intervals are not given in Bk. I, ex. 42.

DIVISION OF ALL THE STEPS IN THE NATURAL FOURTH STEPS Comma Minor diesis Major diesis Accid. minor semitone Accid. major semitone Natural whole tone Accid. major tone Nat. minor third Accid. minor third Nat. major third Accid. major third

Nat. minor semitone Accid. minor whole tone Accid. whole tone Accid. minimal third Accid. proximate Accid. proximate Accid. proximate Accid. proximate

End of the Division of the Steps That Divide the Natural Fourth DIVISION OF ALL THE LEAPS THAT CAN OCCUR IN THE OCTAVE LEAPS Nat. fourth Accid. proximate Accid. fourth Accid. proximate Imper. nat. fifth Accid. proximate Imper. accid. fifth Accid. proximate Accid. proximate Natural fifth Accid. proximate Accidental fifth Nat. minor sixth Accid. proximate Accid. minor sixth Accid. proximate Nat. major sixth Accid. proximate Accid. major sixth Accid. proximate Nat. minor seventh Accid. proximate Accid. minor seventh Accid. proximate Nat. major seventh Accid. proximate Accid. major seventh Accid. proximate End of the Division of All the Leaps That Can Occur in the Octave OCTAVE Example 42 The Tree of the Division of All the Steps and Leaps That Can Occur in the Octave, Generated by the Natural Fourth

Book II on Music Practice

Chapter 1 Proem [27T] It seems clear to me that the total makeup of a sweet and harmonious composition consists in its being organized according to three principal methods. But before a composer constructs any composition, he must consider what he plans to build it on. The first method requires composers to apply tense or slack steps and leaps1 either to the subject of the words or else to other ideas.2 The second method is not inconsequential: when a composer has arranged the steps and leaps, he should match them with tense or slack consonances and dissonances3 so that the steps and leaps are similar in nature to the tenseness or slackness of the consonances. The third and last method is as follows: having matched the steps and leaps with the consonances and dissonances, a composer should then confer on them a rate of motion appropriate either to the subject inherent in the words or to other ideas. Such motion is commonly called air. Thus, if either a composition on certain words or one without a text proceeds at a seemly pace, some people will say, "The work has a fine air"—but this is not proper usage. This air or motion can be achieved in many ways, as will be shown in the chapter on motion [chapter 31]. It is not a good thing if composers should fail to integrate these three methods, for in a poorly organized composition many defects sprout up. Readers are advised furthermore that in compositions the combination of steps and leaps with consonances and dissonances as well as with motion generates six other methods. And these methods produce either good or bad effects. The first of the six methods has a good effect because tense steps and leaps are matched with tense consonances; however, if these intervals lack the proper rate of motion, the composition will not be good. The second method also has a good effect because slack steps and leaps are matched with sad consonances; but should the appropriate motion not 1. The words "i gradi & i salti" denote the linear deployment of intervals. 2. Vicentino often usesfantasia/fantasie to refer to abstract musical subjects or themes— that is, to instrumental ideas not tied to words. See Bk. I, chaps. 17 and 20; Bk. II, chaps. 14 and31;Bk.III,chap. 15; and Bk. IV, chaps. 1,7,14,25,26,28,32,37, and 42. But see also suggietto in Bk. Ill, chap. 24, disegno in Bk. Ill, chap. 43, and cosa in Bk. IV, chap. 15. 3. The words "le consonanze & dissonanze" denote the vertical alignment of intervals.

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be applied, the composition will [not] be good. In the third method, on the other hand, bad effects arise from the juxtaposition of tense steps and leaps with sad and slack consonances. The fourth method also has a poor effect because slack steps and leaps are coupled with tense and lively consonances, again without proper motion. The fifth method produces neither a completely good nor a completely bad effect. In this instance, tense and slack steps and leaps are mixed with slack and tense consonances, so that one quality is confounded with the other with the help of improper motion. This is called disorderly composition. The sixth and last method is very good, even perfect, because tense steps and leaps are coupled with tense consonances as well as with a medium, fast, or very fast rate of motion. Thus combined, they create an excellent composition, provided they are arranged according to the meaning of the words; and they will also be good to play. Composers must take great care with the rate of motion, for motion is so crucial that it can transform the quality of steps and leaps, and that of consonance as well. For example, when the motion is fast or very fast, every leap, step, and consonance—even if slack and sad by nature—[27v] will seem cheerful because of the innate power of rapid motion. If anyone wishes to verify this point and observe a composition closely, let him sing it twice as fast. He will then apprehend how well the steps, leaps, and consonances are suited to the original intent of the composition. Students have now been instructed about methods, motion, steps, and leaps. I have discussed these six methods in the proem because they are the main causes of good and bad composition.

Chapter 2 How to Proceed from the Unison to Other Steps and Leaps, with Examples Whenever a composer is moving from the unison to other steps and leaps, he should follow the method that requires him to be governed by the words. But if he is performing on an instrument, his composition should be sweeter and cleaner of dissonances or ill-disposed steps than is music made to be sung to words. I warn him that playing is very different from singing; thus, when composing he must consider well which compositions are to be played and which are to be sung. True, some words will allow a composition to be sweet and good for both playing and singing, but not all compositions made for words are appropriate for playing because the subjects occurring in them are too diverse. For, as I said, every kind of step—semitone, whole tone, minor third, or major

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third—is good for the purpose of word setting, but only if the words are respected. Indeed, it is the tenseness and slackness of the words that induce a composer to select those steps and leaps that suit his purpose. And he should not prefer the sweeter small step over the harsh big one but use both whenever he needs them. I shall not repeat here which steps are tense and which slack because they were explained in the first book [chapters 14-42], and you can avail yourself of them all. Many times a composer is called upon to write compositions for two voices rather than for three, four, or more. And in a duo for the church, a few of the leaps that go along with steps are good, but others are bad. Example 2.1 shows the good steps and leaps for two, three, four, five, six, and seven voices, as individually indicated by number. Although, as I said above, you may make any kind of step or leap in the setting of vernacular words, it is nonetheless mandatory to have respect for sacred matters and to compose whatever is required by such subjects. Because duo writing is so exposed, it is no mean accomplishment if a composer succeeds in writing two voices that make a good duo and at the same time comply with the exigency of the occasion for which he composes.

Example 2.1 The Unison Going to Other Steps and Leaps [28r] Readers are advised that all steps and leaps combined with consonances that are good for two and three voices are also good—even better—for four, five, or more voices. On the other hand, certain steps and leaps with certain other consonances are good for four, five, and six voices, but not for three and two voices. Example 2.1 is good from six up to nine or more voices. Among such a multitude of voices, every awkward leap is submerged and salvaged, so long as it is not in the soprano or bass, for the extreme ranges of these two parts makes them stand out from the rest. By nature, unison requires union. Thus, if two, three, or more singers sing in unison on one note, they must so blend their voices that they are heard as one voice even though they are many. The composer may leave the unison (as I said above) by ascending by steps and leaps, as shown in example 2.1.

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Students should understand, however, the issue concerning the perfection of the unison. I maintain that the unison has no perfection whatsoever unless it is related by distance to other voices, such as the octave and the fifth. As it happens, practitioners of music include the unison among the perfect consonances, but they forbid it in two consecutive steps or leaps, either ascending or descending. As to its perfection and possible inclusion among the consonances, I argue as follows: I deny that unison is a perfect consonance. As proof I cite the natural number present in the arithmetic progression 1 2 3 4 5 6 7 8 9 . Musicians must realize that just as nature herself has arranged natural numbers, so harmony is born of numbers.4 They should also consider the reinforcement of one number by another, because each exceeds the next solely by one unity. Thus, when nature wished to organize and augment the numbers, she was obliged to use unity, first for the closer number and then for the next one in the sequence. As a consequence, it is clear that unity is not a number but rather the mother of numbers.5 When unity wishes to form the binary number, it counts itself twice to generate two, and when it wishes to form the number three, it multiplies itself three times6 to generate the ternary number, and so on, step by step from one number to the next. The same thing happens with the unison. It has no perfection in itself except as a point of departure for the creation of all consonances and dissonances. When it wishes to generate the first dissonance in the sequence of dissonances, it multiplies itself twice, either ascending or de4. That natural number resided in the arithmetic progression was a received notion. For instance, Boethius, De inst. arith., 1.9, and Franchino Gaffurio, Theorica musice (Milan, 1492), Bk. II, chap. 8, and Bk. Ill, chap. 4. The harmony of music, however, has nothing to do with the arithmetic progression. To be sure, consonances found their formal cause in superparticular ratios, according to Aristotle, Metaphysics, 5.2.1013a, and Physics, 2.3.195a. But the difference between two terms of a superparticular ratio, one or unity, proved the definition of the ratio, not of musical harmony, which was said to arise from the proportionality between ratios. The latter was neither arithmetic nor geometric, but harmonic, as indicated in Nicomachus, Introduction to Arithmetic, 2.24; Boethius, De inst. arith., 2.21, and De inst. mus., 2.7, 12, and 16; Lodovico Fogliano, Musica theorica (Venice, 1529), Bk. I, chap. 9. 5. For example, Aristotle, Meta. 5.6.10l6b, On the Soul, 1.4.409a, and Phys., 4.12.220a; St. Augustine, De musica, 1.11.19 and 1.12.21; Macrobius, In somnium Scipionis, 1.6.7; Boethius, De inst. arith., 1.7, and De inst. mus., 2.3, 7, 15, and 20; Isidore, Etymologiarum sive originum libriXX, 3.3; Gaffurio, Theorica musice, Bk. II, chap. 8. 6. But unity, the monad, or the one, multiplied by itself any number of times, is always one. Unity may count itself or add itself to itself. Vicentino makes the same slip in the next paragraph when comparing three units to the ternary number.

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scending, to give birth to the first in the sequence of dissonances, the interval called the second in practice. And then, when it wishes to create the consonance called the third, it adds itself to itself three times and puts together three steps,7 ascending or descending from the unison to generate the consonance of the third. (This consonance becomes major or minor depending on the collocation of the steps of the whole tone and semitone.) And thus, just as unity multiplies itself three times to give birth to the ternary number, so also the unison takes to itself three other ascending or descending unisons to create a step or leap of the consonance called the third. When unity multiplies itself three times it makes up a number called a ternary number. It does not generate three units, as in 1 1 1, but rather a single figure like this: 3.8 The unison does the same. For it adds to itself two other ascending or descending unisons that, when added together, show a single figure composed of three unisonal steps—not divided, as in example 2.2, but incomposite, as in example 2.3. The latter is the customary notation for the third in music practice.

Examples 2.2 and 2.3 [Thirds] I have now proved with natural numbers that the unison is not a per fect consonance. [28v] It is not even a consonance, for philosophers de mand of music discrete relations to other elements.9 Insofar as the unison—like unity in arithmetic, which is the beginning and creation of other numbers, and the point in geometry, which is the beginning of the line—is not related by distance to other pitches, it cannot be considered a consonance.10 For this reason we should call the unison a unisonance11 and not a consonance. For just as lines and other shapes develop from 7. Vicentino means three pitches or notes. It is difficult to see why the unison should add itself to itself three times to give birth to the third. The analogy is strained. 8. Boethius, De inst. mus., 2.7 and 15. 9. For instance, Vitruvius, De architectural libri decem, 5.4; Pseudo-Euclid, properly Cleonides, Harmonic Introduction, 2; Capella, De nuptiis Philologiae et Mercurii libri II, 9.937; Boethius, De inst. mus., 1.12; Gaffurio, Theorica musice, Bk. II, chap. 2. 10. For example, Philo Judaeus, De opificio mundi, 1.16.49-50; Macrobius, In somnium Scipionis, 2.2.4-10; Capella, De nuptiis, 9.939; Isidore, Etymologiarum, 3.7. 11. The term unisonanza is Vicentino's translation of the Latin unisona, a term taken from Boethius' De inst. mus., 5.6, and Gaffurio's Theorica musice, Bk. II, chap. 2. Denial that the unison could be a consonance was often read into an analogy used by Aristotle (Politics, 2.2.1263b). For example, Gioseffo Zarlino, Le istitutioni harmoniche (Venice, 1558), Bk. II, chap. 11.

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the point and just as numbers are born of unity, so also from the unison are born all the dissonances and consonances.

Chapter 3 How to Approach the Unison by Various Steps and Leaps, with Examples The unison is called a unified point, sung by many voices that are so united that they seem as one. Whenever composers approach the unison from the step of a whole tone, the voice will produce a little harshness with that step. But the step of a major or minor semitone would be a sweeter approach, as would be the enharmonic diesis or the comma, which are both smaller than the semitone. Such a step will be very gentle because smaller steps always produce sweeter harmony than do bigger ones. Students are advised that the unison may be approached from various steps and leaps, as in the sampling given in example 3.1.

Example 3.1 Approaching the Unison by Various Steps and Leaps The steps in example 3.1 are all good. Readers should always keep in mind which steps and leaps are tense and which are slack, so that they may compose with those that suit their purpose. Some leaps are bad as approaches to the unison. But should composers match them with words that intend a bad effect, then these leaps will be good. I shall write a few examples of leaps that are not good, so that composers may use them whenever appropriate. I shall also indicate the good ones, so that they may be used for the goodness of the words and the subject matter. When a composer wishes to approach the unison from a leap that is good and does not disturb the listener, he must follow this rule: always leap on the half of a note or, if it has a dot, on the dotted extension of the note. Observing this rule is a very good idea. In leaping on half of a note, a composer helps singers not to omit any consonance above or below the other note, for singers frequently take a breath on half a breve, semibreve, or minim. Musicians who carefully apply this remedy will never incur any poverty of consonance in their compositions. The same holds true for the dots attached to breves, semibreves, and minims because few

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singers actually sing over the dot. Instead they sneak in a small breath.12 Thus, a good composer often resorts to such remedies, taking into account the many silences made by singers. And he makes frequent use of small and big rests for the sake of the singers, who may then take a breath without impoverishing the harmony. These precautions [29r] are also good for dots and leaps, in that a singer will feel secure when leaping to a unison. For if his colleague has already begun the pitch on half of the note, the first singer cannot help but sing that unison in tune. If the approach is made differently, it is doubtful that the intonation of the two singers will coincide. I offer this small bit of information to composers because I am certain it will be useful in composition, not to mention that it will add to the convenience and security of singers. The many good and bad leaps in example 3.2 have annotations for which are good, not good, or doubtful.

Example 3.2 Approaching the Unison by Various Natural and Accidental Leaps

12. See Bk. IV, chap. 7.

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The leaps in example 3.2 are not all good. Those up to six voices illustrate bad leaps, and the rest are good only so long as they are placed in the middle parts, where they cannot be clearly heard. Composers must use their judgment to foresee the many problems I cannot discuss here. Experience in such problems helps students to evaluate many things. The remedy for having bad leaps go to the unison is this: you should leap on the second part of a note, as I said above and as is shown in example 3.3. When composing for a few voices, any bad leap that goes to the unison is good on half a note. When there are many voices, the bad leap may take up the entire note. This rule applies to natural and accidental leaps alike.

Example 3.3 Approaching the Unison by Various Leaps, Always with Wholly Consonant Syncopation

Chapter 4 On the First Dissonance, Called by Practitioners of Music the Tied or Syncopated Second, Along with the Consonance Called Minor or Major Third [29v] The theory of natural number demonstrates the creation of consonances and dissonances.13 For this reason, in the preceding chapter I discussed how to approach the unison by various steps and leaps. I shall now show the method to be followed when composers wish to go to the consonance of the third by way of the dissonance of the second, an interval that is incompatible without a syncope. We shall thus follow the natural order initiated by the unison, for as in natural number, unity is followed by two, and this two is analogous to the second in music practice. To provide varied fare for the ear, composers have discovered a method of writing dissonances between consonances by passing through such dissonances by means of the grace of syncopation. Syncopation occurs as follows: every time a note is selected to bind the halves of two notes, then the first half will be the second half of the first note and other half will be the first half of the second note. 13. See chap. 2, above.

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Among composers it is customary to bind a syncopation in three ways. The first is called major when the breve combines into one note the halves of two breves; I call this method major syncopation. The second method, called minor syncopation, occurs when a semibreve combines the two halves of two semibreves. And if the semibreve is sung on the upbeat of the measure, so will the breve be. The third method occurs when the minim combines the two halves of two minims in the abovementioned arrangement; I call it minimal syncopation. It follows therefore that the bindings used in music practice to tie the dissonances to the consonances are tied with three different notes. The first is called major syncopation whenever it concerns the breve. The second is called minor syncopation whenever it concerns the semibreve. And the third is named minimal syncopation whenever it concerns the minim. The last kind is called minimal not because it derives from the minim but because it is smaller than the minor syncopation. The dissonance known as the second is always placed on the second half of the syncopated note, which should always descend by step to the consonance of the major or minor third. At the conclusion, the syncope must end with a note worth one-half of the syncopated note. For instance, if the syncope is the length of a breve, it should end with a semibreve moving downward by step; and if the syncope is a semibreve or a minim in length, it should end with a minim or a semiminim, respectively, moving downward by step, as I just said. Example 4 shows how to make such syncopations with the dissonant second, notated in three ways: that is, major, minor, and minimal.

Example 4 The Major, Minor, and Minimal Syncopation

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[30r] Readers will note that some syncopations, while good for from three to six voices, are not good for two voices, as I indicate in example 4. When writing a voice against a syncope, it is much better to approach the syncopated second by means of a semitone rather than a tone. For small steps are sweet with well-placed consonances, and when they are accompanied by dissonances they offend the sense of hearing less than big steps, as everyone can learn from experience. I shall not prolong the discussion of syncopation here, for I plan to explain it in a later chapter [13]. In this discussion my aim is to teach you how to compose the dissonant second accompanied by the consonance called the imperfect third. The rule is as follows. You must never accompany a bad consonance with a perfect one for the following reason: nature does not tolerate extremes.14 Composers are warned, then, not to assail the ear with the worst dissonance followed suddenly by the best consonance, lest nature be confounded by either of these extremes. On the contrary, just as the Philosopher [Aristotle] believed that between two extremes there is a middle,15 so between the worst dissonance and the best consonance there is an interval very close to the latter. And that is the imperfect consonance, for it is in the middle between two extremes and shares in both. The required succession of the second by the third applies also to that of the ninth by the tenth, since they correspond at the octave. However, these two sets of intervals do not have the same nature, as is shown by their ratios and by the experience of hearing them.

Chapter 5 How to Compose the Second and the Fourth in Three Parts, with Examples The method of composing dissonances of the fourth and the second with consonances is as follows. Composers should always reconcile the parts with good consonances—that is to say, with thirds, fifths, and octaves. And if it should happen that a syncope binding a second or a fourth appears with a part making a second above the syncope and a bass below making a fourth with it, then this way of composing results in an excellent concord. The power of the consonance is so strong that the dissonance does not even offend the sense of hearing, as is true, for instance, 14. Probably Aristotle, On the Parts of Animals, 2.7.652a, or Nicomachean Ethics, 2.2.1104a. 15. Aristotle Nic. Eth., 2.2.1104a, 2.9.1109a-b, and 4.4.1125b. This notion also underlies the dictum that a whole or perfect thing has a beginning, middle, and end. Aristotle, Poetics, 7.3.l450a; Pseudo-Aristotle, Physical Problems, 17.3.9l6a; St. Augustine, De musica 1.12.20; Capella, De nuptiis, 7.736. See also Bk. IV, chap. 15.

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when a lesser light is close to a greater light.16 Composers are also advised that in parts going against the syncopation the semitone is better than the whole tone. Example 5 demonstrates good and bad ways of composing these dissonances in three parts. Some examples are better for four and five parts.

Example 5 How To Compose the Second and the Fourth in Three Parts: Alto, Tenor, and Bass

Chapter 6 How to Compose the Syncopated Fourth for Two, Three, or More Parts with a Dot, with Examples [30v] According to philosophers, the fourth should be considered a consonance with inherent perfection.17 Consequently, when the fourth is placed near a fifth or an octave, it is apprehended in exactly the same 16. Gaffurio, Practica musicae (Milan, 1496), Bk. Ill, chap. 6. 17. Gaffurio and Glarean classify the fourth as a dissonance, whereas Fogliano conside it a consonance (Practica musicae, Bk. Ill, chaps. 2 and 5; Dodekachordon, Bk. I, chap. 9; and Musica theorica, Bk. II, chaps. 1 and 4, respectively). The inherent perfection of the fourth resides in its simple superparticular ratio. The authorities for this concept are many: Aristotl Meta., 5.2.1013a, Phys., 2.3.195a; Posterior Analytics, 2.2.90a; Pseudo-Aristotle, Problem

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way as the are latter intervals, for the difference in their harmoniousness is almost equal in perfection. Composers ought to realize that nature receives nourishment from variety and takes no pleasure in consonances that are not varied and mixed in their perfection. Therefore, whenever the fourth is matched with the third, it is preferable to approach it from the semitone rather than the whole tone. Whenever it is matched with a fifth among many voices, the multiplicity of the voices will conceal it. Thus, in five, six, or more voices, the fourth should be put in the middle parts so that it is not perceptible. The fourth comes first in the order of the consonances: that is to say, fourth, fifth, octave. All the other consonances mentioned earlier are born of the fourth. 18 However, it so happens that the pure fourth cannot be considered a consonance in a duo. But if it is accompanied by the fifth, you then perceive how good and perfect it is. Example 6 shows

Examples 6.1 and 6.2 The Syncopated Fourth for Two Voices, Not Syncopated for Three Voices, and with the Dot; How It Should Be Composed for Many Voices, and How It Should Be Composed with a Wholly Dissonant Syncopation 19.23.919b; Philo, De opificio, 1.15.47-48; Vitruvius, De arch., 5.4; Pseudo-Euclid (Cleonides), Harmonic Introduction, 5; Cassius Dio, Roman History, 37.18.3-4; Censorinus De die natali ad Q. Cerellium, 1.10; Macrobius, In somnium Scipionis, 2.1.24-25; Capella, Denuptiis, 9.950-51; Boethius, Deinst. mus., 1.7 and 16; Cassiodorus, Institutions divinarum et saecularum litterarumy 2.5.7; Johannes Philoponus, Commentaria in libros posteriorum Aristotelis, 2.2. 18. See Bk. I, chap. 32.

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how you may compose the fourth for two or more voices in various ways— tied, free, and even with a wholly dissonant syncopation, which is not modern. It is customary to bind several fourths with descending thirds while pretending to complete the syncope now on the first, and then on the second, the third, or a further step, as shown in the third segment (for two voices) in example 6.1. Having experimented with the fourth, I concluded that in three voices this interval sounds better if it is surrounded by a semitone and placed between a major sixth formed by the high and low parts than if it is surrounded by a major third between the high and low parts and placed above the major sixth.19 Whoever makes the same experiment will be assured of the same results. As for me, I sometimes use the fourth not only for variety but also when it suits a tense or slack word, depending on the steps. Consult the second and third segments for three voices in example 6.2. In the fifth segment of example 6.2, the fourth has been used, though it is not too modern. The first segment of example 6.2 shows the fourth composed with the fifth to make up an octave, and it is good for four, five, six, or more voices. Sometimes a fourth with a dot is put in the tenor rather than a syncope against the bass, even though in this case the argument for preferring the dot over the binding is a shaky one. The reason is that singers fail to sing the dot much more often than they fail to finish [31r] singing the syncope, taking a small breath either on the syncope or for the value represented by the dot. In this instance, the tied syncope is a lesser evil than the dot.

Chapter 7 How to Proceed from the Fourth to the Fifth and from the Fifth to the Fourth, With and Without Syncopation, with Examples Every time two similar consonances are used by composers in a musical work, they displease because they lack variety. The same is true of the steps described in the first book [chapters 14-42]. It is now time to discuss movement from the fourth to the syncopated fifth. Let me say again 19. This sentence is a syntactical shambles. However, a comparison of the second and fourth segments in Bk. II, ex. 6.2, clarifies the text. In the former, the fourth in the tenor is approached and resolved by semitone, and it forms the middle note inside a major sixth. In the latter, the eleventh (read fourth) appears in the alto, which forms a tenth (read third) with the bass before and after the eleventh. And this eleventh appears above, not between [the text hzsfra] the major sixth formed by the two lower voices.

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that the fourth is reputed to be perfect by philosophers, and that the fifth is the interval possessing the perfection of optimum harmony.20 If these two intervals are placed one after the other without the insertion of another consonance, the result will not make good listening unless it is redeemed by the subject matter of the words. Without some relevance to words, the fourth and the fifth are not good in a duo, but if they are positioned in the middle of other parts in works for five, six, or more voices, they are then not so obvious. The remedy for three voices calls for the fourth to be syncopated and followed by the fifth; from this interval the bass moves to the sixth below the tenor and the tenth below the soprano, while the tenor goes from the fourth to the fifth against the soprano. This method is demonstrated in example 7.1 for three voices. Moving without syncopation from the fourth to the fifth in more than four voices is salvaged when effected in the middle parts, as I said. And in three voices, movement from the fifth to the fourth may occur with the semitone above or below, as in example 7.2.

Examples 7.1 and 7.2 How to Proceed from the Fourth to the Fifth and from the Fifth to the Fourth With and Without Syncopation Above I explained why two similar intervals, such as the fourth to the fifth and vice versa, do not make good listening. But I cannot resist of20. On the fourth, see note 17, above. As for the fifth, Vicentino's characterization could be based on comments made by Gaffurio and Glarean (Practica musicae, Bk. Ill, chap. 2, and Dodekachordon, Bk. I, chap. 8, respectively).

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fering a small example of several fourths in a composition. These fourths should not be used unless you couple them with harsh words or an otherwise provocative mode of speech, because so many fourths together produce a harmony that seems strange to our ears. Many years ago these fourths were considered very good indeed. Today, some rather old-fashioned people use them as if they were sweet; but for the reasons just given—namely, that there is no variety in the procession of so many fourths—they should not be composed in this way. Above all, composers must take care that variety is never lacking in their compositions and, for this reason, they should always vary the steps and the consonances. These fourths are shown in example 7.3.

Example 7.3 Composing Many Sixths and Thirds for Three Voices, Which Many People Call the Way to Compose "Faulx Bordon"

Chapter 8 How to Compose the Tritone and Its Nature, with Examples [31v] When the low F fa ut and the high F fa ut ascend to the high and very high B fa B mi, respectively, either by step or by leap, they generate the tritone. As I have already said, these constitute either composite or incomposite tritones [Book I, chapter 35]. The tritone is a minor semitone bigger than the natural fourth. Occasionally, the syncopated tritone is used in compositions instead of the fourth; and this happens in music for two and for three voices. Considering the harsh nature of the tritone, the words must move composers to use this interval. I show how to compose the tritone in example 8.

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Example 8 How to Compose the Tritone

Chapter 9 How to Compose the Imperfect Fifth in Various Ways for Two, Three, or More Voices, with Examples The imperfect fifth must be counted among the dissonances because it is a species of tritone. The latter is composed of three natural whole tones, likewise in its incomposite form. Hence the composite imperfect fifth contains two natural whole tones and two major semitones that joined together form a major whole tone.21 The imperfect fifth may also be made up of three whole tones and one minor enharmonic diesis.22 This fifth is used in various ways in compositions. It is redeemed through the major semitone placed above or below the imperfect fifth, which is to be followed by the major third by means of two conjunct parts. Moreover, example 9 shows that the imperfect fifth is better than the perfect fifth as long as it is well accompanied. For instance, if the minor sixth precedes the imperfect fifth, which goes on to join itself to the major third by way of two semitones, then the imperfect fifth is much better than the perfect fifth [example 9.la]. But if the major sixth precedes the perfect fifth, and the perfect fifth is followed directly by the minor third, then this fifth, though perfect, is not so pardonable as the imperfect fifth because the duet proceeds via two ascending and descending whole tones [example 9.1b].23 In contrast, the imperfect fifth produces one semitone and one whole tone in 21. For the major whole tone, see Bk. I, chap. 24. 22. See Bk. I, chap. 37. 23. Ex. 9.1b is my reconstruction of the condemned perfect fifth.

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the upper and lower voices. And the redemption of the imperfect fifth is brought about by the progression of these two major semitones. Therefore, composers must bear in mind, from this example, that the two semitones [32r] redeem the imperfect fifth and make a bad consonance seem good. As a consequence, any good consonances accompanied by many semitones must seem vastly superior and gentler. For this reason, chromatic music, which is full of semitones, produces sweeter harmony than music filled with whole tones. Example 9 shows how to compose the imperfect fifth in various ways.

Examples 9.1 (a and b), 9.2, and 9.3 How to Compose the Imperfect Fifth in Various Ways for Two or More Voices

Chapter 10 How to Compose the Dissonance Called Seventh, Syncopated with the Sixth, with Examples In the previous chapters I discussed dissonances, and how and with which consonances they are accompanied. Because the dissonances of the second, the pure fourth, and the seventh are found within the octave, it now remains to talk about the seventh and how it is accompanied. Readers have already learned the order of natural numbers. In accordance with this order, I now turn to the seventh, a dissonance that the ear cannot tolerate. Therefore, the method of composing this dissonance among the consonances is as follows.

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Every time the seventh is salvaged through the syncope and the syncope resolves by step, as clarified in the preceding chapter, this dissonance may be placed among consonances. Take note that, on account of the natural order of numbers, this seventh would greatly welcome the company of the sixth, more so than any other perfect or imperfect consonance, because the sixth is the imperfect consonance closest to the seventh. The seventh should be placed exactly on the second minim of the syncope, as I explained before regarding the syncope used for the second and third. This dissonance may be used in two, three, four, five, six, or more voices. In three voices the seventh is followed by the minor or major sixth; the bass should be a fifth below the tenor, which makes a sixth with the soprano,24 and thus it can be accommodated with any part. The same holds true for four or more voices. I provide one example for two voices and one for three, which also serves for more than three voices, as you can see in example 10.

Examples 10.1 and 10.2 How to Compose the Dissonance Called Seventh, Syncopated with the Sixth

Chapter 11 Explanation of the Seventh That Almost Produces Two Parallel Octaves or Unisons in Composition) Although Neither Actually Occurs [32v] Let me emphasize to my readers that nature has arranged the elements in many systems, and that accidents often cause these elements to exceed their limits. For this reason, there exist certain means between accidents and nature that are common to two extremes. These means bind and unite any disorder so tightly that, for instance, the limit and 24. This description makes sense only if one imagines the whole-note pitches, c g c, in the bass in ex. 10.1. Ex. 10.2 has different voice-leading.

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order of the consonances are not disturbed by the diversity of the sense of hearing.25 As a consequence, experienced musicians do not concede that the trained ear should accept any dissonance in compositions, nor even two ascending or descending perfect consonances, such as two or more fifths or octaves. There is, however, some sort of remedy for every problem. Composers are advised that whenever they find it convenient they may insert a seventh in a composition, so that the interval creates the illusion of two parallel octaves [example 11.2]. This method is used in compositions for more than five voices, because with fewer voices such sevenths are too obvious. The same goes for unisons, which may seem to be two parallel unisons but are not [example 11.1]. When arranged by means of the semitone, these intervals offend the sense of hearing less than by means of the whole tone, as in example 11. The latter shows both methods for the unison and the octave, that is, with and without the semitone.

Examples 11.1 and 11.2 Composing the Seventh in Two Tenors That Produce Two Parallel Octaves, Although Neither Actually Occurs

Chapter 12 How to Compose Free Dissonances Without Syncopation and Dots, with Examples In the octave there are three consonances—the third, fifth, and sixth— and three dissonances: the second, fourth, and seventh. In order to follow the sequence of natural number,26 I shall now discuss dissonance without syncopation. These free dissonances have been and continue to be put into practice in various ways. You should know, readers, that in music some gains are made gradually. Thus it happens that in old-fashioned works composers used free 25. On the variety of musical apperceptions, see Bk. I, chap. 1. With regard to shared means, the importance of melodic major and minor thirds (from the enharmonic and chromatic genera, respectively) is obvious in ex. 11. 26. See chap. 2, above.

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dissonances of the value of one semibreve within the long by making the first note consonant on the downbeat and the second dissonant on the upbeat. Later on, composers abandoned this method because they felt that the harsh sound lasted too long. In order to cause less dissonance to the ear, they used minims instead, the first consonant on the downbeat and the second dissonant on the upbeat. This arrangement lasted for a while. But in these times we have relinquished the technique of deploying one consonant and one dissonant minim. For today it is thought that the minim is too obvious to the ear—and not only the minim but also the semiminim, whenever it is not positioned well. We are thus accustomed to using only dissonant semiminims and cromas in our compositions. Counting four semiminims per measure, we make the first semiminim consonant, the second dissonant, the third consonant, and the fourth dissonant. Thus the consonant semiminims [33r] are on the downbeat and the upbeat in a succession of four consecutive semiminims. When there are two descending semiminims next to a syncopated semibreve or minim, the second of the pair should be consonant but not the first. When they ascend, the first is consonant and the second dissonant. The same is true of two cromas, as I show in example 12.

Example 12 Free Dissonances for Two Voices with Old-Fashioned and Modern Diminutions

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Chapter 13 On Wholly Consonant Syncopation and How It Can Be Composed in Many Ways During the demonstration of the dissonances I showed how we should use and compose the syncope one-half of which is consonant and the other half dissonant. It is now necessary to discuss the wholly consonant syncope, a syncope that has no restrictions in ascent or in descent, unlike the syncope that is half consonant and half dissonant. The syncope in question is always consonant both ascending and descending, and thus attention need be given only to the movement, so that you do not to cause all the parts to move simultaneously in breves, semibreves, or minims. I warn you that with more than one or two simultaneously syncopated notes, you must not proceed with all the parts because the syncopation will not then be apparent. For syncopation can be discerned only when at least one voice sings on the downbeat while the others are on the upbeat; thus the differences in their movement become recognizable. Therefore, one set of notes should move on the downbeat and another set on the upbeat, as in example 13.

Examples 13.1 and 13.2 Numerous Ways to Use Wholly Consonant Syncopation for Two or More Voices27

27. One assumes that the comment under ex. 13.2 alerts the reader that this simultaneous syncopation must by accompanied by at least one other nonsyncopated part.

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Chapter 14 Several Ways to Accompany the Consonance Called the Minor Third, and Its Nature Now that I have discussed the two ways of syncopating as well as all the dissonances within the octave, it is time to talk about the consonances found within that interval. These consonances are of two kinds, perfect and imperfect. To adhere to the order of the consonances, I shall begin with the imperfect consonance [33v] called the third. There are two kinds of third, the minor and the major. And to follow the order mentioned above, I shall now discuss the minor third and its nature. The minor third is very weak and rather sad, and it descends easily. This step seems a little cheerful when coupled with a fast or very fast rate of motion, but when it ascends at a slow pace it resembles a man who is exhausted. Quite often, singers make mistakes because they cannot tolerate such weak thirds in singing; and occasionally they expand minor thirds, causing them to become major thirds. So if by chance a composer has not been alerted to this problem and places an octave above or below a minor third, the error of false octaves will occur. To avoid uncertainty, he should compose the minor third in descending motion whenever it has an octave above or below. Thus singers will not fall into the error, described above, and make the composition discordant and disorderly. The consonance of the minor third is very useful for sad words, as it is rather static. It is quite important for musicians to know how to change imperfect to perfect consonances, as the circumstances may dictate. The change from perfect to imperfect consonances is not at all important when effected according to the subject of the words or other ideas. For the student's better understanding, I shall later give some examples starting with the consonant minor third and leading to another consonance by a slack or tense step or leap. But I shall not repeat the discussion of the nature of the steps because it was presented in "Book I on Music Practice." Pupils should realize that some things cannot be taught by a teacher. These things a student will learn for himself. From his own work and the experience of having done many things, the student will develop a fine and perfect judgment. A master cannot impart more than the judgment he himself possesses. But a student learns from his own labors and adds this knowledge to his master's. Thus, with unremitting study, every eager and diligent pupil comes to know more than his master. But not all students manage this well, for not all of them study their profession equally.

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My argument can be proved by the musical works written by former pupils who are alive today. Their compositions are far superior to those made by their masters thirty or forty years ago. The same process occurs from master to pupil as time goes by. And thus, the practice and theory of all professions are amplified and enriched at different times by the studies of many people. I have offered this little discourse to encourage students not to abandon the fine enterprise of study, no matter how arduous it may be, and also not to despair of attaining the competence of men who are learned and expert in the sciences. Proof to the contrary I have given by comparing the past to the present time and the works of the past to those of the present, which can be seen and heard today. Rather than lingering any longer on this argument, I shall now give several examples of how to compose the minor third. Example 14 is for two voices, or for as many voices as composers may wish.

Example 14 Several Ways of Accompanying the Minor Third

Chapter 15 On the Major Third and Its Nature and the Various Ways to Accompany It, with Examples for Two Voices [34r] The major third is an imperfect consonance. By nature it is lively and cheerful, and it ascends easily on account of its vivacity. As an ascending step or leap it is tense, whereas in descent it is slack, as I said in the discussion of the steps. The major third can be composed in various ways. You are advised that when the major third moves to other consonances by small steps, such consonances become sweeter and gentler. Numerous ascending and descending major thirds are shown in example 15.

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Example 15 Various Ways of Accompanying the Major Third

Chapter 16 On the Consonance of the Perfect Fifth and Its Nature, with Examples Adhering to the order of the consonances, I have discussed the minor and major third. Now comes the fifth, which is a perfect consonance. Its nature is so harmonious and sonorous that even though players tune the fifth a little blunted and scant, the sense of hearing is not disturbed by the small amount customarily removed when tuning tempered fifths on instruments. As I explained before [Book I, chapter 6], the reason for blunted tuning is to make available four more kinds of consonances than were used by the ancients,28 and hence to make music more rich and abundant, as we enjoy it today. But we cannot produce as many miracles as those recorded by the ancients.29 And yet, we ought to be able to move the listeners more than did the ancients because we have more steps and consonances. We cannot do so because the overabundance and profusion we experience today fails to make any miraculous effect on listeners. The truth is that fine, well-crafted music is embraced by good musicians, and it delights those who have a musical ear much more than those who have merely a natural ear. I made this small digression to calm the minds of those people who read music histories and insist that it would be a great thing if we could produce the music of the ancients. Now that I have enlightened them on this score, they should keep quiet from now on. I have also explained to them the reason why the fifths on instruments are not tuned perfectly, a practical matter of concern to players. As for singers, they should know the reason for the tuning of the fifth, an interval so sonorous that it remains perfect even when blunted. Practitioners 28. That is to say, major and minor thirds and sixths. 29. Here Vicentino repeats the arguments put forward at the end of "Music Theory," chap. 16. See also the introduction.

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of music forbid the writing of two parallel fifths, either ascending or descending by step or by leap [example 16.2], not because two fifths are not good but rather for the sake of variety of consonances. But you should know that you may write two parallel fifths by leaping, as in example 16.1; however, a small rest does not eliminate either two parallel fifths or octaves [example 16.3].

Examples 16.1-16.3 Parallel Fifths

Chapter 17 Explanation of Similar Thirds, Major and Minor, with Examples [34v] Just as nature herself, by means of number, has arranged the consonances in an orderly way one after the other without two consecutive similar ones, so it is evident in natural number that one number follows the other, as in the numbers 1 2 3 4 5 6 7 8 9.30 Anyone wishing to make certain of this fact should go to the monochord, take these numbers, and strike a string. With the division of the string, let him relate one number to another, following naturally from one to the next. He will discover that 1 related to 2 gives the duple ratio [2:1], which is called octave in practice. And from 2 to 3 he will generate the sesquialter ratio [3:2], which in practice is called fifth. Next, 3 related to 4 begets the sesquitertial ratio [4:3], called fourth in practice. After 4 comes 5. When related to each other, these numbers produce the sesquiquartal ratio [5:4], which in practice is sung as the major third or ditone. When 5 and 6 are related to each other they create the sesquiquintal ratio [6:5], which in music practice produces the consonance practitioners call semiditone or minor third.31 30. See chap. 2, above. 31. The ratios given here are those found in the diatonic syntonon tuning of Ptolemy, a tuning Vicentino probably encountered in Fogliano's Musica theorica, Bk. II, chap. 1. See also note 38, below. Like Fogliano, Vicentino realized that most temperaments, meantone in particular, were capable of producing relatively pure thirds and sixths on keyboard instruments. See Bk. I, chap. 6.

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This is how natural number itself orders the consonances, which are created consecutively by their ratios without a single one being similar to another. As a consequence, experienced composers must not disrupt the fine system generated by nature; they must not make two similar consonances, such as two octaves, two fifths, two fourths, or two similar thirds, either major or minor, because of the way these intervals are generated by number. Although custom permits two or more similar imperfect consonances, these should not be used in compositions. If a composer needs to write several imperfect consonances, he can make them different from one another—one major, the other minor, and the next major. Thus, the diversity of inequality will delight listeners much more than similar imperfect consonances, even if there are only two of them. Minor thirds are better descending than ascending, whereas major thirds are better ascending than descending. Composers must pay great attention to variety. If they wish to make a fine composition, they will always make consonances that seem varied to the ear. Some samples of similar and dissimilar thirds appear in example 17.

Example 17 Similar and Dissimilar Thirds

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Chapter 18 On the Imperfect Consonance of the Minor Sixth and Its Nature, with Some Examples [35r] The nature of the minor sixth is as follows. It is somewhat sonorous and rather sad. It inclines readily toward the fifth. Indeed, it is so close to the latter that when these two intervals wish to be joined together, they require but one step, that of the major semitone, to pass from one to the other. Moreover, because the minor sixth lacks intrinsic harmony, it is greatly obligated to the fifth. The fifth has so much intrinsic harmony that it bestows harmony upon the minor sixth owing to the proximity of the two, just as the sun gives splendor to the moon. For the moon lacks intrinsic light, and it is through the benevolence of the sun's light that the moon seems to us to be full of light.32 And as the sun moves farther away from the moon, the latter appears less visible and less bright to us. The same happens to the minor sixth, for it gives us less harmony if it is far away from the fifth and more if it is close to it. For this reason composers must be careful with the consonance of the minor sixth. It is distinctly preferable to follow the fifth with the minor sixth and then, in antithesis, to move from the minor sixth to the octave, the third, or the tenth. This movement can be made by a leap or in various other ways, as will be understood from example 18. Whenever the sixth uses the smaller step to go to the fifth, it is more harmonious. Some sixths can be tolerated in compositions for three voices, whereas others are acceptable only in two voices. But all of them may be used, the well and the badly composed, for a composer selects them according to the subject of the words. A player, however, cannot do this. When he plays he must make the sweetest and most harmonious music he can because on an instrument there is no verbal subject matter to induce a player, for whatever reason, to compose an awkward or misplaced step. Indeed, his course of action is to advance with sweet steps, unless he intends to provide a little harshness to the ear at the start of his playing and then to enter the pathway of gentle and sweet steps. Players are advised to create variety by passing from big to small steps and vice versa, but not for the sake of any misplaced step. Example 18 demonstrates some ways of composing the minor sixth. Readers should note that imperfect consonances that are poorly positioned near perfect consonances are more obvious when ascending than when descending because they have more of an impact in ascent than in descent. 32. For example, Macrobius, In somnium Scipionis, 1.15.12 and 1.19.8.

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Example 18 The Minor Sixth Composed in Various Ways for Two Tenors

Chapter 19 On the Minor Sixth Going to the Octave, with Examples [35v] Quite often, the minor sixth goes to the octave by step or by leap in compositions. When it moves by the ascending step of the whole tone, the minor sixth makes a gloomy, listless, and harsh effect [example 19.1]. This procedure occurs in diatonic composition.33 But the minor sixth also moves to the octave by the descending step of the semitone [example 19.2]. Should minor sixths be poorly situated, they can be salvaged and appear less strange by the use of the same leaps that save any other bad composition, as is evident in examples 19.3 and 19.4. 33. In diatonic composition, at least by Vicentino's definition, there are no linear semitones except natural ones. For his definitions of the diatonic genus and of diatonic as opposed to tempered music, see Bk. I, chap. 6. For an example of a pure diatonic composition, see Bk. Ill, chap. 26.

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Examples 19.1-19.4 How to Compose the Minor Sixth in Various Ways

Chapter 20 On the Major Sixth and Its Nature and How It Can Be Used in Many Ways in Composition, with Examples Nature has endowed everything. If all things, therefore, utilize their proper and legitimate order, they themselves provide the proper and proportionate limits for their natural operations.34 Thus, the nature and the limits of the major sixth are such that it easily ascends or descends, depending on how the voice above or below prompts it to behave. Between two extremes there is always a mean, which mean proffers a remedy for disorderly things.35 This mean also makes something disordered seem almost orderly; for example, it causes the listener to forget the disorder of a consonance by making it seem rather remote. To salvage all imperfect consonances that do not proceed to perfect consonances through the proper steps, make them leap. Now some leaps redress disorder completely, but not all do so, for some are good in as34. For example, Aristotle, On the Parts of Animals, 4.10.6871, and Phys., 1.5.188a. 35. This concept is also found in chap. 4, above. See note 15 for possible sources. The rest of the discussion about order and disorder repeats material from chap. 11.

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cent but not in descent, others are good in descent but not in ascent, and still others are not good in either direction. This matter will be explained in the chapter on leaps [29]. Example 20 demonstrates the many ways of using the major sixth, both by step and by leap.361 do not need to explain the reasons because one method is no better than the other. And inasmuch as students know the nature of the steps and leaps, the nature of the consonances requires no further discussion. Still, students should note that the major sixth acts more like a dissonance than a consonance. Because it arises between the minor sixth, which has little intrinsic harmony, and the seventh, which

Examples 20.1 and 20.2 How to Compose the Major Sixth in Many Ways 36. In ex. 20.2, segment 5 contains no sixth at all; if the second note in the upper part is changed to d1, this segment then duplicates segment 6. In ex. 20.1, segment 6 contains a minor sixth, as do segments 1 and 4 in ex. 20.2.

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is an utter dissonance, the major sixth receives only a little help from the minor sixth and even less from the seventh. Consider the following consecutive sequence: seventh, major sixth, minor sixth, and fifth. Here the minor sixth seems to breathe a little because the fifth is nearby, while the seventh, a very bad dissonance, makes the major sixth seem rather good. And because of its paucity of harmony, the major sixth, when sung, seems to call for help from the perfection [36r] of its neighbor, the octave. For the latter is always as close as a semitone away, either above or below, as shown in many ways in example 20.

Chapter 21 The Many Ways of Composing Similar Sixths, Major and Minor, with Examples During the earlier discussion of similar major and minor thirds I spoke about natural number, which follows its own organization.37 In the ratios of natural number there never arise two similar ratios in succession that could generate two similar consonances, as I have already stated. The same ordering obtains for the major and minor sixth. In the natural number from 4 to 5, which generates the major third, and from 5 to 6, which creates the minor third, it is clear that the difference between the numbers is unity. Exactly the same ordering occurs in the ratios of the major and minor sixth. From 3 to 5 there occurs the superbipartienttertial [5:3], which generates the major sixth, and from 5 to 8 there arises the minor sixth, whose ratio is the supertripartientquintal [8:5].38 If readers pay attention to the excess of the difference between the major and minor sixth, they will discover unity. The difference between 3 and 5 is 2, and the difference between 5 and 8 is 3. Therefore, the difference of the excess that exists between the major [36v] and the minor sixth is unity [3 - 2 = 1]. The same difference was formed between the other consonances, as I explained before. We follow the order of natural number. Just as such numbers do not provide similar ratios capable of generating two similar consonances, so composers should by no means write two similar sixths, neither major nor minor. Two minor sixths succeed better in descent than in ascent, whereas the major ones are better in ascent than in descent. But for the sake of variety, it is better to write one major and one minor sixth. A composer may conveniently change the major to a minor sixth, or vice 37. See also chaps. 2, 4, and 10. 38. Like those of the major and minor third, these ratios correspond to the diatonic syntonon of Ptolemy, a tuning Vicentino found in Fogliano s Musica theorica, Bk. II, chap. 1.

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versa, by means of accidentals, as can be seen in example 21, which shows several ways of composing sixths, both naturally and accidentally. To restore them in accordance with their positions, a composer should write the signs, as I said before in the chapter on signs [Book I, chapter 12].

Example 21 Similar and Dissimilar Sixths

Chapter 22 On the Octave and Its Nature, with Examples There are four unisons that are used naturally—that is to say, the unison, the octave, the fifteenth, and the twenty-second. Of the unison enough has been said. There remains to discuss the octave and how good practitioners use it. First, the octave by nature contains such a close union that its two voices seem as one. It is, moreover, so perfect that in the tuning of instruments the octave tolerates no deficiency, not even the slightest. But the fifth, even though it is a perfect consonance, nonetheless allows a very slight discordance.39 It thus follows that if the fifth is called perfect, then the octave can be called utmost perfect because of its supreme unity. When composers write two ascending or descending octaves, these intervals do not create a discord but neither do they offer any variety to the sense of hearing. For this reason, practitioners of music have prohibited the writing of two fifths or two octaves, whether ascending or descending, unless another consonance is placed between them. Pairs of fifths or octaves may even be salvaged by an intervening consonance of a semiminim, as is shown is examples 22.2 and 22.3. Students are advised never to write an octave against a note in the middle of a cadence, for this note requires an imperfect consonance. It is also possible to pretend to write two parallel octaves and yet not do so, as I demonstrated with regard to dissonances and shall not fail to show again in this context [examples 22.3 and 22.4]. Such dissimulation is effective with five or 39. That is to say, the shortening effected by tempering the fifth. See Bk. II, chap. 16, and Bk. I, 6.

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more voices. It is mandatory that composers be very careful with octaves. When there are enough octaves on one line or space, they should be distributed among the parts. Thus, even though octaves are encountered constantly in singing, they are permitted because they appear now in one part and now in another. Example 22 provides a few samples of octaves, some allowed and some disallowed.

Examples 22.1-22.4 Octaves for Two Voices

Chapter 23 On Double Octaves and on the Octave, the Fifteenth, and the Twenty-Second, with Examples [37r] In order to avoid making two fifths and two octaves, or twelfths, in compositions, the soprano or contralto often makes an octave with the tenor or another middle part. This procedure does not sound well if the octaves over middle parts are placed above a minor third, for the minor third is too weak and susceptible to expansion,40 If it is necessary to put double octaves over thirds, it is better to place them over major thirds than minor thirds. However, the double octave is more secure over the fifth or the octave than over any other consonance, and it is much worse over sixths then thirds. So that my readers understand clearly, let me say that the double octave is nothing more than one part on top of another; the part that has the octave above it also has another part below it, and this part corresponds to the part having a consonance of the minor third, major third, fifth, minor sixth, major sixth, or octave. When a composer wants to write an octave over a minor third, he should employ the following remedy: sound the minor third on a semiminim—or a minim at most—but not on a semibreve or a breve, for there is some danger of expanding the minor third and hence of sinking and withdrawing. But over a major third there is less danger of this happening. Nevertheless, as I said, such octaves placed over imperfect consonances do not sound well when sing40. See chap. 14, above.

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ers must stay on them too long. Over perfect consonances there occurs no uncertainty nor any danger of raising the pitch. When played, all kinds of double octaves are satisfactory because the well-tuned instrument responds accurately and without any uncertainty to direct vocal intonation, in imperfect and perfect consonances alike. Example 23 illustrates some natural and accidental octaves. In music sung with a full choir it is difficult to tune accidental octaves over accidental octaves. However, in chamber music—that is to say, with a small ensemble—it can be done, but not without toil. Because accidental octaves are difficult to sing accurately, the voice is more secure when accompanied by an instrument.

Example 23 Some Double Octaves [37v] In example 23 I have supplied a few illustration of double octaves so that on their model composers may construct many others on both imperfect and perfect consonances. The latter are so outstanding that the Pythagoreans did not want to hear any harmony other than that of perfect consonances, as I said earlier.41 The amity among consonances 41. This assertion does not occur verbatim anywhere in the text before its appearance here, although it is implied in several places. See Bk. II, chap. 16; "Music Theory," chaps. 6 and 8; and Music Practice, Bk. I, chaps. 6 and 8. But see also Foglianos Musica theorica, Bk. II, chap. 1.

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that have been combined together is so great that when there are many pitches, the consonances appear completely united and thus create a unified and well-proportioned body with many members. So perfect is the union of the unisonance42 of the octave and the fifteenth that in this perfection the nature of numbers is shown to be a wonderful thing. And, it might be said, it is a divine rather than a natural thing that even though it involves three pitches, the collocation of the unison, octave, and fifteenth seems to be one pitch and that the fifth within the octave and the tenth within the fifteenth, whether sung or played simultaneously, generate such a union of the body that it fills the listener with harmony and wonder. Should anyone desire to show with a superlative example the vestige of the ineffable nature of God, the being of all creation in God, how creation is united in itself, how it cannot sustain itself unless joined to God, and other similar matters, he could do it just as well with these consonances as with anything else. For like all other things (to eyes capable of examining the matter), these consonances bear the impression that, from his goodness, his order, and his glory, the seal of the hand of God has made in all things, of all things, and especially by his own person.43 As to the first point [the ineffable nature of God], we may speak as follows. From the unison and the octave joined together there proceeds the fifteenth, and all three together make a perfectly concordant unisonance. So also from the Father is born the Son, and from the Father and the Son joined together there proceeds the Holy Spirit; and all three persons are one single divinity.441 do not mean that the Son is signified by the octave and the Holy Spirit by the fifteenth as if, like the Platonists and Arians, I believe that the Son is less perfect than the Father just as the octave is less perfect than the unison, and that the Holy Spirit is less perfect than the Father and the Son just as the fifteenth is less perfect than the unison and the octave.45 On the contrary, because the octave 42. See chap. 2, above. Here the term takes on a theological resonance of cosmic dimensions. 43. This last reference is to the Incarnation. 44. The first part of this sentence paraphrases the affirmations of the Nicene Creed about the Holy Trinity. The second part presents a brief catechism on Trinitarian doctrine: three persons in one substance or essence. Vicentino knew the doctrine on the Holy Trinity expounded by St. Thomas Aquinas in his Summa theologiae, la.29.4. This is not surprising, since Thomistic dogma was the standard explanation of the revelatory operation of the Holy Trinity. For example, The Catechism of the Council of Trent, also called Roman Catechism (Rome, 1566), 1.2.10. 45. The association of Platonists with Arians in the heretical belief that Christ was superior to the Holy Spirit but inferior to God comes directly from the Summa theologiae (la.32.1)

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precedes the fifteenth with respect to the unison, just as the Son precedes the Holy Spirit with respect to Father, I affirm that the unison is first before the octave and the fifteenth. Likewise, the Father is first before the Son and the Holy Spirit.46 First is not to be taken to mean a temporal sequence but rather the distribution existing in the incomprehensible unity of three persons in which, as Athanasius says [38r], nothing is before nor after but all is coeternal.47 As to the second point, the being of all creation in God can be shown with these consonances. Universal creation is divided into two universal parts, that is to say, incorporeal and corporeal.48 The incorporeal com prises the angels, or intelligences, and the rational animals. The corporeal comprises the celestial bodies and the elements. Just as the octave and the fifteenth are in the unison—rather like trees, trunks, branches, flowers, leaves, and fruit are in the seed, or effects in the cause49—so in God is the incorporeal creature that I mean to signify by the octave and the corporeal creature that I mean by the fifteenth. By the great difference existing between the nobility and perfection of the unison, as opposed to the octave and fifteenth, I mean the infinite and totally inestimable difference existing between the nobility and perfection of God as opposed to any creature whatsoever. By the difference between the octave and the fifteenth, I mean the great difference existing between the nobility of the incorporeal creature as opposed to the corporeal. As to the third point [the unity of all creation], there are three creatures in general according another division: incorporeal, incorruptible corporeal, and corruptible corporeal. Just as a woman is called beautiful not because she is simply beautiful but rather in comparison to other less beautiful women, so the incorporeal creature may be called one not because it is simply one but rather in comparison to other creatures that are less integrated than it. Thus, whoever wishes to denote with some sort of example the intrinsic union, beauty, and concord that creatures possess, of St. Thomas Aquinas. In his Expositio super librum Boethii De trinitate (3.4) the Angelic Doctor cites St. Augustine as his authority (De civitate Dei contrapaganos, 10.24). 46. Quicumque vult (The Creed of St. Athanasius), 21-23. This creed was recited every Sunday at Prime until 1965, after which it has been reserved for Prime on the feast of the Holy Trinity. St. Athanasius, the leader of the struggle against the Arians, is no longer thought to be the author of the creed named after him. 47. Quicumque vult, 25-26. 48. For instance, Cicero, "Somnium Scipionis" (Rk. VI of De republica], 4.3; Macrobius, In somnium Scipionis, 1.17.19; St. Thomas Aquinas, Summa theologiae, la.65.1-3, 66.2-4, and 70.1. 49. For example, St. Thomas Aquinas, Summa theologiae, la.46.1, 104.1, and 105.1.

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let him consider the intrinsic union and unisonance possessed by the unison, octave, and fifteenth. Let him imagine that the incorporeal creature is the unison, the incorruptible corporeal the octave, and the corruptible corporeal the fifteenth. Let him also imagine that these three pitches sing together like three flutes that receive breath from the mouth of the wisdom of God.50 Then let him declare of his own accord whether the unisonance of the unison with the octave and the fifteenth is as great as this. What intellect can comprehend how great is the unisonance and alliance within that supreme and substantial unison, that unison which comprises incorporeal creation, the heavens, and all the elements? Cer tain it is that the union of the unison, octave, and fifteenth is nothing but a feeble image or shadow of that union. Blessed be the hand that in all things somehow represents all things in order to make them aware of the creator of all things. As to the fourth point—that is, that a creature cannot sustain itself by itself nor accomplish its operations unless it is joined to God—this point is manifestly exemplified by the unisonance under discussion here. For just as eight and fifteen cannot exist without unity,51 nor the octave and the fifteenth without the unison (because the necessary foundation and element of the former is unity and of the latter the unison), so also the octave, or the incorporeal creature, and the fifteenth, or the corporeal creature, can neither exist, sustain themselves, nor accomplish any natural operation without God. And just as the unisonance of the octave and fifteenth without the unison—that is, without that through which each of them becomes nothing less than a unisonant pitch—is imperfect and deficient, whereas with the unison it is perfect and complete, so the operations of any creature whatsoever are imperfect and futile without God, whereas with God they are perfect and complete. Thus we learn that just as a musician wishing to make the finest unisonance will join the octave and fifteenth to the unison, so every man wishing to create truly praiseworthy works must devote himself with the utmost care to conform his octave (or soul) and his fifteenth (or body) to that eternal unison that is 50. Vicentino's analogy is based on the sapiential myth of a personified Wisdom who proceeded from God at the beginning of time, who is associated with the act of creation. For instance, Psalm 103/104:24; Proverbs 3:19-20 and 8:22-31; Job 28:23-27; Baruch 3:2735; Ecclesiasticus 1:1-10 and 24:1-7 (especially 24:3: "I came forth from the mouth of the Most High"). Wisdom was traditionally interpreted as the Holy Spirit insofar as the third person of the Holy Trinity was said to be produced by spiration, and the Holy Spirit (the Breath) and the Son (the Word) were preexistent with the Father at the Creation. The Catachesis, 1.9.3 and 1.2.23. 51. On unity, one, or the monad, see chaps. 2, 17, and 21, above.

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the will of God.52 This discussion suffices to show the nobility that contains the hidden unisonance of the unison with the octave and the fifteenth.

Chapter 24 On the Minor and Major Tenths and Their Nature, and How They Can Be Composed in Various Ways, with Examples [38v] Some people say that because minor and major tenths correspond at the octave, they have the same nature as minor and major thirds. But in truth it cannot be said that they have the same nature. In my opinion, the pure unaccompanied minor third cannot have the same nature as the minor tenth, for the minor third is the sesquiquintal ratio, that is 6:5, whereas the minor tenth is the supertripartientoctaval, that is 11:8;53 likewise, the major third is the sesquiquartal ratio, whereas the major tenth is the duple-sesquialter ratio [5:2].54 Since thirds are close to the unison and the fifth but tenths are far away from them, how can tenths have a nature similar to thirds? They are dissimilar not only in ratios but also in the distance from the companionship of the unison and the fifth. Readers should know that by nature the minor tenth is weak and it descends easily, for it is more favored by the octave than is the minor third by the unison. The reason is that the octave, formed by the duple ratio, is associated with distance, whereas the unison has no association with distance.55 Consequently, tenths are more potent than thirds. It follows that the major tenth is very lively compared the major third, and it ascends easily. I show how tenths may be composed in various ways with the usual examples [example 24]. Even though the arrangements of the steps and leaps of the tenth are similar to those of thirds, the intervals are not similar in nature, as I said, for pure thirds near the unison seem impoverished in harmony, whereas tenths close to the octave sound better and richer in harmony than thirds. In conclusion, tenths and thirds are similar neither in ratios, nor in proximity, nor in harmony.

52. For example, Clement of Alexandria, An Exhortation to the Greeks, 1.5.1 and 5.3, and 12.120.4. 53. Vicentino is wrong. The minor tenth is 12:5, the duple-superbipartientquintal. 54. The major tenth belongs to the class of duple superparticular ratios. 55. See chap. 2, above.

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Example 24 How Major and Minor Tenths May Be Composed in Various Ways

Chapter 25 On the Twelfth and Its Nature, with Examples In the preceding chapter I discussed imperfect consonances beyond the octave, that is to say, the minor and major tenth. I should now talk about the nature of the twelfth, a perfect consonance. I aver that the twelfth is not like the fifth (as some people think), for the twelfth is in the triple ratio [3:1], whereas the fifth is in the sesquialter. The fifth is much more sonorous than the twelfth even though the latter [39r] is favored by the octave. For such a full harmony is perceived in the fifth that no other consonance can surpass it in plenitude or in aural nourishment.56 Moreover, it is possible to adduce another reason why the twelfth is not similar to the fifth: when calculating and locating the harmonic mean between two extremes, you always find that within the duple ratio comes the sesquialter, which is the fifth within the octave; but within the quadruple ratio [4:1] you find the duple-sesquialter, which in practice is called the major tenth within the fifteenth. Thus, in calculating the harmonic mean within the octave you find the fifth, whereas within the fifteenth you find the tenth. Where the twelfth should have been there appears the tenth.57 How then can these intervals be similar if their ratios 56. See chaps. 7 and 16, above. 57. The harmonic mean within the fifteenth is the major sixth (8:5), not the major tenth (5:2). Vicentino is wrong in calculating from the top instead of the bottom note.

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are different and if the fifth is the harmonic mean within the octave but the tenth is the harmonic mean within the fifteenth? How can the twelfth be similar to the fifth since they correspond at the octave but not in their natures or their ratios? Example 25 shows some of the ways you may compose the twelfth. The evidence pertaining to the fifth is also relevant to the twelfth, even though on account of the distance certain unsuitable differences arise. My examples are for four voices, so that readers may better examine the nature of the twelfth apart from practice.

Examples 25.1-25.5 [The Twelfth] Example 25.1 has an excellent effect because the fifth is above the octave with the major third in between, which sounds good. Example 25.2 does not sound bad because the double octave appears over the fifth. Example 25.3 is not as good as examples 25.1 and 25.2, since it is not so well proportioned and therefore sounds insipid. Example 25.4 is fairly good, since the double octave is over the fifth. Example 25.5 fails to have a good effect, all the more so because the double octave is above the major third. When the twelfth is accompanied by the minor third with the double octave above, the effect is worse. I have offered ample information on the minor and major tenth to everyone so that composers will take great care with the companion notes allocated to these consonances—that is to say, between them—and acquire experience with both kinds.

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Chapter 26 On Major and Minor Thirteenths and Their Nature, with Examples™ The ratios of the major and minor thirteenth are not the same as those of the major and minor sixth. The major sixth is the superbipartienttertial ratio, as in 5:3, whereas the major thirteenth is the triple-sesquitertial, as in 10:3. [The minor sixth is the supertripartientquintal, as in 8:5], but the minor [thirteenth] is the [39v] supersexcupartienttridecimal, as in 19:13.59 Thus, it is clear that their ratios are not the same, and their natures therefore cannot be compared. It seems that the distance from the unison and the octave causes the nature and harmony of consonances to change, as experience on the archicembalo and even in singing will show. I offer no examples of these intervals. However, you should follow the method and arrangement for minor and major sixths [chapters 19 and 20] and apply to major and minor thirteenths whatever appears in the chapter on major and minor sixths [chapter 21]. From the latter you will learn how to accompany steps and leaps, according to the information I have already given for both kinds of examples.

Chapter 27 On the Fifteenth and Twenty-Second and Their Nature, with Examples The octave, of which I have spoken earlier, produces such unity that its two pitches seem to be one voice. The fifteenth does the same, but it appears to be more lively and cheerful than the octave because the higher unisonances60 or consonances present more cheerfulness and vivacity to the listener. But when they are lower, they produce a sadder harmony. When a composer writes three well-integrated octaves one on top of the other, either for instruments or for voices, these octaves seem to be one and the same voice, since they are similar in nature and unity even though their ratios are different. This arrangement must be followed in composing: never make two consecutive fifteenths or twenty-seconds, ascending or descending, either by step or by leap, because these most perfect intervals are like the octave, as is evident in example 27.

58. There are no examples. Vicentino refers the reader back to chaps. 19 and 20. 59. Once again, Vicentino is wrong. See note 53, above. The minor thirteenth is formed by the 16:5 ratio, which belongs to the triple-superbipartient class. 60. See chaps. 2 and 23, above.

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Example 27 The Fifteenth and Twenty-Second for Three and Four Voices

Chapter 28 Many Illustrations of the Two-Note Step Called in Practice Mi-Re and Re-Mi; Also of the Fa-Sol and Sol-Fa Step Placed Above and Below Even though I have already explained and demonstrated with examples the steps of the whole tone and their nature [Book I, chapters 21-24], I shall not refrain from discussing four steps of the whole tone that are rather difficult to accompany. Because these steps generate two similar consonances among the imperfect ones,61 I have gathered together numerous illustrations of them. These examples are useful to composers, who will not only learn to employ various consonances, either steps or leaps, above or below these steps, but also will know when to use them for good or baleful words and thus how to compose good or bad accompaniments according to the circumstances of the subject.

61. For a discussion of similar imperfect consonances, see chap. 17, above.

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Example 28.1 Many Illustrations Below and Above the Two Notes Mi-Re

Example 28.2

Many Illustrations Below and Above the Two Notes Re-Mi

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Example 28.3 Many Illustrations Below and Above the Two Notes Fa-Sol [4lr] Sixteen62 illustrations of mi-re and nineteen of re-mi as well as twenty-two of fa-sol and twenty-seven63 of sol-fa have been given. I provided these numerous examples so that students can more easily achieve an understanding of the practice of these steps and leaps.

62. Misprint: text has tredici. 63. Misprint: text has 30.

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Example 28.4 Many Illustrations Below and Above the Two Notes Sol-Fa

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Chapter 29 On Various Steps and Leaps Placed Above and Below, Ascending and Descending Together It is just as useful as it is necessary to demonstrate two parts, one making steps and the other leaps. Although the nature of all steps and leaps have

Example 29 Many Examples of Various Leaps, Above and Below, Ascending and Descending Together with Steps

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been described in "Book I on Music Practice," pupils will be more motivated now by examples of steps and leaps accompanied by consonances than by pure unaccompanied examples without any consonances. I was therefore prompted to collect many steps matched with leaps, so that with experience students could distinguish the good, the better, and the bad step or leap, either well or badly accompanied, as seen in example 29.

Chapter 30 Many Illustrations of Various Leaps When Two Parts Leap Together [4lv] In the preceding chapter I gave thirty-three examples of one part moving by step and the other by leap. I shall now demonstrate two parts leaping at the same time. Even though the same leaps and steps were shown in other places with respect to other consonances or another argument, these repetitions should annoy no one except he who writes them. I have done this so you may observe the orderly arrangement of the steps and leaps, how they may be better composed with consonances and unisonances, and which of them are weak, which good, and which bad. When I give the numbers 2, 3, 4, 5, 6, or higher, it is to be understood always that such leaps, steps, and consonances are not good for any number of voices lower than the given number, though good for any higher number. Thus, when I indicate that a particular step, leap, or consonance is good for three voices, it is not good for two voices, and so on through the sequence. When you are composing sacred material, such as motets and masses or other such things, the illustrations in example 30 are to be seen as acceptable.

Example 30.1

Two Parts That Leap Together

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Example 30.2 Two Parts That Leap Together

Example 30.3 Two Parts That Leap Together [42r] I did not select leaps that jump the same distance of three steps up or down, four steps up or down, and five steps up or down, for few of them go the same distance in either direction, except in the case of imperfect consonances. However, those going from an imperfect to a perfect consonance, or vice versa, cannot move the identical distance. The greatest possible difficulty facing a composer is that of distinguishing good from bad leaps—that is to say, well and badly accompanied leaps— in order to know how best to accommodate steps and leaps that move from imperfect to perfect consonances. Movement from perfect to im-

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Example 30.4 Two Parts Notated as Tenor and Bass, Soprano and Bass, and Tenor and Bass perfect consonances is not very important, except when the words prompt you to make various strange steps and leaps. Therefore, all good and bad steps and leaps are good when they create tense and slack effects because they are relevant to the words. I have provided forty-eight64 different illustrations in example 30 of different leaps matched with consonances, so that pupils will learn enough about them. Even though they have received previous information about which leaps are tense, slack, and pure, leaps accompanied by consonances are nonetheless very useful. Composers are advised that in composition there are three ways of leaping. The first occurs when the two parts leap upward. Regarding such parts, it is crucial to point out that when leaps are badly arranged and out of place—without being necessitated by the words—they are much more prominent going up than going down. The second is when both parts leap downward. If any poorly placed consonance occurs in this method, it does not make as much noise as does an ascending one. The third and last way occurs when one part leaps up and the other down. This way does not frequently entail either bad effects or passages that are difficult to accompany. To conclude, the composer who takes heed of these examples and of his own experiments with tense and slack leaps will write fine compositions.

64. Misprint: text has 46.

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Chapter 31 On Motion and Its Nature, and on How Many Ways Motion May Be Used in Composition, with Examples Motion is extremely important in compositions, for it is so potent that it transforms the nature of steps, consonances, words, and instruments. A composition lacking the pace appropriate to the subject of the words or the design of other ideas will not gratify listeners, for it will seem to have been made without care and judgment. The chapters on various compositions in Book IV cover the topic of motion—when, how, and what sort of motion should be used [chapters 9, 14, 15, 20, 26, 27, and 29]. Motion in eight note-values occurs in compositions [42v]. The first motion is represented by the maxim shape, |, and it is called very slow motion. The second motion is called slow when composers present the shape that is named long, ^. The third is called natural motion, for it is neither fast nor slow, like the pace of the breve, H. The fourth is called average motion, and it is represented by the semibreve, O. The fifth, represented by the minim, ^, is above average. The sixth, represented by the semiminim, ^, is called quick motion. The seventh is called rapid motion, and it is represented by the shape named croma, |. The eighth and last motion occurs with the shape semicroma, R, and it is called very rapid motion. These then are the eight note-values and the eight rates of motion used in music practice. If a composer puts into practice tense and slack steps and leaps matched with tense and slack consonances, following all the above rules of motion according to each subject, and if all these elements are well coordinated, then his composition will be among the best and rarest works that could be composed and heard. End of Book II on Music Practice

Book III on Music Practice

Chapter 1 Proem [43r] Many celebrated musicians have recorded many rules for music, and almost all have discussed the composition of fourths, fifths, and octaves, as well as how the modes or "tones" (as practitioners call them) are collocated out of these intervals. Nevertheless, I shall not refrain from speaking about some matters already discussed by our predecessors, even though in the Proem to the first book I promised not to write down published rules.1 In this regard I am certain I shall not be reproved by good practitioners if I restate the occasional known item. Since I shall talk about the formation of the modes and their nature, I may be forced from time to time to repeat something that has been already discussed by some other person pertaining to the modes and their formation. I shall talk about fourths, fifths, and octaves, in keeping with their systematic exposition, and then about whatever remains to be said. I also expect to speak about the modes, as well as about a few that I have added to them, something no one else—neither Boethius nor any other philosopher— has ever done, either with examples or with annotations. In this book I discuss the formation of fourths, fifths, and octaves, out of which are formed the eight modes or tones. I shall also discuss the modes used in measured polyphony to compose in the hard and soft hexachords.2 In addition, I shall talk about the modes notated with three and four flats with their cadences as they have been used up to now, a procedure practitioners call writing in feigned music. After these modes, there appear twenty-four newly recorded modes, published by me, along with the formation of their fourths, fifths, and octaves, and an explanation with examples inspired by the music in use up to this day. I shall not forget to talk about which diatonic modes are pure, which are mixed with some large parts and some species of the three genera,3 and which are the eight pure chromatic modes. Nor will I omit the eight enharmonic modes, both pure and mixed, showing how they are comprised of their fourths, fifths, and octaves, with their notational features. There also appear seven different kinds of examples of compositions for four and l.Bk. I, chap. 1. 2. See Bk. I, note 22. 3. Mixed diatonic modes, which include major and minor thirds and minor semitones, create what Vicentino calls tempered music. See Bk. I, note 49.

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five voices. I shall discuss which steps are movable or stationary and which are neither completely movable nor completely stationary. I have aspired to write about and explain all these topics as simply as possible, with examples and reasons to instruct the students of our profession.

Chapter 2 Demonstration and Explanation of the Three Composite and Incomposite Diatonic Fourths The first persons to ponder how they might accommodate the semitone in the natural fourth realized that it is possible to situate the semitone in not more than three ways: at the beginning, in the middle, and at the end of the fourth. This positioning of the semitone generates three arrangements of fourths. Among practitioners of music, the first arrangement is as follows: the semitone is placed in the middle of the fourth. In the second arrangement, the semitone is written in the beginning of the fourth. The third [43v] arrangement shows the semitone at the end of the fourth. 4 These can be observed in example 2, which shows all the fourths in sequence, both composite and incomposite.

Example 2 The Three Composite and Incomposite Diatonic Fourths

Chapter 3 Demonstration and Explanation of the Three Composite and Incomposite Diatonic Fifths There are four natural fifths, and they differ because of the placement of the semitone in various locations, as in the formation of the fourth. According to practitioners of music, the first species of the first fifth occurs when the semitone is put on the second step of the ascending fifth. The second species of fifth occurs when the semitone is written at the beginning of the fifth. The third arrangement of fifth is seen with the semitone at the end of the ascending fifth. The fourth species of fifth is governed by the semitone written on the third step of the fifth.5 Example 3 helps you understand the sequence of the four fifths. 4. See Bk. I, chap. 32. 5. See Bk. I, chap. 39.

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Example 3 The Four Composite and Incomposite Diatonic Fifths

Chapter 4 Demonstration and Explanation of the Seven Composite and Incomposite Diatonic Octaves In the preceding chapters I discussed the three fourths and four fifths that, when joined together, form the seven octaves. The following arrangement defines the first octave: it derives its beginning and creation from the first fourth and first fifth; these, when placed together, create the first species of the first octave. This species is the start of the second order of the hand, called by music practitioners A re or the lowest A la mi re, and ascends through the steps of one octave.6 In composite form, the steps create the first arrangement out of the first species of the first octave composed, as explained above, of the first fourth and first fifth. A better understanding of these octaves may be had from example 4. The [44r] second octave begins on B mi in the hard hexachord or the lowest B fa ^ mi. It ascends through one octave up to the low B fa B mi, with the second fourth placed below the second fifth to form the second octave. The third octave is formed by the third and last fourth plus the third fifth. It ascends through eight pitches up to C sol fa ut, with the third fourth below the third fifth to form the third octave in the same way as the other two described above. The fourth octave is formed by the fourth fifth.7 But because there are no more than three fourths and four fifths in the arrangement of fourths and fifths, it is necessary to go back and choose the above-mentioned 6. See Bk. I, ex. 5.1. 7. This statement contradicts the ensuing analysis of the fourth octave. Yicentino s syntax is often careless; he may have meant to say, "The fourth octave should be formed by the fourth fifth." His description of the seven octave-species follows tradition. Still, his most likely source was Gaffurio's Practica musicae, Bk. I, chap. 7. Vicentino reproduced the octave-species as described by Boethius (De inst. mus., 4.14) in the "Music Theory," chap. 11. Hence the confusion evident in chapter 12, below; see note 24, below.

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fourths and place them above the fifths in order to form the remaining octaves. Thus, to form the fourth octave, you place the first fourth over the first fifth. The fourth octave begins on D sol re and ascends stepwise through the pitches up to D la sol re. The fifth octave is formed by the second fifth with the second fourth placed over it, beginning on the low E la mi and ascending through eight pitches up to the high E la mi. It is in this way that the formation of the fifth octave is discovered. The sixth is formed by the third fifth with the third fourth placed over it, as in the preceding arrangement. These intervals form the sixth octave, beginning on the low F fa ut and ascending through eight pitches up to the high F fa ut. The seventh and last octave is the highest. It is formed by going back and choosing the first fourth and then placing it over the fourth fifth, which begins on G sol re ut. These two intervals create the seventh octave.

Example 4 The Seven Composite and Incomposite Octaves Thus, in the octave arrangements of all diatonic music, there are no more than three fourths, four fifths, and seven octaves—all of them natural—even though some people would like to form other sorts of octaves, fourths, and fifths.8 But because they are composed of the tritone and diminished fifth, such octaves, fourths, and fifths are not accurate. I do 8. This paragraph is one of three puzzling references to the system of twelve modes put forward by Glarean in the Dodekachordon. The other two occur in chaps. 23 and 49, below. Vicentino was conversant with the number of added modes and had a notion, however mistaken, that Glarean's method entailed coming to terms with the false fourths and fifths in the F-f and B-b octaves. Glarean of course rejected the arithmetic and harmonic divisions in these octaves, thus reducing the practicable number of modes from fourteen to twelve

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not wish to speak at length about these intervals, for others have dealt with them. True, some people say there are four other kinds of modes or tones, making a total of twelve altogether. But inasmuch as these are formed by false fourths and fifths, I shall not discuss them now. I can omit them for the moment, since they have been described by others, as I said above. Example 4 will help students understand the octaves better.

Chapter 5 Explanation of the Eight Pure Diatonic Modesy First of the First Mode and Its Nature, with an Example [44v] As was demonstrated in the preceding chapter, the formation of the three fourths combined with the four fifths produced seven octaves. Just as these fourths and fifths were the causes of the formation of the seven octaves, so from the seven octaves is derived the formation of the eight modes. These modes produce various effects on listeners9 depending on the diverse placement of the semitones. The first mode is formed by the fourth octave,10 and therefore it frequently uses the extremes of its fifth and fourth by step or leap in order always to stay within its boundaries. When fourths, fifths, and octaves of another mode are mixed with it, they create among themselves a certain diversity and thus change the goal and nature of the manner of singing. When a composer wishes to retain the exact extremes of each of the eight pure diatonic modes, he should write them in keeping with their natures without adding to them other fourths and fifths that do not belong to the pure mode itself. As for the modes composed with other parts of other genera, I shall discuss them in the appropriate chapters [15, 18, 23, and 32]. The first mode, then, is of an agreeable and devout nature, and it seems more virtuous than wanton. This mode was very honored by the Dorian people who sang their songs in praise of great deeds in it. For this reason Boethius and other philosophers called it the Dorian mode after this people.11 (Bk. II, chaps. 5-7). See Bk. Ill, chaps. 14 and 21, and Bk. II, chaps. 18 and 25. As is clear from the examples in chap. 23, below, Vicentino knows how to construct Glarean's Ionian and Aeolian modes (see note 38, below), but somehow in the text he confuses them with the illegitimate modes that contain false fourths and fifths. 9. Aristotle mentions this idea with respect to harmoniae or tonoi in Pol., 8.5.1340a-b. 10. Error: text has prima ottava. 11. Boethius does not give the ethnic derivation of the Dorian mode, although he mentions the Lydian and Phrygian in this context (De inst. mus., 1.1). Gaffurio, on the other

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In our practice it is called the first mode, even though up to now there has been scarcely a single plainchant that is truly diatonic. The reason is that all plainchants and all measured polyphony have revealed themselves to be mixed with the fourths and fifths of other modes as well as with the larger parts of the other genera.12 Still, in the examples these are shown in their pure form with their extremes ascending and descending to the octave. Some people, however, insist that the first mode may descend one pitch below its beginning note, thus containing, from one extreme to the other, nine pitches in all. The reason, they say, is that just as the numbers eight and nine generate the whole tone called in practice ut-re, re-mi, fa-sol, and sol-la, so the tone or mode may contain between its extremes either eight or nine pitches.13 This reasoning pleases me, although when the mode reaches the ninth pitch it seems to exceed its proper limits. The first pure diatonic mode is notated in example 5.

Example 5 The First Pure Diatonic Mode, Called Dorian by the Greeks

Chapter 6 Explanation of the Second Pure Diatonic Mode and Its Nature, with an Example The second mode is akin in nature to the first, the only difference being that the first is more cheerful, whereas the second possesses more modesty because the fourth is below the fifth. Such modes make a stronger effect in compositions for four voices than in their pure form. Moreover, they exhibit their nature better when [45r] mixed with the large and small parts of the other genera14 rather than in the diatonic genus hand, refers specifically to the Dorian people, along with the Phrygian and Lydian (Practica musicae, Bk. I, chap. 7). Of course, the Dorian described by Boethius was not the same as the Dorian in the eight church modes. Just as Gaffurio overlooked this inconvenient fact, so did Vicentino. The nomenclature of exx. 5-12 in Bk. Ill, fancifully attributed to the ancient Greeks, embroiders the contemporary misconception of the modes. 12. The larger parts are the minor third and major third, from the chromatic and enharmonic genera, respectively. See Bk. I, note 49. 13. In elaborating a minor point made by Gaffurio, Vicentino distorts the main point of his source, namely, that it is possible to add a whole tone below the final in the Dorian and Mixolydian modes and a semitone below the final of the Lydian (Practica musicae, Bk. I, chap. 8). 14. As was said earlier, the large parts are the thirds in the chromatic and enharmonic genera. The small parts are the minor semitones and dieses of these genera. See Bk. I, note 49.

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unmixed with the other genera. The second pure diatonic mode is placed opposite the first because it has the fifth below the fourth. The ancient philosophers called it Hypodorian mode, that is, placed below the Dorian, solely on account of the difference of the fourth, as I said above.15 In fact, example 6 demonstrates this mode.

Example 6 The Second Pure Diatonic Mode, Called Hypodorian by the Greeks

Chapter 7 Explanation of the Third Pure Diatonic Mode and Its Nature, with an Example In the preceding chapter I discussed the second mode. Now I should talk about the third mode and how it is to be written in its pure form. I should also state that practitioners of music have called the first mode authentic, the second plagal, the third authentic, the fourth plagal, the fifth authentic, the sixth plagal, the seventh authentic, and the eighth plagal. All the authentic modes ascend first with their fifth and then above that with their fourth, whereas all the plagal modes have their fourth below their fifth. This arrangement pertains to all eight modes. The third mode is cheerful by nature when composed for four voices with a mixture of all the genera.16 But the pure diatonic mode shows little cheerfulness, for it is alone and bereft of any company. Example 7 shows its melodic contour with the terminal notes of its fourth and fifth. Philosophers called this mode Phrygian, from the Trojans who sang in this mode.17

Example 7 The Third Pure Diatonic Mode, Called Phrygian by the Greeks

15. For example, Gaffurio, Practica musicae, Bk. I, chap. 7. 16. See Bk. I, note 49. 17. For example, Boethius, De inst. mus., 1.1, and Gaffurio, Practica musicae, Bk. I, chap. 7, although neither mentions the Trojans. In the Aeneid Virgil repeatedly refers to Troy as being located in Phrygia and to Aeneas as a Phrygian. Also Isidore, Etymologiarum sive originum libriXX, 14.3.

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Chapter 8 Explanation of the Fourth Pure Diatonic Mode and Its Nature, with an Example I have discussed the third authentic mode. Its plagal is the fourth mode, which is sad. It is more funereal when accompanied by four voices than by itself. Composers are advised that composed modes18 should have as companions sad consonances if the modes are sad but cheerful consonances if they are cheerful. Moreover, the words should be well matched with the nature of the modes. Let us leave this discussion now and turn to the composition of the fourth mode. I point out that its fourth is below its fifth, descending and ascending. [45v] Philosophers called this mode Hypophrygian, that is, placed below the Phrygian.19 It is illustrated in example 8.

Example 8 The Fourth Pure Diatonic Mode, Called Hypophrygian by the Greeks

Chapter 9 Explanation of the Fifth Pure Diatonic Mode and Its Nature, with an Example It now behooves me to talk about the nature of the fifth mode, which shows itself to be haughty and cheerful. Philosophers called it Lydian from the nature of the ferocious and prideful Lydian people.20 This mode has its fourth above its fifth. Along with the Dorian and Phrygian, the Lydian was greatly honored by ancient philosophers. There can be no doubt that this mode is capable of demonstrating its nature in its pure and its accompanied form. Example 9 illustrates the Lydian mode.

Example 9 The Fifth Pure Diatonic Mode, Called Lydian by the Greeks 18. That is to say, modes used in polyphony. 19. Probably Gaffurio, Practica musicae, Bk. I, chap. 7. 20. For instance, Boethius, De inst. mus., 1.1, and Gaffurio, Practica musicae, Bk. I, chap. 7. Neither source singles out the Lydians as a particularly fierce people. As Vicentino says below, on the authority of Gaffurio, the Lydian was one of three modes celebrated by the ancients. Gaffurio gives as the reason the appropriateness of the Lydian to vehement affections of the soul. Perhaps Vicentino had in mind the Asiatic origin of the Lydian mode and its first use by Olympus as the auletic funeral nomos on the death of the Python, as described in Pseudo-Plutarch, On Music, 15.1136c.

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Chapter 10 Explanation of the Sixth Pure Diatonic Mode and Its Nature, with an Example The philosophers who arrange the authentics and plagals two by two do not leave the sixth as an odd mode, for it is called Hypolydian, that is, placed below the Lydian.21 Although the plagal is somewhat sadder than the authentic, nevertheless, the sixth mode is still relatively cheerful and ferocious. Its composition placed the fourth below the fifth. Example 10 shows it to everyone.

Example 10 The Sixth Pure Diatonic Mode, Called Hypolydian by the Greeks

Chapter 11 Explanation of the Seventh Pure Diatonic Mode and Its Nature The seventh mode is the one that has its fourth over its fifth, and this fourth is borrowed from the first mode to go with the fourth fifth. This mode is very cheerful and rather haughty. Philosophers called it Mixolydian.22 It is the highest of the authentic modes. Example 11 gives it in notation.

Example 11 The Seventh Pure Diatonic Mode, Called Mixolydian by the Greeks

Chapter 12 Explanation of the Eighth Pure Diatonic Mode and Its Nature [46r] Many times nature is deficient in some things, which can be replaced by means of the natural talent of mankind for using the accident.23 In ancient times there were only seven modes in music practice. Ptolemy, more shrewd, noticed that there were three fourths and four fifths and that three of the fifths matched with the three fourths above and below, the fourth fifth being matched only by a fourth above but 21. Probably Gaffurio, Practica musicae, Bk. I, chap. 7. 22. Gaffurio, Practica musicae, Bk. I, chap. 7. 23. On nature and accidents, see Bk. I, note 91; also Bk. I, chap. 23.

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none below. Ptolemy matched the same fourth above the fifth by placing it below that interval. He thus made up the eighth mode, which was later called Hypermixolydian, that is, placed below the Mixolydian.24 This eighth mode is by nature quite lively as well as pious. It was not used by ancient musicians, as stated by Boethius in Book IV, chapter 16, of his Fundamentals of Music,25 because it was added by Ptolemy, as I said before. Its melodic contour and nature have a better effect accompanied by four voices than in pure form. Example 12 shows how it goes purely.

Example 12

The Eighth Pure Diatonic Mode, Called Hypermixolydian by the Greeks

Chapter 13 Explanation of the Three Fourths, Four Fifths, and Seven Diatonic Octaves Composed in the Soft Hexachordy and How to Name Correctly the Two Letters B-Natural and B-Flat Even though fourths and fifths may be written with a flat in the key signature, they are nonetheless of the same nature as those written with a natural. When a student names these two "B" letters, and says "natural B" for the one, he must say for the other "flat B." But when he calls the round B "flat B," he must call the square B "hard B," though it would be better to say "raised B." Let us look at the fourths, fifths, and octaves in example 13. Although they are written with a flat, the ear distinguishes no transmutation from B-natural to B-flat, because no other alteration of the steps occurs in the melodic contour. It is only to the eye that the singing is transmuted, that is, lowered a minor semitone down from B-natural to B-flat. Such a composition cannot be called chromatic music, for it lacks any transmutation from the beginning to the end. On the other hand, it may truly be called chromatic transposition, that is to say, a change from B-natural [46v] to B-flat. Example 13 demonstrates this transposition so that pupils may more easily write it either way. 24. Not only does Vicentino fail to notice that Hypermixolydian means "above the Lydian," but he also fabricates an explanation, which he attributes to Ptolemy, for the composition of the eighth mode. The ordering of the modes with the eighth given as the Hypermixolydian follows Gaffurio (Practica musicae, Bk. I, chap. 7), though Gaffurio changes the name to Hypomixolydian toward the end of his chapter. 25. Bower translation (New Haven, 1989), Bk. 4, chap. 17.

Example 13.1 The Three Composite and Incomposite Diatonic Fourths with a B-Flat

Example 13.2 The Four Composite and Incomposite Diatonic Fifths with a B-Flat

Example 13.3 The Seven Composite and Incomposite Diatonic Octaves with a B-Flat

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Chapter 14 Illustration of the Three Fourths and Four Fifths Written with Four Flats and of the Seven Octaves Commonly26 Called Feigned Music, with Examples Written Diatonically; Also an Easy Method of Raising and Lowering a Composition by a Whole Tone or a Semitone Some people fail to recognize that music written with four flats27 is the same as that written in the hard and soft hexachords. The invention of this notation was occasioned solely by the need to show where the hard hexachord could be played on the organ. To enable a performer to play a minor semitone lower for the choir's needs, the melody has been notated with a [47r] flat. Since voices are unstable, it often happens that the choir will lower the pitch sung at the beginning by a semitone as they proceed toward the end. And later, when the singers reach the end, they sometimes go down a whole tone. So that pupils may know how to play compositions a whole tone lower, the music is written with four flats. Thus, with these rules, a student can lower any sort of composition by a minor semitone or a whole tone whenever the song is written in the hard hexachord. Likewise, whenever it is written with four flats, he may also raise it by a whole tone or a minor semitone, for the melodic contour will remain the same. If a student wishes to find the species of the fourth and fifth when the song is in the hard hexachord, he can raise it a fourth to locate the exact fourths and fifths; when the song is then in the soft hexachord and he lowers it a fifth, the species of the fourth and fifth will be one whole tone below the level of the fifths and fourths in the hard hexachord. So, by going up a fourth and down a fifth, players will find that the melodic contour of the fourths and fifths is always identical on ordinary instruments.28 But my archicembalo is more useful. I have offered these few words not only to advise players but also to make novices understand this system. As for the fourths, fifths, and octaves written with four flats, they are shown in example 14.29 26. Instead of dal vulgo, the original table of contents has daprattici. 27. As ex. 14 demonstrates, the key signature involves three flats, one of which is duplicated; which flat is duplicated depends on the clef. 28. Although the general drift of Vicentino's notion of transposition is clear, the details of his method are incorrect. First, the addition of one flat (which lowers B by one minor semitone) does not transpose a melody down a semitone; rather it raises it up a fourth. The subsequent lowering by a fifth from the transposed pitch does bring the melody one whole tone below its original level, as Vicentino states. However, one must add one, not two, flats to the key signature. In other words, Vicentino has missed one step in the circle of fifths. 29. In ex. 14, one flat is always duplicated to cover a pitch with two locations on the staff. In the alto or tenor clef, this pitch is Ek. In the treble clef, it is A1*.

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Example 14.1 The Three Pure Diatonic Fourths Written with Four Flats

Example 14.2 The Four Pure Diatonic Fifths Written with Four Flats

Example 14.3 The Seven Pure Diatonic Octaves Written with Four Flats [47v] Earlier I demonstrated how the eight modes are derived from the seven octaves and how the latter are created from the three fourths and the four fifths in the diatonic disposition, even though they can be written in three ways: in the hard hexachord, in the soft hexachord, and with four flats. I also discussed the alteration of notation, so-called feigned music. And yet it should not be called feigned music but rather feigned transposition, for music notated with four flats seems to the eye to be completely altered by the notation, whereas the ear discerns no difference between music with and without flats, as I said in Chapter 13. Lest

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anyone call a composition notated with four flats chromatic music, I have already explained in Book I what chromatic music is—namely, the transmutation perceived when we first hear a whole tone that is subsequently altered into a semitone, or vice versa, effected by the chromatic species and the lack of movement through the natural steps [chapters 7, 10, and 12]. About all this I have already said enough. There remains the discussion of plainchants. However, these rules have been published and rehashed many times by many persons. I shall therefore omit them and turn instead to the ordering of the eight tones, or modes, and to how their limits are used in polyphonic music in three ways: in the hard hexachord, in the soft hexachord, and with four flats, the latter called feigned music.

Chapter 15 Explanation of the First Mode of Tempered and Mixed Music Written in the Hard and Soft Hexachords, with an Example in Feigned Music The most important foundation a composer must have in mind is this: he should consider what he plans to build his composition on, in keeping with the words, be they sacred or on another subject. The foundation of this building is the selection of a tone or mode suitable to the words or to another idea.30 On that foundation, then, he will use his judgment to measure well and to draw over this good foundation the lines of the fourths and fifths of the chosen mode, which lines are the columns that support the building of the composition and its boundaries. Even though the fourths and fifths of other modes may be placed between them, these do no harm to this edifice when they are disposed and matched gracefully in a few locations in the middle of the work. It is with such architectural variety that composers adorn the building of their composition, as do good architects, who dazzle the vision of men with their refined manner of using the lines of the triangle.31 For with the latter they paint the facade of some lovely palace or other in such a 30. See Bk. II, note 2. 31. Vicentino alludes here to the science of perspective, and a little later he introduces the topic of modeling or shaping by means of color. The visual triangle and the illusion of perspective were discussed by Leone Battista Alberti in the first book of Delia pittura (Venice, 1535-36). On Painting, translation John R. Spenser (New Haven, 1973), pp. 47, 50, and 53, and // trattato della pittura, edited by G. Papini (N.p., 1934), pp. 21, 25, and 32. Vicentino s striking analogy to architectural method was probably inspired by the Hexaemeron, 1.7.25, of St. Ambrose: "Bonus artifex prius fundamentum ponit: postea, fundamento posito,

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way that it seems to the onlooker to be far away from him, though it is not, since it is painted close to the vision of the person looking at such a picture. This illusion conies from knowing how to match colors with lines.32 Moreover, architects often match in one edifice the diverse styles of the structural orders,33 as is shown by the celebrated Vitruvius, who said that the Doric order may be accompanied by the Attic, and the Corinthian by the Ionic.34 They are so well connected and united that, even though the styles are diverse, nonetheless the expert artificer [48r] may use his judgment to construct the edifice and proportion it with various ornaments. Likewise, composers of music may use artifice to make various mixtures of fourths and fifths from other modes and thus to adorn the proportioned composition with a variety of steps according to the effects of the consonances applied to the words. However, composers must always sustain the mode carefully whenever they write sacred works that anticipate the response of choir or organ, such as masses, psalms, hymns, or other responses expecting a reply. There are, moreover, a few other Latin compositions that seek to maintain the design of the mode, whereas other vernacular compositions enjoy great latitude in treating many and diverse passions; for example, sonnets, madrigals, and chansons, which begin cheerfully and then at the end are full of sadness and death, or vice versa. On such words, a composer may forsake the modal order in favor of another mode, for no choir needs to respond to the mode. On the contrary, the composer's sole obligation is to animate the words and, with harmony, to represent their passions— now harsh, now sweet, now cheerful, now sad—in accordance with their subject matter. This is why every bad leap and every poor consonance, depending on their effects, may be used to set the words. As a consequence, on such words you may write any sort of step or harmony, abandon the mode, and govern yourself by the subject matter of the vernacular words, as was said above. aedificationis membra distinguit, et adjungit ornatum" (The good architect first lays the foundation, and after the foundation has been laid, he marks off the parts of the building and then adds the embellishment). 32. See Bk. I, note 55. 33. Throughout the treatise Vicentino uses tono/toni or modo/modi to refer to the church modes. In this passage, modo/modi has the technical meaning of the orders of classical architecture. Just where Vicentino got the idea of using these words to translate from the Latin is not clear. See the introduction. 34. It must be said that Vitruvius did not sanction the indiscriminate mixing of architectural orders and styles. But in the opinion in Vicentino's day, these had been mixed in classical architecture, in particular in Roman antiquity. See the introduction.

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It is now necessary to take up the explanation of the first mode as composers should use it in ordinary music, that is, the style in which all professionals of music compose today. I have described the division of the first mode in [chapter 5]. At this point a discussion of the mixture of modes found in polyphony is very opportune, for it will prove that no composers have observed or observe the mode. Furthermore, their compositions show everybody that they know neither the nature, limits, nor structure of the modes, according to what Boethius wrote. On the authority of many celebrated philosophers, Boethius said in the treatise on the modes in Book IV, chapter 15,35 that these modes should be notated in the diatonic genus. But in the compositions created a long time ago and in those appearing in our times, no one has written either in polyphonic music or in plainchant a melody that observes the order of the diatonic genus. For in these melodies there occur not only the steps of the diatonic genus—that is, whole tones and natural semitones—but also steps of a minor third, which in practice we call mi-sol and re-fa, and leaps of a ditone, which in practice we call ut-mi and fa-la, not to mention that in polyphonic music two whole tones are cut, making a semitone out of a whole tone or a whole tone out of a semitone. The latter species are not diatonic, as was said earlier [Book I, chapters 9-11]. How then can the tones or modes be respected if no composition is written in the diatonic order? For this reason, music of the past and of today ought to be called tempered music, mixed with certain species from all three genera. It is not diatonic music, for the many reasons given above.36 I shall now demonstrate the first mode of tempered and mixed music in three ways: in the hard hexachord, in the soft hexachord, and in feigned music. Example 15 gives some of the main ambits of its fifth and fourth in the lowest part, because this part, as the base and foundation of the structure, supports and preserves the first and second modes, as well as all the others. When getting acquainted with a composition, many composers look at the soprano, from which part they cannot securely judge the mode of the work. Let students first rely on the bass, for in that part there appear the fourths and fifths that form all the modes, as [48v] I said above. From example 15 it is possible to learn better how to form the mode with its boundaries.

35. Bower translation, Bk. 4, chap. 16. 36. See Bk. I, chap. 6.

Example 15.1 The First Mode of Tempered and Mixed Music in the Hard Hexachord in the Octave Below the Normal One

Example 15.2 The First Mode of Tempered and Mixed Music in the Hard Hexachord in the Normal Location

Example 15.3 The First Mode of Tempered and Mixed Music in the Soft Hexachord

Example 15.4 The First Mode of Tempered and Mixed Music, Called Feigned Music by Practitioners

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Chapter 16 Explanation of the Second Mode of Tempered and Mixed Music in the Hard and Soft Hexachords and in Feigned Music Composers are warned that I shall not state how the eight modes of polyphonic music are formed. Their formation was explained in the system of the eight [pure] diatonic modes. Even though many species from the three genera appear in the former, the modes are nonetheless formed with their fourths and fifths in the same way as the latter. I now show how they are composed in the range of the bass part, in example 16.

Example 16.1 The Second Mode of Tempered and Mixed Music in the Hard Hexachord

Example 16.2 The Second Mode of Tempered and Mixed Music in the Soft Hexachord

Example 16.3 The Second Mode in the Soft Hexachord That, for More Variety, Gives the Fifth Below Its Lowest Melodic Range, Which Is D Sol Re

Example 16.4 The Second Mode in Feigned Music, Being Similar to Tempered and Mixed Music

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Chapter 17 Explanation of the Third Mode of Tempered and Mixed Music in the Hard and Soft Hexachords and in Feigned Music, with Examples [49r] It is not necessary to mention that the third mode, being authentic, is cheerful by nature. As always happens in compositions for four or more voices, when the bass recites the authentic mode the tenor presents the plagal; and in reverse, when the bass part sings the plagal the tenor does not omit the authentic. Thus, the authentic and plagal are always together in measured polyphonic music. Example 17 shows the third mode.

Example 17.1 The Third Mode of Tempered and Mixed Music in the Hard Hexachord

Example 17.2 The Third Mode of Tempered and Mixed Music in the Hard Hexachord

Example 17.3

The Third Mode of Tempered and Mixed Music in the Soft Hexachord

Example 17.4 The Third Mode of Tempered and Mixed Music in Feigned Music

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Chapter 18 Explanation of the Fourth Mode of Tempered and Mixed Music in the Hard and Soft Hexachords and in Feigned Music The fourth mode conveys considerable sadness, and when it is sung in the bass part it is very melancholy. Example 18 demonstrate its ranges in various ways. Readers are advised that I notate these short examples only to show a few of the main limits that are to be observed. However, in lengthy compositions you are to proceed with diverse, gracefully placed fourths and fifths from other modes, just as you hear and see them used every day.

Example 18.1 The Fourth Mode of Tempered and Mixed Music in the Hard Hexachord

Example 18.2 The Fourth Mode of Tempered and Mixed Music at the Octave Below its Final in the Hard Hexachord

Example 18.3 The Fourth Mode of Tempered and Mixed Music Without Its Just Fifth, in the Soft Hexachord

Example 18.4 The Fourth Mode of Tempered and Mixed Music, with Its Just Fifth, in the Soft Hexachord with Two37 Flats 37. Error: caption has tre.

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Example 18.5 The Fourth Mode in So-Called Feigned Music

Chapter 19 Explanation of the Fifth Mode of Tempered and Mixed Music in the Hard and Soft Hexachords and in Feigned Music [49v] There is no doubt whatsoever that the fifth mode is cheerful and lively, for within its fifth the ditone lies below the semiditone. This is evident from the main ranges of this mode in example 19.

Example 19.1 The Fifth Mode of Tempered and Mixed Music in the Hard Hexachord

Example 19.2 The Fifth Mode of Tempered and Mixed Music in the Hard Hexachord

Example 19.3 The Fifth Mode of Tempered and Mixed Music in the Soft Hexachord

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Example 19.4 The Fifth Mode of Tempered and Mixed Music in Feigned Music

Chapter 20 Explanation of the Sixth Mode of Tempered and Mixed Music in the Hard and Soft Hexachords and in Feigned Music [50r] The sixth mode is written in various clefs. Its nature is opposite to that of the other plagal modes, for most of them are sad, whereas the sixth mode is cheerful because the ditone is in the lower position within its fifth. This ditone imparts intensity to the first step of this fifth, as can be seen clearly from the ascending and descending limits of the sixth mode in example 20.

Example 20.1 The Sixth Mode of Tempered and Mixed Music in the Hard Hexachord

Example 20.2 The Sixth Mode of Tempered and Mixed Music in the Soft Hexachord

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Example 20.3 The Sixth Mode of Tempered and Mixed Music at the Octave Below Its Final and with the Fifth Below the Final of Its Fourth, in the Soft Hexachord

Example 20.4 The Sixth Mode of Tempered and Mixed Music in the So-Called Feigned Music

Chapter 21 Explanation of the Seventh Mode of Tempered and Mixed Music in the Hard and Soft Hexachords and in Feigned Music Composition would be extremely crude if it observed the limits of the modes completely: that is, in accordance with the composition of the fifths and fourths of the modes. And so for the convenience of writing for many voices and for the sake of a greater variety of pitches, the fifth below the fourth is added to the plagal modes, with the result that the limit of their fourths and fifths is exceeded by a lower fifth. In addition, the octave below the final is added to the authentic modes, to accommodate many more voices than four. The seventh mode is the highest of all, and it is very cheerful. Its limits are shown in Example 21.

Example 21.1 The Seventh Mode of Tempered and Mixed Music in the Hard Hexachord

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Example 21.2 The Seventh Mode of Tempered and Mixed Music in the Hard Hexachord

Example 21.3 The Seventh Mode of Tempered and Mixed Music in the Soft Hexachord

Example 21.4 The Seventh Mode of Tempered and Mixed Music in Feigned Music

Chapter 22 Explanation of the Eighth Mode ofTempered and Mixed Music in the Hard and Soft Hexachords and in SoCalled Feigned Music [50v] Earlier I explained how there are eight modes and up to this point I have shown seven of them, along with examples. There now remains to discuss the eighth mode, which is cheerful and pious. Its main limits are given in the illustrations of tempered and mixed music in example 22.

Example 22.1 The Eighth Mode ofTempered and Mixed Music in the Hard Hexachord

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Example 22.2 The Eighth Mode of Tempered and Mixed Music with the Fifth Below Its Fourth in the Hard Hexachord

Example 22.3 The Eighth Mode of Tempered and Mixed Music in the Soft Hexachord

Example 22.4 The Eighth Mode of Tempered and Mixed Music in Feigned Music

Chapter 23 Explanation of the Two Modes Mixed from the Fifths and Fourths of Diverse Modes [51r] In the preceding chapters I presented the eight modes with examples of their principal ranges. This was done to educate pupils. Although some people have described four other modes with the formation of false fourths and fifths, as I indicated earlier, I shall offer only a small sampling of the latter. Everyone will thus know how to form them by themselves. Even though these modes have been discussed by others,381 now write them to give students an illustration, so that they can understand the mixture. Should anyone wish to form these mixed modes, he may acquire an easy method from example 23. 38. The words altri and alcuni refer to Heinrich Glarean. See chap. 4, above.

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Example 23.1 The Mode Mixed from the First Fifth of the First Mode and the Second Fourth of the Third Mode

Example 23.2 The Mode Mixed from the [Fourth] Fifth of the Seventh Mode and the Third Fourth of the Fifth Mode These two mixed modes show that the first [example] is made up of the first and third39 modes, as is evident from the main boundaries defining the first fifth, re-la, of the first mode and the [second] fourth, mi-la, of the third mode, and that the second [example] is a mixture of the fourth fifth, which is ut-sol, of the seventh mode and the third fourth, which is ut-fa, of the fifth mode. If example 23.1 were to be presented in the hard hexachord, it would drop down a fourth but remain the same; and if example 23.2 were to be raised up a fifth and sung in the hard hexachord, it too would remain the same.40 Consequently, every kind of composition lowered by a fourth or raised by a fifth retains the identical fourths and fifths in either the hard or the soft hexachord.

Chapter 24 Explanation of the Three Kinds of Cadences I Call Major, Minor, and Minimal and Their Nature, as Used With and Without the Dot in the Composition of Plainchant and Polyphony, with Examples The cadence was invented to show (whenever it appears in compositions) that composers mean to denote the final falling-off at the conclusion of speaking41 or, in other words, the ending of the composition itself. And because the syncope, tied as it is, has this effect (seeming to fall and 39. Misprint: text has quarto. 40. Ex. 23 presents Glarean's Aeolian and Ionian modes transposed once. 41. The translation retains Vicentino's circuitous expression, "di far cadere il fine della

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thus conclude a speech), it is called cadence.42 But because some composers do not take into consideration the reason the cadence was invented, they make cadences at the start of their work, giving the listener the impression that they mean to conclude and close down their composition before it has even begun. Every composer must pay attention to the cadence. For some time now, keyboard players have known that occasionally the cadence can be indicated intending but not making it. This is the method of pretending to conclude and yet not concluding, and it is acceptable in the middle of compositions as long as the cadences are [51v] appropriate to the words or to another idea.43 This way of making cadences was first put into practice with long notes, that is to say, using a breve, and a long time after that it was used with the semibreve, and then in more modern times with the minim. At first, these cadences were sung without any diminution; later, more expert singers and their followers began to apply a little diminution, both with and without dots. Others have used and still use the wholly dissonant syncopation at the cadence, although this method is not modern.44 Others have written the cadences diminished in various ways, with and without the dot. It seems to me that cadences without the dot are intrinsically more graceful. As for the three kinds of cadence—major, minor, and minimal—I shall first write them in the antiquated fashion and then in the way these same cadences were gradually broken up and diminished. I shall place the examples one after the other: the cadence of the breve, then that of the semibreve in several ways, and finally different cadences of the minim, with and without dots as well as with and without diminution. As it happens, the disposition of pitches in some of the examples diminishes the cadences in various ways, in imitation of instruments. Example 24 shows these cadences with the arrangements mentioned above.

Example 24.1 Major Cadences of the Breve Without the Dot and Diminished with the Dot conclusione del parlare," in order to convey the sense of the passage—an allusion to the kind of vocal inflection used by a speaker to signal the ending-point of his discourse. 42. See Bk. II, chap. 4, where Vicentino describes the major, minor, and minimal syncopes. 43. See Bk. II, note 2. 44. See Bk. II, chap. 6, and the fifth illustration in Bk. Ill, ex. 6.2.

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Example 24.2 Minor Cadences of the Semibreve and Minim, Diminished and Undiminished

Example 24.3 Minimal Cadences of the Minim and Semiminim, Diminished and Undiminished, With and Without the Dot

Chapter 25 How to Compose Diatonic Cadences for Four or More Voices, with Examples The proper system for leading a pupil to a knowledge of all eight diatonic, chromatic, and enharmonic modes requires that he attain an understanding of the cadences of these eight modes. For the sake of brevity, I shall give examples in four voices of all the cadences customarily used in the eight modes of mixed and tempered music. Thus, in this chapter, I explain only the way to write a few diatonic cadences (whenever they must be composed diatonically) and how many kinds there are in the first mode, in the second, and so on, in all eight modes. Pupils will draw on these cadences for all eight modes of tempered music and use them to form the diatonic cadences in all the eight modes. The natural and diatonic cadence is that which never has an accidental semitone and is always made by the whole tone, except for the occasional occurrence of the natural semitone. But it does not stop [52r] being a diatonic cadence because of the association of the natural semitone with both the diatonic and chromatic genera, according to what Boethius and other philosophers have written.45 Example 25 demonstrates a few diatonic cadences. Composers are advised further that they must not only observe the cadential mode in the soprano but also maintain the modes in all the parts. Any steps of the minor and major third are for45. De inst. mus., 4.6. The reference to other philosophers seems more a rhetorical device of emphasis than a citation of corroborating authorities. Other possible sources are Vitruvius, De architectura, 5.4; Capella, De nuptiis Philologiae et Mercurii libri II, 9.958; Glarean, Dodekachordon, Bk. I, chap. 5.

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bidden, though leaps of the fourth, fifth, sixth, and so on are acceptable because they are common to all the genera, as was stated earlier [Book I, chapters 6-11].

Example 25 Diatonic Cadences for Four Voices

Chapter 26 Demonstration of Diatonic Music Composed for Four Voices Lest readers remain in doubt, I wish to offer a completely diatonic example for four voices such that, when a student sings it, he will be more certain about diatonic music [example 26]. Such music may be composed for as many voices as suits the composer's purpose. However, considerable harshness is felt in this music, compared to that which is tempered and mixed. Composers are advised that the insertion of a minim

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rest nullifies the step of a major or minor third.46 This composition is apt for both singing and playing.

Example 26 Diatonic Example (continues) 46. For an analysis of ex. 26, see the introduction.

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Example 26 Continued

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Chapter 27 Demonstration of Cadences for Two Voices, Diminished and with Full Note-Values, as well as Dubious Cadences [52v] The matter of cadential technique—that is to say, how they are accompanied and how they show the way to make cadences—was discussed when the syncopes were listed. Nevertheless, it is now time to describe the method of making a cadence, even though the syncope already demonstrated it. To help students learn this method easily, [53r] I shall give examples of how cadences are to be composed for two voices and which cadences are diminished better in one way and which in another. Those cadences written with natural diminutions are more manageable for singers than the ones diminished with accidentals, as is evident in example 27. Also shown are some false cadences, which are dubiously sharpened and hence better diminished than when full note-values are retained.

Example 27.1-27.3 Cadences with Full and Diminished Note-Values, and Inconclusive Cadences for Two Voices47 47. Inconclusive cadences for two voices form the subject of the next chapter; however, two such cadences are illustrated in ex. 27.3.

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The rule for cadences is that when a note has to be raised, it should be marked with a sign—sharp, flat, or natural—to prevent the many errors made by singers. When such mistakes occur in performance, they can even ruin the intent of the composer who wanted to represent harshness on a particular cadential note, which singers have raised, making the music sweet.48 In dubious cadences it is a gross error to expand a major sixth, for it will probably become a minor seventh and create great discord. The remedy for salvaging dubious cadences is to save them with diminutions or, if the notes must retain their full value, to make them leap either upward or downward. All dubious cadences are salvaged in this way.

Chapter 28 Demonstration of Natural and Accidental Cadences That Do Not Conclude To avoid a multitude of errors, it is a good idea in cadences to mark all notes requiring accidental signs, as I said in the preceding chapter. To develop fluency with inconclusive leaping cadences, I shall show the novice many leaps that redeem cadences that become dubious when sharpened, demonstrating when he needs to leap before or after accidental signs. Composers should write such cadences so well that singers cannot bungle the intonation. Indeed, in a good ensemble you can sing any awkward leap, both natural and accidental, as in example 28. There I show natural and accidental cadences that leap by means of various and diverse leaps.

Example 28 Natural and Accidental Cadences of Tempered and Mixed Music for Two Voices That Evade Their Conclusion 48. For a longer discussion of this problem, see Bk. I, chap. 19.

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[53v] A diversity of cadences occurs in compositions. The cadences notated in example 28 are as good in one tone or mode as in another. Good for two voices, they would be better for three or more voices. The notes of these leaps may be either lowered by applying flats or raised by sharps, as composers see fit. The ear should learn every bad leap with practice, so that there will come a time when all the natural and accidental modes and leaps will be sung as effortlessly as we sing the good leaps of the octave and the just fifth nowadays. Today we sing a few awkward and very strange leaps. Therefore, the more we use my archicembalo, the easier will be the difficult leaps.

Chapter 29 Demonstration ofTwo-Voice Cadences for Soprano and Tenor, with Examples When composing cadences for two or three voices, a procedure other than the one applicable to cadences for four voices is sought because two singing voices are deprived of ensemble and therefore of harmony. For this reason, it is necessary to hold the parts in check, for when the parts are too remote from each other they produce less harmonic fullness—all the more so when there are only a few voices. Two-voice cadences, consequently, are constructed more closely and tightly than are cadences for three voices. In example 29 I indicate that the upper part is the one that performs the cadential action in the soprano cadence, whereas the lower part performs the tenor cadence. Because of their parts, these cadential actions

Example 29.1 Various Types of Two-Voice Cadences for Soprano and Tenor (continues)

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Example 29.1 Continued are suitable for three, four, or more voices, even though the actions are many and diverse. Example 29 also shows which are good, bad, and better. [54r] The Cadential Action of the Soprano on Top Will Now Be Taken Over by the Tenor Beneath the Contralto, Sometimes Using Wholly Consonant Syncopation for Two Voices

Example 29.2 [Examples of Cadences for Contralto and Tenor]

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Example 29.3 Cadences for Contralto and Bass That Evade Their Conclusion

Example 29.4 Cadences for Contralto and Tenor That Evade Their Conclusion

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Chapter 30 Demonstration of Some Cadences That Avoid Their Conclusion Through Natural Leaps [54v] In the preceding chapter, sixteen varied cadences were shown, along with fourteen inconclusive cadences that avoided their conclusion by step.49 I here write eight sorts of cadences50 that evade their conclusion through natural leaps, as seen in example 30.

Example 30 Cadences That Evade Their Conclusion Through Natural Leaps Either Upward or Downward

Chapter 31 Demonstration of Some Three-Voice Cadences of Tempered and Mixed Music To help students of the music profession learn with ease, I offer music for three voices in example 31. The music is composed with as much closeness as possible among the voices so that these cadences will be more sonorous and serve as models of good practice for students. Depending on which part has the cadential action, various steps and leaps are taken, as will be seen in the cadences for four voices: the so49. Errors: text has 17 essempi di cadentie variati: & anchora altre tante cadentie che non concludeno. 50. Error: text has 10.

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Example 31 Three-Voice Cadences of Tempered and Mixed Music

prano proceeds with its proper action; the contralto performs an action that suits it; and both the tenor and the bass hold to their boundaries according to the nature of the steps and leaps.

Chapter 32 Demonstration of Many Four-Voice Cadences Used in the Eight Modes of Tempered and Mixed Music [55r] In tempered and mixed polyphony, many cadences occur outside the main limits of the tones or modes, and these cadences are placed in the midst of the course of a composition. For instance, when a composer has provided the principal cadential points for a composition, he may then write other cadences from other modes between these points. He must, however, proceed gracefully: that is to say, if somewhat beforehand he proceeds in good order to reach the cadence outside the mode, then this cadence will not seem strange to the listener when the singers reach it. If a composer proceeds in this way, he can devise any kind of cadence whatsoever outside any mode. The principal limits of a mode fall on the first and last note of its fifth and fourth. When writing, composers should bear in mind that (as the Philosopher says) nature cannot tolerate excessive things; for example,

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man cannot be always laughing, nor always weeping, nor always running, nor always resting.51 On the contrary, because moderate things endure, you must select a middle course between extremes to reach a desired goal. Similarly, composers lay out a refined unfolding, with varied cadences from other modes carefully planned so as not to seem outlandish, as was said above. The sequence of these cadences is seen in example 32.

Example 32.1

Some Four-Voice Cadences in the First Mode of Tempered and Mixed Music in the Hard Hexachord52

51. The concept that man is capable of laughter but does not laugh continuously comes from chap. 4 of the Introductio in Aristotelis categorias a Boethio translata, by Porphyry; the extremes of motion and rest are mentioned in chap. 3 of this tract. See Bk. I, notes 44 and 82. Similar ideas are found in Plato, Laws, 5.732c, and Republic, 10.6l9a-b, and Aristotle, Nic. Eth., 2.5.1106b and 4.10.1125b. 52. Misprint: caption has Quarto modo. Exx. 32.4 and 32.5 are on p. 56r; incorrectly numbered 54r.

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Example 32.2 Some Four-Voice Cadences in the Second Mode of Tempered and Mixed Music in the Hard Hexachord

[55v] Readers are advised that the bass is the governing part. It endows all the parts with a gracefully refined unfolding and varied harmony, not only when approaching the cadences but also when moving to other passages.

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Example 32.3 Some Four-Voice Cadences in the Third Mode of Tempered and Mixed Music in the Hard Hexachord

Example 32.4 Some Four-Voice Cadences in the Fourth Mode of Tempered and Mixed Music in the Hard Hexachord (continues)

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Example 32.4

177

Continued

Example 32.5 Some Four-Voice Cadences in the Fifth Mode of Tempered and Mixed Music in the Soft Hexachord

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Example 32.6 Some Four-Voice Cadences in the Sixth Mode of Tempered and Mixed Music in the Soft Hexachord [56v] Almost all modern composers usually write the fifth and sixth modes in the soft hexachord, for they find it very convenient. This hexachord contains the just fifth between B mi with a flat and F fa ut. Composers should use the identical cadential points for the fifth and sixth modes in the hard hexachord.

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Example 32.7

179

Some [Four-Voice] Cadences in the Seventh Mode of Tempered and Mixed Music in the Hard Hexachord

Example 32.8 Some [Four-Voice] Cadences in the Eighth Mode of Tempered and Mixed Music in the Hard Hexachord (continues)

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Example 32.8 Continued

Chapter 33 Demonstration of the Soprano Cadence Placed in the Alto, Tenor, and Bass of Tempered and Mixed Music, and Five Kinds of Varied Cadences as Made by the Bass with All the Other Parts [57r] Since many cadences in the eight modes have been demonstrated with examples, it remains to discuss soprano cadences placed in the alto, tenor, and bass. Sometimes a composer needs to move cadential actions from one part to another for the sake of variety.53 Every time a part takes over the technique of making a cadence from another part, the former adopts the cadential action of the latter. For instance, should the contralto make the cadential action of the soprano, the latter makes the cadential action of the contralto; and should the tenor make the cadential action of the soprano, the soprano makes the cadence of the tenor; and the same occurs in the bass when the soprano makes its cadence. Thus, all parts must do as follows when one part takes over the technique of another—for instance, when the bass makes the cadence of the tenor, the latter should make the cadence the bass ought to have made, and the same goes for the contralto and tenor. In this way, whenever cadences belonging to specific parts are not placed in their normal location, they are always transported to another location, as I show in example 33.54 Example 33.2 in particular shows five kinds of cadences made by the bass with the soprano. 53. See chap. 29, above. 54. In ex. 33 the designation of parts refers to their cadential action, not their range.

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Example 33.1 [Cadences in the Soprano, Tenor, Contralto, and Bass]

Example 33.2

[Five Kinds of Cadences in the Bass]

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Chapter 34 Demonstration of Three Kinds of Four-Voice Cadences, the Major, Minor, and Minimal, All in Tempered and Mixed Music [57v] In chapter 24 I demonstrated the three kinds of cadences in their purest form: the major, minor, and minimal. It remains to illustrate them, accompanied, in four voices. I shall also show the four-voice cadence with the wholly dissonant syncopation. Even though such syncopation is not too modern, some persons, ignorant of modern technique, use it in their compositions. They also use major cadences, which are not acceptable in our time. Example 34 demonstrates these cadences for four voices.

Example 34.1 Antiquated Major Cadences for Four Voices With and Without the Dot and with Wholly Dissonant Syncopation

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Example 34.2 Minor Cadences

Example 34.3

Minimal Cadences

Chapter 35 How to Compose a Fifth Part Below the Cadences of Mixed and Tempered Music, with Examples [58r] Students should take note of the nature of those cadences that require an imperfect consonance on the middle note of the three notes that perform the cadential action of the soprano: that is, the note immediately following the syncope, which is half consonant and half dissonant. Although some are accustomed to putting the octave below this note in the fifth tone or mode in the soft hexachord from A la mi re to G sol re ut, nevertheless such an accompaniment is not pleasant to the ear, and this despite the fact that this cadence cannot be managed in any other way.

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The nature of the cadence is such that it always desires imperfection. It seems to the ear the the cadence can tolerate neither the unison nor the octave above or below, even in six or seven voices. An alert singer, hearing such an accompaniment, is likely to decide that the cadence has been robbed of its delightful sound. An error may thus arise in the cadence, for if the soprano is making a cadence and raises the middle note against the octave above or below, then the resulting disorder will be too great a discord for the ear. Of this let the student beware. In example 351 show which cadences are dubious and which are good or false. Whatever arrangement is used for five voices, it will also hold for six or more voices. Students must take care to accommodate properly the fifth and sixth voices. Seven and eight voices—such as, for instance, two sopranos, two contraltos, two tenors, and two basses—do not occur except in compositions for two choirs. And the lowest part is always the bass, even if it acts as the soprano.55 Example 35 presents some cadences for five voices.

Example 35

[Some Cadences for Five Voices]

55. That is, when performing the cadential action of the soprano. See chap. 33, above.

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Example 35 Continued

Chapter 36 Demonstration and Explanation of the Three Chromatic Fourths [58v] I have described the formation of the three diatonic fourths and the four diatonic fifths, how the seven octaves are formed with them, and finally how these octaves create the eight diatonic tones or modes. In addition, I went on to discuss and demonstrate the limits of the eight modes of tempered and mixed music, along with their cadences for four and five voices, which I organized in many and varied ways in the hard and soft hexachords and in feigned music. I also presented examples of these cadences for four voices. Not to abandon the ordering of the three genera, I shall now describe and demonstrate how to form the chromatic fourths, fifths, and octaves, as well as the eight chromatic modes. I shall also explain the eight modes of the enharmonic genus and demonstrate them with examples. And I shall follow this precise system, a system no one else in music practice has ever described and demonstrated before. In the previous discussion of the eight modes it was stated that Ptolemy added the eighth mode to the seven modes in use before his time.56 But I add twenty-four to these modes—in sum, eight diatonic, eight chromatic, and eight enharmonic, as well as the eight mixed modes of tempered music. These modes were 56. See also, "Music Theory," chap. 12.

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first created from the seven octaves, which were themselves generated from the three fourths and four fifths. I shall adhere to the same sequence for the eight chromatic and eight enharmonic modes. Insofar as I shall construct these other modes with the same elements that formed the modes of mixed and tempered music, it is necessary to begin by talking about the creation of the three chromatic fourths, for these are based on the same reasoning and ordering as the diatonic modes. Even though I discussed the making of the three diatonic fourths, I shall not recoil from enumerating their composition, for the pupil's greater understanding. As he recalls, the explanation was as follows. Philosophers constructed [59r] three fourths. 57 The first proceeds through the step of a whole tone, then through a semitone and a whole tone, just as in practice we are accustomed to singing re mi fa sol. In this sequence of steps, you see, there occurs in the first step from re to mi the big step of the whole tone, in the second from mi to fa the small step of the semitone, and from fa to sol the big step of the whole tone. And this is how the diatonic fourth is made up first of a big step, followed by a small step, and finally by a big one. The chromatic fourth has all its steps placed differently and contrary to the sound of the diatonic steps. For the diatonic steps produce a harsh sound, whereas the chromatic restore a gentle sound to the ear. The latter are called different on account of the differences between the juxtaposed big and small steps, in keeping with their genera. They are called contrary in sound because the steps of one genus are harsh and those of the other are gentle. Just as fire is the opposite of water, or the bitter is the opposite of the sweet, so it happens with the sounds of the different steps of the genera. Let us now return to the first chromatic fourth [example 36.1]. At its beginning, the first step is small, the distance of one major semitone. In the middle comes the step of a minor third, which step is big, the distance of three semitones. The third and last step is smaller than the small one [the major semitone], for it is a minor semitone. These chromatic steps are all placed differently from those of the diatonic, as I said before. For the first diatonic step is big, a whole tone, whereas the first chromatic step is small, a semitone; the second diatonic step is as small as a semitone, whereas the second step of the chromatic sequence in the fourth is a step as big as three semitones; and the third step of the ascending chromatic fourth is small, a minor semitone, [whereas the third diatonic step is big, a whole tone]. 57. Probably Gaffurio, Pmctica musicae, Bk. I, chap. 5.

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So that pupils may better understand the rule, I shall illustrate two fourths, one after the other, one diatonic and one chromatic. Thus will they understand how diverse steps make one fourth different from the other. Students will recall the explanation I gave previously about the name chromatic, when I stated that chromatic means nothing more than the transformation of one sequence into another [Book I, chapter 7]. It is from this sequence that the chromatic fourth will be recognized as being distinct from the diatonic.

Example 36.1 First Fourth We now proceed to the second chromatic fourth, which follows the process of transforming all the steps of the second diatonic fourth. Where there were small diatonic steps, there are now placed [big steps] on the same degree in the chromatic fourth. And where there were big diatonic steps, I now place small chromatic ones in the sequence of these steps. To show this change I present in example 36.2 the two second fourths, one diatonic and the other chromatic, in the same way I illustrated the sequence of the first chromatic fourth.

Example 36.2 Second Fourth When comparing one fourth with the other, students will note how the sequence of the steps differs, for where the small step lies in the diatonic, there begins the big step of the chromatic. In the same way, all the fourths are constructed in opposition to each other, as I said above. Thus, in the third fourth, both the big and small steps are placed differently from each other, as seen in example 36.3.

Example 36.3 Third Fourth

Example 36.4 The Three Chromatic Fourths

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Chapter 37 Demonstration and Explanation of the Four Chromatic Fifths [59v] In the preceding chapter I discussed the three chromatic fourths constructed differently from the diatonic ones, and this in imitation of the name chromatic, which (according to Boethius) 58 means a step that is different from the diatonic. Insofar as the steps of the chromatic genus were to be exactly opposite to those of the diatonic, it was necessary to insert the big step, so as to effect a change in the chromatic fourth precisely where the small step of the diatonic fourth likewise effects a change. We must now discuss the four chromatic fifths, in which I have inserted the big step of the chromatic genus. This is the step that forms and generates the four different kinds of chromatic fifth, just as the small step of the major semitone does in the case of the diatonic fifths.59 To illustrate the chromatic fifths, I present in example 37.1 the first diatonic fifth, along with the first chromatic fifth, so that students may learn them easily.

diatonic

^

chromatic

Example 37.1 First Fifth In a similar way I demonstrate the second chromatic fifth together with the second diatonic fifth.

8

diatonic

• chromatic

Example 37.2 Second Fifth The third chromatic fifth is also illustrated in juxtaposition to the diatonic.

diatonic

chromatic

Example 37.3 Third Fifth Finally, the fourth chromatic fifth is not bereft of the company of the last diatonic fifth, that is, the fourth diatonic fifth. 58. De inst. mus., 1.21. See also Bk. I, chap. 7. 59. Misprint: text has quarte. See chap. 3, above.

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diatonic

189

chromatic

Example 37.4

Fourth Fifth

In example 37.5 I write all of them one after the other for the student's information. Second Fifth

First Fifth

[?o ho l"> fr Fourth Fifth

Third Fifth

Example 37.5

The Four Chromatic Fifths in Consecutive Order

Chapter 38 Demonstration and Explanation of the Seven Chromatic Octaves It has been noted that the creation of the seven diatonic octaves was made by the three diatonic fourths and the four diatonic fifths. The same process obtains in the formation of the seven chromatic octaves, which are formed by their three chromatic fourths and their four chromatic fifths, as in example 38. [60r] All seven are written and read differently from the diatonic octaves. For where the whole tone in the diatonic was First Octave

^ » o kp° bo q° s

"9

0

,

7C">

TO—'

i

I

,

U^ U^. V^ *\**

0

Second Octave

_e—o

Third Octave

,

i

'

bo

Fourth Octave

~ lo fro

1,0

enharmonic

r-£ fo

I

U^ U^ bo ~

-o 1

!"» ^

Sixth Octave U £-v

0—o—

U x-v

Seventh Octave

Example 38

*^*

7O

t]O

bo

—o—PO—b-o—ku_h

AJ

bo

[The Seven Chromatic Octaves]

L fc o t?° qo

e—

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read, in the chromatic you read the semitone, and where the semitone in the diatonic was read, in the chromatic you read the step of the minor third. These changes are shown in example 38.

Chapter 39 Demonstration and Explanation of the Eight Chromatic Modes and How They Should Be Used in Plainchant and Polyphony; First, Concerning the First and Second Modes Earlier I discussed the eight diatonic modes and the eight modes of tempered and mixed music, as well as the way the steps of the minor and major third from the chromatic and enharmonic genera have been randomly placed alongside the diatonic genus in the tempered modes. Up to now these thirds have been used by composers who, lacking the erudition required to distinguish which steps belong to which genus, have put one after the other solely on the basis of mere custom, without understanding the wealth of reasons behind this practice.60 But in the future, with the help of the Holy Trinity and the aid of my labors, people may be able to recognize from among all sorts of compositions which is diatonic, which chromatic, and which enharmonic, not to mention to discern which composition is made up of various species from the genera and which genera are mixed with other genera. It is now necessary to make known the eight chromatic modes. These modes are formed by arranging their fourths and fifths exactly in the same way as the diatonic modes and the tempered and mixed modes. The formation of the first mode begins on D sol re with the first fifth and, ascending to A la mi re through the sequence of this fifth, it then proceeds with its ascending fourth, whose steps terminate on D la sol re. Its outside limits may be exceeded above or below by one semitone. The authentic and plagal modes will be recognized by their fourths and fifths, which are placed either above or below one another, as was noted earlier regarding the diatonic modes. The process of arranging the fourths and fifths in the chromatic modes is the same as in the eight diatonic modes. If composers adhere to this arrangement in forming the chromatic modes, they will be able to recognize which melodic contours belong to the first mode and which to the second. Thus, as each composition requires, a determination is made as to which genera and species best suit the purpose. Example 39 presents the notated illustrations of the first and second modes. 60. For a longer diatribe on this subject, chap. 15, above.

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Example 39.1 The First Chromatic Mode

Example 39.2 The Second Chromatic Mode

Chapter 40 Demonstration and Explanation of the Third and Fourth Chromatic Modes [60v] The formation of the modes indicates that they cannot remain isolated in compositions. That is to say, if a composer writes an authentic mode in one part, the plagal will appear in another part, or vice versa, as is seen in polyphonic music. I turn now to the third and fourth modes. When ascending, the arrangement of the fifth with the fourth above it creates the third mode, whereas the fourth below the fifth creates the fourth mode. Both arrangements are demonstrated in example 40.

Example 40.1 The Third Chromatic Mode

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Example 40.2 The Fourth Chromatic Mode

Chapter 41 Demonstration and Explanation of the Fifth and Sixth Chromatic Modes The fifth and sixth modes are composed of the third fourth and the third fifth, as are the parallel diatonic and mixed modes. The arrangement is identical in that the authentic has its fourth above its fifth, whereas the plagal has this same fourth below its fifth. Example 41 illustrates both arrangements.

Example 41.1 The Fifth Chromatic Mode

Example 41.2 The Sixth Chromatic Mode

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Chapter 42 Demonstration and Explanation of the Seventh and Eighth Chromatic Modes [6lr] Since the number of the diatonic modes, as well as that of the mixed modes, is eight, the number of the chromatic modes must also be eight. In the preceding chapter, the formation of the fifth and sixth modes was demonstrated. It remains to talk about the seventh and eighth chromatic modes. These are formed by the following arrangement: [in the seventh mode] the fourth fifth is put below the first fourth, sung "sol-re" in practice, whereas the eighth mode has the identical fourth below the fourth fifth. These two arrangements, then, form the seventh and eighth modes, as is evident in example 42.

Example 42.1 The Seventh Chromatic Mode

Example 42.2 The Eighth Chromatic Mode Readers are advised that the eight chromatic modes notated here and in previous chapters can be written in both the hard and soft hexachords and in feigned music, as in the case of the tempered and mixed modes, provided the boundaries of their fourths and fifths are retained.

Chapter 43 Explanation of Four-Voice Chromatic Cadences with the Cadential Action of the Soprano in All the Parts, with Examples Chromatic cadences in all parts are exceedingly pleasant. The reason is that no whole tones occur in any of the parts, which have instead semitones and steps of the minor third as well as leaps of the fourth and

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fifth. The latter, of course, are common to all the genera. Some chromatic cadences are shown in example 43.

Example 43 Chromatic Cadences61 [61v] A composer can, on his own, write chromatic cadences in all eight modes, provided that there never appears a whole tone like the one found between ut and re, re and mi, fa and sol, or sol and la. He can also observe the technique of making varied and diverse cadences in the first and second modes as well as in all the modes, according to the cadences I demonstrated for the eight mixed modes. Whenever the whole tone appears in a composition, the remedy is as follows: divide the whole tone into two parts, one major and one minor semitone. As to which of these semitonal divisions should come first, this decision rests on the composer's judgment, depending on either what suits him best or how he is moved 61. Each part with the soprano cadential action is labeled "soprano."

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by the words or another idea.621 have now said enough about the modes and cadences of the chromatic genus and species.

Chapter 44 Demonstration and Example of a Completely Chromatic Composition for Four Voices Having decided that it would benefit pupils if I were to give an example of a completely chromatic composition, I present in example 44 a cheerful little motet, which is completely chromatic. We sing it in church on the day of the Resurrection of Our Lord, thus showing everyone that chromatic music can be sung in church with a full choir.63 A composer may write any sort of chromatic music he wishes, to suit the words, for there are many kinds of chromatic music—sad, cheerful, harsh, gentle, and tempered, depending on the mixture of the genera and of the species of these genera, as is evident in those of my compositions that mix various kinds of elements to suit the words. God willing, I shall publish them immediately after this work so that everyone will see the great abundance of steps I have brought to light in villotte and madrigals for three, four, five, six, seven, and more voices, as well as in motets, the complete Passion, and the Lamentations, all written with and without fugues, in keeping with the subject of the words.64 Example 44 provides a partial advance notice of this publication. Some persons may wish to point out that this little motet is not completely chromatic. But I have kept only [62r] two big steps from the enharmonic genus in the soprano, on account of the intensity of the words, as well as one in the contralto, two in the tenor,65 and one in the bass. These may be corrected with a flat; however, I have left them in because of the abovementioned intensity. When the singers have finished this motet, they should return to the beginning and finish at the first proportional sign [measure 6]. 62. See Bk. II, chap. 1. 63. See Bk. II, chap. 23, for another comment on singing a plena voce. But see also Bk. IV, chaps. 1,26, 28, and 29. 64. These works, along with a few others mentioned in Bk. Ill, chaps. 51-55> and Bk. IV, chap. 33, are not extant. Some fragments of four madrigals for four voices from Bks. I and II (date and place of publication unknown) were reproduced in the Discorso intorno amadrigali etalibri dell'antica musica ridutta alia moderna prattica da D. Nicola Vicentino, by Gandolfo Sigonio, and //Melone secondo, by Ercole Bottrigari, which were published together (Ferrara, 1602). 65. There is only one major third in the tenor (mm. 15-16), not two. For an analysis of this work, see the introduction.

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Example 44 A Completely Chromatic Little Motet66 66. The text combines the Alleluia and Gradual for Easter Sunday: "Alleluia. Haec dies quam fecit Dominus: exultemus et letemur in ea" (Alleluia. This is the day the Lord hath

Book III on Music Practice

Example 44 made; let us be glad and rejoice in it).

Continued

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[62v] The rules that teach us to recognize major and minor semitones were explained earlier in this work [Book I, chapters 16-20]. Only those notes having some sort of accidental sign are to be sung according to that sign; the rest of the notes (without signs) are to be sung under the sign of their normal clef, either in the hard or soft hexachords. If anyone thinks it is not possible to write a purely chromatic composition, let him look at the madrigals, motets, and other works printed in chapters 52 and 55. The singing should not be faulted for lacking grace because of so many leaps, for these avoid the steps of the whole tone, which is rough and harsh, as experience tells us. On the contrary, the harmony will be all the gentler because of these leaps.

Chapter 45 Demonstration and Explanation of the Three Enharmonic Fourths I illustrated eight chromatic modes by imitating the diatonic ones, with different steps in their respective fourths, fifths, and octaves, as was seen earlier. I shall now bring to light and disclose for the first time the formation of the eight enharmonic modes with their octaves, fifths, and fourths. I begin with the formation of the three enharmonic fourths, which are arranged in the same way as the chromatic fourths—by putting the big step in the location of the small diatonic one, and the small steps in place of the big diatonic ones, all fourths in every genus are made up of three steps written with four notes. The first enharmonic fourth in example 45.1 consists of a minor enharmonic diesis as the first step and an incomposite ditone as its second step. The third step is another diesis, an enharmonic major diesis67 that completes the first fourth. To help pupils understand easily, I shall put the steps of the diatonic and chromatic fourths together with those of the enharmonic fourth. Thus, these fourths can show their melodic contour, so that the differences between them may be observed.

Example 45.1 The Three Different Fourths in the Three Musical Genera of the First Species of Fourth

67. The major enharmonic diesis is the same size as the minor semitone. See Bk. I, chap. 16.

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[63r] In example 45.2, the second fourth begins on B mi, and its first step is the distance of the incomposite ditone. Then, to complete the fourth, come two enharmonic dieses. The first is major and the second minor, for these dieses make up a major semitone. The second enharmonic fourth is accompanied by the second diatonic and chromatic fourths so that, in comparison to the others, it will be easy to understand.

Example 45.2

The Three Different Fourths in the Three Musical Genera of the Second Species of Fourth

It remains to describe the formation of the third fourth. This fourth has as its first step a minor diesis and as its second a major diesis, these two steps making up a major semitone. The remainder, which completes the fourth, is the interval of the incomposite ditone. In example 45.3 I present the third fourth in all three genera.

Example 45.3 The Three Different Fourths in the Three Musical Genera of the Third Species of Fourth

Chapter 46 Explanation of the Four Enharmonic Fifths, with Examples The three enharmonic fourths were formed in the preceding chapter, so I shall now discuss the four fifths. This explanation, along with the examples, will teach their formation. The first fifth begins on D sol re and climbs up to A la mi re through [six] small steps and one big step. I shall retain the system for the enharmonic fourths, that is, I shall accompany the first diatonic fifth with the chromatic and enharmonic fifths [in example 46.1] so that pupils will understand them better.

Example 46.1 The Three Different Fifths in the Three Musical Genera of the First Species of Fifth

[63v] Composers are warned that all fourths, fifths, and octaves in every kind of genus must be constructed within the identical dimensions. The diatonic fourths therefore consist of two whole tones and one

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major semitone; likewise the chromatic and enharmonic fourths consist of two whole tones and one major semitone, even though they are divided by differently made steps. The diatonic fifths consist of three whole tones and one major semitone. And the chromatic and enharmonic fifths are also the same size as the diatonic. Their steps may be larger or smaller, but they still make up three whole tones and one major semitone. Moreover, the diatonic octaves consist of five whole tones and two major semitones. And of such dimensions also are the chromatic and enharmonic octaves. Thus, if readers understand the method and put the major and minor semitones, and the major and minor dieses, together with the semiditones and ditones, they will discover that each genus contains as many whole tones and major semitones as every other genus. The second fifth has as its first step the distance of the ditone, and the remainder, which completes the fifth, consists of enharmonic dieses. The first diesis is major, the second minor, the third minor, the fourth major, the fifth minor,68 and the sixth major. These steps can be enumerated in example 46.2.

Example 46.2 Second Fifth Perhaps readers will be surprised by the duplicated examples of the diatonic and chromatic genera that have been added to the enharmonic set of fifths. This was done to impress deeply on the student's mind an understanding of these fourths and fifths when placed together. For I am quite certain that any new invention in these systems is somewhat baffling. I therefore do not intend to excuse myself from work but rather to demonstrate diligently by means of examples and explanations whatever is necessary regarding these new inventions. The third fifth follows this order [example 46.3]: It begins its ascent with six steps of major and minor dieses. The first step is minor, the second minor, the third major, the fourth minor, the fifth minor, and the sixth major. However, a composer may at his good pleasure arrange the order of these major and minor dieses, as well as the major and minor semitones, in any way he sees fit. The remainder of the fifth that comes after the dieses is the step of the incomposite ditone.

Example 46.3

Third Fifth

68. Error: text has maggiore. The fifth diesis is minor. See Bk. I, ex. 18.1.

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Finally, we come to the formation of the fourth fifth. It begins on G sol re ut and climbs two consecutive dieses, the first minor and the second major. The third step is the incomposite ditone, after which come four dieses to complete this fifth. [64r] The first diesis is minor, the second minor, the third major, and fourth minor. The enharmonic fifth called the fourth fifth is notated with the other fifths in example 46.4.

Example 46.4 Fourth Fifth

Example 46.5 The Three Enharmonic Fourths and the Four Enharmonic Fifths

Chapter 47 Demonstration and Explanation of the Seven Enharmonic Octaves The arrangement followed in the formation of the seven diatonic and chromatic octaves with their three fourths and four fifths has shown us the way to form the seven enharmonic octaves with their three fourths and four fifths. These are written in example 47. [64v] I decided not to combine the examples of the diatonic, chromatic, and enharmonic octaves because it seems to me that a pupil can construct the latter, with their fourths and fifths, on his own and without further comparison with other sorts of genera just as was done for the fourths and fifths. If students were to measure these enharmonic octaves, they would discover that enharmonic and chromatic octaves consist of five tempered whole tones and two major semitones, as was stipulated earlier for the diatonic octaves. But on examining the

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Example 47 [The Seven Enharmonic Octaves] enharmonic octaves, readers will find that some of them have eleven steps and twelve notes, whereas others have ten steps and eleven notes. Yet one octave is not larger than another, for the quantity of minor and major dieses plus ditones in each is equivalent to the five whole tones and two major semitones that when placed together make up a perfect octave.

Chapter 48 Demonstration of Many Fourths and Fifths, Starting with the First Fourth and First Fifth, Mixed Together from the Species of the Three Genera; and an Explanation of the Many Ways They Can Be Formed in Polyphonic Music Up to this point I have discussed the fourths, fifths, and octaves of all three genera by demonstrating them in each genus. I have also illustrated the eight modes of composition in each genus—diatonic, chromatic, and enharmonic. It is now necessary to demonstrate a few mixtures among the species of the three genera, mixtures that occur often in compositions, so that every student can use in his music every sort of step found in the three genera. Just as it is possible to write eight pure modes in each of the diatonic, chromatic, and enharmonic systems, so is it also possible to compose steps mixed from the species and systems of the genera. Thus, you may form all eight modes from these mixed steps. Here is the reason: in our day we use the big steps or parts of the chromatic and enharmonic genera together with the diatonic, as I have said many times before. From these mixtures of generic steps in polyphonic music, practitioners have formed eight modes and called them tones.

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Indeed, these practitioners fail to realize that they compose the many and diverse steps of the species of these genera in a haphazard way.69 They do not hold to any system whatever other than to make one step similar rather than dissimilar to another, or one smaller rather than bigger, and likewise to cause leaps to whirl about these muddled steps. As a result, they do not understand how this mixture of various steps and leaps, accompanied gracefully by consonances, can make a fine harmonic consensus. Nor do they realize [65r] that the more the steps are altered in a composition, the more attentive and moved will be the listener, in contrast to [the reaction to] a composition that proceeds by always arranging its steps and leaps in one way.70 Every time a composer writes the pure diatonic, chromatic, or enharmonic modes without mixing in another one of the genera or species, then that composition will not please as much as one with a great variety of steps. If, therefore, a variety of steps and leaps gratifies men so much, it cannot be denied that a much greater variety of steps and leaps also pleases their ear. Thus, we must conclude that a composition having many different steps and leaps gives more delight than one with fewer. From the compositions of fifty years ago, we can see that composers in those days used fewer steps—such as the divisions of the whole tone made by flats, naturals, and sharps—than we do now and that for the past ten years or so they have used more flats and sharps than before, and today use even more. No one worries about spoiling the arrangement of the diatonic fourths and fifths. For this very reason, you can compose a fourth or a fifth out of many varied steps, be they diatonic or chromatic or enharmonic, provided that in using them you do not destroy the order of the eight modes with many unruly steps. Some people think that when compositions contain one, two, or more enharmonic dieses, the organization of the tone or mode is disordered, and that the same goes for two or three consecutive semitones in one part because they too destroy modal order. Such people do not understand that up to now no one has obeyed the organization of the tones or modes—that is to say, no one has written a composition entirely in the diatonic,71 entirely in the chromatic, or entirely in the enharmonic genus. Very little thought has been given to this matter. But I shall explain it. A composer writes a fourth (or fifth) in a specific mode. Regardless of 69. See chap. 15, above, and Bk. I, chap. 6. 70. On the element of surprise, see "Music Theory," chap. 16, and "Music Practice," Bk. I, chap. 24. 71. For a test case of a composition in the pure diatonic genus, see Bk. Ill, ex. 26.

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whether this fourth (or fifth) contains many or few steps, if their total makes up a perfect fourth of two whole tones and one major semitone, the composition will be good because it abides by the boundaries of the fourths and fifths of its modes or tones, even though the composer has disrupted the order of the modes by inserting unruly steps as well as unruly fourths, fifths, and octaves in them. In truth, the modes that have been used and are still being used today in polyphonic music and plainchant may be properly called disorderly tones or disorderly modes on account of the mixture of steps from the genera and the unruly fourths and fifths in any one tone or mode. I have provided so many arguments time and again that I am sure my readers have thoroughly understood the matter of the many or the few steps that can be inserted within a fourth (or fifth), provided the steps are enough to make up a perfect fourth of two whole tones and one major semitone. To help students grasp this matter, I have provided in example 48.1 the arrangement of the first fourth made up of diverse types of unruly steps. All the same, with steps and leaps of the minor and major third, sometimes fewer, sometimes more, the fourths remain true. o

o l?o |?o fao

f\»

^°t"

" 0

O

o

0

l?o o ———-©—o—o—

O

-*-*

jy

Example 48.1 The First Ascending and Descending Fourth Mixed from the Three Genera and from Their Varied Sorts of Species

[65v] Example 48.1, the first fourth, allows a reader to understand that other fourths, fifths, and octaves are similar. Thus he may on his own examine the ordering of the octave made up of unruly steps and mixed from the various species of the genera. The component steps are named according to their transformation. So, if whole tones are transformed beyond the natural system, they are called chromatic tones in the diatonic order. The same holds true for the other genera, depending on their conversion; for instance, a semitone or whole tone transformed by an enharmonic diesis is called a chromatic enharmonic species. I now provide a few illustrations of the first fifth mixed with various ascending and descending steps, as can be seen in examples 48.2 and 48.3.

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Example 48.2

The First Fifth with a Mixture of Ascending Species from the Three Genera

"1M0 ol>o o I " °

Example 48.3

'ci«m»* o—1>-

The First Fifth with a Mixture of Descending Species from the Three Genera

Chapter 49 Demonstration and Explanation of the Eight Ascending Enharmonic Modes Up to now the big step of the enharmonic genus, called in practice "ut-mi and fa-la," has been used in plainchant and polyphony. But now, even the two small steps of that genus are used. Because these steps are very gentle, they are sung in the chamber with a small ensemble.72 Thus, the entire enharmonic genus, with its eight modes, is sung today. Should anyone object that if the chromatic and enharmonic modes were suited to musical performance, philosophers would have written about the subject, there is an answer. It was no small matter to discover the seven diatonic modes in those early beginnings and then to have the eighth mode added by Ptolemy, as Boethius wrote.73 It is evident that Ptolemy completed the octave. Moreover, in modern times, some authors have written down four other modes made up of false fourths and fifths, as I showed earlier.74 Had such people penetrated these matters more profoundly, they would have written the same things about them as I. For the ancients discovered many things, and afterward, from time to time, many philosophers gradually added many other things. Today one should not be astounded by such inventions. For if the diatonic genus has opened the way to composing the eight diatonic modes, why should the chromatic and enharmonic genera not have their own eight modes to serve each genus? When a composer has the freedom to 72. See Bk. II, chap. 23, for a similar comment on chamber music. In this chapter, con bassa voceis used in contrast to a plena voce, the term for a full choir. See chap. 44, above, and Bk. II, chap. 23. 73. De inst. mus., 4.17. On Ptolemy and the eighth mode, see "Music Theory," chap. 12, note 29. 74. As in the case of the general references in chap. 23, above alcuni authori refers to Heinrich Glarean. See also chap. 4.

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write in the first mode of the diatonic or of the chromatic or of the enharmonic orders, he will have compositional resources of such richness, so many steps and various species adorned with so varied a set of procedures, that his compositions, on account of their great diversity of mixed steps, will be marvelous things to hear. The first mode of the enharmonic genus is composed of its first fourth and its first [66r] fifth, just as the fourths and fifths for the first diatonic mode are arranged. Thus, in their formation, all the enharmonic modes follow the arrangement described earlier. The fourths and fifths that ap-

Example 49 [The Eight Enharmonic Modes]

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pear most frequently in particular modes help us to recognize which mode the composition is in, be it the first, the second, or any other mode. I therefore notate all eight modes one after the other in example 49, so that readers may recognize the differences between them. These differences are seen in the melodic contour of the fourths and fifths in both the authentic and plagal modes.

Chapter 50 Explanation of Some Four-Voice Enharmonic Cadences in All the Parts, with Examples [66v] The enharmonic genus contains a semitonal division that is disproportioned and irrational. And the other parts accompanying this division cannot contain proportioned and accurate leaps because they must correspond to this irrational ratio. Thus, the steps and leaps in the parts are disproportioned. Let no one be astonished that the nature and division of the genus allow this to happen. The nature of the diatonic genus goes along with its own steps and leaps, which are true in their ratios. But the nature of the division of the chromatic genus permits the disruption of the diatonic order and the creation of two semitones from the whole tone as well as the step of the incomposite trihemitone. Likewise, the nature of the enharmonic genus disrupts the order of both the diatonic and chromatic and permits the creation of steps and leaps beyond the rational. For this reason such a division is called an irrational ratio. A pupil must learn such disproportioned steps and leaps for singing in order to become a perfect musician and a perfect singer. Also, he should know how to match and accompany with harmony all sorts of disproportioned and irrational intervals, and also how to sing them so as to show the world that he is exceptional and can accomplish with artifice that which cannot be done by reason. It is now time to provide the model for enharmonic cadences in all the parts.75 Composers must never put the whole tone or the major semitone in any part; however, the divided semitone and the leaps of the irrational fourth, fifth, and so on occur in enharmonic compositions. So that students will be thoroughly informed, I provide illustrations of some enharmonic cadences in all the parts in example 50. Just as they will understand how to compose some such cadences by way of these ex75. As in previous examples (chaps. 33 and 43, above), the cadential formula of the soprano migrates to other parts. Hence the bracketed designation "soprano" under the voices in ex. 50.

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amples, so they may write these cadences on their own in all the eight modes.

Example 50 [Enharmonic] Cadences for Four Voices: Soprano, Alto, Tenor, Bass

[67r] Enharmonic cadences must not be accompanied by any dissonant syncopation because the nature of this very small step [the minor diesis], it seems, is so gentle it cannot tolerate any disturbance to the ear either before or after it. It is also apparent that such small divisions go with neither a fast nor a slow rate of motion, for the divisions in such steps are rendered imperceptible by rapidity and unrecognizable by retardation. This is especially true of instruments that are not of the wind class, such as monochords, harpsichords, clavichords, cembalos, and archicembalos, because, unlike the organ, they cannot sustain the pitch.

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The pace must agree with the nature of the steps. Chromatic steps should not run too quickly; being larger than enharmonic steps, they require a medium pace. To help students better understand enharmonic composition, I offer an explanation, together with an example, in the next chapter.

Chapter 51 How to Write an Enharmonic Composition, with an Example Enharmonic composition contains some completely irrational combinations that render diatonic steps and leaps false and imperfect: for instance, steps of the minor and major tone, the minimal third, and the third larger than the minor and larger than the major, and leaps larger than the fourth, smaller than the fifth, larger than the fifth, and other irrational leaps.76 In example 51, I present the beginning of a madrigal for four voices. God willing, I shall print many diverse kinds of music along with the ones I give here as examples.77 It therefore suffices to give a bit of the beginning by way of illustration so that it may be sung with the archicembalo. In this small example, there occurs a fugue built on the ascending and descending enharmonic dieses.

Example 51

[The Beginning of an Enharmonic Madrigal]78 (continues)

76. See Bk. I, chaps. 14-42. 77. See note 64, above. 78. The text has two seven-syllable lines: "Soav'e dolc'ardore,/Che fra piant'e sospiri" (Gentle and sweet passion,/Which among laments and sighs). For an analysis of this fragment, see the introduction.

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Example 51

Continued

Chapter 52 Demonstration of a Four-Voice Example of Mixed Chromatic and Enharmonic Music Without the Diatonic, Which Can Be Sung in Five Different Ways [67v] To recapitulate the order of the examples in the preceding chapters, I followed the explanation of completely diatonic composition by the explanation of chromatic music, illustrated by a little motet; and finally, to demonstrate composition in each of the genera, I did not omit a small example of enharmonic music. To help pupils learn more easily by experience about all the generic systems, both separate and mixed, I decided to present as an example the first part of a little madrigal that is completely chromatic but includes a few notes of the enharmonic sys-

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tern.79 Thus, students who sing these two systems combined together will be able to judge their diversity and difference. Students are advised that wonderful secrets are found in such compositions, for every work based on this method can be sung in three ways. To make the comparison and to permit the composition to improve and make better listening, you begin by singing it without any accidentals— that is, without flats, naturals, sharps, or enharmonic dots. The result will be music without much harmonic sweetness because of the diatonic mixture. The second time, the composition is sung with the flats, naturals, and sharps but without the enharmonic dots. The entire composition will become sweetly chromatic. And the third time, when sung with all the accidentals as written, the composition will become mixed chromatic and enharmonic, both sweet and gentle. Thus any sort of enharmonic and chromatic composition can be sung either with or without the accidentals, so as to change its nature. Furthermore, you can benefit contemporary compositions by adding sharps and enharmonic dots between their whole tones and semitones. In such works the great advantage of rich harmony is perceptible. Example 52 illustrates this kind of madrigal.

Example 52 The First Part of a Four-Voice Madrigal That Can Be Sung in Five Ways: Diatonic, Chromatic, Chromatic and Enharmonic, Diatonic and Chromatic, and Diatonic, Chromatic, and Enharmonic80 (continues) 79. See note 64, above. 80. The text is treated rather freely in the four parts; however, it is possible to discern a stanza of four lines of eleven, eleven, seven, and eleven syllables, respectively: "Dolce mio ben, son quest'i lumi, / Che tanto dolcemente mi consumi, / Che tanto dolcemente / Fanno che dolcemente mi consumi./Hayme" (Sweet treasure mine, these are the sweet lights,/ That so sweetly consume me,/That so sweetly/Cause me sweetly to pine away./Alas). For an analysis of this madrigal and the five ways of performing it, see the introduction.

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Example 52

Continued

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Example 52

213

Continued

Chapter 53 Demonstration of the First Part of a Four-Voice Madrigal, Which Is Mixed with the Unruly Species of the Three Genera in Keeping with the Words, and Which Can Be Sung in Five Ways [68r] Because of its variety, the mixture of steps arranged in keeping with the words is most delightful. Insofar as examples are more convincing than words, I write in example 53 the first part of a madrigal for four voices,81 which is an experiment in music mixed from the species of all the genera. With experience, pupils will develop sureness and confidence in using this mixture. 81. See note 64, above.

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Example 53

[A Mixed Madrigal for Four Voices]82

82. The text of this madrigal has the same structure as that of ex. 52 (see note 80, above): "Madonna, il poco dolce e il molto amaro,/Il breve riso, il troppo lungo pianto / M'hanno

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Continued

ridotto a tanto,/Che'l pianger sempr'e mi e caro" (My lady, the meager sweetness and the great bitterness, /The brief laughter and the long lament/ Have reduced me to such a state, /

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Example 53

Continued

That forever to weep and sigh is my delight). For an analysis of this madrigal and the five ways of performing it, see the introduction.

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Example 53 Continued

Chapter 54 Demonstration of a Four-Voice Composition in All Three Genera, Each Separated by Its Species, on Three Latin Verses: the First Verse Is Set to Diatonic Music, the Second Illustrates Chromatic Music, and the Third Enharmonic Music [69v] The diversified music of four different compositions has been illustrated.83 Having found some finished examples, I printed them in this work so as not to have to stop to write some completely chromatic and completely enharmonic compositions, for I lack the time to do so. In my view, it suffices that I have discussed the rules and the method for 83. See exx. 44, 51, 52, and 53. Note that the diatonic exercise (ex. 26) is not considered a composition.

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composing these genera individually. Pupils may thus compose them at their leisure. I know that readers will derive more pleasure from my persevering in this work than if I were not to finish it because of some trouble or other and because of the time lost in devising such precise examples. Indeed, time is short and our ambition long.84 And because the music includes Latin and the vernacular, this work requires considerable time. So I decided to use the finished examples ready to hand. Let us go back to example 53. It was mixed together from the three kinds of species of the three genera, so that singers could hear the effects made by the diversity of the steps. To illustrate the species of the three genera in a single work, so that a comparison can be made between the various species, I offer in example 54 a four-voice setting of three Latin verses.85 As I said above, the first verse is set to the species of diatonic music, the second is sung in the species of chromatic music, and the third is represented by the enharmonic species. These three Latin verses were written in honor of my lord and patron, the Most Illustrious and Very Reverend Cardinal Ippolito II d'Este. Example 54 illustrates the diversity of the three musical systems.

Example 54 [A Four-Voice Latin Composition in All Three Genera]86 84. A version of the well-known aphorism "ars longa vita brevis," itself a translation of a saying attributed to Hippocrates. 85. See note 64, above. 86. The anonymous Latin encomium has three lines of seventeen, fifteen, and seventeen syllables: "Musica prisca caput tenebris modo sustulit altis, / Dulcibus ut numeris priscis certantia factis, / Facta tua, Hyppolite, excelsum super aethera mittat" (Ancient music of late has raised her head out of the darkness, / So that, with antique and sweet numbers, to compete with ancient deeds, /Your great deeds, Hyppolitus, she might send high above the heavens). For an analysis of this composition, see the introduction.

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Example 54

Continued

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220

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Continued

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Example 54

Continued

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Example 54

Continued

Chapter 55 Demonstration of the Chromatic Genus and Its Species, Composed for Five Voices [70v] Perhaps some people are still doubtful about the genera and whether they can be demonstrated in compositions with the accompaniment of four, five, or more voices. Pupils should be aware that all the genera can be so composed. When the work is for more than four voices, a composer has greater flexibility. Therefore, having discovered that I had written some lamentations for five voices, I selected the example of "Hierusalem" because it is a short work.87 This composition is completely chromatic, without any mixture from other genera. It begins with the 87. See note 64, above.

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chromatic genus, and all the other parts reply in fugue, one after the other. These fugues are beautifully varied, for one part begins the genus with the two semitones followed by the incomposite trihemitone, whereas the other part replies in the reverse, starting with the incomposite trihemitone followed by the two semitones. This is shown in example 55.

Example 55 The Chromatic Genus and Its Species for Five Voices88 (continues) 88. The text, associated with the Lamentations of Jeremiah, was sung as a refrain for the first lessons at matins during theTriduum of Holy Week: "Hierusalem, Hierusalem, convertere ad dominum deum tuum" (Jerusalem, Jerusalem, return to the Lord thy God). For an analysis, see the introduction.

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Example 55 Continued

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Example 55 Continued

Chapter 56 Explanation of the Movable and Stationary Steps and Those That Are Neither Completely Movable Nor Completely Stationary, with Examples [71r] The explanation of the movable and stationary strings or pitches appears in Book IV, chapter 12, of Boethius' Fundamentals ofMusic.^ I discussed those steps—which are neither completely movable nor completely stationary—in my book on Boethius' Music, in ["Music Theory,"] chapter 13. I believe, however, that pupils have not been entirely satisfied, for the discourse was rather obscure on account of its Latinity and also because it was not possible to introduce examples of my practice along with those of ancient practice. But now that these steps have been adapted to practical music, I shall say all that is necessary with examples. So that students [71v] may understand more easily those [modern] steps that are neither completely movable nor completely immovable (besides those of Boethius), I shall explain them better with my practice. As my readers know, in order to cover every aspect of the subject on which they write, philosophers not only discuss the subject but also provide examples of it. For this reason, Boethius decided to illustrate in his book the explanation of those pitches that are written in one stable and 89. Bower translation, Bk. 4, chap. 13.

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firm location: the ones serving as stationary pitches in the genera without alteration either by semitone or by enharmonic diesis. A few other pitches served the species of both the diatonic and chromatic genera without being moved or notated differently in either genus. Others moved in only one genus, whereas still others moved in all three genera. According to what Boethius writes,90 the characters of the stationary pitches were written without ever moving them by any semitonal sign—such as A re, B mi, the high A la mi re, and the first D la sol re—because there were two pitches, B fa and B mi, one written for the diatonic and one for the chromatic genus. The reason was the disjunction of the tetrachords, as was said earlier ["Music Theory," chapter 3], a disjunction permitting the fourths and fifths to correspond exactly at the octave in many locations. Therefore, all sorts of consonances in any location are seen to correspond in my chromatic hand and on my archicembalo.91 To return to the present topic, philosophers invented B fa after the high B mi92 because B fa was changed in its notation. We also use it with the flat to change the whole tone to a semitone; for instance, in our practice, where first they said "mi" for the note, the name was changed by the flat sign and pronounced "fa" with the singing of a major semitone. And after B mi the same was done for E la mi.93 Such pitches were always written in the same way, and since they were not altered in any genus, they were called stable by philosophers [examples 56.1 and 56.2].94 Now on to those pitches that permutate according to the genera, which in my practice are: C fa ut, the second D sol re, and—in the first rank— F fa ut, G la sol re, C sol fa ut, D la sol re, the high F fa ut, and the high G la sol re.95 Having listed these eight pitches, I shall now discuss those that are not completely stationary: the low and high C fa ut, and the low and high F fa; and those that are completely movable in all the genera: 9Q.Deinst. mus.,4.13. 91. For the chromatic hand, see Bk. I, chap. 5. The chromatic pitches on the archicembalo are discussed throughout Bk. V. 92. See Bk. I, chap. 3 and ex. 5.1. 93. Vicentino discussed the application of a flat on E la mi in Bk. I, chaps. 3 and 4. 94. This statement refers to the stable pitches listed in the previous paragraph. Exx. 56.1 and 56.2 show that, the "acquired" low A aside, the diatonic tetrachords are framed by B-E and E-A, respectively, whereas the chromatic tetrachord is framed by A-D. 95. Such terms as D la sol re secondo and nel primo ordine refer to the keys of the archicembalo. But in an effort to stick to the definitions of Boethius, Vicentino becomes confused and does not give the full range of permutations for any of the partially or completely movable pitches listed here. And some of the examples have nothing to do with the text. Moreover, even those pitches here defined as stable become movable on his archicembalo. See Bk. V, chaps. 4 and 5, and App. V and VI.

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the second high D la sol re, the first low D sol re, and the high G sol re ut [example 56.3]. Among the pitches that are neither completely movable nor completely stationary, the ones that are stationary in two genera, the diatonic and chromatic, are: the low and high F fa ut, and the low and high C fa ut [example 56.4]. These are stationary pitches in two genera, that is, in the chromatic and the diatonic. But when C fa ut and F fa ut are written in the enharmonic genus, they come close to D sol re ut and G sol re ut, respectively.96 This is how F fa ut and C sol fa ut move up and down, not through a descent by the minor semitone associated with the ancient diatonic and chromatic genera. Be advised that the movable and stationary steps I use are different from those recorded by Boethius.97 For as I have already indicated [Book I, chapter 6], philosophers used to sing the minor semitone, whereas we use the major semitone, as is seen and heard on instruments. Now on to the explanation of the characters used by philosophers in ancient times to write down the fourths, fifths, and octaves. Whether these notes are written in a particular way in one genus or are associated with two genera, I shall furnish examples of my practice so that students will understand me. After all, examples are useful—but the Greek explanation avails us nothing. In our practice it is unnecessary to learn the mutation of the Greek notes, for we do not use them. I have already put into practice some of the mutations on the hand with the naturals, flats, and [72r; incorrectly numbered 69r] sharps, associated with two genera,98 as well as the sign connected with a single genus, that is to say, the superscript dot associated with the enharmonic genus. These will be amply demonstrated in Book V, on the archicembalo. I decided to provide this discussion of the Boethian pitches with examples of contemporary practice, lest anyone think, merely because of the Greek terms, that Book IV, chapter 12, in Boethius' Fundamentals of Music" states something important. Since nowadays we write these notes with characters different from those used by Boethius, the examples of my practice illustrate which of their notes we write, which notes are not altered in one genus, and which are associated with two genera.100 If pupils experiment with all the rules previously given, they will discover much more by working them out than I have imparted, because in 96. What Vicentino says is that C and F written in the enharmonic genus become C and F. Ex. 56.5 shows the same operation regarding B and E, which move closer to C and F. 97. De inst. mus.y 4.6. 98. The diatonic and chromatic genera. 99. Bower translation, Bk. 4, chap. 13. 100. See notes 97 and 98, above.

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Example 56.1 Stationary Steps in All Three Genera

Example 56.2 Stationary Fourths and Fifths

Example 56.3 Movable Steps in All Three Genera

Example 56.4 Stationary Steps in the Diatonic and Chromatic Genera

Example 56.5 Movable Steps in the Enharmonic Genus

music practice it is mandatory to do and make many things. Having made some compositions in one fashion, let students embark on another fashion, in order to achieve more diversity and thus to gain continuously from composing. It seems to me that I have now written sufficiently on the subject matter of this third book. So, with the help of the Lord our God, I end it here and start the fourth book, which follows directly. End of Book HI on Music Practice

Book IV on Music Practice

Chapter 1 Proem [72v] Having recorded many diverse matters concerning music practice in the three previous books, I shall now in Book IV treat the clefs and show how they are notated in plainchant and polyphony for two or more voices with major or minor modus and with perfect or imperfect tempus. I shall also discuss the following: perfect and imperfect prolation in perfect and imperfect tempus; minim and semiminim rests and other proportional signs; various ways of beating the measure and the patterns for writing colored and white notes as well as notes that contain tied and free dots; different manners of composing various ideas for playing1 and for singing on plainchants or measured polyphony with various canons; how to make many fugues, with a few remarks on accommodating singers; the extreme ranges of composition convenient to singers, that is, compositions for two, three, four, five, six, and seven voices, and for two choirs that are neither too low nor too high for singers; composing a single part; motion and repose; and how to write double counterpoint. Nor shall I omit the following: how the words are fitted under melodies; fitting the pronunciation of long and short syllables to the notes; duplicating and triplicating a passage; how never to lack a compositional subject for various and diverse kinds of music; composing a work in which one part starts at the beginning and another at the end; how a composer should govern himself when writing such varied compositions as motets, psalms, masses, hymns, madrigals, dialogues, and other works that can be sung with a full or with equivalent voices;2 how to set introits, responses, and lamentations; the reliable way to check whether there is an error in all sorts of compositions, even if they are for more than four voices—that is, for five, six, seven, eight, nine, ten, eleven, twelve, or however many seem appropriate to the composer; and many other conditions to be observed in compositions for the convenience of singers. l.SeeBk. II, note 2. 2. The term a voceplena refers to singing in a natural range with full chest voice (see Bk. II, chap. 23, and Bk. Ill, chap. 44) whereas a vocipart means parts that may substitute for missing voices. Elsewhere in this book Vicentino uses a voce mutata and voce mutabile to denote high parts sung in falsetto (chaps. 26, 38, and 39).

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Thus can everyone easily learn my music practice. A pupil who wishes to make a start in comprehending it must first understand the signs of the clefs, which will later open his senses to those elements that lead to the knowledge of my practice.

Chapter 2 Demonstration of the Signs Called Clefs by Practitioners When the door of a house is locked with a key and someone wishes to enter through that door without breaking it, he must have the proper key to open the door. The same thing happens in music practice, for its practitioners have invented some signs that they write at the beginning [73r] of the music. These are called clefs, because it is by their means that pupils learn to open the locked door of compositions. To help pupils learn more easily to recognize the signs, or clefs, of polyphony and plainchant that have been and are still in use, I shall demonstrate them with examples. I write first the natural soprano clefs we use and after them the other clefs. These, then, are read according to the soprano clefs, for the latter make intelligible all the clefs of the other parts. Moreover, the natural soprano signs help you to recognize other clefs written with accidental signs, for the identical names of the soprano notes are likewise read as the notes of the other parts. Even though I showed the signs of the clefs in Book I [chapter 3] of my "Music Practice," I shall not refrain on this account from showing those clefs used in polyphony, in order to adhere to the organization of my demonstrations. Lest anyone say that I promised in the first Proem ["Music Theory," chapter 1] not to repeat things said by others, I have excused myself on a previous occasion [Book III, chapter 1]. I explained then that to observe the order of the rules, I am forced to say a few things said by others. I shall not, however, say them in the same way, nor without adding something new for my readers. Signs or clefs are usually written in all the parts of polyphonic music. Therefore, the sign of the high G sol re ut is written on the second line. Although some people are in the habit of occasionally writing it in the

Example 2.1 Examples of the Clefs

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bass, this is not done frequently. In addition, the clef of C sol fa ut is written in the soprano as well as in the contralto, tenor, and bass; and in the latter part, F fa ut is written as its clef, as seen in example 2.1. You will also find the clefs and the models for learning to read them in any other clef from the pitch series in the soprano.

Example 2.2 The Soprano Clefs That Teach You How to Read All Other Sorts of Clefs in the Natural and Soft Hexachords and in Feigned Music3 [73v] Example 2.2 demonstrates that the soprano clefs, each with its own pitch series, show you how to read the other clefs. The first series has below it two sets, one for the contralto and one for the bass, both of which are to be read similarly to the soprano. In the same way, the second and third series have two sets beneath them, both indicating that 3. On feigned music, see Bk. Ill, chap. 14.

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their series should be read according to the notes of the soprano. The exception is the fourth series, which has four sets beneath it. I shall now demonstrate some other natural examples, in addition to those given in example 2.2. The sets written below these series are to be sung like the natural set, as is evident in example 2.3.

Example 2.3 [Other Natural and Accidental Clefs] [74r] These are the clefs that have been and are still used now. In the next book [Book V, chapter 59], I shall show with many series how you can read the clefs written for compositions intended for my archicembalo; and also how all of them are read differently from the ones given here.

Chapter 3 Demonstration and Explanation of the Major and Minor Modus, Both Perfect and Imperfect Many writers on music have given information on the signs of the cut and uncut circle and semicircle with the prolation, as well as the major and minor modus. They have juxtaposed these signs against one another

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in so many ways that it seems almost superfluous for me to repeat them, for today we do not usually juxtapose them in that way. Nonetheless, I shall discuss a few of the less frequently used signs, even though today we should concentrate on new inventions in composing musical steps and leaps that create gentle or harsh harmony. Indeed, because these circles and semicircles do not make any harmony whatever, many composers have abandoned them all. Instead, they use a certain rule whereby compositions are measured, causing a notational shape written as a breve to be sung as if it were a semibreve. The same effect arises from the proportions that diminish or augment the value of notes. Whenever a composer wishes to make a canon of some sort, he avails himself of these juxtaposed signs. Today he takes care to make difficult things simple rather than to behave as was customary before—namely, in making simple things excessively difficult4 without any harmonic enrichment. We come now to an explanation of a few of the signs. Readers should know that in polyphony there occur some signs of the major perfect and the major imperfect modus that are called pauses by practitioners. The major perfect modus is written with three strokes of pauses that span three or four lines. When they span four lines, the maxim has the value of three longs. But in the major imperfect modus, the maxim is worth two longs; then we write two strokes of long pauses that span three or four lines, as seen in example 3.1. Sometimes, the modus becomes minor perfect when the long is equivalent to three breves with one stroke of pauses spanning four lines. But when the long is worth two breves and the stroke of pauses spans three lines, then the modus is minor imperfect, as in example 3.2.

Examples 3.1 and 3.2 [The Major and Minor, Perfect and Imperfect Modus]

4. Vicentinos variant of a popular slogan attributed to Aristotle is probably taken from Franchino Gaffurio, Pmctica musicae, Bk. I, chap. 3, and Bk. II, chap. 8.

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Chapter 4 Demonstration and Explanation of Perfect and Imperfect Tempus [74v] Philosophers have reckoned that all things in the world consist either of time or of measure or of weight.5 And so, practitioners of music decided to represent pauses by short lines, perfect tempus by the circle, and imperfect tempus by the semicircle. Because philosophers call the mathematical disciplines pure, musicians decided to select three geometrical figures—the line, the semicircle, and the circle—that are closely related through arithmetic, so to speak.6 When a musician wishes to indicate the perfect long and breve, he writes the circle, for practitioners use the perfect semibreve in perfect tempus. Moreover, when two semibreves are located between two breves, the second semibreve is always equivalent to two semibreves. In the case of two identical breves, the first is perfect because it precedes the second one. If the second of these breves precedes a semibreve, it becomes imperfect because the latter is not the same value as the semibreve, which is then worth two semibreves of the perfection. Many people have written at great length about alterations. They have talked also about imperfect tempus, in which the long is worth four semibreves, the breve two semibreves, and the semibreve two minims; about perfect tempus, in which the long is worth six semibreves, the breve three semibreves, and the semibreve two minims; and about the stroke for the pauses that spans three lines worth six semibreves in perfect tempus and four in imperfect tempus. These matters are so well known and so banal to every practitioner of music that any pupil may have his doubts about them allayed by any mediocre music practitioner.7 Example 4 presents examples of perfect and imperfect tempus. 5. A paraphrase of well-known words from the apocryphal Book of Wisdom, also called the Wisdom of Solomon, 11:20: "Thou has measured all things by measure, and number, and weight." Likely sources are St. Augustine, Confessiones, 5.4, and De civitate Dei contra paganos, 12.19; Cassiodorus, Institutiones divinarum et saecularum litterarum, 2., "Praef," and Isidore, Etymologiarum, 3.4. 6. Vicentino puns on Germane (pure) and germane (closely related). The latter referred to siblings born of the same mother and, by extension, to anything pure or unadulterated. The primary meaning is given by Isidore in his Etymologiarum, 9.6. He also calls certain types of geese germane because they nourish their young more than other types (12.7). The notion that arithmetic, the science of abstract numbers, should nourish the existence of subsidiary sciences, such as geometry and music, is an esoteric but not implausible inference in the text. 7. See chap. 31, below, for more on this subject, with a direct reference to Gaffurio.

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Example 4 [Perfect and Imperfect Tempus]

Chapter 5 Explanation of Perfect and Imperfect Prolation in Perfect and Imperfect Tempus Earlier I discussed modus and tempus. There now follows prolation, which is indicated by musicians by a dot in the middle of the circle or semicircle. This prolation is called either perfect or imperfect depending on which sign accompanies it. When the dot is in the circle, the prolation is perfect in perfect tempus, whereas when it is in the semicircle, the prolation is perfect in imperfect tempus. In addition, imperfect prolation in perfect tempus is indicated by a circle that lacks a dot in the middle; when the semicircle appears without a dot, the prolation in perfect tempus is such that the semibreve is worth three minims. The same equivalence occurs in imperfect tempus with perfect prolation. Imperfect prolation in perfect tempus occurs when the semibreve is worth two minims, and the same happens in imperfect tempus when the prolation is perfect, as in example 5.

Example 5 [Perfect and Imperfect Prolation]

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Chapter 6 Demonstration and Explanation of Some Juxtaposed Signs [75r] Many times it is necessary for composers to take these signs and juxtapose them in order to be able to double or halve the value of the notes in canons. They can thus triple and quadruple the value of the same notes by signs and proportions. In example 6 I have written down which signs are worth one-half more or one-half less when one sign is notated opposite another. These signs are notated with and without prolation, with and without perfection, with major or minor modus, with the circle or the semicircle, and cut or uncut. When the uncut circle is juxtaposed against the cut circle, the former is worth one-half more than the latter, as here, O (j). Likewise, the uncut semicircle is worth one-half more than the cut circle, as seen here, C . The same goes for the uncut semicircle, C D, which in reverse is worth one-half less. When a composer wishes to restore a sign so that the previous one no longer obtains as before, he puts this sign below the first, which will then lose its value. I have gathered many signs juxtaposed against one another in example 6.

Example 6 [Proportional Signs]

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Chapter 7 Explanation of the Breve and Minim Rests, and the Order in Which They Must Be Placed [75v] Whenever a composer writes a composition, he is advised not to give singers too much trouble but rather to accommodate them with frequent rests (called pauses by the Greeks), which occur after the periods or endings of Latin or vernacular speech. Every time one or more pauses are made with the breath, listeners think that the singer has made a period or an ending to the subject or idea previously begun. But some people often compose twenty-five to thirty tempora without a single resting place, be it the value of a minim or breve.8 A singer is thus forced to stop singing and take a breath because he can proceed no farther in this lengthy passage without resting a little with either a breve or a minim rest. Two errors arise from this unsuitable situation. The first occurs when a singer takes a breath by means of an unwritten minim rest, which could occur between two fifths or octaves. But listeners will hear the two fifths or octaves. For a minim rest does not cancel these intervals unless the composition is for more than five voices, in which case the error is not perceptible owing to the multitude of voices. The second error happens when a singer decides to breathe on a note and, as a result, the composition is missing a consonance. Such harmonic impoverishment will be noticeable unless the work is for six or more voices. But if he is silent on an octave when there are only a few voices, a singer does no damage to the composition. Composers should therefore insert breve or minim rests at frequent intervals for the sake of singers. Moreover, rests are useful in composition, especially those for more than four voices, because silence is always preferable to unseemly singing. It is good to hear the parts entering one after the other in Latin and vernacular works for five or more voices. 8. Vicentino's sloppy use of sospiro/sospiri here and elsewhere creates a terminological muddle. First, sospiro is used in the then-common sense of "breath" (see Bk. II, chap. 3). Second, sospiro and mezzo sospiro refer to notational values for rests: to be precise, those of the minim and semiminim (see Bk. IV, chap. 1). In this chapter mezzi sospiri are not named although they appear in exx. 7.1 and 7.2. Third, even when the technical (i.e., notational) meaning of sospiro is easily distinguished from the ordinary one, it is difficult to ascertain the exact value designated by the term. Most of the time, it seems to mean a smaller rest as opposed to a larger one, generally called pausa. The technical meaning ofpausa is a breve rest, ofsemipausa a semibreve rest. The latter appear in the examples without being listed in the headings. To complicate matters, Vicentino also uses pausa in the general sense of pause or rest.

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Besides all this, composers are advised when notating rests to write them out in an order that looks good to singers, whether they are two minim rests or two breve rests in the major or minor, or perfect or imperfect modus, as in example 7.1. As it happens, some composers are in the habit of writing disorderly rests, but others write in an orderly way, so that a binary unit falls on the downbeat of the measure. Thus the ear perceives no clash between even and uneven rests. However, even though they are traditionally supposed to be even, whoever fails to make them so commits no sin against the Holy Spirit. For such usages do not offend the ear, only the customary obedience to the binary number. Let us now attend to the matter of helping singers (if possible) by means of rests. It seems to me useful for singers to see a breve or minim rest written between awkward leaps—such as of the tritone, major sixth, seventh, or ninth—in place of a proper leap or consonance. For instance, if a singer has to leap a tritone after a breve or minim rest, he may then imagine that same breve or minim rest to be a leap of a third or fifth; and if the leap in question is a seventh or a ninth, then he will imagine the rest as a leap of an octave. For in the singer's imagination, the breve or minim rest points the way to a proper leap. A singer who has the mental image of the proper leap can accurately sing any kind of awkward leap easily and without much effort.9 Minim and breve rests act as guides leading singers down the path of good intonation for awkward leaps, as is seen in example 7.2.

Example 7.1 Rests Notated in Perfect and Imperfect Tempus

Example 7.2 Awkward Leaps with Breve and Minim Rests Written in the Place of Proper Leaps

9. See chap. 11, below.

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Chapter 8 Rule for Beating the Measure in Three Patterns, with Examples [76r] Beating the measure is a certain rule to which all composers and experienced singers submit, for without measure it is impossible to sing musical compositions. By beating the measure, experienced singers agree with one another when performing together, so that none of them goes faster or slower than another. This measure has three patterns. The first pattern is called beating alia breve, because one breve or two semibreves fall under one beat in minor imperfect tempus. The second pattern is called beating to the measure of the semibreve in perfect tempus, because it was once customary to sing three semibreves per beat, in emulation of the ternary number. Today it is no longer used except in equal proportion. The third pattern of beating the measure is called sesquialter proportion. When a composition is marked with the sesquialter ratio, both the semibreves and minims are sung two against three. These patterns are shown in example 8.

Example 8 [Beating the Measure]

Chapter 9 Rule for Writing Note-Values in an Orderly Way, with Examples [76v] All systems governing things were instituted first by nature, then by men. In music we have eight note-values observed in the compositions of our predecessors. These composers kept the following order: they notated the long after the maxim, the breve after the long, then the semibreve followed by the minim, then the semiminim and the croma, and finally the semicroma [example 9.1]. Today this order is not followed completely as regards the maxim and the long, because nowadays few composers write these note-values in their compositions. These notes afford little variety. For instance, having written a third, fifth, sixth, or octave below or above, a composer cannot provide other consonances below or above these notes except for the octave of these consonances,

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and these octaves are identical to the consonances mentioned before. Thus the maxim is not used by the moderns except as a cipher to indicate lessening by one-half. And very few longs appear in compositions because (as was said) little advantage is gained from them. But it is true that longs are used in canons and other severe compositions. In these cases the long is followed by the breve, then by the semibreve, minim, and semiminim. This order is appropriate to severe matters. However, in certain other compositions, you may break the order, in keeping with the subject matter and the words. Composers should manage things so as to use certain median terms that lie between extremes; for instance, wholly consonant syncopes made of semibreves that can be followed by semiminims, as in the modern manner of composing. But some other methods are not good, as I show in example 9.2.

Example 9.1 The Order of Proceeding with Note-Values

Example 9.2 [Good and Bad Methods of Ordering Note-Values]

Chapter 10 Rule for Writing Black Notes Under the Perfect and Imperfect Sign, Under Major and Minor Hemiola, and Under Equal and Sesquialter Proportion [77r] Black or colored notes are used in both plainchant and polyphony. The black notes of plainchant can be mixed with those of polyphony. All plainchants have their own colored notes, both square and round [example 10.1]. Because many people have recorded the rules for the latter,

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I shall not embark on a discussion of them except insofar as they are mixed in polyphonic music; for instance, when the long, the breve, and the semibreve are black in perfect tempus (the latter to imperfect the others whenever they are perfect). In addition, minims are colored to make semiminims, and cromas to make semicromas in perfect and imperfect tempus. Right now I do not want to take time to repeat what many others have said. To proceed in an orderly way, however, I state that in imperfect tempus semibreves and minims are colored; the latter are sung four against one semibreve, whereas colored cromas are sung eight to the beat and semicromas sixteen to the beat. It is customary to color all the notes in a composition marked by the number 3, although some people omit the number because all the notes are black. Practitioners call a composition written all in black notes major hemiola because three semibreves or one breve and one semibreve are sung per beat. When three black minims or one [black] semibreve and one black minim are written per beat, such a composition is called minor hemiola by practitioners. Others mark completely black songs with the uncut imperfect sign, and when performing any such composition singers refer to "singing to the measure of the breve." All these are seen in example 10.2: colored notes in perfect and imperfect tempus with and without proportions.

Example 10.1 Colored Notes in Plainchant

Example 10.2 [Colored Notes in Polyphony]

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Chapter 11 How to Teach the Singing of Upward and Downward Leaps of the Tritone, Minor Sixth, Major Sixthy Seventh, and Ninth It is often necessary for composers to write very bad leaps that are awkward for singers. Such leaps, either ascending or descending, are required as much by tenseness as by slackness.10 When a composer wishes to make a bad leap, he is advised to write [77v] either the octave, fifth, or another proper leap just before it with the note before the one making the [bad] leap, upward or downward. As to the master who teaches singing and the pupil who learns it, if both are alerted to make the proper leap on the note antecedent to the one that will make the [awkward] leap, they will never fail to sing that leap accurately. Here is an example: on a part located on C col fa ut, you plan to make a cadence such as fa-mi-fa. When a singer produces the first "fa," he must keep in his memory the octave of that fa. And when he sing the "mi," he will then remember the first fa, which easily directs him to the intonation of the upward leap of a ninth or a downward leap of a seventh. This way of learning to make an awkward leap of a seventh or a ninth also serves as a guide for doing the same with all other leaps—that is, imagining the octave, third, fifth, or fourth above or below such leaps by means of the imaginary note. A singer must imagine to himself everything required to use the imaginary note according to the leaps. Very often a leap of a seventh or a ninth occurs on an entrance, and in this case you must imagine its proper consonance either above or below. A singer, therefore, has two ways of singing awkward leaps, one demonstrative and one imaginative. The demonstrative way occurs when the note before the leap demonstrates what constitutes the proper leap either by its octave or else by another consonance above or below. In the imaginative way, any [awkward] leap is initiated at the start of a composition or immediately after one or several pauses, without an antecedent guide for the imagination, but rather with a subsequent guide. Both are demonstrated in example 11.

Example 11.1 The Demonstrative Note Antecedent to the Note Initiating the [Awkward] Leap 10. See Bk. I, chaps. 35-42.

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Example 11.2 The Imaginative Note Subsequent to the Note Ending the [Awkward] Leap

Chapter 12 Demonstration of the Tied and Free Dot Used in Music Some authors have written that the dot in music practice is used in three ways. The first is called the dot of augmentation: it is written directly after the note and augments it by the addition of one-half its value. The second dot is called the dot of division: it is customary to write it in perfect tempus to divide or separate perfect from imperfect notes. Some call this the dot of transportation, because it transports the note far away from its companions on account of the ternary number. This dot neither diminishes nor augments the note but merely separates it, as is seen in example 12. The third dot is called the dot of perfection: it makes the note perfect, as in the case of two semibreves in the dotted circle or semicircle of perfect prolation. In this instance, when two semibreves follow each other, the first becomes perfect by virtue of the power of this dot. In addition, when there are two minims between two semibreves, the second becomes perfect [78r] and has the value of two minims in perfect prolation.11 Other dots are used at the end of a composition, along with vertical lines: these tell you to return and repeat the same music. I have invented two signs. One of these, called the comma, is written with a small reversed "c" and it raises the note over which it is placed by one comma. The other sign that is put over the note is a dot I call the dot of elevation of pitch. For when it is placed above a note, either to the right, in the middle, or to the left, it raises the pitch by one-half of a minor semitone. The dot representing this kind of division is called enharmonic diesis, as I said earlier [Book I, chapter 13]. These dots are notated in example 12.

Example 12 [Tied and Free Dots] 11. Probably Gaffurio, Practica. musicae, Bk. II, chap. 12.

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Chapter 13 Some Comments on the Dot of Augmentation Written in Various Ways The dot is used in various ways in compositions to make varied and diverse effects when matched with consonances or dissonances. Composers are advised that the dot of augmentation, when tied to a note, must always be consonant, except for cadences using diminutions that show the dissonant dot of the seventh, second, fourth, ninth, eleventh, or fourteenth, as in example 13.1. When the dot is against the dissonance of the second, it is better with the step of a semitone than with that of a whole tone. This is true of all dissonant dots, with and without syncopation. Sometimes the dot is used with a wholly consonant syncopation on the beat. But be careful that the dissonant dot is not made against the beat unless the words oblige you to use it to represent fatigue or anguish, because it will seem as if this dot cannot be sung. Composers should take great care with these dots, especially the dots for the semibreve, because almost all singers sneak a small breath instead of singing over the dot, except when these dots are at the start of a composition or directly after a rest.12 To remedy this defect, composers should superimpose an octave or a unison on the dot, so that compositions will not have sparse harmony, lacking either the fifth, third, tenth, or twelfth, as I said earlier [Book II, chapters 3 and 6]. Another remedy can be effected if composers are careful not to put these dots in places where a singer has been singing for too long a time and therefore omits the dot in order to take a breath, as happens in the middle or near the end of a composition, when singers are exhausted. This advice is useful with respect to composition, for I have heard such errors many, many times. In my two-voice examples, dots of augmentation of the value of a note, both consonant and dissonant, are [78v] shown along with a reminder of a minim dot, above or below which is placed a different consonance, and dots between two octaves or fifths that salvage these [parallel] pairs of intervals.

Example 13.1 The Dot in Syncopation 12. See chap. 7, above.

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Example 13.2 Dots That Salvage Two Octaves or Fifths

Chapter 14 The Method to Follow When Beginning a Composition Before devising the start of any kind of composition, a composer must first consider what he is going to write about. If, for instance, the subject at hand is a Mass, he will construct it on a plainchant or a motet or other ideas. The beginning of a Mass ought to have a somewhat severe character, and this goes for all things Latin. In contrast, a medium pace is customary in such secular items as madrigals, sonnets, chansons, and other similar compositions. And there are other secular items that require a rapid beginning, such as villotte, Napolitane, and the like. Whenever the beginning is to be written with a fugue, or without a fugue but with one voice entering after the other, the composition will sound well if the voices follow each other at the same distance, be it a minim or one, two, or three breves. It should be noted that a distance of five or six breves is not good; even a distance of four breves is a little too much. The pitches for the first entries must be well chosen so that singers can produce secure intonation upon entrance, especially in compositions for the church. Consequently, the beginning of a composition may have entries at the unison, fourth, fifth, octave, tenth, twelfth, or fifteenth, but not at the second, minor sixth, major sixth, seventh, or ninth. Such dissonant entries, however, are acceptable at the start of the second part of the composition, since the ending of the first part will have already prepared the singers' ears to tackle any kind of awkward note. It is also good occasionally to hear the deception whereby one voice enters on the downbeat, the second on the upbeat, the third on the downbeat, and the fourth on the upbeat. This kind of metrical variety is a source of pleasure.

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It is also important to note that at the beginning [79r] of a composition, the voices should not enter at extreme ranges—for instance, a soprano very high and a bass very low. This kind of opening, heard in compositions that are not very modern, strikes the ear as crude. You should always begin with voices that are most appealing to the ear, as are tenors and contraltos. As for basses and sopranos, they should be in a medium range so as to avoid extremes that sound strange to the ear. When a composer opens on a plainchant, he should not begin with a minim, for it sounds poor. But a minim rest before the minim makes a good beginning. Nor should a composer begin a composition at a rapid pace. Rather, in a graceful way he should gradually persuade his audience by his elegant and fine beginning. The aural effect will be much better if the beginning is made on the consonance of the third or the fifth rather than on the unison and the octave.

Chapter 1513 The Method to Follow in the Middle of Any Sort of Composition The Philosopher [Aristotle] says that between two extremes there is a middle.14 In compositions, therefore, there exist the appropriate boundaries of the beginning, the middle, and the ending. Having discussed the beginning in the preceding chapter, I must now talk about the middle. This is the part that keeps the range of the melodic contour of the mode on its feet, especially when the composition is to be a sacred work that is followed by a response from the choir. But in the parts between the beginning and the middle, and between the middle and the end, it does not much matter whether you insert some passage or other that lies outside the mode, provided you approach the final part elegantly, by starting in good time and moving gradually and surely toward the pitches and location of the tone or mode. Thus, will you proceed in an orderly way and in keeping with the subject of the composition. If the work is for five, six, or seven voices, it is sometimes good to write a duo, trio, or quartet in the middle. It seems to me, however, that in a composition for many voices a duo is too weak to satisfy an ear that has been sated by many voices, as in the case of a sextet or septet. In short, you must give some thought to what sort of composition you are writing and show some judgment about it, whether it is on a sacred or other subject. When a composer introduces a duo, trio, or quartet in the 13. Misprint: text has XVI. 14. See Bk. II, note 15.

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middle of a work, in keeping either with the words or with the arrangement of the idea,15 he may cause the parts to enter one after the other, or altogether, or sometimes to be silent. It is the subject matter and the words that lead to an understanding of how the entire composition should be written, for certain incidental things cannot be taught unless you see the subject first. Of course, some commonplace things, such as certain stable limits in the ordering of cadences, can be regulated. But as to the procedure for motion and diminutions, any student with a little judgment will govern himself so as to accommodate the subject on which he must write his composition. When a student wishes to make one part enter after the other in the middle of a composition, he must not wait for one part to finish before introducing the other. Rather, he must introduce the second part by at least the second half of the last note of the part that is finishing. Also, it is good to hear the parts in the middle sections enter all together on an identical consonance placed in various locations; for instance, it is good if all the parts enter on a third or a fifth, so that one enters in the high range and another in the low, while others touch on various pitches in between. The student is advised not to make an entry on the unison or octave, because listeners always expect something new.16 Because the unison and the octave produce the same consonance they made previously with each other, the parts should not enter with either one. Composers should not conclude the middle of a work with a minor consonance the length of a breve. This ending sounds poor unless it is occasioned by a sad word. Moreover [79v], ascending minor consonances are rather inappropriate at the beginning because they are unreliable and prone to expansion;17 they are, however, acceptable when they descend with sadness. In the middle of a composition a part may enter over a syncope on one-half of a dissonance, such as the second, seventh, or ninth. However, it is preferable to have a minim rest than to enter on the syncope. But this does not go for the fourth, because it sounds well under a syncope. Above all, let the composer strive to please the listener. He should not cause a part to begin on a minim without a preceding minim rest, nor should he end with a minim after breve rests in Latin or sacred composi15. In this context, cosa seems to be a synonym for fantasia, the most frequent noun referring to instrumental or abstract musical themes. See Bk. II, note 2. 16. On the element of surprise, see "Music Theory," chap. 16, as well as "Music Practice," Bk. I, chap. 24, and Bk. Ill, chap. 48. 17. On the problem of minor thirds raised to major thirds, see Bk. II, chap. 14.

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tions. It is true that often the words constrain a composer to do such things. Nevertheless, the less such things occur the better. And so, with the many comments made above on the procedure for the middle of a work, you can move on elegantly to the ending, about which I shall speak in the next chapter.

Chapter 16 The Method of Devising the Ending of Compositions The ending of a thing is the conclusion of its beginning and its middle. Moreover, the ending is the perfection of the thing initiated, a perfection developed from its imperfect beginning and middle. Some old-fashioned composers consider it a mistake if a composition begins with an imperfect consonance. They do not realize that the perfection of a thing consists of a good, elegant, and perfect ending. If every composition had an elegant beginning, a bad middle, and a worse ending, it would not be pleasing. But a composition in which the beginning is not too good, the middle an improvement, and the ending remains elegant, good, and perfect to the ear would gratify everyone. However, when the beginning is good, the middle better, and the ending best and perfect, the entire composition is then most pleasing. As a consequence, it is not a grave error to begin a composition on an imperfect consonance in order to arrive subsequently at the perfect ending. For the beginning of an oration is not so important as the ending.18 It is now time to steer composers to the perfect ending. When a composer plans the beginning of a work, he should at the same time consider the middle and the ending so that the direction of the subject easily leads to its own direct and perfect ending. If a composer has not first decided on the purpose and goal, so to speak, toward which the subject will be directed, how then will he, without having first discovered it, proceed by a direct path to the determined ending? Many times it is necessary to make the ending of a composition before the beginning. Thus, the goal established, you can lead up to it with ease. A composer, therefore, acts like a good traveler who, before his voyage, first decides on its goal. Having gathered together everything necessary, the traveler sets out and tries to reach the destination by the most appropriate routes possible. The same goes for composers. Whenever a composer must set to music hymns, psalms, or other material to which a choir must respond, he 18. For a similar but not identical pronouncement on the conclusion, or peroratio, in oration, see Quintilian, Institutio oratoria, 6.2.1 and 6.1.51—52.

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should take care that the tone or mode is present in the ending so that the choir can respond to the ending in the proper mode. However, in setting madrigals and other vernacular texts that do not require response from a choir, a composer may finish outside the mode for the sake of imitating the words, for there will be no disagreement except with the initial mode. But experienced composers, who first write the ending, work up to it so elegantly that the listeners are not aware that the piece does not end on the initial mode. Such a composition proceeds by means of a sure and elegant technique of gradually leaving one mode for another in a leisurely way, without disturbing the audience, whose sense of hearing is left satisfied. Composers [80r] should govern themselves by the rules and by their judgment, depending on the subject proposed to them. When a composer plans to finish with a particular passage, he must take care that this passage is in the mode in which he must end—again, depending on the composition required of him. If this passage is to proceed with the bass, tenor, contralto, and soprano, composers should not transfer the effect19 of the tenor or bass to the other parts. Indeed, it would seem that such a passage is better in the middle than at the end of a composition. For you must not abandon the technique of ending the work while taking into account the nature of the parts, especially in a composition for two, three, or four voices. If, however, a work has more than four voices, it is acceptable for one part to take over the action of another at the end—if, say, the soprano provided the tenor or contralto action in six, seven, or more voices.20 It is much better to end with the fifth than the third over the fifteenth. In approaching the conclusion, neither a single nor several breve rests are used, because the repose granted to the parts indicates to listeners that the composition will continue for some time rather than come to an end. But a minim rest near the end is acceptable. For it is not as bad to write a minim rest without losing a consonance as it is for singers to make an unwritten minim rest and lose a consonance.21

19. Elsewhere Vicentino uses atto/attito identify the cadential motion of individual voices. See Bk. Ill, chaps. 33 and 43, and below in this chapter. 20. See Bk. Ill, chap. 29. 21. See chap. 7, above.

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Chapter 17 How to Keep to the Limits of the Parts in Measured Composition, with an Example The convenience of singers demands that there be limits to the parts of a measured composition, so that any ordinary voice can easily sing its part. This convenience is owed both to good voices and to those that are neither too flexible nor vigorous. To understand how to proceed with each part, composers should observe the following system. The tenor may ordinarily ascend twelve to thirteen steps above the bass, the last step being more accessible by semitone than by whole tone. The contralto may ascend above the bass fifteen to sixteen steps, the last by semitone. The outer limit between the soprano and bass is nineteen to twenty steps, the last one also a semitone. These outermost limits are convenient for compositions for four, five, six, and seven voices. But when a work is for eight voices, the soprano may ascend twenty-two steps above the bass for the greater accommodation of the parts. No line should ever be added above or below the five staff lines in any part. Nor should clefs be changed in the middle or at the end of a composition, because this is the same as adding another line to the five. Such a part will be either too high or too low for the singer. For this reason, composers must stay within the limits imposed by the lines and spaces of the staff.

Example 17 The Limits [of the Parts]

Chapter 18 How to Compose a Single Part ofPlainchant [80v] It is often necessary to arrange a plainchant in order to build some kind of canon on it, or else to write a plainchant for the service of the church, a chant to which an antiphon, an introit, or some other Latin text in prose or verse will be set. A composer must first consider on which mode, whether authentic or plagal, he will build his chant, and then he will select the boundaries of its fifths and fourths so as to form that mode

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in a refined manner. He should take care never to linger unduly on a tritone in the melodic contour, for this interval really bothers the listeners. Rather, he should proceed with true fourths so that everyone can sing the plainchant with ease. Example 18 shows the perfect mode, as well as the contour of the tritone. I shall not at this time talk about which modes are perfect, imperfect, or pluperfect, nor which pitches are final or judicial, nor which tones are mixed or commixed, nor the many beginnings possible in plainchant, which must always be judged by their endings. For many authors have filled entire books with these matters.22 Nor shall I embark on a discussion of the many errors of plainchants. If I were to describe the errors in notes and words imposed on plainchants by barbaric pronunciation,23 it would cause everyone too much agitation and bother. For instance, syllables that should be long are made short, and vice versa. How crude it is, too, to hear many notes sung on one vowel with the reiteration of those notes pronounced in this way: a-a-aa-a-a; e-e-e-e-e-e; i-i-i-i-i-i; o-o-o-o-o-o; u-u-u-u-u-u. Thus singers move listeners more to laughter than to devotion. Example 18 demonstrates the perfect mode and the contour of the tritone.

Example 18.1 The First Perfect Mode

Example 18.2 This Contour Is Not Good Because of the Tritone

Example 18.3

This Contour Is Good Because It Avoids the Tritone by Means of the Flat

22. In addition to the authors on polyphony whom he had read (e.g., Gaffurio, Practica musicae, Bk. I, chaps. 7-15; Glarean, Dodekachordon, Bk. I, chaps. 11-15, and Bk. II, chaps. 36-37; and Stefano Vanneo, Recanetum in aurea (Rome, 1533), Bk. I, chaps. 47-56), Vicentino may refer to such instruction books on plainchant as Cantorinus ad eorum instructionem: Qui cantum ad chorum pertinentem breviter et quamfacillime discere concupiscunt (Venice, 1540). 23. On barbarisms, see Quintilian, Inst. ora., 1.5.17—33, and Isidore, Etymologiarum, 1.32.

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Chapter 19 How to Put the Flat, Natural, and Sharp Accidentally into Latin Compositions, with Examples To help the consonances, it is often necessary to assist them with a natural, flat, or sharp in order to make minor consonances major and vice versa, and to make fifths perfect. So that these inflections [81 r] will not seem strange to the ear, it is a good idea for composers, before sounding the pitch with the flat or the natural, to write above or below it a note that corresponds to the fifth or the fourth of the antecedent note. I shall not stop to discuss the nature of either sign, for I have already stated that every time certain signs are placed in compositions they accidentally change the nature of the melodic contour: the flat imparts melancholy, whereas the sharp makes a composition cheerful and also alters the nature of the work when it is inserted accidentally [Book I, chapter 10, and Book II, chapters 16-19, 27, 30, 33, 36-38, and 40]. The system to be followed for one sign is the same as for the other in Latin and sacred works. But in vernacular pieces, owing to the words, this restriction is sometimes not observed in the endings or in other similar passages in the middle of compositions. The flat is better positioned after a lower note. The natural and sharp, on the other hand, are better before a descent rather than an ascent. These rules are illustrated in the two-voice sacred Latin settings in example 19.

Example 19 The Antecedent and Subsequent Fifth with Good and Better Progressions for Naturals, Flats, and Sharps

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Continued

Chapter 20 How to Stand Still and How to Move in Compositions Movement and repose bestow much grace on compositions. A certain amount of repose in keeping with devout words in motets induces considerable devotion, whereas motion induces cheerfulness. When a composer is writing a cheerful motet, he must see to it that the parts move continually, right up to the end, and that of the four singing parts at least one is in motion. If the others are in motion as well, they will have a good effect. When all the parts [81v] move at one time, the aural effect is bad. Some composers have the habit of moving all the parts in their compositions, frequently syncopating them together. But this motion is not unequal, and it is unsuitable because there is no difference among the parts that move at the same pace. Therefore, the technique of syncopating simultaneously could almost be called standing still. It should be used sparingly in motets and in madrigals with minims, which are less unsuitable than other note-values. Sometimes it is good to hear simultaneous motion, as in villotte, Napolitane, and madrigals as well as in French chansons with a fast pace. Depending on the words, repose and movement lend grace to compositions. When a composer requires repose on a consonance in the middle of a composition, it is infinitely better to stop on a major than on a minor third. If all the parts stop in the middle with a pause, listeners will think the composition is finished. For this reason, composers should be wary of stopping the parts simultaneously in the middle of a work. Some composers even write a breve rest for all the parts at the beginning of a composition, which is truly unsuitable. For when the singers are about to start singing and glance at one another, this rest induces more laughter than singing. If all the parts have a minim rest, it is less unsuitable, though not much better. It is best when among four singing parts, one begins while the others have a breve or minim rest.

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Chapter 21 How to Write a Harmonious Composition That Is Cheerful or Sad Without Poverty of Consonance The entire substance of music consists of knowing how to provide the motion, steps, and consonances appropriate to the subject on which you are composing.24 First, let me warn you that consonances are the most important of the three resources, for the following reasons. As composers should realize, the ear feeds on consonances, and if it hears steps with motion but without consonances, as produced by someone who sings alone with steps and motion but without consonances, it will not be satisfied. The same happens in the opposite situation. In singing, it is not good to work with motion and steps but without consonances. If the ear feeds more on consonances than on hearing a single voice composed of steps and motion, then consonances must be the most important, because they create harmony without any subordination to steps or motion. But when consonances are matched with steps and motion according to the subject, the composition will be good. Lest pupils fail to learn these three systems and how to match them together, it is necessary to talk first about the main consonances that occur in music. For if these are lacking in a composition, it remains harmonically impoverished. Moreover, the piece remains insipid not only when both the third and the fifth are lacking but also when only one is missing. Composers are advised to so devise the composition that it never lacks these consonances—that is, the third and fifth, the fifth and tenth, or the tenth and twelfth. For when it is made in this way, the composition will always be full of harmony. If a composer wishes to make a work cheerful, he should always match a fast or very fast rate of motion with tense steps and take care that the major third and major tenth are never missing among the consonances and unisonances.25 On the other hand, if he wishes to make a [82r] melancholy composition, he should do everything exactly the opposite to that in the cheerful work: he should select a slow pace and slack steps and use minor consonances. But daily we hear the contrary in compositions, for on a sad word certain composers use fast motion, tense steps, and major consonances. Moreover, many errors are also committed by singers. For instance, to show off their talent for embellishing a passage, they have no qualms 24. See Bk. II, chap. 1. Motion refers to pace or tempo, steps to linear intervals, and consonances to vertical intervals. 25. See Bk. II, note 11. For a description of tense and slack steps, see Bk. I, chaps. 14-42.

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about ruining a sad passage by making it seem cheerful, contrary to the composer's intention. I have noticed that they do the opposite as well, for when a composer prescribes a cheerful passage with diminutions, the same singers fail to show off this talent. As a result, any sort of music sung without attention to the words and the subject may well become uncoordinated. It is appropriate to touch on this topic, because this reminder is useful to many singers as well as to composers. We now continue with the technique for writing a harmonious and well-made composition. Composers are advised that all consonances are good when well placed and appropriate to the words, as are descending minor thirds and minor sixths. The major sixth next to the fifth is good for harshness, and next to the octave it is not unpleasant to the ear, as I explained earlier concerning the nature of all the consonances [Book II, chapters 20 and 21]. To make a fine composition with all three systems, the consonances and unisonances should be well positioned, and great care should be taken with the parts when they pause and when they are about to enter on the unison or octave. This last progression is not too modern, as I said before. However, if the parts must enter on the unison, hide the unison in the second half of each note, the octave likewise. In this way, the composition will always be harmonious. If you wish to give a composition a sad character, place the minor consonances in low positions. Although the minor third is of a sad nature, when it is put in a high position it does not seem entirely sad, especially when it has the octave below it and is accompanied by motion. When writing for five, six, or seven voices, minor thirds should not be used much in the low parts except when descending for they are dubious and likely to be raised by the singers.26 If you wish to stop any parts near pauses or endings, see to it that the consonance of the major third is in the low parts, even if the composition requires sadness. If a stop entails neither motion nor step, and one part is to enter cheerfully, it will always enter sooner in the high than in the low position among the parts. Be warned that when the consonance of the major third enters in the low parts, it loses its nature, though not completely. It is like the minor third in this situation. When the minor third is placed in high positions and does not stop longer than a semibreve, it has neither a completely sad nor a completely cheerful character. Likewise, the major third in low position has neither a completely cheerful nor a completely sad character. These major and minor consonances are like our health. For when we do not enjoy health in the right locations of the body, our body changes 26. See Bk. II, chap. 14.

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and seems to lose the vigor and power of its native condition. The same thing happens to the body of compositions. When the consonances just described are not put in the right places, the body of the work changes its countenance. When a composition that at first seemed cheerful and lovely to listeners goes on to reveal badly placed consonances, it appears completely transmogrified and crude. It now remains to discuss the fine variety of consonances arising from the system of sounding various pitches in the bass or in the lowest parts. These cause all the parts to appear [82v] full of harmony and of a variety of consonances: when, for instance, the bass or the lowest parts change their pitches or locations, ascending or descending to the extreme limits above or below, always sounding now in one location and now in another. But if one note stays in one location longer than the value of a breve, it does not please as much as do semibreves, minims, and semiminims. If, however, you can provide three or four different consonances below or above one note, the result makes a good aural effect, for nature delights in variety and renewed expectation. If a composer wishes one part to enter after a rest in the middle of a work, it is much better to deceive the ear by having it enter at a second, fourth, sixth, seventh, or ninth from the antecedent part than at a fifth, octave, third, or unison from the antecedent note, called the leader. Entering on the fifth, third, octave, or unison sounds banal to the ear. However, for variety, you may enter with the consonance of the third if another part can enter on the fifth, another on the tenth, and another on the twelfth, thus achieving variety when matched with the steps and motion appropriate to the composition. In such combinations, may the consonances of the third, fifth, and sixth within the body of the octave never be lacking. Within the twelfth, let there be placed the tenth, the fifth, and octave.27 And within every extreme and large consonance, may there never lack the major or minor third or its replicates, the major and minor tenth, and the fifth and its replicate, the twelfth. In place of the fifth you may use the sixth or its replicate, the thirteenth, as I said earlier [Book I, chapters 18 and 19]. By keeping in mind the consonances named within every large consonance, a composer will always have a composition that is full of harmony and that is sad or cheerful according to its subject. I have repeated these many things more to facilitate the student's learning than for my own satisfaction. 27. The text here is garbled: "& fra la Decima, che sia posta la quinta & ottava, 6 la Duodecimal'

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Chapter 22 How to Compose on a Plainchant The methods of composing on a plainchant are many. If a composer wants to make fugues on a plainchant, he may do so, more or less, but such a method is not modern. He should compose according to the modern method: choose a segment of the plainchant and make the parts imitate that segment, perhaps by an upward or downward fugue such that the parts are fuguing with one another and not with the plainchant. If the plainchant is long, he can make some duos, trios, and quartets, provided that the composition is for more than four voices. When one part enters after another, it is good to hear in a subsequent part a passage as it was sung by a previous singer, if a composer can do it. All the parts should do likewise, always making fugue, one after the other, either above or below the plainchant. This is a fine method, and it is not bad to hear. Sometimes the parts join together against the plainchant, depending on what happens in it. The more consonances there are on one note to the plainchant, the more pleasing to the ear they will be. At the very least, there should be two consonances, one below and one above the plainchant. If a composer wishes to write a motet on a plainchant, he should take care to maintain the tone or mode in the bass or the lowest parts, because they govern the mode. And he should be careful not to sound any pitches in the bass that would detract from the design and mode of the plainchant. If it is his pleasure [83r; incorrectly numbered 80r] to compose a short antiphon on a plainchant that has a text, and he must make a second section, a composer can select a plainchant in another mode and move it up or down a fourth or a fifth at his convenience, using it as if it were a single plainchant. He could also, for variety, compose on the plainchant of a hymn. Because the plainchant repeats many times, it may be stated now in the tenor, now in the soprano, now in the contralto, and even in the bass, either at the fourth or fifth. With this variety, a composer will give much pleasure, even while keeping the boundaries of the tone or mode so as to allow the choir or organ to respond appropriately to the mode. It is possible to make duos and trios on any plainchant, and sometimes to set the last verse for five or six voices, according to circumstances. The same is true of other compositions on plainchant, as in the examples heard every day in churches on solemn feasts.

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Chapter 23 How to Improvise on Plainchants It is good to hear improvised singing on a plainchant in church, if the members of the group are well-coordinated and if all the parts keep to their ranges—that is, if the sopranos, contraltos, and tenors make their passaggi over the bass, which is the plainchant. Indeed, every part must observe its own patterns. But it is difficult to avoid the incidence of errors, and not just a few of them. True counterpoint, or better, true composition on a plainchant occurs when all the parts that might be sung extempore are written down. Even so, a composer who does so takes on no small task to make such a composition correct and errorless, all the more so if it is for more than four or five voices. Any such work, being free of errors, will be good to hear. As for variety and satisfying many people, nowadays one person likes one pattern and another likes another. To expand on this, let me say that many techniques of improvised singing are used over plainchants. Some sing in two voices, and having invented an ascent or descent of four or five pitches, they make fugue by sixth and by fifth up and down by step [example 23.1].28This is crude to hear because refined contrapuntal procedure consists of presenting as many consonances as possible on one note. But this technique of making fugue by sixth and fifth has no variety whatsoever, whether of consonances or steps, for singers always present the same consonances and the same steps to the audience. Therefore, this technique should be avoided, not only because of the reasons already given but also because it is so common. Besides, it is not modern.

[Example 23.1 Lusitano, Introdutione facilissima, fol. C4r; facsimile edition, pp. 13r-13v] 28. Vicentino's discussion of improvised counterpoint on a preexistent melody is derived from material found in a treatise written by Vicente Lusitano, his rival in the 1551 Rome debate: Introdutione facilissima drnovissima di canto fermo, figurato, contraponto semplice dr in concerto, con regole generali per far fughe differenti sopr'il canto fermo . . . (Rome, 1553).

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Among the old-fashioned singers there are others who sing their fugues by leaping continuously up a fourth and down a third, persisting through many notes with these two leaps [example 23.2]. They rise from the octave to the fifth and vice versa without at all varying the consonances and the steps.

[Example 23.2 Lusitano, Introdutione facilissima, fol. C4r; facsimile edition, p. 13v] They also do this from a fifth to a third, and vice versa29 [example 23.3]. This technique has a few more consonances and a few more varied steps than the previous one. Nevertheless, because it always repeats the same consonance and steps, it is not too modern. Still, it is not as bad as the others.

[Example 23.3 Lusitano, Introdutione facilissima, fol. C4v; facsimile edition, p. I4r] Lusitano's excursus appears in a section entitled "How One Can Make a Fugue on a Plainchant" (Introdutione facilissima, fols. C4r-D3v). In the facsimile of the 1561 edition by Giuliana Gialdroni (Lucca, 1989), this section is on pp. 13r-16v. 29. The text has a redundant "di quinta in sesta" interpolated between "di quinta, in terza" and the reversed direction. Ex. 23.3 is the fourth example given by Lusitano. The intervening one, at the top of fol. C4v (facsimile ed., p. 13r), exemplifies the second type of improvisation, but on the same chant used in ex. 23.2.

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Some others make a practice of singing in church in three voices on a plainchant. While the soprano is entirely in tenths against it, the person singing in the middle observes the ban on making two imperfect consonances.30 But if the middle part does make two sixths with the bass, the soprano makes two fifths; and if the middle part makes two thirds with the bass, it makes two octaves with the soprano.31 This technique of singing is easy [83v] to follow. But because so many tenths are heard, it is apparently not very pleasing [examples 23.4 and 23.5]. Nonetheless, with its tenths set in either three or four voices, it is not so bad as the other patterns, with fifths and sixths, discussed above.

[Example 23.4

Lusitano, Introdutione facilissima, fol. D2v; facsimile edition, p. 15v]

30. This prescription repeats the one in Lusitano (Introdutione facilissima, fol. D2r; facsimile ed., p. 15v). 31. Lusitano calls this type of improvised singing "contraponto in concerto sopral basso" (Ibid., fol. D2r; facsimile ed., p. 15v). Although Vicentino does not go on to describe in detail the four-voice contraponto in concerto, it is given here as ex. 23.5 because it exemplifies many of the shortcomings noted by Vicentino. Moreover, this example becomes double counterpoint, called contraponto in accordio by Lusitano (fol. D3r; facsimile ed., pp. 15v16r).

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[Example 23.5

261

Lusitano, Introdutione facilissima, fols. D2v-D3r; facsimile edition, p. 16r]

There are other singers, moreover, who intensify their counterpoint with a number of ostinatos, whereby they produce one and the same passaggio over the plainchant. This is done with such utter clumsiness that plainly these singers are prepared to keep track of their ostinato and their passaggio but not of any harmony. And they use such velocity in their delivery that the most common note-value we hear is the semicroma.32 This is what happens when one is bent on sustaining an ostinato and maintaining a passaggio throughout the performance [examples 23.6 and 23.7]. 32. Lusitano calls this technique Taria di cantar il contraponto" and describes it as an alternation between the tirata, a stepwise diminution, and thepasso largo, or leap (Ibid., fols. Dlr-Dlv; facsimile ed., p. I4v). Here, in ex. 23.6, there are four distinct parts, each to be sung over the same chant in the bass. Ex. 23.7 provides a single counterpoint under the chant, now placed in the soprano.

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[Example 23.6 Lusitano, Introdutione facilissima, fols. Dlv-D2r; facsimile edition, p. 15r] Such a practice is neither good nor useful for the choir, and in the chamber it is worthless. Indeed, counterpoint or composition should be charming and possessed of a certain grace that is born of elegance and of refined passaggi accompanied by harmony. For the goal of music is to delight the ear with harmony. These ostinatos and repeated passaggi are difficult to learn and, besides, they are devoid of harmony. Music that is

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[Example 23.7 Lusitano, Introdutione facilissima, fol. D2r; facsimile edition, p. 15r-15v] somewhat difficult to learn but is full of harmony is the kind that offers rewards in harmony and singing. Therefore, since ostinato technique and repeated passaggi are useless, students need not toil over them. However, should a student wish to try his hand at improvised singing on a plainchant, he must never exceed the limit of twelve steps above or below the chant in two-voice counterpoint. Extremes do not succeed in a duo, as is clear when some singers rise frequently to the fifteenth. Such a distance in a duo is not at all graceful.

Chapter 24 How to Compose for Two Voices, with Examples The system for composing for two voices is as follows. First, composers should take care to observe the mode that governs the response to the choir or to others. The duo, placed in the midst of a motet, should imitate the phrases and boundaries of the mode of the motet or another subject.33 When planning the entrance of the duo, composers are advised not to use the boundaries of another mode at the beginning and not to ascend more than fifteen steps between the outermost limits, so that at most the consonances will be the tenth and twelfth. They should also bear in mind that the duo is devoid of harmony and ensemble; therefore, every poorly ordered and maladroit consonance is obvious. With respect to compositions for three, four, and five voices, the duo is comparable to the difference between the nude and the clothed figure 33. See Bk. II, note 2.

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in painting. Every painter depicts a completely clothed figure quite well, whereas not all painters can do the same with a nude. The same is true of composers of music. Many write works for four or more voices, but few possess the refined manner required to combine the steps and consonances in a duo. In a duo it is good to make the octaves few and far between. It is also useful to devise varied and dissimilar consonances, such as alternating minor and major thirds or vice versa, and major and minor sixths or vice versa, for the absence of two similar consonances is a good thing. You must be careful with the two steps, fa-sol and mi-re, because both present similar consonances above and below—that is, major or minor thirds and sixths. The remedy is to use the flat, natural, or sharp to make the major ones minor and the minor major. The cadences of duos should end either on the fifth or, passing through the sixth, seventh, and sixth, on the octave. You can make a cadence of the fourth and third followed by the sixth on the low and middle parts. The end should always be on the octave or the unison. Even the imperfect fifth can be accommodated, as is shown by some phrases in example 24.

Example 24

[Some Cadences in Duos]

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Chapter 25 How to Compose for Three Voices, with Examples [84r; incorrectly numbered 79r] When a pupil is beginning a trio, either on a plainchant or another idea,34 he can start with the part that he finds most amenable to making a fugue with it. It is good to arrange a lovely bass part under the tenor subject, as in the case of compositions whose bass exhibits a refined procedure and often sounds a variety of notes. Such works delight the ear. It is also possible to insert a duo in a trio. Insert some well-placed and rather strictly bound dissonances in a trio, for they provide the ear with variety when they are composed with their appropriate companions. Even the imperfect fifth can be accompanied extremely well, as seen in the third illustration in example 25. You must not make consonances that proceed from fourth to fifth because they seem like two consecutive perfect consonances. The fewer octaves the better. In three voices, the octave with the enclosed fifth is always preferable to the octave with the tenth above or below. If there is a duo within the trio and the third part is to enter after a rest, see to it that it enters on a fifth that has within it a major third. This arrangement makes a better aural effect than does a fifth with a tenth.

Example 25 [Trios]

Chapter 26 How to Compose Diverse Four-Voice Compositions for Full and Falsetto Voices Earlier I discussed the nature of the consonances, as well as which steps are tense and which slack [Book I, chapters 14-42, and Book II, chapters 2-30]. I also indicated that because it is poor in harmony, the music in a duo should be more purified and refined. And because the 34. See Bk. II, note 2.

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trio has one more companion than the duo, it is conceded a few more liberties, but [84v] not too many. For whatever is not well arranged will sound just as bad in one texture as in the other. Thus, considerably more is perceptible in a trio than in a quartet, of which I shall now speak. Depending on the subject, composers should adhere to the proper system and respect conditions in accommodating the parts and certain consonances that are not easy to accompany. They must consider the words or other ideas.35 So, for instance, Masses, psalms, hymns, motets, madrigals, French chansons, and other texts set to four voices entail certain conditions in going from the fourth to the fifth and vice versa— to avoid having them sound like two [consecutive] perfect consonances—and in writing steps and leaps that produce sweet or harsh effects, as was described earlier. Four-voice settings of the Mass and Latin words should be serious and not too intemperate in character. For the procedure of Masses and psalms, being sacred, must of necessity be different from that of French chansons, madrigals, and villotte. As it happens, some composers proceed contrary to the subject of the Mass, which requires a gravity full of devotion rather than lasciviousness. Some even compose the Mass on a madrigal, a French chanson, or a battaglia, so that when such compositions are heard in church they make everyone laugh. It almost seems that the temple of God has become a place for the recitation of wanton and ludicrous matters, as if the church were a stage where it is permitted to recite any sort of ridiculous and lascivious buffoons' music. It is not surprising that in these times music is not valued, for it has been applied to lowclass items such as ballets, Napolitane, villotte, and other silly things. This practice goes against the opinion of the ancients, who restricted music to the singing of hymns to the gods and about the great deeds of men.36 Certainly, we must have great respect for such subjects, for great is the difference between composing a piece to be sung in church and one to be sung in the chamber. A composer should keep his judgment finely honed and compose his works in keeping with the subject matter and the purpose of the words. As to writing for four voices, a composer may prefer to begin with a duo, trio, or quartet. The kind of beginning depends on whether he decides to start with or without a fugue. In continuing the composition through the middle and up to the end, he will arrange it according to the words or other ideas. Vernacular texts should be pleasant and intelligible 35. See Bk. II, note 2. 36. See my introduction.

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in their setting, without canons and overly cunning proportions, because the words, like those in madrigals, demand nothing but the imitation of nature by means of the consonances and steps applied to them. When composing a work for falsetto voices,37 that is to say, without a soprano, be careful that the range does not exceed fifteen steps, or at most sixteen with the extra semitone. Provide the gravity and motion appropriate to the subject on which you are composing. Accommodate the parts so that they leave room for one another in an elegant way and without inconveniencing one another. If a composer is required to write psalms, Masses, or hymns, he should keep the mode so that choir or organ can respond to that mode. I shall give no more examples of steps, leaps, and consonances, because I have already stated repeatedly which were good in two, three, or four voices.

Chapter 27 How to Compose for More Than Four Voices It is possible to compose effortlessly for four voices, making the words intelligible regardless of whether the voices proceed simultaneously or make fugues. However, in five, six, or more voices, making the words intelligible even when the parts move together is difficult. For it is necessary to make some of the [85r] parts rest rather often or else to conceal the pitches through the parts, making unisons now in one part and now in another. The system of well-placed unisons among the parts has been described earlier [Book II, chapters 2, 3, and 11], And the same problem occurs when octaves are distributed now in one part and now in another. When a part must rest, it should not do so before having reached the conclusion of the words of the discourse—that is to say, when the text has a period. In compositions for five or more voices, it is possible to make trios, quartets, and quintets. The more voices a composition has, the greater is the possible variety of quartets, quintets, and sextets. Progressions from the fourth to the fifth and the reverse can be put in the middle parts, where they will be hidden by other voices. The total range of such compositions should not exceed nineteen or twenty steps. Depending on the composition, the subject of the words will govern the slowness or rapidity of the motion.

37. See note 2, above. For a more detailed discussion of this technique, see chaps. 38 and 39, below.

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Chapter 28 How to Compose Psalms, Dialogues, and Other Works for Two Choirs In churches and other big, spacious places, music composed for four voices makes a small sound, even when there are many singers per part. Because it is necessary to make a large sound in such places, and for the sake of variety, you may compose Masses, psalms, dialogues, and other works to be played with various instruments mingled with the voices. For an even bigger sound, you can also compose for three choirs. A composer must take care first to choose the mode for his setting of the words and then to respect the tone or mode of the composition, which may be composed on a plainchant or on an idea of his own, with or without fugues. Where the first choir is to begin, he should see to it that the first pitches are easy to sing—that is, the unison, fourth, fifth, octave, tenth, twelfth, or fifteenth. After the first choir has sung and is about to rest, thus finishing its first section, the second choir should begin halfway through the last note of the first choir, either on the unison or on the octave of all the other parts. To illustrate, choose for the tenor a unison with the other tenor and for the contralto a unison with the other contralto; the soprano—a changed voice that seems like a contralto—could be given a unison, or the consonance of the third or fifth below the soprano; and for the bass choose a unison with the other bass or else an octave, depending on what seems more convenient. If one choir does not take up the pitch of the other, either at the unison or at the octave, the aural effect will not be good because the entrance of the voices is bound to be faulty. The entrance of a voice must occur halfway through the last note, after a minim rest, a breve rest, or several such rests. Thus the voice that is singing will be a sure guide for the one that is about to intone and maintain the mode. For variety, the soprano of the second choir may be a changed voice, in contrast to the full-voice choir.38 As I said before, the choir that has to enter after the rests never begins after the first choir has finished but rather in the middle of the last note of the first choir. When planning for two or three choirs to sing at the same time, it is advisable to make the basses of two or of all three choirs agree with one another. Never put one bass a fifth below the other when all three are singing at once, because then the parts in the third choir, having the fourth above, will be unable to hear the fifth below if this choir is somewhat far away. Hence the third choir will discord with the rest. To make 38. Here a voce mutata is contrasted to a voceplena. See note 37, above.

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all the basses agree, always keep them at the unison or the octave. Sometimes a major third is used but never for longer than a minim, for the major third is too weak to support so many voices. This is the way to avoid discords among the parts. The choirs may also sing separately [85v], even if the singers are placed far away from each other, provided they agree in the way described. On the other hand, in dialogues it is customary to have the singers form a circle. Because they then stand close to one another, it is possible to compose fifths in the basses, so that the bass having the fourth above will not discord with the lower bass as if it were far away. The same arrangement pertains to the entrance of voices, as I said above. Composers should be governed by the subject of the words. As to harmonizing two basses, I point out many notes at the unison, octave, and third in example 28. Thus, pupils will learn more from examples than from words.

Example 28 Two Basses That Harmonize with One Another When Singing in Two Choirs

Chapter 29 How to Pronounce Long and Short Syllables Under the Notes, and How Their Nature Should Be Imitated, as well as Other Useful Remarks Many composers are so absorbed in working out a personal compositional procedure that they have no consideration for the nature of the words, or their accents, or which syllables are long and short, whether in the vernacular or in Latin. But you should observe the long and short accents according to the usage and the rules of Latin and Tuscan speak-

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ers. For if long syllables were pronounced short and short ones long in, say, the French, the Spanish, or the German language, that nation would laugh at such pronunciation. The same thing happens in the musical text-setting of any nation. A composer must be careful when setting French words to observe their accents, and for Latin words to observe Latin usage, for Tuscan words to pay attention to Tuscan pronunciation, and similarly for the nature of the words of every other nation. Thus will he follow the pronunciation of the languages of the nations throughout the world. Moreover, all nations represent their own way of singing by means of the steps found in the division of my archicembalo. But with the music in use nowadays it is not possible to write French, German, Spanish, Hungarian, Turkish, or Hebrew songs—or songs of any other nation—because, when spoken in the mother tongue, the steps and leaps of the nations of the world proceed not only with the steps of the whole tone, natural semitone, and accidental semitone, but also with dieses as well as enharmonic semitones, tones, and leaps. This is why I have devised my division, which allows all nations of the world to write with their own accents and to compose in as many voices as they like.39 [86r] Music set to words has no other purpose than to express in harmony the meaning of the words, their passions and their effects.40 If the words speak of modesty, you proceed modestly, not intemperately, in the composition. When they speak of joyfulness, you do not make the music sad, and when they speak of sadness, you do not make it joyful. When they are about harshness, you do not render it sweet. When they are gentle, you do not set them otherwise, because their meaning will seem distorted. When they speak of speed, the music will not be sluggish and slow, and when they speak of standing still, it will not run. When they depict going together, see to it that all the parts unite in a breve, for the latter is more obvious than a semibreve or a minim. When a composer is writing something sad, slow motion and minor consonances help him. When he is writing something joyful, major consonances and rapid motion are appropriate. Even though minor consonances are sad, rapid motion nonetheless will make them seem almost joyful: the ear does not apprehend their sadness and weakness on account of the pace, as I said earlier [Book II, chapter 1]. 39. A similar claim was made later by Vicentino for his arch-organ in section 11 of the [Descrizione dell'arciorgano] (Venice, 1561). See my introduction, note 41. 40. The ensuing discussion of harmony and rates of motion calls to mind the famous remarks of Plato concerning the primacy of logos over harmonia and rhythmos. Republic, 3.398d and 400d.

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Some composers think it is clever to match the vowels of syllables of words with the vowels of solmization syllables.41 Since the method has few advantages, this sort of matching would not have found favor, were it not that the words can be pronounced with a little more agility by singers.42 All the same, a good singer pays no regard to such matching because he knows it is of little importance. These are the very vowels that give composers trouble in the making of elisions, because every time you meet two consecutive vowels in the vernacular, you must always utter the second and omit the first. Thus, two elided vowels make up one syllable, except at the end of a verse. The same is true when two vowels occur at a minim or breve rest, for at that point you maintain the usage of speech, making the intervening minim or breve rest an ending. As sometimes happens, a verse may end without a minim or breve rest and lead directly to the next verse. In that case, you should be wary of making an elision with the next verse lest there be no resting point after the first verse—for to join the ending of one verse to the beginning of the next creates a pattern more appropriate to prose than to verse; therefore, separate the two vowels. Moreover, elisions are never made when two vowels appear next to each other in the Latin language, even though Latin and Italian employ the same five vowels—a, e, i, oy u—that are so useful to singers. In setting these vowels, composers are advised that some, such as a, oy and Uy are amenable to runs in the low registers and support the delivery of a big tone, especially in church, where the choir has full voices43 and a multitude of singers. Some other vowels, like ay ey and 0, are good in the middle registers, whereas in high and very high registers the vowels at ey and / are appropriate. The vowel / is acute in accent and pronunciation. For this reason, it seems that singers using a full voice cannot manage to utter it when making runs in the low register. And so, to get a bigger tone, some of them pick another vowel, o or «, instead of /. Many friars do this when singing plainchant in the choir: they open their mouths so as to give the voice greater resonance. Because the formation of the letter a and the vowel o is very comfortable for an open mouth, which makes a bigger tone, the friars always say these two vowels, a and 0, regardless of what vowel they encounter. 41. This is the technique Gioseffo Zarlino was to call "Soggetto . . . cavato dalle vocale" in Le istitutioni harmoniche, Bk. Ill, chap. 66. 42. This concession echoes an earlier remark on the advantages Guido s hand gives to the novice singer. See Bk. I, chap. 2. 43. The phrase here is "con le voci pieni." See Bk. Ill, note 72.

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But let us return to the technique of elegant pronunciation in the high, very high, extremely high, middle, and low registers. Composers who pay attention to these vowels can help singers a great deal. Just as the vowel i is awkward to pronounce in the low registers, the same goes for the vowel u [86v] in the high and very high registers. Let composers also note that ascending and descending steps and leaps cause the quantity of these vowels to change, so that a long one becomes short and a short one long. This attention to pronunciation is very useful. A composer who experiments with the upward steps and leaps of the fourth, fifth, sixth, and octave, and then with the same syllables and the same downward steps and leaps, will discover that the pronunciation of the syllables changes because of the change in direction, except for the vowel u> which is pronounced the same way going up and going down. Moreover, so great is the difference in pronunciation on the upbeat and downbeat of the measure that it changes from short to long and from long to short. When beginning a composition, a student should be aware that as a rule, you start at a slow pace, unless compelled to do otherwise by some sort of swiftness depicted in particular words. The exceptions are French chansons, Napolitane, and other similarly inconsequential texts, as I said before. Do not introduce repose by rests or slow motion near the end of a composition, because the end is the repose of the composition and the conclusion of the subject, as indicated before. You may perhaps make two, three, or more sections in a composition; however, these stops are not called endings but rather intermediate endings, because the rest of the composition will follow almost immediately and bring the work to its conclusion. It is sometimes effective to present the words simultaneously. If one part begins to sing with a breve and then continues with a semibreve followed by two minims, and the other parts adhere to the same textsetting one after the other, the ear will be satisfied. The same happens when the parts enter one after another with an identical pattern of minim and breve rests or of equal rests. The part that finishes first should be the first to resume. Be careful not to put any syllable under notes that are not consonant, for discordant notes are too obvious when they have a pronounced syllable. But a syllable is tolerated under a fourth because the latter, particularly when syncopated, is considered to be almost a consonance. The goal of elegant text-setting is to match the words with appropriate motion and consonances. It is also to set texts in a refined manner.

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When the words speak of repose, you make a breve rest, and when of sighs, you make minim rests to imitate the words. An experienced composer will learn a thousand other clever devices because one will lead him to another. He will also understand that it is impossible to teach everything that occurs in composition, for the act of composing teaches things that a student cannot imagine.

Chapter 30 Rules for Writing Words Under Notes So That They Are Convenient to Singers Singers often make mistakes in pronouncing syllables placed under the notes. Some of them repeat a syllable or an entire word even though it is not written. But sometimes it is the composer who causes the singer to say a word twice, which he ought not to do because such repetition does not signify anything. Furthermore, singers sometimes cannot put all the syllables under the notes because the composer has omitted one of them. Such confusion can be attributed to both singers and composers. Whenever a composition has more notes than syllables, requiring one vowel to run under several notes, composer and singer should be careful to adhere to the following method. When making runs of semiminims and cromas with one vowel, do not pronounce the next syllable on the first white note directly after a black note but rather [87r] pronounce it on the second white note, for this procedure is more immune to barbarisms. However, it is no great error if sometimes you cannot avoid pronouncing a syllable under the second of two minims that are close either to rests or to the ending. Nor is it a grave fault to pronounce a syllable on a black note that follows a dotted minim. But as a general rule, the method described earlier holds sway—that is, in singing, pronounce the syllable on the second white note after any ascending or descending black notes. In my opinion, when you write a leap of an octave, you should not utter one syllable on the low note of the leap and another on the high note. This kind of pronunciation sounds bad because the leap is too big [example 30.2]. You should rather begin the verb, noun, participle, or pronoun after the leap. If you must break off a word in the middle, it is not as bad to do it in a leap of a fifth as it is in a leap of an octave. But it is better if you manage to pronounce the word after leaps of at least a fifth or fourth. The shorter the leap, the less offensive the split pronunciation is to the ear, as shown in example 30.

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Example 30.1 Universal Rule for Placing Words Beneath Notes

Example 30.2 [Bad Pronunciation in the Octave]

Example 30.3 Syllable Pronounced Under Black Notes by Necessity

Chapter 31 On the Musical Proportions Used Today by Practitioners of Music Many things change with the times, as may be observed in the practice of music. Fifty years ago, men expert in music toiled to master and compose with the many and diverse proportions. Such exertions, however, have become almost useless in music. Our more recent forebears selected a few more practicable proportions, abandoning the many proportions given by Franchino Gaffurio in his book.441 limit myself to the proportions used today, First, what is a proportion? According to Euclid, a proportion consists of two numerical quantities belonging to the same genus that have a certain affinity between one number and the other.45 Moreover, be warned that proportion is one thing and proportionality is another.461 shall not speak of proportionality at this time because it is irrelevant to the present discussion, which concerns proportions and whence they arise. 44. Practica mitsicae, Bk. IV, chaps. 1-15. 45. Elementa, 5. Dif. 3. But probably from Gaffurio's Practica musicae, IV, 1. 46. A proportion is a relation between two numbers, whereas a proportionality is an identity of proportions or an equality of the numerical relation between two numerical extremes and their mean(s). For example, Boethius, De inst. arith., 2.40-53, and De inst. mus., 2.12; Gafrurio, Practica musicae, Bk. IV, chap. 1; and Lodovico Fogliano, Musica theorica, Bk. I, chap. 2.

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Philosophers have set up five genera under which fall, they believe, all the proportions possible among numerical relations.47 According to what Boethius wrote in his Fundamentals of Arithmetic48 the first genus is called multiple because it multiplies the numbers, as in the case of one to two, called duple proportion; one to three, or triple proportion; one to four, or quadruple proportion; and, in like sequence, the quintuple and the sextuple proportions. The progression of these numerical relations [87v] goes on to infinity. It is under the multiple genus that composers are accustomed to singing and writing musical notes, using no numerical characters and only the eight note-shapes: that is to say, maxim, long, breve, semibreve, minim, semiminim, croma, and semicroma. These note-values are sung in compositions within the measure of the breve and semibreve without subscript or superscript numbers. They are also sung with proportions under the multiple genus, as in the case of a semibreve against which you sing the duple, quadruple, and octuple proportions, consisting of two semiminims, four cromas, and eight semicromas against this semibreve. Likewise, you can sing two semibreves, four minims, eight semiminims, sixteen cromas, and thirty-two semicromas against the breve; or two breves, four semibreves, eight minims, sixteen semiminims, thirty-two cromas, and sixty-four semicromas against the long; or two longs, four breves in imperfect tempus, eight semibreves, sixteen minims, thirtytwo semiminims, sixty-four cromas, and a hundred and twenty-eight semicromas against the maxim. All these proportions, designated by the eight note-values mentioned above, belong to the multiple genus. As was stated in "Book I on Music Practice" [chapter 4], this system of note-values was invented by Jehan des Murs, the very eminent Parisian philosopher. Insofar as the practice of all things and all professions expands through being exercised, more recent practitioners wished to increase and amplify the musical proportions. Realizing that these note-values could be neither augmented nor diminished except by some sort of continuous quantity, they inserted dots, lines, circles, and semicircles. With these signs, they meant to augment and diminish the notevalues, depending on how the note-shapes had been written down in the first place, as is demonstrated by a great many authors. Under perfect 47. This statement is true only of unequal proportions. For instance, Boethius, De inst. arith., 1.22, and De inst. mus., 2.4; Jehan des Murs, Notitia artis musices (also known as Ars nova musica), Bk. I, chap. 2; Gaffurio, Practica musicae, Bk. IV, chap. 2; and Fogliano, Musica theorica, Bk. I, chap. 2. 4S.Deinst. arith., 1.23.

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prolation the semibreve is worth three minims; under perfect tempus the breve is worth three semibreves; under major perfect modus the maxim has the value of three longs. But I shall not discuss these signs, because many rules have been already printed in a great many books.49 At any rate, such were the signs by which the followers of des Murs gradually augmented the note-values under the multiple genus. But more modern practitioners have been more discerning in their desire to further their understanding, and to augment and diminish the eight note-values by means of the numerals of discrete quantity. So they added numbers with many varied proportions to the perfect and imperfect signs used up to that time. Fifty years ago composers wasted considerable time in the study of these proportions. But in these times, when experience has made men certain of all things, practitioners of music have realized that nothing useful is found in such proportions. Thus, they retained in practice only the sesquialter proportion, the major and minor hemiola, and the proportion of equality.50 These are shown in example 31. How should a reader understand the sesquialter proportion in compositions? He will recognize it when one or more parts sing two semibreves per beat and, in opposition, one or more other parts sing three semibreves. This is true sesquialter: when three are sung against two. Composers should make the sesquialter consonant on the downbeat and upbeat of the measure, just as semiminims are consonant on the downbeat and upbeat in polyphonic music.51 Another kind of sesquialter occurs in music practice when [in] experienced composers cause three semibreves to be sung against three other semibreves. But this proportion is improperly called sesquialter. Because three are sung equally against three, it ought to be called a three against three proportion of equality, not a sesquialter. Someone may wish to defend this proportion by saying that the beat goes at the rate of the breve and that this breve is understood in the measure [88r], thus proving that this proportion is properly called sesquialter. The rebuttal of this line of reasoning is that it is necessary to hear the singing of two against three rather than the beating of two against three, no matter what is being sung. For proportions consist of two related numbers: in this instance, the sesquialter of two and of three, whereas in this kind of equal proportion the relations of two different numbers 49. Besides Gaffurio (see note 44, above), other candidates are: Pietro Aaron, Libri tres de institutione harmonica (Bologna, 1516), Bk. II, chaps. 10-32, and Vanneo, Recanetum, Bk. II, chaps. 1-37. Continuous quantity is measured by geometric calculation, and Vicentino links the line, circle and semicircle to geometry. 50. See chap. 10, above. 51.SeeBk. II, chap. 12.

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are not audible in the singing. To conclude, the proportion of three against three is an equal, not a sesquialter, proportion. The sesquialter is written with a cut circle, called minor imperfect by practitioners, which has next to it the number ~- When written with breves and semibreves, the value of the perfect notes is said to be in perfect tempus, for it is the same in this proportion. It is customary to write the sesquialter not with the sign of minor imperfection but with that of perfection. The sesquialter should always begin at the end of a cadence that finishes on the measure of a breve, so that the starting beat is not left hanging in the air. This pattern occurs in the middle of a composition, and the cadence, be advised, should be in the mode of the composition. If the sesquialter proportion is to finish in the middle, it should conclude with a cadence, just as at the end of a composition. When a sesquialter occurs at the start of a composition, a composer can make it with or without fugues, as he pleases. When the sesquialter has finished in the middle, the initial sign is repeated without a subscript number. I show how to notate these proportions in example 31. In addition, I show how to write the major hemiola and the minor hemiola with all black notes: breves, semibreves, and minims. Since no perfection is found in the major or minor hemiola because of the power of the color, these proportions are not marked with the sign of perfect tempus. Example 31 also shows equal proportion and the true sesquialter that produces two against three.

Example 31.1 How to Deal with Equal Proportion

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Example 31.2 Sesquialter Proportion, Two Against Three

Example 31.3 Major Hemiola

Example 31.4 Sesquialter Proportion Consonant on the Upbeat and the Downbeat

Example 31.5 Minor Hemiola

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Chapter 32 Rule for Making Fugues in Various Ways [88v] When a composer is beginning a fugue, he should first think about the subject on which it will be made, either with words or to be played, on a Mass, a motet, a madrigal, or some other idea.52 He first selects the tone or mode and then stays as close as possible to its limits. He also matches the words to the fugue, observing the conventions of the Latin or Tuscan language. In planning the beginning of a fugue, he selects a passage that can be repeated by the other parts. The second part should enter either after a minim rest or else after one, two, three, or four breve rests. But it should not be delayed for more than four breves, for even four breve rests are almost too long, as was pointed out earlier. Moreover, it is good to hear all the parts of a fugue enter after each other at the same time-distance, as would happen if one part entered after a rest of one, two, three, or four breves and the same rest occurred between it and the next part. Or if one part had entered after a two-breve rest, the next could do the same after the entrance of the preceding part. Thus one would follow upon the other. It is a good idea occasionally to deceive listeners by causing the first part in a fugue to enter on the downbeat of the measure, the second on the upbeat, the third on the downbeat, and the fourth on the upbeat.53 Fugues constructed in different ways are good except at the unison and the octave, because these intervals do not provide enough variety. Therefore, the technique of making fugues at the unison and the octave should be used seldom and only when necessary. In four voices, when the bass makes fugue with the tenor at the fourth, the contralto and soprano will be at the fifth. Conversely, if the bass and tenor make fugue at the fifth, the contralto and soprano will make fugue with each other at the fourth. Furthermore, when a fugue is about to begin and the part that is to adhere to the fugue cannot do so for a while, composers will match the initial voice with a [free] counterpoint on it. It does not matter if the beginning starts off in fugue but does not continue that way for longer than four or five notes.54 These techniques are used in motets, 52. See Bk. II, note 2. 53. See chap. 14, above where this device is called I'inganno. In this chapter Vicentino uses the infinitive ingannare. 54. Vicentino s technical vocabulary is muddled. Nonetheless, it may be assumed that he is making a distinction between the strictly canonic deployment of voices on the one hand and, on the other hand, free points of imitation, where only the initial notes duplicate each other. This distinction is the same as the one made later by Zarlino between strict (legato)

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madrigals, French chansons, Masses, and psalms. But it cannot be done in canon—when two, three, or four voices sing from one part—because then it will not succeed. To make fugues by contrary motion at the octave in such a way that the beginning of one part leaps up a fifth is bad technique, because it will seem that the composition has been forced to leave its mode. When one part leaps up a fifth [89r], the other should leap down a fourth, and when one part leaps up a fourth, the other should leap down a fifth. Thus, the species of the octave comes out right. There are other techniques for making fugue at the second, third, sixth, and seventh that

Example 32.1 The Contralto Makes Fugue at the Fifth, the Tenor at the Octave, and the Bass at the Twelfth and free (sciolta) fugues, or imitations (Le istitutioni harmoniche, Bk. Ill, chaps. 51 and 52). Two sentences later, Vicentino usesfaga for what we call a canon. But at the end of this and in the next chapter, he also uses canonlcanoni.

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sound well. But be careful of the mode, for the technique of fugue at the second is unreliable, owing to its tendency to leave the mode. It is also possible to make mixed fugues in which two parts converse in one way and two in another. Other fugues can be made in inversion, that is to say, the semitones ascend in one part and descend in the other; in this procedure there are as many whole tones below the semitone in one part as there are above the semitone in the other. Fugue by inversion is shown in example 32.3. The technique of fugue is easy if composers invent an elegant beginning that can be effortlessly continued. And it is artful if the end of the composition can arrive with the same fugue as was used at the beginning. Be warned that it is far better to make a harmonious composition with elegant contours in the parts than to write fugues that sound clumsy in their harmony and are even worse to sing.

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Example 32.2 Mixed Fugue in Two Parts, Two on One, for Four Voices

Example 32.3 Inverted Fugue at the Second with Semitones and Tones in Contrary Motion So many fugues have been and are being written that I shall not prolong the discussion. Rather I shall give a few examples, in order to initiate students. With the slight enlightenment and exercise afforded by these examples, students may with practice discover other ways of making fugue, without relying on techniques that have been used so often in the past. Not too many more these types of fugues can be fashioned, for there is almost none that has not already been made.

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Example 32 shows the beginnings of some less-common fugues. The world is full of the common ones. We now proceed to canons.

Chapter 33 Rulefor Composing Various Canons on Plainchants and Measured Melodies Among the many and varied techniques of composition are some schemes of singing the same notes in two, three, four, or more voices from one part, either a plainchant or a measured melody. The rule for singing from one part is called canon, which means rule or method of singing the same notes and making the [89v] same rests that are written in that part, even though, for the sake of variety, the part that came first could be sung second and the part that came after could be sung first. The rule can be made with rests and note-values so as to accommodate them to plainchants or measured songs with the application of appropriate canons. If the rests are not repeated, the same tune will nonetheless be reproduced. Lest anyone object that this technique of changing the rests is not used in canon, it is now put into use. For if canon means rule, this system of changing rests is a canon or rule made in that system. In this regard, therefore, you should have a little consideration for the singer and place some kind of verbal rubric over the canon to give him direction and information as to how he should proceed. To demonstrate this variety, I have made ten canons on the plainchant Dapacem Domine, as well as a Mass for six voices on the same subject.55 Thus, no one will find it unbecoming that it is not a grave error to alter the rests of a canon in order to acquire variety in the music. For to seek diversity and variety in melodies gives more pleasure than to annoy the ear with the silence produced by rests. We come now to the discussion of the method to be followed in making canons. Canons are more suited to plainchants than to measured melodies, because a severe demeanor corresponds to and resembles more closely the former than the latter, as in the case of Masses, motets, hymns, psalms, and odes. Such canons can be made in different ways and for a number of voices. They can be sung at the unison, second, third, fourth, fifth, sixth, seventh, octave, ninth, and tenth. But canons at the second, 55. See Bk. Ill, note 64. There are two chants with the incipit Dapacem Domine in diebus nostris that are sung during the Missa Pro pace, and Dapacem sustinentibus te, the introit of the mass for the eighteenth Sunday after Pentecost. The first chant was a very popular canonic theme.

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third, sixth, seventh, and ninth are more modern than the others. If a composer plans to construct a canon for a Mass, he should select from the Mass a chant or passage that seems to him appropriate, or select another subject. If it is a psalm, he should imitate the psalm tone or the hymn he is planning to compose. If it is to be a hymn in Latin, either in verse or in prose, he should select the chant of a hymn, because the word hymn means praise. A composer should take great care with the words, for they tend to be one-fourth or at least one-third shorter than the required length of the composition. He should also apportion all the parts without many repetitions, so that they can lead elegantly to the conclusion. The canon should never begin before the other parts; rather, the other parts should begin by imitating the canon. Note that when the tenor that is making canon with the contralto at the fifth is in the soft hexachord, the contralto will appear in the hard hexachord. Therefore, the fourth should be avoided, so as not to introduce the tritone in the canon. When composing for five, six, seven, or more voices, always work with the most convenient vocal parts. For instance, two tenors are more readily used than two sopranos or two contraltos because there are always enough tenors around, more than any other type of voice. Do not use two basses unless you are composing for two choirs or making a sad composition in the fourth mode56 with two, three, or four basses. A single bass—that is, the lowest sounding part—is always audible. If a canonic part has enough rests, the canon then has sufficient freedom to allow refined singing. However, it would be even better if refined singing were accommodated with only a few rests. The closer the canon and the closer the parts follow after one another, the better will be the aural effect. Be warned that plainchants should never be transposed. Nor should flats, naturals, and sharps be added to them, for their nature will change. It does not matter if two or three notes of a plainchant are altered by stepwise motion, but this is never done by leap. If the [90r] canon can finish by repeating the the same fugue, it is very effective. If this is not possible, the canon should conclude with a free counterpoint that sticks as closely as possible to it. Note that a canon should not include extreme note-values—that is, the maxim, long, semiminim, croma, and semicroma—for it seems that the breve, dotted or not, and the minim suit better. These are the three note-values that suit canon. And to place two or three semibreves over a minor third in the middle of a canon is bad; it is worse if the semibreves are over a 56. See Bk. Ill, chap. 18.

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double octave. If at the end the soprano cadence tends to be low, it should be replaced by the contralto, while the soprano acts as the contralto an octave higher.57 Sometimes a composer must make a canon in which three parts sing from one, with one part ascending and another descending. Practitioners call this technique arsis by ascent and thesis by descent,58 as if one part were to say "ut-re-mi-fa-sol-la" by arsis and the other to reply "lasol-fa-mi-re-ut" by thesis. In this case the semitones are always inverted, so that the first part says "mi-fa," to which the other should answer, "fami." If the canon comes across an accidental flat to which the second part replies with a sharp, then the third part should be at the unison or the octave, so that the canon will come along by itself without too much cogitation. But be careful to make the same number of rests in every part, so that the rests between the first and second parts are as many as those between the second and third parts. Note also that canon by inversion cannot be sung at the octave because it will come out wrong. Let no one wonder, when one part leaps by a major third and another by a minor third, whether these leaps are contrary, because they are not. But all leaps that are either major or minor, one ascending and the other descending—the same goes for the leaps of the fourth and fifth—must pass the test of the whole tone and semitone, so that both parts ascend and descend the same number of steps. If a canon descends to the octave, see to it that the second part proceeds by making the same fourths as the preceding part, for alteration of the fifths will cause an error in the canon. And do not make a sixth followed directly by a fourth, for two fifths will then occur against the bass. Having begun the canon with as many rests as necessary, a composer is free to make as many or as few as he likes in the middle. Should it prove necessary to make a sixth followed by a fourth, you can find a remedy for avoiding two fifths with the bass. But it is difficult to salvage them. You will be forced to leap to a unison with the tenor, which will become the sixth with the canon above and at the octave. Furthermore, when planning an inverted canon, you are advised that if the tenor is low and reaches C fa ut, it would be most convenient for the composition to raise that voice up a fourth to avoid the tritone—an excellent device in canon at the seventh, as shown in the examples.59 57. See Bk. Ill, chaps. 37 and 43. 58. For a more detailed discussion of "fuga per arsin et thesin," see Zarlino, Le istitutioni harmoniche, Bk. Ill, chap. 51. 59. Since there are no canons at the seventh, perhaps Vicentino had in mind ex. 32.1, above, a double counterpoint at the second.

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Care should be taken with the rests so that when beating the measure alia breve you do not begin on an odd beat. For then the part that sings on all the breves will come on the upbeat, which is awkward for the singer. And this holds true for the ending as well. As to the ordering of rests, let me state that a breve rest is acceptable in the middle as long as two or more parts come together on the notes at the end. In addition, the words ought to considered. Thus, when planning a canon on Latin verse or prose, it is necessary to measure and divide the beats by the syllables of the verse or prose so that they come out right, and more words are not repeated in one verse than in another. If a composer is writing a motet on Latin verse and plans to make a canon, he should choose two poems whose subjects are as compatible as possible, in order [90v] to avoid the undue repetition of words. I should like to make one more observation. If a pupil makes a canon that requires one part to sing at the fifth below, he should raise these same notes up an octave, for they will then come out eminently well at the fourth. I shall not extend this discussion any further because almost every composer knows how to give students information on various fugues. But for the their benefit, I thought I would discuss some fugues that are less common. In example 33 I demonstrate two canonic parts, one of which ascends and the other descends, as well as the technique of inverting certain intervals that occur in such canons.

Example 33.1 [Canon] at the Eleventh

Example 33.2

[Invertible Intervals]

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Chapter 34 How to Compose Double Counterpoint or Double Composition Double counterpoint or double composition partakes of the nature of fugue without being fugue. Sometimes it is fugue between the lower and upper parts, depending on their mutual accommodation to the plainchant. What is called double counterpoint or double composition occurs when a counterpoint can be made either above or below a chant, after which the same notes or the same melodic contour can be uttered yet another time below or above the chant. If the counterpoint appears the first time above the chant at the tenth without a breve or minim rest, the second time it can be repeated at the third or the octave with a minim, breve, or several such rests [examples 34.3 and 34.4]. Moreover, the counterpoint can be made at the third above and then at the sixth after a minim or breve rest; and the part above is placed below, whereas the part below is placed above [examples 34.6 and 34.7]. There is also an example of two parts singing on a plainchant, the second of which repeats the first after a minim rest; though the parts singing over the chant seem to be in octaves against each other, they are not, as I show in example 34.5. As I explained with regard to these examples on plainchant, it is possible to make double counterpoints in many ways, even on measured melodies. The parts can be made to sing at the octave and the twelfth, as well as at other intervals. It suffices for me to provide a little enlightenment to the clever pupil, who will discover many things for himself through hard work and experience. In a composition at the tenth below,60 do not make two thirds or two sixths. You can make double counterpoint on the downbeat and the upbeat of the measure by moving one part by a minim rest. Example 34 presents some illustrations.

Example 34.1 At the Octave Above the Chant for Two Voices

60. Misprint: text has disotto di duodecimo,.

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Example 34.2 At the Third Below the Chant for Two Voices

Example 34.3

At the Tenth Above the Chant for Two Voices

Example 34.4 At the Third Above the Chant for Two Voices

Example 34.5 At the Octave for Three Voices with Two Octaves Apparently but Not Really Formed by the Tenor and Soprano

Example 34.6 At the Third Above the Chant for Two Tenor Voices

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Example 34.7 The Same Contour and Steps [at the Sixth Below] with a Minim Rest

Chapter 35 How to Invent a Composition with Double Counterpoint [91r] In order to exploit the great diversity of procedures in compositions, it is possible to invent many ways of composing the steps of the whole tone and the semitone. Composers must consider all the parts together when planning a composition that can be sung with and without rests and whose semitone steps ascend in one part and descend in another with the same inverted whole tones and leaps. Composers must also be careful with the parts that sing with rests and those without rests, so as to avoid all errors between them. To help pupils learn more easily, I provide examples for two and four voices. I also show which parts are to sing first and which second, as well as which are to sing with rests and which without. Thus, in example 35.1, for four voices, the soprano may begin with the rests while the other three voices can all sing without rests. Then, on returning to a second rendition [example 35.2], the opposite is done—that is to say,

Example 35.1 The First Time the Soprano Has Two [Semibreve] Rests

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the soprano begins and the other parts observe the rests.61 If a student wishes to invert the plainchant, example 35.3 shows him that the first time the chant can be presented at the fifth below the soprano and the second time the tenor voice can be presented at the fifth above, inverting

Example 35.2 This Time the Three [Lower] Parts Have the Two Rests of the Soprano, Which Sings Without Them

Example 35.3 The Soprano a Fifth Above the Tenor

Example 35.4 The Inverted Tenor in the Soprano and the Inverted Soprano in the Tenor a Fifth Below the Plainchant

61. Exx. 35.1 and 35.2 can be sung one after the other. But if the tenor substitutes the two semibreves at the start of ex. 35.1 for the breve at the end of ex. 35.2, then all four voices can go back to the beginning.

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the chant at the tenth above, as seen in example 35.4. With these little examples, students will understand how to make a beginning; and this beginning, with study, will lead easily to the final goal of discovering many inventions, one by one.

Chapter 36 Rule for Duplicating, Triplicating, and Quadruplicating a Passage, and Also for Readily Inventing Compositional Material Without Too Much Thought62 [91v] It is good to hear a passage duplicated on the downbeat and upbeat of the measure in a composition. So that a composer will not find himself entangled in thought, trying to find the way and the means of inventing new passages, here is a handy rule for the performer of instruments, particularly the organ. This rule will always give the performer something to work with: once a player has accompanied the fugue [subject], he uses the accompanying passage—or some other opening material—as a beginning or guide, assigning it to whatever part seems most convenient, and giving the same passage to the other parts one by one, so that the passage always seems to make fugue. Thus he always has material on which to compose without continually searching for and pondering on the invention of new passages. This rule cannot be applied to a composition with words, because the words themselves provide the rule, as was shown in the discourse on the imitation of the nature of the words matched with steps, leaps, and consonances. As I have already stated, the repetition of a passage is good on the upbeat and downbeat. The repetitions of steps and leaps have the opposite effect to the repetitions of words. The reason is that a repeated word means nothing, whereas a repeated text should mean something. When a text is repeated more than two or three times in a motet, the effect is poor in Latin and even worse in the vernacular. But when the musical repetitions are alternately placed on the upbeat and downbeat of the parts, such repetitions are pleasing. In example 36, the bass takes up the passage of the soprano after the fugue has begun. This organization of passages can be taken up in all the parts at the composer's pleasure. 62. The translation of this chapter title preserves the noun inventione, important because the so-called commonplaces (loci communes) were essential to theories of invention and memory as they pertained to extemporaneous classical oration, and later to musical improvisation. The sources on these interrelated topics are many. Three major ancient works Vicentino may have known are: Cicero, De oratore, 2.86.351-54 and 357-58; Pseudo-Cicero, AdHerennium, 3.16.28-20.34; and Quintilian, Inst. ora., 11.2.17-26.

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Example 36 Composition for Four Voices

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Chapter 37 Rule for Writing a Composition with One Part That Starts at the End and the Other at the Beginning at the Same Time, Which Can Be Sung in Circular Fashion and Ended at the Pleasure of Singers [92r] It is possible to invent diverse ideas63 for compositions with fugue in mind or to have two, three, or four voices sing from one part. But since the obligation of fugue is an impediment, such fugues cannot contain much harmony and elegant singing. In truth, such fugues and canons please less because of their harmony than for their clever fugal niceties. If such fugues or canons also turn out to have harmonic fullness and a refined manner of proceeding, they are good to hear; however, never or rarely do they achieve this balance. Such fugues or canons could be pleasant to the ear if they were accompanied by well-coordinated parts that are not obligated to present the same notes. It must therefore be concluded that a composition made up of canons or fugues accompanied by free parts is considerably better than one made merely from canons. Not only is there variety in the parts, but also the advantage of there being no loss of harmony in the composition, which remains rich—not to mention no loss of stylishness in the behavior of the parts. The rule for writing this kind of composition, described in the chapter title, is as follows. A pupil should never write a dissonant syncope, a dissonant black note, or a dot after a note because, when singing the part backward, all the notes after the dot will be syncopated in the reverse

Example 37 [Circular Composition for Two Voices] 63. See Bk. II, note 2.

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direction. He should first compose ten or more tempora up to the middle of the composition. On the half already established, a composer then begins to build in such a way that he imagines this beginning to be the ending. And he goes on to compose until he reaches those notes that came at the beginning. In the middle a composer may use the consonance of the third, or any other consonances. The resulting composition will be circular, and you can stop wherever you please, as in example 37.

Chapter 38 Rule for Writing Any Composition So That It Can Be Sung with Full or Falsetto Voices by Lowering the Soprano an Octave to Become a Tenor ^ It is now necessary to discuss the rule for writing a composition in which one part can be sung by two falsetto voices. It transpires that often some singers gather together and among them there is no one who sings soprano. Having at hand one or several compositions written for full voices, the group stops singing because it lacks a soprano. [92v] To ensure that everyone has a chance to sing, any type of composition may be so arranged that it can be sung when there are sopranos as well as when there are none. The rule is as follows. Write a soprano part and then lower it an octave, converting it into a tenor, and make the contralto similar to a falsetto soprano. Composers should take care that all the consonances of the fifth in the soprano are converted to fourths when this voice is lowered by an octave. All major thirds become minor sixths, and conversely all minor thirds become major sixths. If it is necessary to have a duo with the falsetto part, never make a fifth, for when that part is lowered by an octave the fifth becomes an exposed fourth without any support. The twelfth in the falsetto part becomes a fifth. Whenever the falsetto soprano makes a tenth in cadences going from the sixth to the tenth between bass and contralto, this tenth becomes a third in the lower octave, making a false fourth or tritone with the contralto. It is not a good idea to use the succession of consonances, fourth to fifth, in such compositions. The less of these you make, the better; and they should be used in the middle rather than the outer parts. If this succession of fourth to fifth appears in the falsetto part when it is on top, the succession reverses itself to become a fifth going to a fourth when the 64. See note 2, above. When an ensemble is described as singing with full chest voices, the soprano must be either a boy, a woman, or a castrate; otherwise this part is sung falsetto ("a voce mutata, voce mutabile, soprano mutabile") by a tenor or bass.

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part changes and descends an octave. This is neither a gain nor a loss because the leap consists of either three or four steps. Examples 38.1 and 38.2 show the falsetto soprano and also the soprano written as the tenor an octave below.65

Example 38.1 Four-Voice Composition with Falsetto Soprano

Example 38.2 Four-Voice Composition with Soprano Changed to Tenor an Octave Below

65. The single line of text reads: "Of almost all my wealth have I been deprived."

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Chapter 39 Rule for Writing Any Sort of Composition So That It Can Be Sung with Falsetto or Full Voices by Raising the Tenor an Octave to Become a Soprano It may please composers to write Masses, motets, madrigals, chansons, psalms, hymns, or other works that can be sung in two ways, that is, with full or falsetto voices. If, for instance, you want to compose a motet or madrigal in this way—to be sung in two ways—you then write two tenor parts. The [93r] tenor voice that takes the falsetto should be like a soprano in that it performs the soprano's cadential actions.66 Be warned that the falsetto tenor, that is, the one to be sung an octave higher, should never descend a fifth below the bass because at the octave above it will become a discordant fourth. If the tenor is a third below the bass and is then sung an octave higher, that third becomes a sixth. All octaves above the falsetto tenor will become unisons, and in the falsetto part the unisons will become octaves. All minor and major thirds below the tenor will become major and minor sixths, respectively, when this tenor is raised an octave above. If the falsetto tenor is a minor sixth below the bass, it becomes a major third when raised an octave. If the tenor makes an octave with the bass,67 at the octave above it becomes a fifteenth.68 If the tenor makes a fifth with the bass, it becomes a twelfth at

Example 39.1 [Four-Voice Composition with Full-Voice Tenor] 66. See Bk. Ill, chap. 29. 67. Error: text has "et quando il Tenore sara sotto il Basso un'ottava." 68. Error: text has quinta instead of quintadecima, which appears in the next phrase.

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Example 39.2 [Four-Voice Composition with] Tenor Changed to [Falsetto] Soprano an Octave Above the octave above. If the tenor rises to the thirteenth above the bass, it was a minor sixth at the octave.69 And the syncopated fourth becomes a fifth when raised an octave. It is necessary to observe these rules to ensure that compositions are sonorous and attuned to the falsetto part that is to be raised an octave.70

Chapter 40 Rule for Discovering an Unwritten Canon9 and How It Should Be Sung Some composers make canons and then display them with nothing written above them, as if that were sufficient for rather inexperienced musicians. But the opinion of philosophers is that man should strive to make his compositions more excellent and marvelous than those of all other men in his profession.71 He should also force himself to make them as easy as possible, because difficulty leads only to annoyance. This is especially true with regard to certain things that could be easy and yet are made difficult by the addition of certain signs and other impediments that impede the student's understanding. Such things are sooner to be censured than praised, for every philosopher concludes that it is 69. This utterance is not very clear: "et se quello ascendera alia quintadecima con il basso egli rimarra sesta minore all'ottava." 70. The single line of text reads: "O blessed one, if such liberal gifts you bestow." 71. On excellence and superiority, see Aristotle, Meta.> 2.1.993b, and Nic. Eth., 5.16.1021 and7.1.1H4a.

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useless to accomplish with more what can be done with less.72 Thus you must [93v] always elucidate and facilitate all difficult things lest it be said that anything is lacking in the composition. Composers ought to make their canons and any other such fancies as easy as possible. If a student wishes to discover unwritten canons and other sorts of devices, he should take them and test the parts according to the canonic systems: that is, at the second, third, fourth, fifth, sixth, seventh, octave, and ninth. Though this is an annoying and tiresome task, man is not excused from hard work where honor is at stake. At times, the fugue or canon cannot be discovered through the systems mentioned above, either because of the impediment of rests, or because one part is going up while another is going down, or because one part starts at the beginning and the other at the end. In such cases a student can begin at the end and work back to the beginning in order to find where and in which voice he should begin the canons. The same can be done if the composition is faulty in the middle or near the end. I have offered these remarks to make this task easier. In the same vein, a student must examine cautiously all the parts and consider the opinion of whoever made the device or canon so that everything will be easily discovered. A composer of such fancies must try to make canons and fugues that are pleasant and full of sweetness and harmony. He should not make a canon in the shape of a tower, a mountain, a river, a chessboard, or other objects,73 for these compositions create a loud noise in many voices, with little harmonic sweetness. To tell the truth, a listener is more likely to be induced to vexation than to delight by these disproportioned fancies, which are devoid of pleasant harmony and contrary to the goal of the imitation of the nature of the words. According to the Philosopher [Aristotle], all those who act do so for a reason.74 The purpose of music is to satisfy the ear, and this will not be accomplished by means of colors, chess, or other fancies more enticing to the eye. On the contrary, only those fancies that are well accompanied by harmony and the words for 72. Another version of this idea occurs in chap. 3 (see note 4, above). The aphorism as stated here is an almost verbatim borrowing from Gaffurio's Practica musicae, Bk. II, chap. 8: "Cum apud Philosophum Frustra fiat per plura quod fieri potest per pauciora." 73. Vicentino s irony is exaggerated. However, Ghiselin Danckerts did write an enigmatic set of twenty-one canons in the shape of a chessboard on a set of Marian texts beginning with the words "Ave maris Stella." Considering Danckerts' role in the 1551 debate with Lusitano (see chap. 43, below), Vicentino must have enjoyed inserting this veiled barb. The canon is preserved in Pedro Cerone, El melopeo y Maestro (Naples, 1613), Bk. 22, chap. 1129.

74.Nic.Eth., 1.1.1094a.

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the purpose of aural satisfaction are worth a hearing. But few fancies are so fashioned, rather their steps and leaps are serviceable neither to harmony nor to words.

Chapter 41 A Reliable Way to Check a Composition for Few or Many Voices; Should It Contain the Errors of Two Fifths or Two Octaves, These Can Be Discovered with Great Certitude by Using the Rule Given Here The scant experience of music students often gives rise to errors and mistakes in compositions for three, four, five, or more voices. For instance, when an untutored pupil must compose two sixths, the danger is that he will compose two fifths. The inexperienced student makes frequent errors because he fails not only to concentrate when composing but also to review his composition. So those who are not very experienced should adopt the following rule. To be certain that there are no errors in the case of a composition for four or five voices, a student should begin with the soprano and check it diligently note for note with all the other parts. When he has finished checking the soprano with all the parts, he should then take the contralto and check it with the tenor, with the fifth part, and finally with the bass. The same is to be done with the tenor. Several tenors, several contraltos, or several sopranos should all be checked according to this [94r; incorrectly numbered 88r] rule, part by part and note by note. If a pupil wishes to check a composition for six, seven, eight, or more voices, he should realize that it does no discredit even to a well-experienced person to bar [and score] the composition by breves and longs.75 Checking a composition in this way constitutes a reliable method of correcting mistakes.

Chapter 42 Rule for Coordinating the Singing of Any Sort of Composition Compositions differ according to the subjects on which they are made. All too frequently, however, certain singers pay no attention to this in their singing. They sing unheedingly and, depending on their nature and custom, using their own specific technique. But compositions made 75. In this context, the verbpartire means to score a composition by putting bar lines in each part, so as to facilitate lining up the notes mentally as one checks each voice against the others.

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on various subjects and various ideas76 demand different styles of writing. Singers, therefore, must consider the intention of the musical poet and whether the poet writes in the Latin or vernacular tongue, and they must imitate the composition with their voices by using as many diverse techniques of singing as there are diverse styles of composition. When they use such techniques, they will be considered by the audience to be men of judgment and masters of many styles of singing. They will also demonstrate the abundance and richness of their many singing techniques with their talent for gorgiay or diminution, matched to the appropriate passages in the composition. There are some singers, however, who display to listeners scant judgment and consideration in their singing, for when they come upon a sad passage they sing it joyfully and, conversely, when the passage is joyful they sing it sadly. Such persons are advised that diminutions made in the proper places and in tempo will seem good. Moreover, such diminutions should be used in more than four voices, because diminution always causes the loss of numerous consonances and the burden of many dissonances. Even though the diminution may seem smooth to inexperienced listeners, it nevertheless impoverishes the harmony. To avoid losing harmony in compositions while singers display a refined talent for diminution, it is a good idea to have such diminution accompanied by instruments that play the composition accurately, without diminution. For harmony cannot be lost through diminution if the instrument holds the consonances for their full values. Sometimes while a player diminishes a composition, the singer also decides to diminish the work they are both performing. In this case, if both performers diminish simultaneously but fail to produce an identical passaggio in agreement with each other, they will truly not be in accord. But if they are well-coordinated, they will be good to hear. Moreover, in compositions sung without instruments, diminutions sound good in works for more than four voices, because wherever a consonance is missing it is replaced by another part, either at the octave or the unison. The composition will not be left bereft of harmony, because the singers making the diminution proceed by wandering among the parts, sometimes at the unison, sometimes at the second, third, fourth, fifth, sixth, or octave—touching now one part and now another with various consonances and dissonances—which dissonances seem consonant without being so owing to the rapidity of the singing. 76. See Bk. II, note 2.

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Each singer should take care not to make any diminutions when singing lamentations or other mournful compositions, for then these sad works will seem joyful. Conversely, he should not sing joyful works sadly, be they in the vernacular or in Latin. He is also advised that in coordinating vernacular works, he should sing the words in keeping with the composer's intention, so as to leave the audience satisfied. He should express the melodic lines, matching the words to [94v] their passions— now joyful, now sad, now gentle, and now cruel—and adhere to the accents and pronunciation of the words and the notes. Sometimes a composition is performed according to a certain method that cannot be written down, such as uttering softly and loudly or fast and slow, or changing the measure in keeping with the words, so as to show the effects of the passions and the harmony. This technique of having all the singers at once change the measure will not seem strange, provided the ensemble agrees on when the measure is to be changed, thus avoiding any errors. A composition sung with changes of measure is pleasing because of the variety, more so than one that continues on to the end without any variation of tempo. Experience with this technique will make everyone secure in it. You will find that in vernacular works the procedure gratifies listeners more than a persistent changeless measure. The measure should change according to the words, now slower and now faster. It is well to take care when the measure is changed through the proportion of equality77 in the middle or at the end of compositions. Although some believe that you should not change the measure when beating alia breve, it is nonetheless changed in singing, which is not such a terrible thing. When the equal proportion is finished, you return to the previous measure, so that the change of the measure is not disconcerting in any composition. The experience of the orator can be instructive, if you observe the technique he follows in his oration. For he speaks now loud and now soft, now slow and now fast, thus greatly moving his listeners. This technique of changing the measure has a powerful effect on the soul. For this reason music is sung from memory, so as to imitate the accents and effects of the parts of an oration.78 What effect would an orator have if he were to recite a fine oration without organizing accents, pronunciations, 77. See chap. 31, above. 78. Although the parts of a speech varied by genre and author, the standard scheme has six parts: exordium, narratio, divisio, confirmatio, confutatio, and conclusio. But see chaps. 14-16, above, where Vicentino discusses a tripartite structure (beginning, middle, and ending)—an Aristotelian concept.

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fast and slow rates of motion, and soft or loud levels of speaking? He would not move the audience. The same is true of music. If the orator moves listeners with the devices described above, how much greater and more powerful will be the effect of well-coordinated music recited with the same devices, but now accompanied by harmony. The experience of listening to the organ teaches us that it is wonderful to hear only the intonation of pitches matched with consonances, without the pronunciation of words. O how immeasurably excellent would music be if singers, by means of the delivery of pitches and words, could intone and sing a composition as accurately as the organ! And even if singers cannot attain so accurate an intonation, at the very least they should be diligent in harmonizing as much as possible in their ensembles. It is much more pleasing if music is sung from memory than from written parts. Take the example of preachers and orators. If they recited their sermons or orations from a script, they would lose favor and face a dissatisfied audience. For listeners are greatly moved if glances are matched with musical accents. Refined and learned compositions move those who are expert in this profession much more than the inexperienced. A merely instinctive listener lacks that subtle judgment acquired through much hard work. In order for an entire ensemble to be flawless, the singer who sings the bass should harmonize well at the octave with the other parts. For in the bass part lies the complete substance of perfect accord.

Chapter 43 The Musical Disagreement, Debated and Adjudicated, Between Don Vicente Lusitano and Don Nicola Vicentino, as Recorded Below [95r] I, Don Nicola Vicentino, being in Rome in the year 1551, was present at a private academy where there was singing.79 During a discussion on music there arose a kind of dispute between the Reverend Don Vicente Lusitano and myself. The gist of our discourse was as follows: The said Don Vicente was of the opinion that the music sung at the time was diatonic. I, on the contrary, maintained that it was not purely diatonic80 and that the compositions then in use were a mixture of the larger parts of the chromatic and enharmonic genera as well as of the diatonic 79. The musicale, during which an ensemble sang a composition on the Regina coeli antiphon, took place at the home of Bernardo Acciaiuoli-Rucellai. See App. IV and my introduction. 80. See notes 87 and 92, below, and my introduction.

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species and genus.81 Not to be prolix and stray beyond the substance of our debate, I shall omit the many words spoken in our argument. To be brief, we wagered a pair of gold scudi82 and agreed to elect two judges to hear our disagreement and to give an inappealable verdict for one side or the other. The judges were the Reverend Messer Bartolome de Escobedo, priest of the diocese of Segovia, and Messer Ghiselin Danckerts, clerk of the diocese of Liege, both singers in the chapel of His Holiness [Pope Julius III].83 The matter was debated once in the presence of the Most Illustrious and Very Reverend Lord Ippolito II d'Este, Cardinal of Ferrara, my lord and patron, and an audience of many learned men. Subsequently, in the chapel, before all the singers who happened to be in the chapel of His Holiness that morning, the reasons for this disagreement were presented by both sides to the two judges whom we had elected, in the presence of many persons in addition to the aforesaid singers. When the Very Reverend and Most Illustrious Cardinal of Ferrara, my lord and patron, was present, our disagreements were heard by only one judge, namely, Messer Bartolome de Escobedo. Because the other judge, Messer Ghiselin, was prevented from attending that time by some personal business, I sent him the very same day a letter narrating in a few words how in the presence of my patron, the Most Illustrious and Very Reverend Cardinal of Ferrara, I had proved to the said Don Vicente that the music sung at the time was not purely diatonic,84 as he said it was, but rather a mixture of the larger parts of the chromatic and enharmonic genera as well as the diatonic species and genus. Since I had sent a few words about our disagreement (though I cannot be certain that the said Don Vicente had been advised that I had written those words to the judge, Messer Ghiselin), it transpired that Don Vicente himself likewise wrote the judge many words in a letter of his own. Four or six days later, the said judges came to a unanimous agreement and pronounced the sentence against me, which everyone can see copied below. The judges sent the sentence to be presented to the Most Illustrious Cardinal of Ferrara in my presence, by the hand of the said Don Vicente. My Most Illustrious Lord, after reading the sentence, told me that I had 81. The phrase "larger parts of the chromatic and enharmonic genera," refers to minor and major thirds, respectively, and music incorporating these intervals is called tempered and mixed music in contradistinction to the pure diatonic. See Bk. I, chap. 6, and Bk. Ill, chaps. 5 and 15. 82. See Introduction, notes 17 and 26. 83. The names of the judges are rendered Bartholomeo Escobedo and Ghisilino Dancherts. 84. See notes 87 and 92, below, and my introduction.

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been condemned to pay the two gold scudi, and so I paid them then and there. I have no wish to recount the words the Most Illustrious Cardinal rightly and justly addressed to Don Vicente about the injustice and wrong done me by the judges, for I should not have wished to win one hundred scudi and been the recipient of such a just rebuke from such a prince in the presence of so many witnesses as were then present, who will bear true witness and testimony as to what happened. Nor do I want to overtax myself by enumerating how many times, after the Most Illustrious Cardinal had read the sentence [95v], the said Don Vicente requested it back from His Most Illustrious Lordship. Since the said sentence was in favor of the aforesaid [Don Vicente], I begged His Most Illustrious Lordship to show me mercy and to permit me to print and publish it to the world to his honor and glory as well as to that of the two judges. I shall refrain from describing how insistent Don Vicente was to have the sentence back from the Most Illustrious Cardinal when he heard that I planned to publish it, and how many days he importuned the rector, Monsignor de Troti, to whom the Most Illustrious Cardinal had entrusted the sentence.85 A few days later my lord and patron had to leave for Ferrara. We stayed there for some time, and then it was necessary for His Most Illustrious and Very Reverend Lordship to go to Siena, where the Sienese were at that time waging war. We lived in Siena with much anxiety but not for long. After returning to Ferrara for a short stay, my lord and patron had to go back to Rome where, with God's help, we now reside. I have written these few words lest the aforesaid Don Vicente Lusitano reprove me for my tardiness in printing the said sentence, which I had promised him to do some time ago. This delay was caused by the concerns and reasons given above. Even though four years have elapsed since that sentence was issued, this delay is not inappropriate because the sentence now comes out together with this, my work. Hence, it will be better understood than it would have been earlier without my work. As a consequence, everyone can properly adjudicate our disagreements and consider whether the sentence was pronounced justly and whether the judges understood our disagreement. So the arguments sent in writing by me and by the said Don Vicente Lusitano as well as the sentence are copied faithfully below without the fraudulent subtraction or addition of a single word. Indeed, they are 85. No information on Monsignor de Troti is available, other than the title of his position, Preposto, which means rector or provost. The Trotti family was a distinguished one with branches in the major cities of northern Italy, including the Trotti of Ferrara.

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copied down to the last period from the authentic copy made by the judges and sent to the Most Illustrious and Very Reverend Cardinal of Ferrara, as everyone can read in the following documents.86 The Contents of the Information Sent by Don Nicola to Messer Ghiselin as His Evidence to the Honorable Messer Ghiselin: I have proved to Messer Vicente Lusitano that the music we all ordinarily sing today is not purely diatonic,87 as he says. I have explained to him the rules of the three genera. I have also explained that the diatonic proceeds by being sung with the steps of a tone, a tone, and a semitone and that it must never have steps other than the tone and the semitone, as he himself confessed to be true. On the other hand, it is public knowledge throughout the world that our singing and melodic lines proceed in our songs with the incomposite ditone—for instance, ut-mi—and also with the incomposite trihemitone—for instance, re-fa and mi-sol—without anything intervening by way of a tone or semitone, as happens with re-mi-fa in the diatonic genus. Thus, this re-fa or mi-sol is the trihemitone, or semiditone, or step of the minor third in the chromatic genus. And the incomposite ditone, called ut-mi and fa-la in practice, belongs to the enharmonic genus. I have thus explained that the music sung today is composed of a mixture of all three genera but without the many species of the chromatic genus, such as the sharps and flats, that are accidentally placed to aid the consonances and that disrupt the diatonic system. Therefore, according to my explanation, which you may examine in Boethius, the music we sing today is a mixture of the three genera rather than purely diatonic, as Messer Vicente Lusitano avers. Rome, 5 June 1551 Devoted to Your Excellency, Don Nicola Vicentino The Contents of the Information Sent by Don Vicente Lusitano to Messer Ghiselin as His Evidence The Very Reverend and Magnificent Lord Ghiselin [96r] On Thursday June 4, I believe I proved before the Very Reverend Cardinal of Ferrara that I understand the genus of the music composers 86. The copies of Vicentino's and Lusitano s submissions differ in insignificant details from copies of the same preserved in Danckerts' Sopra una differentia, Bk. I, chaps. 3 and 4. Of the two, Vicentino's is the more complete and accurate version. 87. In the version of this document printed by Danckerts (Sopra una differentia, Bk. I, chap. 3), the wording is Diatonicha, not Diatonica semplice. In his letter "To the Readers," Danckerts indignantly points out this addition, imputing malicious motives to Vicentino: he changed the grounds of the original debate in order to strengthen his claim that the verdict against him was unfair. See Introduction, note 34. It must be said that although Danckerts' versions of the documents are also inaccurate in some respects, the addition of the word semplice here and at the end of the document seems to be a deliberate and substantive alteration on the part of Vicentino. See also note 92, below.

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88. The third reference to De inst. mus.—that is, 4.6—is mentioned in the paragraph that follows the lengthy quotation from 1.21. The translation of the material from Boethius, cited by Lusitano and Vicentino in Latin, is taken from Calvin M. Bower's translation with a few minor changes, duly noted. The text gives Lusitano s first reference as Tundecimo, del primo Libro," a misreading of "per il ii del primo libro." However, neither 1.2 nor 1.11 have anything to do with the genera. Perhaps Lusitano meant 1.22 ["per il xxii del primo libro"], though 1.23 is also relevant to the issue. See Vicentino's rebuttal below. 89. That is, in the five tetrachords: hypaton, meson, synemmenon, diezeugmenon, and hyperboleon. 90. The "etcetera" is Lusitanos; Boethius' text ends as follows: "(a diesis is half a semitone)." 91. Bower translation, Bk. 4, chap. 6. 92. The version of this document printed by Danckerts (Sopra una differentia, Bk. I, chap. 4) does not record the word semplice. Vicentino made the identical alteration in his own deposition. See note 87, above. 93. Boethius makes no such statement, although it may be inferred from the context of Deinst. mus., 1.21.

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[Don Nicola] lacked the true knowledge of the chromatic, which is the progression by semitone and semitone, and of the true progression of the enharmonic by diesis and diesis. As to the ditone and semiditone, they existed in the diatonic genus before any of the others, for the diatonic was the primary and most natural [genus], according to what Boethius said.94 And though Don Nicola himself wants to call it mixed, he does not desist from initially calling it the diatonic genus. I likewise maintain that one should never desist from speaking of the diatonic genus, and I so declare. I beg Your Excellency to confer with your colleague about these my arguments and, as was promised to the Most Illustrious Cardinal of Ferrara, to pronounce the sentence on Sunday. Completed on this day, 5 June 1551 Vicente Lusitano,95 servant to Your Excellency

Having perused my arguments and Don Vicente's reply, readers now understand that the two chapters he cited from Boethius constitute the very explanations of my arguments. Let me first discuss Book I, chapter 21, where Boethius says: "In all these, the pitch progresses according to the diatonic genus of song." The title of this chapter is "Concerning the Genera of Song," and it begins with these words: "Now that these things have been explained." In this chapter you will find the explanation of the three divided genera: the diatonic divided by the chromatic, and the chromatic and diatonic divided by the enharmonic. You will also see how in this chapter Boethius gave all those explanations I sent to Messer Ghiselin, the judge. And he [Don Vicente] cited this very chapter in my favor and against himself, as every connoisseur of music, theorist or practitioner, can judge for himself. That this is the truth can be seen by every connoisseur who reads chapter 23, which follows shortly after the previous citation from Boethius, for it explains everything in chapter 21, the chapter cited by the aforesaid Don Vicente. The title of chapter 23 reads as follows [96v]: "Which Ratios Are Between Pitches in Each Genus." So that everyone may understand thoroughly the chapter in question, I shall expound it section by section and compare it with music practice, in order that it can be understood by practitioners of music as well. "In this manner, then, the division is made through each tetrachord according to the special character of the genera, so that we divide all five tetrachords of the diatonic genus into two tones and a semitone." By beginning with these words, Boethius wants to show students which pitches and which characters pertain to each genus. Readers are advised 94. De inst. mus., 4.6. 95. In Latin, Vincentius Lusitan.

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that in each tetrachord—that is, in each fourth in the character of the genera—the division is made in this way: we divide all five tetrachords, or all five fourths, of the diatonic genus into two tones and a semitone. The chapter then continues as follows: "In this genus the tone is called 'noncomposite,' since it is considered whole, and no other interval is added to it; rather, the tones in each interval are integral." Pupils are warned that in this diatonic genus the whole tone must be integral, that is, incomposite, and without any division by other pitches or intervals. On the contrary, both these intervals of a tone are integral and not divided, as is done in music practice. For many composers divide whole tones with flats, sharps, and naturals. Given such divisions of the whole tone, music made in this way is not diatonic according to the rule and division presented above. And this section of Boethius goes against the sentence of the judges. The rest of the chapter continues: "In the chromatic genus the division is set forth as semitone, semitone, and noncomposite trihemitone. We call this trihemitone 'noncomposite,' because it is put together in one interval." Having discussed first the division of the diatonic genus, Boethius then goes on to explain the division of the chromatic genus. He states that we arrange the division by semitone, semitone, and incomposite trihemitone. We call this trihemitone incomposite because it is made up in one interval. In other words, the step of this trihemitone has no division within it, as, for instance, is the case in music practice with the step or leap of the minor third, re-fa and mi-sol, and the reverse, fa-re and sol-mi, which are the same size as the first pair. These intervals have been used and are still used by composers, and since they disrupt the diatonic system, the music that was and is being sung is not purely diatonic.96 This section also goes against the sentence. The chapter goes on to say: "In the diatonic genus a semitone-plus-tone can be called a trihemitone, but it is not noncomposite, for it is made out of two intervals." In addition, then, the author explains the incomposite and composite trihemitone. He says, you will note, that the trihemitone can be called composite when it is composed of two intervals. But it belongs to the diatonic genus, as when in music practice you make up re-mi-fa or fami-re, and mi-fa-sol or the reverse, sol-fa-mi. This trihemitone is composed of two intervals—one between the first and second notes and the other between the second and third notes—both in ascending and descending. Proceeding to the enharmonic genus, the expositor [Boethius] says: [97r] "Likewise in the enharmonic genus it [the trihemitone] con96. See note 87, above, and my introduction.

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sists of a diesis, a diesis, and a noncomposite ditone. We call this ditone 'noncomposite' for the same reason, for it is brought together in one interval." Boethius explains briefly that the enharmonic genus is the one that consists of two dieses and an incomposite ditone, and as he states, the same arrangement is followed for the ditone as was explained for the trihemitone. In this genus we call the ditone an incomposite ditone for the same reason we call the trihemitone incomposite—namely, that it is made up of one interval or leap without any intervening interval, as in music practice we say "ut-mi" or "fa-la." This step of the ditone has been and is being used as an incomposite interval. Don Vicente did not understand this explanation when he wrote in his deposition that the step or leap of the trihemitone and ditone occurred first in the diatonic genus. According to the present chapter, as Boethius so well explains and avers, the genera have different divisions. Therefore, his [Don Vicente's] deposition speaks against himself and against the sentence. If readers consider the chapter copied above, they will find that these same words were written by me in my deposition addressed to Messer Ghiselin, as my arguments above have shown. The other chapter cited by Don Vicente in his statement addressed to the judge, Messer Ghiselin, is Book IV, chapter 5, in the Fundamentals of Music by Boethius, although the said Don Vicente cites it as being Book I.97 The title is "Partition of the Monochord of the Netai Hyperboleon Through Three Genera," and it begins in this way: Now the diagram of the diatonic genus has been presented in that mode which is first and rather basic, the mode we call Lydian. The modes should not be discussed at this time. In order that a diagram might integrate the three genera and that a specific numerical value may be given in all cases, even the numbers holding the ratios of tones and the diesis, the number that will allow all this to be accomplished has been computed. The largest number, which should be 9,216, is written down at the proslambanomenos, while the smallest number should be 2,304. The ratios of the remaining sounds will be interposed between these two. We proceed from the lowest, and we designate all the notes not only by words, but also by letters placed alongside. The partition must be made in three genera.98 97. Lusitano did cite 4.5 (Bower translation, Bk. 4, chap. 6), not 1.5, as Vicentino says. 98. Vicentino took the last phrase, "scilicet ita ut quoniam trium generum est facienda partitio," as an independent sentence. In Bower's translation it is a part of a clause: "But since the partition must be made in three genera and the number of notes exceeds the number of letters, . . . "

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In what follows in this chapter Boethius explains the divisions and partitions of the three genera on a string called the nete hyperboleon by philosophers." In our practice it is called the highest A la mi re, for it is the first and highest in the order of the tetrachords. It is now clear that this chapter, as cited by Don Vicente, is irrelevant to the question I put to him: Is the music sung in compositions diatonic or a mixture of the three genera, that is, of some of their parts? I cannot make up my mind as to which of the two I should believe, considering the sentence passed by the aforesaid judges. But I do not wish to lose time over this now, nor state that the judges have done me wrong, nor insist that they failed to understand the aforementioned chapters [from Boethius]. I would never be capable of saying such things of anyone. But the courtesy of Don Vicente Lusitano has been such that, having overcome me and taken the two gold scudi through the sentence formerly passed, he has also overcome me by deliberately speaking against the sentence and the aforesaid judges who did him such a favor. Truly, he has vanquished me and put me in such bondage that I shall be obliged to him in perpetuity. I should never have believed that the aforesaid Don Vicente would have agreed and stated that the sentence that was handed down was unjust. But he has indeed made known to the world that they passed an unjust sentence against me.100 What is more [97v], in one of his chapters he has proved that the sentence as passed was against himself, thus demonstrating the truth to the world. Truly, it seemed to me to be a dream. Yet the truth is that he himself has confessed it publicly to everyone. So that people will believe me in what I have said, Don Vicente himself has decided to print and publish to the world the argument I presented in my deposition to the judge, Messer Ghiselin, thus providing stronger confirmation and corroboration of what I said. This he did to unburden his conscience, for he himself came to realize that he had stolen the two scudi. May God forgive us all as I forgive him because his action was that of a good Christian. For assurance, let everyone take a look at his work on music entitled Introdutione facilissima & novissima di canto fermoy figurato, contraponto semplice etc., printed in Rome at the Campo di Fiore by Antonio Blado, Apostolic Printer, September 25, in the year of Our Lord 1553. 99. For instance, Capella, De nuptiis, 9.931; Gaffurio, Practica musicae, Bk. I, chap. 2; and Glarean, Dodekachordon, Bk. I, chaps. 2 and 5. 100. This sardonic passage refers to what Vicentino saw as an act of capitulation on the part of his adversary, documented in Lusitano's explanation of the three genera in his treatise of 1553. See note 101, below.

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The aforesaid Don Vicente discusses a number of matters in this work, and near the end of it he discourses on the three genera of music. Beginning with these words, he says:101 The genera or linear progressions of pitches are three: that is, the diatonic, which proceeds through four pitches by tone, tone, and minor semitone; the chromatic, which proceeds through four pitches by minor semitone, major semitone, and three semitones, making a total of five semitones according to Boethius' definition in chapter 21.102 And according to the same Boethius in chapter 23, the chromatic genus proceeds through minor semitone, major semitone, and an adjoining minor third, as in re-fa rather than re-mi-fa. Minor third means the incomposite trihemitone, which should be put together in one integral interval, such as re-fa or mi-sol. The enharmonic is the genus that proceeds through four pitches by diesis, diesis, and the single interval of a major third, as in ut-mi rather than ut-re-mi. The signs for these intervals are like those I have already described. For the minor semitone, the tt designates the four commas it contains. The sign for the major semitone, ^,103 designates the five commas it contains. This sign is not used except after the minor semitone to instruct us to make a major semitone at that spot on either a line or a space, as will be shown below. The sign for the diesis, +, designates the two commas it contains.

It is evident in the above chapter that Don Vicente confirms that the leap of the semiditone or minor third belongs to the chromatic genus and gives as examples re-fa and mi-sol. He took these examples from my written deposition, sent to the aforesaid Messer Ghiselin and reproduced above. This action goes against him and against the judges. He then goes on to explain the enharmonic genus and gives an example, saying that ut-mi is the ditone or the leap of the major third. This example also he learned from my written deposition addressed to the aforesaid Messer Ghiselin. Again, this passage goes against Don Vicente himself and against the judges. That Don Vicente truly learned it from my written deposition can be seen by anyone who reads the paper he sent to Messer Ghiselin. For near 101. Introdutione facilissima, "De tre generi della musica," fols. F2v-F3r; facsimile ed., pp. 22v-23v. The copy in Vicentino s text presents only insignificant typographical variants, except in one case noted below. 102. De inst. mus., 1.21. In the next sentence, the reference is to De inst. mus., 1.23. 103. Error: tt. Someone, author or printer, failed to notice that the sign for the major semitone has five strokes, in comparison to the four strokes of the minor semitone. Though firm conclusions cannot be drawn from punctuation, it is nonetheless worth noting that commas are consistently inserted before the word come in this citation from Lusitano, thus making nonsense of his prose. The word come has been interpreted as an adverb rather than the plural of coma/comma.

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the end of it he says boldly that I do not understand what the chromatic genus is. But I say boldly that the said Don Vicente understood very well what the chromatic genus is, that is to say, he understood it from my paper addressed to Messer Ghiselin. For whoever compares his aforementioned printed treatise on music with my deposition will find that it is the same as what I said in explaining the three genera. And his declaration that he knew beforehand how to give a practical example of the chromatic genus is not to be believed. Nay, with his treatise he shows that beforehand he did not know how to do this, at least not before he had seen my written statement. [98r] Furthermore, it is true that at the end of his paper to Messer Ghiselin he writes the following words in his argument and defense: the ditone and the semiditone first belonged to the diatonic genus. But in this treatise of his he declares the complete opposite: re-fa does not belong to the diatonic but rather to the chromatic genus, and he then adds that re-mi-fa belongs to the diatonic genus. He says the same things about the enharmonic genus: he advises you that in the enharmonic genus we have ut-mi, not ut-re-mi. Clearly, he has printed the complete opposite of what he had previously written as his argument in his deposition. His arguments were based on what he wrote in that paper, as was the sentence pronounced by the judges. I am ashamed on his behalf and deeply grieved that this work by Don Vicente should be made public, for it constitutes overwhelming evidence to the world, evidence that forces everyone to recognize that this Don Vicente contradicts the judges as well as himself. There are many other reasons as well. For instance, at the end of his work the author shows that he neither understands nor knows how to harmonize the enharmonic diesis with consonances. What is worse, he gives an example of false fifths and false thirds. And when speaking of the minor semitone, he gives two notes, mi-fa or fa-mi, as an example. He is of the opinion that the semitones sung or played on instruments is minor, whereas it is major, as in fa-mi or mi-fa.1041 have presented the explanation and proof of these steps in the chapter on major semitones dealing with how many ways and with what signs they are written [Book I, chapter 19]. To assure everyone, I shall give the example of false fifths and bad thirds printed by Don Vicente at the end of his work [example 43].105 Not to tire my readers, I shall not linger further on his work, leaving 104. From the beginning Vicentino has maintained that the modern diatonic species contains a major semitone plus two sizes of whole tone (16:15 plus 10:9 and 9:8). See Bk. I, chap. 6. 105. The example is transcribed from Lusitanos Introdutione facilissima, fol. F2v (fac-

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whatever more needs to be said to those who have studied my work. Should there be many errors in it, they can be noted and corrected by understanding my labors.

Example 43 How the Aforesaid Don Vicente Has Arranged False Consonances How it grieves me to have to show this example, so false in harmony! But I am comforted by two reasons why no one may reprimand me: first, because it is printed and I am not the first to make it public; and second, it permits everyone to judge the erudition of the pretensions of [some] men. It now remains to present the copy of the sentence pronounced against me, faithfully and accurately copied from the original, with signatures in the two judges' own hands and countersigned by the witnesses who checked our depositions and the sentence. Let no one think that I have transcribed and printed it to suit my own purposes. To whoever wishes to examine and verify that the depositions and the sentence are printed accurately word for word, I undertake to give the said sentence and let him read and examine it.106 Witnessed and agreed: their investigations submitted in writing, written and signed in their own hands, and inspected by the writers themselves in the presence of the entire aforesaid assembly. simile ed., pp. 22v-23r), rather than from Vicentino's text, because the latter fails to reproduce accurately the accidentals as printed by Lusitano. For an analysis of this example, see my introduction. 106. The copy of the sentence is virtually identical with the one presented by Danckerts in Sopra una differentia, Bk. I, chap. 5.

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Sentence [98v] After invoking the name of Christ, etc., we, the aforesaid judges, Bartolome de Escobedo and Ghiselin Danckerts, by this our final sentence and decision pronounce in the presence of the said assembly and the aforesaid Don Nicola and Don Vicente, the petitioners for the said sentence, being now present, of sound mind, and listening. We pronounce, decide, and judge the said Don Nicola not to have proved, either orally or in writing, anything on which the idea of his proposal can be founded. How much more, on the contrary, has the said Don Vicente, in speech and writing, proved that he, for one, competently knows and understands which is the genus of composition normally used by composers today and sung everyday, as all can clearly see above in their respective investigations. For this reason, the said Don Nicola must be condemned, as we sentence him in the wager made between them, as above. And thus we, the undersigned, Bartolomeo and Ghiselin, affix our signatures below in our own hands. Dated at Rome in the Apostolic Palace and the aforesaid Chapel, the seventh day of June, in the inscribed year of the pontificate of Our Most Holy Lord of God, Julius III, Pope, being the second year. And we testify: I, Bartolome de Escobedo, have pronounced as above and sign my name with my own hand. I, Ghiselin Danckerts, have pronounced as above and signed my name with my own hand. I, Don lacopo Martelli, bear witness that the sentence and the two depositions given above have been faithfully printed and copied from the copy of the same sentence of the aforesaid judges. I, Vincenzo Ferro, confirm the above. I, Stefano Bettini, called "II Fornarino," confirm the above. I, Antonio Barre, confirm the above.107 I have no wish to say anything about the sentence printed above, for I leave this task to the judgment of the world and of the good Lord, who is Supreme Justice. For by his intervention, everyone has learned the right and the wrong insofar as he inspired the aforesaid Don Vicente to publish my arguments to the world in his printed work, which goes against himself and the judges as well. End of Book IV on Music Practice 107. Of the four witnesses who signed at the bottom, the last three were musicians. Bettini and Barre were composers as well as singers in the papal choir. Bettini joined the papal choir in 1562, and in 1570 he became choir director at San Petronio in his home city of Bologna. Barre began his printing business in 1555. There are some extant madrigals by Ferro. Nothing is known about the prelate, Don lacopo Martelli. Martelli, Ferro, and Barre also signed the copy of the sentence reproduced by Danckerts in Sopra una differentia musicale, Bk. I, chap. 5.

Book V on Music Practice About the Instrument Called the Archicembalo

Chapter 1 Proem [99r] I have labored for the benefit of rare and exceptional talents in order to give greater encouragement to students of music practice to study not only how to play but also how to learn composing for and singing with the archicembalo—the foremost and perfect instrument, in that none of the keys lacks any consonances. And I have adapted the new practice of chromatic and enharmonic music, facilitated with many examples, some presented in the preceding books and some in this one. Moreover, the examples are written so as to be easy for everyone, with explanations chapter by chapter and with intelligible notational signs as well as documentation of the structure of the archicembalo that provides measurements of its length, height, and width. I also provide drawings of the length and width of all the keys fitted together in the six ranks,1 as well as the measurement of the board in which to put the holes for the jacks that hit the strings with their quills, and also the measurement of the latter. Also I describe the arrangement of the holes for the iron pegs around which are wound the strings, and of the bridge above which they lie, as well as the measurement of the rose to be carved and how far it should be from the keyboard, as viewed from the outside of the instrument. Once the above-mentioned measurements and information have been absorbed, the six ranks on the keyboard and how to tune or temper them will be understood. With reference to the tuning, you will understand where many kinds of thirds are found on this instrument and discover certain unusual locations of fifths. The number of systems contained in this instrument will be discussed, as well as the number of steps of the enharmonic diesis, major semitone, and minor semitone, and also how many kinds of whole tones the archicembalo contains—all of these given with examples and ratios. There follows an explanation of the movable strings or steps; those that are neither completely movable nor completely 1. See figures 1-3. In the facsimile edition by Edward E. Lewinsky (Kassel and Basel, 1959), the unnumbered pages found at the end of the original print are put together in foldout format. There are eight pages in all: pp. 1-2 show the holes for the jacks (figure 1), pp. 3-5 show the lower keyboard divided into three segments (figure 2), and pp. 6-8 show the upper keyboard, also divided into three segments (figure 3).

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stationary; and those that are completely movable; together with the demonstration of the seven series that teach you how to read any type of clef written with any sort of notational sign that could occur on the archicembalo. This is easily done by means of many examples of the first series, followed by seven other examples written a major semitone higher than the natural series and by yet another seven series written a minor semitone higher. Seven other series are written with dots that denote a raising by one enharmonic diesis, an amount equivalent to one-half of the minor semitone of the naturally sung series. I also give examples of the seven series of notes written one major semitone higher than the natural enharmonic as well as the seven series written one minor semitone higher. In addition, I explain twelve different kinds of steps or leaps of a third, illustrated by examples of both the major and minor third. I also explain the seven ways of representing fourths, as well as the different ways of writing the ten leaps of the fifth, the ten leaps of the minor and major sixth, and the seven leaps of the octave. There follow the system and formation of the seven octave-species, which can be formed on the lowest A re or A la mi re2 [99v] without ever leaving the initial note. Likewise, on the lowest B fa B mi, or B mi in the hard and then in the soft hexachord, and also on the lowest C sol fa ut, and directly after, on the lowest D la sol re, then the low E la mi, the low F fa ut, and G sol re ut. On the archicembalo, all these form the seven octave-species without changing the first initial note on which the first octave began. All the remaining octave-species are made from the same initial note but by proceeding quite differently in their formation, as seen in the examples. Subsequently, seven other octave-species are written on each of the above-mentioned locations. Thus every location reveals its seven octave-species; for instance, a minor semitone lower3 when the first initial note is on the lowest A la mi re in the third rank of the keyboard [SA^j/The system explained above is followed in a subsequent example with the seven octave-species one major semitone lower than the initial natural system shown at the outset; [these are on A la mi re in the second rank (2G*)]. The formation of the seven octave-species is also seen in the fourth rank on the lowest enharmonic A re or A la mi re [4A], and these are one enharmonic diesis higher than the octave-species in the initial natural system. Thus, as2. For A la mi re in the lowest octave, see Bk. I, ex. 5.1. 3. Error: text has alzate. The same mistake occurs in the next sentence. 4. Vicentino explains his terminology in chaps. 4 and 5, below. See App. V.

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cending through seven pitches we form seven octave-species on each pitch. Leaving the lowest A la mi re [4 A] and going up a minor semitone, we begin on B fa B mi or B mi in the soft hexachord in the system explained above, but now on the initial note of the second rank [2B1*]. This system has no duplicate. But if we ascend from the fourth A la mi re [4 A] by a major semitone, we then enter the fifth rank—which is the lowest enharmonic B fa B mi on the fifth B [5w]—and form seven octavespecies. The same formation occurs in the seven octave-species starting on the subsequent fifth F fa ut [5G^] 5 and [fourth] G sol re ut [4G]. To minimize the novelty of using the archicembalo, I have collected the consonances that could occur above and below in these octave-species. Thus a choir in church may take full pleasure in this perfect practice, so suitable to every choral voice. As for facility in locating major and minor thirds, I refer to the locations, which are handy and convenient to the player as well as to how he should move from one rank to another. Moreover, I explain the defects in the division of the lute, the bowed viol, and other similar instruments. Nor do I omit the names of all the keys with their ranks, which withstand many defects. A student should spare himself no labor to acquire so rare and marvelous a music practice in playing, composing, and singing. For students of such a practice will always be more honored and acquire more profit and fame than those who do not wish to study further and to progress to a higher level of knowledge. Indeed, the playing practiced in these days is common to everyone, in that all players go through the same routines and the same keys. What is played by one student is likewise played by another, except for a difference in velocity. The same goes for the different, sweeter manner of playing diverse fugues. But no one has discovered how to play on a keyboard that is different from all the rest. My keyboard, therefore, being perfect and without defect, will bring fame to the student who exercises in singing with the archicembalo, composing music on it, and playing it. For he will be celebrated by everybody as a perfect and most exceptional musician.

5. See note 29, below and my introduction.

Figure 1. Board with strings and jacks for the archicembalo. From L'antica musica ridotta alia moderna prattica (Rome: Antonio Barre, 1555). By permission of the British Library (Hirsch I, 591 and 785, m.33).

Figure 2. Lower keyboard of the archicembalo with the first, second, and third ranks. From L'antica musica ridotta alia moderna prattica (Rome: Antonio Barre, 1555). By permission of the British Library (Hirsch I, 591 and 785, m.33).

Figure 3. Upper keyboard of the archicembalo with the fourth, fifth, and sixth ranks. From L'antica musica ridotta alia moderna prattica (Rome: Antonio Barre, 1555). By permission of the British Library (Hirsch I, 591 and 785, m.33).

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Chapter 2 Demonstration and Documentation of the Length, Width, and Height of All Measurements Necessary to Make the Archicembalo [lOOr] As a permanent record and to leave a firm model in the world for my contemporaries and posterity, I have decided to print drawings of the shape of the archicembalo,6 including the lines seen here below. These comprise the measurements that teach every practicing instrument-maker to build the archicembalo with ease. Beside the measurements of the lines, I present the drawings of the two keyboards made with accurate measurements [figures 2-3]. All the builder needs to do is incise them on the wood with a little care in measuring, for in joining together the sheets [of the drawing] of the first keyboard, he will form the first frame, which can be removed in one piece. The second frame is movable, for it, like the first one, can be taken out and put back without moving the keys. The second keyboard is pierced, on account of some long jacks that pass from top to bottom, as shown in that keyboard. The drawing of this second keyboard is on other sheets that, joined together, make the keyboards fit together properly. Nearby, other sheets are printed, and these contain the pierced division of the jacks on the board, which has been measured carefully and accurately because the division of the register is all-important for accommodating the strings and the jacks of the instrument. The first keyboard should have 69 jacks and the second 63 for all the keys, making a total of 132 jacks.7 When a student or builder plans to begin making the archicembalo, he must first select appropriate wood, good and dry, which has been cut a long time ago. If he can figure out and obtain the part of the tree that faced the sun, that part would be better. He then prepares the wood, in order to be able to make the instrument. Next he takes the measurement of the length [9.75 cm.]8 represented by the line given below, which goes twenty times into the length of the archicembalo [195 cm.]. The same line, furthermore, goes eight times into its width [78 cm.]. 6. See figures 1-3. 7. See figure 1. There seem to be 132 jacks, though the drawing of the holes on the board is not too accurate. The instrument has 130 keys in all, 68 on the first keyboard and 62 on the second. See figures 2-3. The two keys missing on the instrument but found in some of the music examples are C and F in the sixth rank. See notes 32 and 91, below, and my introduction. 8. One cannot be sure that the lines in the text are exactly to scale. Nonetheless, they do give a sense of the dimensions in general and some proportioned sizes in particular.

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I likewise show all the measurements with lines and explanations. The line [10.7 cm.] that enters twice into the depth or height of the instrument [21.4 cm.]. The line for the height between the surface [of the keys] and the board, where the keys or the iron pegs that hold the strings rest. This same line serves as the height between the first keyboard or frame and the top of the instrument. [Missing The line [6.8 cm.] for the height of the upper works of the instrument, or that part beginning with the edges of the keys. The line [5.2 cm.] for the height of the two keyboards, placed one above the other. The line [13.55 cm.], taken twice [27.1 cm.], that shows the distance between the incision of the rose and the jacks. The same length, taken once, is almost the upright height of the instrument. [lOOv] The line [9 cm.] for the width of the rose. The line [10.7 cm.] for the width where the strings lie near the curved length of the instrument. This width should be maintained up to the middle of the instrument, after which it gradually increases toward the end of the instrument. Line [6.9 cm.] for the length of the white keys of the first rank visible outside the instrument. Line [3.9 cm.] for the length of the black keys of the second rank visible outside the instrument. Line [2.1 cm.] for the black keys of the third rank visible outside the instrument. These three ranks belong to the first frame. Line [6.15 cm.] for the length of the white keys of the fourth rank visible outside the instrument. Line [3.8 cm.] for the black keys of the fifth rank visible outside the instrument.

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Line [2.1 cm.] for the length of the black keys of the sixth rank visible outside the instrument. These three ranks—the fourth, fifth, and sixth— are placed on the second frame, which can be conveniently removed and replaced because it is fastened with two iron keys from the edges of the instrument. Line [3.4 cm.] for the height between the first frame and the first black key in the second rank. Line [4.1 cm.] for the height between the first frame and the first black key of the third rank. When they are adjacent, these two ranks of semitones [the second and third] are placed one above the other in order to facilitate the accommodation of the two keys. The width and length of the surfaces of the white and black keys are to be arranged according to the judgment of a good master. A player should be able to run over all the keys nimbly with his hands and easily reach the bottom and top keys. The keys should not be so narrow that a player can touch two of them at one stroke. Thus, by means of all these measurements, a master should strive to make a good instrument that is convenient to play. It is not necessary to give lines for the length of the wood of the keys as far as the jacks, because this length is accurate in the drawing of the keyboard. You are advised to put a little lead at the end of the long jacks so that they are quick to come up, for they tend to be slow because of their length. Wherever the jacks lie on the wood, put a bit of chamois on the wood so that the jacks are quiet going down. There are four holes around the middle of the first frame, in which you place four iron pegs to support the second frame. Every key has its hole for the iron peg that supports it. Line [15.8 cm.], taken twice, for the length of the first soprano string [31.6cm.]. [lOlr] Line [6.1 cm.] for the length from the resting point of the string to the first jack. Line [11.2 cm.] for the length of the long jacks. Line [7.2 cm.] for the length of the short jacks.

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There are some holes in which the iron pegs that fasten the strings seen in the drawing [figure 1] fit, and they are at a distance from the lid that lies over the keys. This lid is closed so that the entire length of the wooden keys, as it enters into the body of the instrument, is not visible. The distance between the pegs and the lid is represented by this little line [1.9 cm.]. The first series of jacks contains both long and short ones, whereas in the second series they are all the equally long. The frame is pierced underneath according to the piercing of the keys. All the iron pegs have some chamois or white female chamois, except those near the end of the keyboard; these have some cloth to dampen the noise. On the wood beneath all the jacks there should be some chamois. A master who makes the archicembalo should be careful to make the keys agile, quick, and noiseless. The quills put on the jacks should be soft and short to match the strings. Above all, you should put in good and perfect strings, because bad strings make even a good instrument seem bad. The strings for the first frame should be as thick or as thin as those for the second frame, for the difference in pitch between them is small, no more than one-half of a minor semitone. If a master is diligent in his use of the above measurements and remarks, he will make a good and perfect archicembalo. If it is made a little smaller, you can then sing with it, for in the dimensions given here the instrument is a whole tone too low. The archicembalo will be good and perfect if the strings are well stretched over the instrument. Finally, whether any of the above measurements should be bigger or smaller is left to the judgment of the good instrument-maker.

Chapter 3 On the Six Ranks of the Archicembalo Now that we have constructed the instrument, we must understand its six ranks.9 So as not to confuse tuners, I shall make it a firm rule that every time I say the first natural rank I refer to the rank of white keys (without the black ones) on the keyboards of organs, monochords, harpsichords, and other similar instruments. As to the black keys, my second rank refers to the black keys commonly used on all organs and keyboard instruments. Continuing in sequence to name the ranks of my archicembalo, I call the rank added by the builder of the common keyboard the third rank; all its keys are shorter than the other white and 9. For a diagram of the six ranks within the F-F octave, see App. II.

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black keys. The above are all the keys in the first frame. Next in sequence is the fourth rank, and it refers to the white keys in the second frame above the third rank. The [lOlv] black keys placed between those of the fourth rank are called the fifth rank, and the black keys superimposed on the black ones of the fifth rank are called the sixth rank. It is now clear that the archicembalo has six ranks of keys. To be better understood, I shall have to refer many times during the discussion to the first rank as the diatonic order and sometimes as the natural order. Thus, the first white keyboard is referred to in three ways: as the first rank, as the diatonic order, and as the natural order. In this keyboard, none of the pitches has been split or cut in any way. But when the natural or diatonic order is split and cut by the placement of many divisions, I then refer to it as the second rank, which is commonly called chromatic order, because artificial pitches have been placed accidentally10 in the locations of natural pitches. Yet it is possible to speak of proceeding naturally in this rank if you begin in this chromatic nature—that is to say, in this rank of semitones—and go on with semitones right up to the end. This way of proceeding is called natural chromatic. Furthermore, if you proceed in this uninterrupted way, you can call it diatonic in the natural chromatic, depending on the conjunct or disjunct melodic contour. Whole tones placed in this natural chromatic are referred to as chromatic whole tones, since they are transformed from the first natural diatonic order. With this procedure, you locate the steps of the minor third, major third, and whole tone. The latter two are called chromatic steps of the enharmonic genus and the former, chromatic steps of the diatonic genus.11 Finally, with regard to the third rank, it is not necessary to discuss it as other than the third rank, because its steps cannot encompass any imperfect consonances—to be precise, no major thirds and only one minor third,12 as will become clear in the order of thirds on the archicembalo [chapter 62]. The fourth rank I call enharmonic order, fourth rank, and natural enharmonic. This fourth rank is explained in various ways, for depending on how the steps progress, you apply a name to the melodic contour. For instance, if you proceed by diesis in the fourth rank, the procedure is called proceeding naturally in the enharmonic. But if steps of a semitone are played in this rank, the enharmonic order is then transformed, and 10. For Vicentino's definition of accident and his use of accidentally see Bk. I, chaps. 23 and 25. 11. See Bk. Ill, chap. 15. 12. 3B»-3D». SeeApp.VII.

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these steps are now steps or species of the chromatic genus in the nature of the enharmonic order. If steps of a whole tone are sung, they are called chromatic diatonic steps in the enharmonic order. The same goes for steps of the minor and major third, for they are named according to their divisions. Minor thirds are called steps or species of the chromatic genus in the enharmonic order, and major thirds are called steps or species of the chromatic enharmonic genus in the enharmonic order. To explain the fifth rank we need a division of whole tones similar to the one between the first and second rank. There is one progression that is different in certain locations: when the player ascends from the fourth to the fifth rank while continuously alternating white and black keys, the semitones become major, whereas between the first and second ranks, that is, when the player ascends between white and black keys, he meets now minor and now major semitones. It is therefore clear that the fifth rank produces major semitones. It is moreover possible to proceed with whole tones that are called chromatic tones in the chromatic enharmonic order. As to the sixth rank, it is called simply the sixth rank or the order of the just fifths.13 This rank is similar to the first diatonic order. I shall deal with the differences among all the steps and all these ranks, along with their ratios, in the explanations of each. The present chapter suffices for an understanding of the six ranks of the archicembalo.

Chapter 4 Explanation of the Names of All the Keys Within the Octave of the Six Ranks of the Archicembalo [102r] Philosophers have given names to all things so that they may be known and distinguished from one another.14 It is therefore necessary to give names to each key of the archicembalo so that the great number of keys does not confuse students, who can then easily study this profession. I begin with the lowest A re or A la mi re, and I call it the first A la mi re or the first A re because it belongs to the first rank and also because it is like the goal, point, or sign that endows this key with its name.15 Its note is written on a line or a space. Students will observe that the point or sounding of A la mi re or A re is not a whole tone but rather the beginning of a whole tone. It becomes a whole tone when the sounding of two points, or rather two sounds, occurs, beginning from the same A 13. See note 47 and chaps. 13, 14, 17, 21, 22, 24, 26, 29, 31, and 37, below. 14. See, for instance, Genesis 3:20 and Isidore, Etymologiarum, 1.7. 15. See the discussion of the unison and the geometric point in Bk. II, chap. 2.

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la mi re or A re and ending on G sol re ut, or from A re to Gamma ut. The latter note is the beginning of the whole tone that finishes on F fa ut. Thus, the end of one whole tone is the beginning of the next whole tone or semitone, depending on the required divisions of the steps. When a composer is splitting this whole tone to make two semitones, one of them major and the other minor,16 he begins with the sound on A la mi re. If he is making a descending major semitone, he writes on the space where G sol re ut is written [2G*]; in the case of a descending minor semitone, he writes it on the line [3Ak]. Many call the sign or the division of this major semitone the semitone of G sol re ut. But it is the semitone of A la mi re, as can be seen example 4.1.

Example 4.1 [The Descending Major and Minor Semitone from A La Mi Re]

This example shows that the minor semitone is placed in the location of the first sound, for it is shorter than the major semitone. The length of the major semitone tells the singer to enlarge the semitone, for the representation of the note, written in the location of G sol re ut, is farther away from the first sound. This semitone is lower than the minor semitone, which is written in the location of A la mi re and is therefore closer to its starting point. The next semitone, which finds its ending on the same tone of A la mi re, is also the semitone of A la mi re, being either major or minor, as is shown in example 4.2. For the end of the major semitone [2G, 6B above 3D«, and [6C] above 3E«. See App. VIII. 37. For a tabulation of the triads produced by this tuning, see App. IX. 38. When discussing natural number, Vicentino gives the ratios of 5:4 and 6:5 for the true major and minor third. See Bk. II, chap. 7. He also suggests that the goal of tempering a keyboard is to produce some true major thirds. See Bk. I, chap. 6. In the second tuning system, Vicentino tries to approximate the diatonic syntonon tuning of Ptolemy. It is likely that his information came from the Musica theorica of Lodovico Fogliano. See Bk. I, note 47, and Bk. II, note 31. 39. In Venice in 1561, Vicentino published an advertisement for a two-manual arciorgano with 126 pipes and 126 keys [Descrizione deWarciorgano, section 5]. See Introduction, notes land 41.

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Chapter 7 How to Find Seven Fifths That Do Not Stay Within the Steps of Their Rank as Do the Natural Fifths There are seven fifths on my archicembalo that do not stay within the rank of their steps, as do the natural fifths. To begin with, we have on the ordinary keyboard two such fifths that cross over from white to black keys and vice versa. In the case of B mi in the hard hexachord [IB], its fifth should keep to the system of going from one white key to another white key, as do the other fifths—but it does not. I speak here to the experts who do not understand the logic of going from black to white keys. The fifth in question crosses over the white rank and goes to the first system of black keys [the second rank]. And likewise, the other fifth crosses over from a black key to a white key. These two fifths are: first, the upper fifth from B mi [IB] tuned with the second G sol re ut [2F*], which in practice is called the sharpened F fa ut; and second, the lower fifth from the first F fa ut [IF] to B mi in the soft hexachord [26^]. Both these fifths cross over the natural system of the first rank to the second rank. Next come two other fifths, one between the second and third ranks and one between the third and second ranks. To temper the fifth from the second A la mi re [2G&], a player ascends and finds its fifth on the high third E la mi [3D*]. To tune the fifth of the high second E la mi [2E1*], which in practice is called E la mi in the soft hexachord, he descends to tune its fifth on the third A la mi re [3A1*]. Both of these fifths also cross over the ranks, that is, from the second to the third and vice versa, just as the fifths listed above move from the first to the second and vice versa. If a player plans to proceed by going from the second to the third or from the third to the second rank, he must follow the system outlined above. But there is no key that allows him to carry on with this system from the third to the fourth rank. The obstacle is the tuning of the fourth rank with respect to the first rank, for there is a difference of one-half of a minor semitone between these two ranks. Consequently, to carry on with aligning fifths, we must start with the third rank and show the fifths that cross over to the fourth. We begin with the second C fa ut in the third rank [3B«] because its fifth is the fifth G sol re ut [5 G^].40 This fifth goes from a black to a black key. The fifth from the third F fa ut [4F] is tuned with the fifth B mi41 [56^], which fifth goes from a black to a 40. Error: text has "F fa ut quinto." See note 29, above. 41. Error: text has "B mi quarto."

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white key. The low fourth F fa ut42 [4F] is tempered by the fifth from the low B mi in the soft hexachord, that is, on the fifth B mi [SB1']. The latter two fifths have the same tuning at the [105r] octave above and below. I wished to gather these fifths together and discuss each one separately in order to make the tuning of the archicembalo easier. For tuners will have less work to do if they are apprised of the location of these fifths, even though I listed them in the preceding description of the tuning system. But because these fifths were jumbled in the course of outlining this tuning, I decided to explain them separately for the benefit of whoever tunes this archicembalo.

Chapter 8 Rule for Finding All the Perfect and Imperfect Consonances Above and Below on All the Ranks So that students may find it easy to learn, I shall not shirk the labor involved in devising rules for finding all sorts of consonances above and below every key in every rank.43 Therefore, I begin with the low first A la mi re [1A] and the minor third below, which is the second G sol re ut [2F*]. The major third is the natural diatonic F fa ut on the first rank [IF]. The fifth below the same A la mi re [1A] is D sol re [ID]. Its minor sixth is the second D sol re [20], its major sixth the first C fa ut [1C], and its octave A re [1A]. All these consonances are applied downward. There are also two other kinds of thirds that can be used, even though they do not have the just measurement of the others. Nonetheless, they can be employed more readily in playing than in singing, because the minute difference between the third we normally use and those we shall now adopt is not audible if players do not linger on them. It may be argued, moreover, that if totally dissonant seconds and sevenths are used, the proximates of the minor and major third are much more serviceable, 44 since they seem consonant when newly composed on the archicembalo. If a player fails to pay attention to the proximate and most proximate consonances, he will be deceived by them, for they are so proximate to imperfect consonances that they seem identical to them. Thus, when playing the archicembalo, you may use the third larger than the minor 42. Here Vicentino means the low third F fa ut in the fourth rank [4F]. 43. To verify the consonances, see App. IX. 44. On proximates and most proximates, see Bk. I, chap. 41. The former are one minor diesis larger and the latter one comma larger than the regular intervals.

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third, that is, the proximate third that is one minor diesis larger than the minor third.45 This step resembles the major third without being a major third, and the minor third without being a minor third. The minor third we use below the low A la mi re [1A] is the second G sol re ut [2P]. Its proximate is on the third F fa ut on the fourth rank46 [4F], and it seems better than the minor third because it is not as weak as the minor third in comparison to the major third. Still, the proximate is somewhat weaker than the major third because it is smaller by one enharmonic diesis. Thus, the proximate or most proximate to the minor third sounds acceptable and can be played.471 believe that some people sing proximate and most proximate thirds as they sharpen these minor and major consonances when performing compositions, and they do not create discords despite the fact that the former are not the same size as the latter. Moreover, the same thing happens with the proximate to the major third, which seems to be both a major third and a fourth without being either.48 This proximate third is less tolerable to the ear than the proximate of the minor third. The reason is that the minor third itself moves toward the major third so that its proximate tends toward this good third, whereas the proximate of the major third moves toward the fourth as if tending toward a dissonance.49 Thus, the proximate of the minor third below A la mi re [1A] is the third F fa ut in the fourth rank [4F], and the proximate of its major third is the second F fa ut in the third rank [3E*]. Its fifth is D sol re [ID]. In addition, there are two other new consonances that occur in the same way: the proximate and most proximate of the major [105v] and minor sixth. Just as the minor sixth below A la mi re [1A] is located on the second D sol re [20] and its proximate on the third C fa ut in the 45. See Bk. I, chap. 28. 46. Error: text has "G sol re ut terzo." In the next paragraph, the proximate minor third is correctly identified as 4F, as shown in ex. 8.1. 47. Because of Vicentino's loose syntax, it is impossible to ascertain whether proximate and most proximate are synonyms or merely appositions. The latter reading may seem more likely in view of the random references to mostproximates in this chapter. Vicentino neither identifies nor illustrates them. But near the end he alludes to this omission, describing "most proximate thirds" as being justly tuned. In Bk. I, chap. 41, these intervals are one comma larger than normal, whereas here they are equated with true thirds. This equation explains the final reference to the second tuning system, in which the tuning of the sixth rank is crucial to producing what Vicentino requires: true fifths and almost true thirds. See note 38, above, and App. VIII and IX. 48. See Bk. I, chap. 31. 49. Vicentino has some trouble with the status of the fourth. See, for example, Bk. II, chaps. 5-7.

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fourth rank [4C], so the major sixth below A la mi re [1A] is the first C fa ut [1C], and the third C fa ut in the fourth rank [4C] has its proximate below A la mi re [1A], which is the second C fa ut in the third rank [3B*]. The latter proximate is harsh, for it tends toward the seventh. But it is salvaged by its sixth. Players are advised that the arrangement of the white semitones disrupts the proper sequential disposition, because when these semitones are split a black semitone is placed in the third rank. For instance, when C fa ut [1C] descends by semitone toward B mi [IB], it first encounters a black semitone that turns out to be the second C fa ut in the third rank [3B*]. After that comes the third C fa ut in the fourth rank [4C]. You may call the second C fa ut in the third rank [3B&] the third C fa ut because it is in the third rank; however, since there is no other division after the first C fa ut [1C], you must refer to this semitone as the second C fa ut because it follows directly upon the first C fa ut, even though it is located in the third rank. The same line of reasoning explains the third C fa ut in the fourth rank [4C]. This rule for the natural semitone applies to all other natural semitones on both the first and fourth ranks. I shall now conclude the explanation of the locations of all perfect and imperfect consonances above A la mi re, along with their proximates. I advise players that whenever I descend below A re with all the consonances, I should begin again with A re and ascend to A la mi re, always locating its consonances. But I do not wish to do this because the minor and major third seem discordant when sounded in the bass, even though they are consonant steps. In order to avoid confusing students, I have begun the ascending sequence with A la mi re, G sol re ut, and F fa ut. To follow this order, I indicate first that the minor third above A la mi re [1A] is the first C sol fa ut [1C], and that its proximate is the third C sol fa ut on the fourth rank [4C]. I also show that the major third is the second D la sol re [20], and its proximate is the third D la sol re [3D1*]. Having described four kinds of thirds—minor thirds and their proximates as well as major thirds and their proximates—I shall set aside the most proximate, which could be called justly tuned thirds.50 As for fifths, I should first list the fifth above A la mi re [1A] located on the high E la mi [IE]. Then, ascending a major semitone, you form the minor sixth on the high first F fa ut [IF]. The addition of one enharmonic diesis to the latter generates its proximate, which is the third F fa ut in the fourth rank [4F]. The major sixth above A la mi re [1A] is the high second G sol re ut [2F*], and its proximate is the third G sol re ut [3G^]. This proxi50. See note 47, above.

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mate produces less harshness than the fifth G sol re ut [5 &], since it is smaller by one diesis.51 Although either could be used, the more proximate of the two is always sweeter. The octave above A la mi re is the very high A la mi re. This discussion of which consonances occur below and above the first A la mi re [1A] has covered both the perfect and imperfect consonances as well as their proximates. They are illustrated in example 8. As it happens, the most proximate consonances occur when the archicembalo is tuned entirely by just fifths, as I indicated earlier.52

Example 8.1 [All the Consonances, with Proximates, Below the First A La Mi Re (1A)]

Example 8.2 [All the Consonances, with Proximates, Above the First A La Mi Re (1A)]

Chapter 9 All the Consonances Below and Above the Second A La Mi Re [2G«], with Examples* [106r] I need no longer repeat and explain how many kinds of thirds and sixths can be found, for this information was given in the preceding chapter. However, there is another third smaller than the minor third.54 But because the minor third is so weak, it becomes too discordant when even a particle is taken away from it, and it resembles a second. I there51. Error: text has un comma. 52. See note 47, above. 53. Having given the reader a sample of Vicentino's prolix method in chap. 8,1 present the description of the consonances in chaps. 9-39 in tables with a modern letter-name for each pitch, preceded by a number to indicate the rank of the key. This reduction is both clear and brief. Discursive material is rendered in prose in the relevant chapters. 54. For the minimal third, see Bk. I, chap. 25.

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fore set it aside, just as the proximate of the major sixth with the added minor enharmonic diesis should be set aside.55 Readers who look closely at my archicembalo will find that I have marked all the semitones with the signs by which they ought to be notated.56 My archicembalo serves as a model for any player who has never had another guide for learning to mark the semitones, whole tones, dieses, and commas for instrumental compositions. For I have marked it completely in sequence, except for the fourth and sixth ranks. The fourth rank is easy to mark by putting a dot over those notes to be composed in that rank according to the rules [Book I, chapters 15-17 and passim]. Nor did I mark the sixth rank with the comma, because it has been so designated in the rules of the comma [Book I, chapter 14]. Its keys provide just fifths for the first rank.57 If a player wishes to find just fourths and fifths, he should stick to moving step by step, climbing the semitones by the dieses notated near them. By moving from one diesis to another, he will discover which are the chromatic instead of the natural semitones. If you strike a key in the first rank that happens to be the boundary for the descent to the natural semitone, a sequence of notated flats in the soft hexachord will ensue, except for the occasional crossing over to the fourth rank.58 The flats and the sharps in the second and third ranks are easily followed in their steps. Thus every experienced player quickly masters performing on my archicembalo. To make things easy, you may do what the first teachers of organ playing did: they notated the letters of the hand on the keys. These letters are useful for inexperienced players.59

55. See chap. 8, above. 56. See Figures 1-3. 57. Only the second tuning system provides true fifths. Moreover, the sixth rank provides true fifths for the third, not the first rank. See chap. 6, above, and App. VIII. The chapters following make it clear that Vicentino alludes to fifths enlarged by a comma, which can be used in the first tuning system. Although larger than true fifths, these "true" fifths (716 cents) sound brighter and richer than tempered fifths. See exx. 13.1, 13.2, 14.2, 21.2, 24.1, 26.7, 29.1, 31.2, 33.1 and 37.1, below. See also notes 89, 90, 92, and 96, below. 58. In a descending sequence of semitones on the flat side, one crosses over to strike 4B and 4E between 1C-IB and IF-IE, respectively. The key of 4B, the same pitch as