Revisiting the Music of Medieval France: From Gallican Chant to Dufay [1 ed.] 1409436810, 9781409436812

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REVISITING THE MUSIC OF MEDIEVAL FRANCE From

Gallican Chant to Dufay

Manuel

VARIORUM

COLLECTED

Pedro

Ferreira

STUDIES SERIES

Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com

Also in the Variorum Collected Studies Series:

JOHN BOE Chant and Notation in South Italy and Rome before 1300

THOMAS

FORREST KELLY

The Sources of Beneventan Chant

NIGEL WILKINS Words and Music in Medieval Europe DAVID FALLOWS Composers and their Songs, 1400-1521 THOMAS

FORREST

KELLY

The Practice of Medieval Music Studies in Chant and Performance

MICHEL HUGLO La théorie de la musique antique et médiévale

MICHEL HUGLO Chant grégorien et musique médiévale

MICHEL HUGLO Les anciens répertoires de plain-chant

MICHEL HUGLO Les sources du plain-chant et de la musique médiévale

TIM CARTER Monteverdi and his Contemporaries

TIM CARTER Music, Patronage and Printing in Late Renaissance Florence ERNEST H. SANDERS French and English Polyphony of the 13th and 14th Centuries Style and Notation RICHARD L. CROCKER Studies in Medieval Music Theory and the Early Sequence

DAVID FALLOWS Songs and Musicians in the Fifteenth Century

VARIORUM COLLECTED

STUDIES SERIES

Revisiting the Music of Medieval France

E vii by

Manuel Pedro Ferreira

Manuel Pedro Ferreira

Revisiting the Music of Medieval France

From Gallican Chant to Dufay

$

Routledge

à

Taylor & Francis Group

LONDON AND NEW YORK

First published 2012 by Ashgate Publishing Published 2016 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN 605 Third Avenue, New York, NY 10017

Routledge is an imprint of the Taylor & Francis Group, an informa business This edition © 2012 by Manuel Pedro Ferreira Manuel Pedro Ferreira has asserted his moral right under the Copyright, Designs and Patents Act, 1988, to be identified as the author of this work. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing in Publication Data Ferreira, Manuel Pedro. Revisiting the music of medieval France : from Gallican chant to Dufay. — (Variorum collected studies series ; CS1007) 1. Music — France — 500-1400 — History and criticism. 2. Music — France — 15th century — History and criticism. I. Title II. Series

780.9'44'0902—dc23 ISBN 9781409436812 (hbk) Library of Congress Control Number: 2012931345 ISBN 13: 978-1-4094-3681-2 (hbk)

VARIORUM COLLECTED

STUDIES SERIES CS1007

CONTENTS Author’s note

vii

Acknowledgements

ix

The lamentation of Asterix: Conclusit vias meas inimicus

125-157

Medieval Sacred Chant: from Japan to Portugal, ed. M.P Ferreira. Lisboa: Colibri / CESEM, 2008

II

The Cluny Gradual: its notation and melodic character

205-215

Cantus Planus: Papers Read at the 6th Meeting (Eger, Hungary, 1993), ed. L. Dobszay. Budapest,

1995,

Vol. I; reprinted with

a Postscript

III

Is it polyphony? [The Versus de Sancto Marciale by Adémar of Chabannes]

9-34

Revista Portuguesa de Musicologia 12, 2002

IV

New light on St Bernard’s chant reform: Guido of Eu and the earliest Cistercian choirbooks

77-82

Cantus Planus-2002. Russkaya versiya 1. St Peterburg: Compozitor,

2004; reprinted with additional illustrations

Early Cistercian polyphony: a newly-discovered source

267-313

Lusitania Sacra, 2nd series, 13-14, 2001-2002; reprinted

with an Addendum

VT

Mesure et temporalité: vers 1’ Ars Nova

66-120

La rationalisation du temps au XIIléme siècle — Musiques et mentalités (Actes du colloque de Royaumont, 1991). Royaumont: Créaphis, 1998

VII

L'identité du motet parisien Ariane: revue d'études littéraires françaises 16 (1999-2000)

83-92

vi

VIII

CONTENTS

Compositional calculation in Philippe de Vitry Studi

IX

musicali

13-36

Anno 37.1, 2008

. Dufay in analysis or — who invented the triad?

27-66

‘New Music’ 1400-1600. Papers from an International Colloquium on the Theory, Authorship and Transmission of Music in the Age of the Renaissance (Lisbon-Evora, 27-29 May 2003), eds J.P. d’Alvarenga and M.P. Ferreira. Lisbon and Évora: Casa do Sul/CESEM/CHAIA,

X

2009

Proportions in ancient and medieval music

1-25

Mathematics and Music, eds G. Assayag, H.G. Feichtinger and JF Rodrigues. Berlin: Springer, 2002

Index of manuscripts Index of names, works and concepts

1-3

This volume contains x + 292 pages

PUBLISHER’S NOTE

The articles in this volume, as in all others in the Variorum Collected Studies

Series, have not been given a new, continuous pagination. In order to avoid confusion, and to facilitate their use where these same studies have been referred to elsewhere, the original pagination has been maintained wherever possible. Each article has been given a Roman number in order of appearance, as listed in the Contents. This number is repeated on each page and is quoted in the index entries.

AUTHOR'S NOTE The essays collected here, written between

1989 and 2007, concern different

aspects of medieval music in France from the 8th century up to the mid-15th, covering a wide range of subjects: Gallican survivals in Gregorian chant, the Cluniac and Cistercian versions of it, rhythm and variation in frouvére song, the origins of Aquitanian polyphony, the evolution of counterpoint up to the 13th century, the intellectual novelty of the Parisian motet, the mathematical underpinning of the Ars nova and the presence of triads in the music of Dufay. Half of these essays have been published in Portugal; this testifies to the international outlook of its small musicological community, but does not favour widespread reading. Of the remaining, only Chapters IV and VIII have been published in well-established journals, yet the English version of the former 1s only accessible as part of a Russian book. This mirrors exactly the lack of publishing strategy that I urge my students to avoid. I have therefore felt justified in reprinting these contributions in order to make them accessible to a wider public. French and French-based sources have been the core of Medieval Music as taught worldwide since the 19th century. Still, it is surprising to discover how much is worth either revisiting (Chapters II and III, on the old hypotheses of microtonal nuances at Cluny and of early two-voice writing at Limoges) or digging into (Chapter IV, on the Cistercian musical reform; Chapters VI to VIII, on the nature of polyphonic thought in the French motet). A larger geographical frame is sometimes needed to make sense of evidence that the remaining French sources reflect only incompletely (Chapters I and V, on the connection between Old-Hispanic and Gallican rites, and the style of early discant). General theoretical questions can also be raised on the basis of well-known repertory (Chapter IX, on the origins of the concept of chord) or panoramic syntheses be inspired by the acquaintance with a wide array of music (Chapter X, on the compositional use of proportions). In the first half of the book, research was triggered off by some notational idiosyncrasy or enigmatic trait observed in a particular manuscript; this then led me to tackle the wider musical and historical implications. From Chapter VI onwards, I sought from the outset to clarify the origins of a particular compositional approach and to place it into a broader historical context. Even if the reader does not subscribe to most of my admittedly provocative insights or proposals (chromaticism and word-painting in a 7th-century melody,

vili

AUTHOR’S NOTE

11th-century enharmonic neumes and instrumental polyphonic voices, 12thcentury work-in-progress palimpsests, 13th-century contrasting temporalities in monodic song, a mathematical-based approach to the motet bridging Ars antiqua and Ars nova, a chordal alternative to contrapuntal writing found as early as c.1430), at least I can be confident that the cases have been thoroughly researched and rationally argued and that, perchance, the reading will not be dull. MANUEL PEDRO FERREIRA Lisbon January 2012

ACKNOWLEDGEMENTS The essays included in this volume would not have been written without the example of, and proximity to, Kenneth Levy and Margaret Bent when I was a graduate student at Princeton University, around 1990. Michel Huglo, then a visiting fellow at Princeton’s Institute for Advanced Study, was an inspiring presence as well. In the ensuing years, I found friendship and scientific appreciation also among other French colleagues, and particularly Marcel Pérès and Marie-Noél Colette, my hosts at Royaumont, Moissac and the École Pratique des Hautes Études in Paris, where I taught for some months in 2004-2005. Grateful acknowledgement is additionally made to the following individuals, journals, institutions and publishers for their help in the preparation of this volume or their kind permission to reproduce the essays included therein: Bernadette Nelson, David Cranmer, Zuelma Chaves, Centro

de Estudos de Sociologia e Estética Musical at FCSH - Universidade Nova de Lisboa (for essays I, IX); László Dobszay} (II); Manuel Carlos de Brito and Revista Portuguesa de Musicologia (III); Alexey Yaropolov and Compozitor: SPB Publishing House (IV); Maria de Lurdes Rosa and Lusitania Sacra (V); Editions Créaphis and Fondation Royaumont (VI); Maria Alzira Seixo and Ariane: revue d'études littéraires françaises (VIT); Agostino Ziino and Studi musicali (VIII); José Francisco Rodrigues and Springer Science+Business Media (X).

Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com

The Lamentation of Asterix: Conclusit vias meas inimicus

To Kenneth Levy The year is 800

A.C.: Gaul is entirely occupied by Roman liturgical books. Well, not entirely...

One small monastery of indomitable Gauls still holds out against the invaders. And, 1200 years

later, trying to find what they sung is not easy for musicologists confined to university campuses...

It is known that, in the second half of the 8* century, the liturgy of Rome served as a basis, in the Carolingian Empire, of the formation of the Roman-Frankish rite which, imposed as a political

decision, replaced the Gallican rite, almost entirely eliminating any trace of it. It is also known that, from this time on, the Roman-Frankish rite was associated with Gregorian chant and that both reached the Iberian Peninsula, taking the place, from the end of the 11% century,

of the Old-

Hispanic liturgy, whose musical legacy, in that it does not record the melodic intervals, is today largely undecipherable. Nevertheless, Gregorian melodies sometimes invite an archaeological

excavation which may lead to surprising discoveries. In 1997, during one of my visits to the Cathedral of Braga, 1 came across a Matins responsory for Palm Sunday, Conclusit vias meas inimicus, where, in two different manuscripts, flats in red ink had

been added to some of its E notes. Both choirbooks, n°s. 10 and 31, date from the early 16" century, but these flats could have been written at any time between then and the early 19% century (Ex. 1).

As with any great responsory, Conclusit consists of two parts, the respond and the verse. The respond is given an individual, fixed artistic melody

(composed

anew, crafted from traditional

materials or somewhere in between), whereas the verse is usually sung to one of eight invariable

formulaic tones, freely adaptable to the length of the text and the position of its initial and medial accents. After the verse is sung, the final part of the respond (often its last third, approximately speaking) is repeated by the choir; this final section will be called here the repetendum.

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Ex. 1: The responsory Conclusit in Braga's choirbooks. In this transcription, flats in red appear above the staff (doubled, whenever found in both codices); editorial suggestions are presented inside square brackets.

In the Braga chant tradition, the piece starts by establishing A, with upper B flat, as an axis, in dialogue with the lower F, which in turn is established as a second axis, before one hears the

melody plunge into C (a typical plagal gesture) and return to F and above. The B flat appears not only in the incipit, but also afterwards, with some prominence:

in fact, it functions as a

third melodic axis, before it is provisionally replaced by the upper C. The cadential formula at abscondito, (ama)ritudine and (vi)tam meam is common to many other chants ending on È' All this is compatible with a 6-mode piece, although the polarity between F/G and B flat/C in its middle part brings an 8"-mode flavour and a modulating character with it. The melody also goes as high as a seventh above the final, thus associating plagal and authentic ranges,

even if internal cadences never end higher than A; the lower notes return only at the end.

! Cf. Theodore Karp, Aspects of Orality and Formularity in Gregorian University Press, 1998, pp. 273-75.

126

Chant,

Evanston,

Illinois: Northwestern

This mixed-range quality, while atypical, is in keeping with the particularly high-pitched behaviour of the sixth responsorial tone; the initial progression in the respond from A

to B

flat and C, and

the final return to E replicates, in a way, the structure of the tonc as it appears in a number of southern

French

and

Iberian

sources?

However,

the E flats which

are called

for above

/eo,

amaritudine, posuerunt, iudica, mee (in the responsorial melody) and tora (in the verse) are totally unexpected, and an exceedingly rare phenomenon. They imply a major second below the final

degree, and therefore, ambiguity between the 6% and the 8^ modes becomes unavoidable. Not every flat appears in each individual choirbook: three appear in only one of them, the remaining three in both. But this was enough for me to infer, first, that the additions werc

made independently of one another, and second, that they depended on an established local tradition, and not just on an individual's whim.

It remained to investigate whether this

tradition corresponded to a late, regional performance practice (exceptional use of musica ficta allowing perfect fifths or fourths between E and B) or if it corresponded to an older, widely disseminated stratum, as the generally conservative character of the Braga chant tradition would

imply. Theoretical references to the responsory

Concíusit by the Berkeley Anonymous

(Goscalcus) and Anonymous XI were recorded years ago by Dolores Pesce; but since only a couple of medieval antiphoners were consulted, she was not able to make sense of these remarks?

? Daris, BN lat. 1090 (from Marseille); Paris, BN lat. 1091 (from Arles); Silos, Bibl. Monasterio, 9 (from Celanova), Paris, BN lat. 742 (from Ripoll); Huesca, Archivo de la Catedral, 2 (from somewhere in Aragón). The version of the responsorial cone found in Braga, with tenors A and C in the first part, and F in the second, is possibly earlier; it is also found in Benevento, Bibl. Cap. V.21, Toledo 44.2 and Huesca 7, with the same melodic turns. The version printed in Paolo FERRETTI, Esthétique gregorienne, Solesmes: Abbaye Saint-Pierre, 1938, p. 250 (which differs from that in the original Italian edition of the book) retains the triple tenor A-C/E. Willi APEL (Gregorian chant, Bloomington: Indiana University Press, 1958, 2365), complains that he has been unable to find an example of the hypothetical ‘original’ tenors, A and F (rather than C and F), in che sixth tone; Alberto TURCO (Jl canto gregoriano: toni e modi, Roma: Torre d'Orfeo, 1991, pp. 269-70), assumes A and F as plagal tenors, but then reproduces the Solesmes version, applied to a short text which uses only tenors C and F (Liber hymnarius cum invitatoriis & aliquibus responsoriis, Solesmes: Abbaye Saint-Pierre, 1983, pp. 509-10, 605). The closest to the hypothetical ‘early’ paradigm chat I know of is the A-C/F scheme, where the A is attained at the intonation but remains the melodic axis afterwards for a short while, if necessary, before it is replaced by the upper C; this scheme possibly evolved to B flat-C/F through the transitional stage A (intonation axis)-B flat-C/F, found in the sources mentioned above. However, there may have been different, early forms of the tone; Toledo 44.1 (from Tavérnoles) already has a B flat axis at the intonation,

and goes immediately to tenor C. Two different modern reconstructions of the B flat-C/F form of the tone appear in Paolo FERRETTI, Estetica gregoriana, Roma: Pontificio Istituto di Musica Sacra, 1934, p. 272; and Bruno STABLEIN, «Psalm. B», Die Musik in Geschichte und Gegenwart, Band 10, Kassel: Bárenreiter, 1962, cols. 1676-90 [Tabelle]. A comparative table, recording some melodic variants, is published as an Appendix in Giacomo BAROFFIO, «I versetti non salmodici dei responsori tra reliquie archaiche e fenomeni tardivi: osservazione preliminari», Musica e storia, vol.

XIV/1 (2006), pp. 143-62. ? Dolores PESCE, The Affinities 190, 194.

and Medieval Transposition, Bloomington: Indiana University Press, 1987, pp. 82, 84,

127

Consequently, I began to collect materials to study this piece, a process which lasted until 2005.‘ Having done it on the side, as it were, and having access only to a small number of microfilms,

my data is not as complete as I would wish; I apologize for any shortcomings that this may bring to my understanding of the music. Examination of more than forty notated manuscripts (with additional information concerning another forty) provides, however, enough evidence to sustain my

argument.

My interest in the responsory started a year before Theodore Karp published his richly documented and insightful book, Aspects of Orality and Formularity in Gregorian Chant, which | saw, being far from well-equipped

research libraries, only in 2004.

I discovered then, to my

surprise, that he had already dedicated ten pages to Conclusit5 This testifies to the interest and

intellectual challenge posed by this melody. However, Karp’s conclusions and mine are not exactly the same. Our disagreement arises mostly from my use of practical and theoretical sources which were not available to, or were unwillingly ignored by Karp, an oversight which is hardly surprising given the enormous task he faced when writing his huge book. The present report comes thus as an expansion and revision of his pioneering observations.

Karp finds the melody unusual and proposes a Gallican origin for it, because (1) " Conclusit does not have a fixed place in the liturgy”; (2) “it does not have a fixed verse”; (3) “one finds

multiple use of the pes stratus, which Huglo designates as symptomatic of Gaulish chant, whether of Gallican or Romano-Frankish origin”; (4) “one finds the descending sequential patterns also

cited by Huglo”; and (5) “its pitch vocabulary displays the richness associated with other chants thought to be of Gallican origin’, among these some offertories with non-psalmic texts singled

out by Kenneth Levy. Karp infers from the incipit provided by the Berkeley Anonymous, taken together with a remark by Theinred of Dover, that the melody “begins a minor third above the final, leaps down to the whole

tone

below

the final, and

then

circulates within

this pitch space”;

from

close

comparative reading of a variety of manuscript sources and discussion of the problematic shifts in notational level encountered there, he concludes that, “faced with the necessity to choose between the maintenance of the large-scale tonal relationships within Conclusit vias meas and the maintenance of the details of individual gestures, most [medieval musicians] opted in favor of

the latter [...]. The majority of the displacements that may be noted retain the basic tetrachordal * Some

microfilm prints were sent to me in 1997 and

1998

by Daniel Saulnier and Ike de Loos; the latter also

provided a list of manuscripts, with the respective modal assignment for Conclusir. After a first version of this paper was read in 2005, Ruth Steiner, Lila Collamore and Giacomo Baroffio mailed additional photos or microfilm prints

which expanded the available evidence significantly. ST. KARP, op. cit., pp. 213-22.

128

and pentachordal shapes at the expense of the overall tonal structure [...] even the individual phrases may be sacrificed for the maintenance of their constituent parts”. Karp then attempts, by analytical reasoning, to identify the causes behind the observed notational shifts, and proposes,

with due reservations, a possible reconstruction of the melody, assuming F final and starting with a descending leap from A

flat to E flat.

At the outset I must say that I find Karp’s suggestion that Conclusit belongs to the sphere of Gallican chant worth keeping in mind; his argument, however, is not altogether convincing. The

responsory is found in the two surviving Old-Roman antiphoners; it appears there in the same liturgical position, on Palm Sunday.‘ Although the manuscript sources are no earlier than the 12" century, they spring, to some extent, from a venerable local tradition; thus, Conclusit may have been known in Rome already in the mid-8" century. The current narrative about the genesis of Gregorian

chant presents it as a Frankish adaptation

of Roman

chant; although

recently

challenged,’ this view implies that one should not exclude the possibility of Roman roots. It is also possible that the responsory was composed in the wake of Carolingian liturgical reform, reaching Rome only afterwards. At the latest, the piece must have been in existence before the partition of the Carolingian Empire in the mid-9" century, for it spread all over Europe. Thus, the hypothesis of a Gallican origin must compete with that of a Roman, or a later Frankish origin. I concede

that the liturgical assignment of the responsory is not completely stable (Palm

Sunday is its most common

location, but the chant may exceptionally appear earlier, or, in many

cases, on the following Monday or Tuesday).* It comes with one of two different verses, or both.” * London, BL add. 29.988, and Roma, Bibl. Var., Arch. S. Pietro B. 79. In the Old-Roman Ondo antiphonarum [Ordo XH] there is no mention of chants sung on Palm Sunday: cf. Michel HUGLO, «Le chant ‘vieux-romain’. Liste des manuscrits et témoins indirects», Sacris erudiri, vol. 6 (1954), pp. 96-124, reprinted in id., Les anciens répertoires de plain-chant, Aldershot: Ashgate, 2005, ch. I; Michel ANDRIEU, Les Ordines romani du baut moyen dge, vol. II: Les textes

(Ordines XI), Louvain: Spicilegium Sacrum Lovaniense, 1960, pp. 459-66 [463]. 7 Nancy VAN DEUSEN writes that ‘since the fundamental premises of the two melodic procedures differ so clearly and significantly, it is difficult to imagine that one melodic type evolved from, was generated by, or became the revision of the other’ (“Formula or Formulation? Old Roman Chant and Italianate Melodic Style”, Max Lütolfzum 60. Geburtstag: Festschrift, Basel: Wiese Verlag, 1994, pp. 21-30 [27]). Kenneth Levy proposes a radical overhaul: that the early attempt to impose Roman music as a model for Frankish singers failed, that Gregorian chant is largely a Frankish creation based on Gallican musical precedent, and that ‘the musical relationship between GREG and ROM [...] results from the arrival of Frankish GREG at Rome, where it was meant to replace the local ROM repertory. But Roman musicians, instead of abandoning their music, effected a compromise. They accepted considerable amounts of GREG music, but

remodeled what they took into conformity with their own ROM style’ ("Gregorian Chant and the Romans”, Journal of the American Musicological Society, vol. 56 (2003), pp. 5-41 [6]). ST. Karp, op. cit, p. 214. For examples of assignment to Palm Sunday or Monday in Holy Week, see René-Jean HESBERT, Corpus Antiphonalium Officii [= CAO], vol. IV, Roma: Herder, 1970, p. 78 (n° 6306); Tuesday in Holy Week (not mentioned by Karp) is found, for instance, in the Worcester Cathedral antiphoner (facsimile in the series Paléographie Musicale, I° série, vol. 12, Solesmes: Abbaye Saint-Pierre, 1922, p. 115). ° The verse Factus sum in derisum... comes from the book of Lamentations, 3.14; Omnes inimici mei... is taken from Psalm 40 (41), 8-9. According to Samuel TERRIEN, The Psalms. Strophic Structure and Theological Commentary, Grand

Rapids, Mich.: Eerdmans, 2003, pp. 343-47 [346], ‘this poem apparently was composed by one of Jeremiah's disciples’.

129

It apparently adds a chromatic degree to the usual pitch vocabulary. None of these facts imply a Gallican origin. In what concerns the Office, local usage frequently implies some degrec of variance

in liturgical assignment. Alternative verse texts are common enough in Office responsories. The presence of degrees such as the E flat or the F sharp, in addition to the usual diatonic gamut, has

been detected in Gregorian melodies which have not so far been suspected of having a Gallican background." Moreover, there are just two pes stratus in the Sarum antiphoner from Barnwell, of

which only the first is corresponded in the oldest sources, instead of multiple use of the neume, as argued (Ex. 2)."!

Ex. 2: The use of the pes stratus in the responsory Conclusit in the Barnwell antiphoner (Cambridge, Univ. Libr., Mm.ii.9).

We are thus left with one pes stratus and two cases of consecutive climacus starting on adjacent degrees, on (inebriavit) me and (deduxe)runt, which Huglo identified as a typically (but not exclusively)

Gallican descending sequential pattern. In so doing, Huglo warned that “purely musical criteria cannot distinguish between the older Gallican repertory and chants composed shortly after the Carolingian

reform”,

since

“after

the

imposition

of the

Gregorian

repertory

in Gaul,

chant

composition continued for a time along traditional lines”.!? Gallican musical features are therefore

compatible with the hypothesis of a late Frankish creation. It may also be supposed that the pes stratus and the sequential pattern observed are traces of 8"-century Frankish remodeling of an imported Roman melody. These alternative explanations, late Frankish composition or idiomatic remodeling,

would still stand if a further link with Gallican musical style is added: the ascending chain of thirds B flat - D - F recalls a reintonation formula which Michel Huglo signaled as a Gallican trait.” The Mont-Renaud manuscript, from Noyon (reproduced in the series Paléographie musicale, I° série, vol. 16, Solesmes: Abbaye Saint-Pierre, 1955), has both verses without neumes (Ommes entered by a second hand, above Factus); according to Karp (op. cit., p. 214), Roma,

Bibl. Vall. MS

C 5 has Omnes followed by Factus, both with music

(complete only above the latter). !° Gustav JACOBSTHAL, Die chromatische Alteration im liturgischen Gesang der abendlándischen Kirche, Berlin: Julius

Springer, 1897 (repr. Hildesheim: Georg Olms, 1970); Rupert FISCHER, «Die Notation von Stücken mit chromatisch alterierten Tônen — Schwierigkeiten der melodischen Restitution», Beiträge zur Gregorianik 29 (2000), pp. 43-78. !! Facsimile: Walter Howard FRERE (ed.), Antiphonale Sarisburiense, 6 vols., London: The Plainsong and Mediaeval Music Society, 1901-1924, repr. Farnborough, Hants.: Gregg Press, 1966. ? Cf. Michel HUGLO, "Gallican rite, music of the", The New Grove Dictionary of Music and Musicians, ed. Stanley

SADIE, 20 vols., London: MacMillan, 1980, vol. 7, pp. 113-25 [117]; 2" ed. (2001): vol. 9, pp. 458-72 [463]. P Id. ibid., and id., «Altgallikanische Liturgie», Geschichte der katholischen Kirchenmusik, Band 1, Kassel: Bárenreiter,

1972, pp. 219-33 [228], reprinted in M. HUGLO, Les anciens répertoires de plain-chant, cic., ch. VIII.

130

On this slim basis, nothing can securely be said about the melody ultimate origins. It may be that the text, common

to Old-Roman

and Gregorian

sources, can shed some

light on the

matter; I give it below, with punctuation added: Conclusit vias meas inimicus; insidiator factus est mihi, sicut leo in abscondito; replevit et inebriavit me amaritudine; deduxerunt in lacum mortis vitam meam et posuerunt lapidem contra me. Vide, domine, iniquitates illorum et judica causam animae meae, defensor vitae meae. *

This seems to be a free centonization of passages from the book of Lamentations, chapter 3.

Different Latin versions of this biblical book circulated in the early Middle Ages; the exact version from which

the text was taken, or adapted, cannot be ascertained on the basis of the available

evidence. The versicles quoted (9, 10, 15, 53 and 58-59) span most of the chapter. In the standard editions of the Vulgate, they read as follows:

3.9: conclusit vias meas lapidibus quadris semitas meas subvertit 3.10: ursus insidians factus est mihi leo in absconditis 3.15: replevit me amaritudinibus (et) inebriavit me absinthio 3.53: lapsa est in lacu(m) vita mea et posuerunt lapidem super me

3.58: iudicasti Domine causam animae meae redemptor vitae meae 3.59: vidisti Domine iniquitatem (illorum) adversum me iudica iudicium meum'®

Note that while verses 9-13 and 15-16 (the larger context of those first quoted) presuppose a

singular subject, 3.53 implies a non-identified plural subject, which in fact is introduced by the previous verse, 3.52:

Venatione venari sunt me quasi avem inimici mei gratis." The text from the

'4 This is the standard, CAO

text, reproduced in the CANTUS

database. For variants, see R.-J. HESBERT,

Corpus

Antiphonalium Officii, cit., and ‘Critical Edition of Respond c6306', in CURSUS: An Online Resource of Medieval Liturgical Texts. 5 Biblia sacra. Iuxta vulgatam versionem. Editio minor, Stuttgart, Deutsche Bibelgesellschaft, 1984, pp. 1251-53. Additional letters or words from the Editio Clementina (Roma, 1592), reproduced in the critical apparatus, appear

between round brackets. ‘6 The online World English Bible translation (Accessed in February 2007): 3.9 He has walled up my ways with cut stone; he has made my paths crooked. 3.10 He is to me as a bear lying in wait, as a lion in secret places. 3.15 He has filled me with bitterness, he has sated me with wormwood. 3.53 They have cut off my life in the dungeon, and have cast a stone on me. 3.58 Lord, you have pleaded the causes of my soul; you have redeemed my life. 3.59 Yahweh,

you have seen my wrong. Judge my cause. !? Additional verses in translation: 3.11

He has turned aside my ways, and pulled me in pieces; he has made me

desolate. 3.12 He has bent his bow, and set me as a mark for the arrow. 3.13 He has caused the shafts of his quiver to enter into my kidneys. [...] 3.16 He has also broken my teeth with gravel stones; he has covered me with ashes. [...] 3.52 They have chased me relentlessly like a bird, those who are my enemies without cause.

131

central part of the chapter, not retained here, tends to have a reflexive character, which would

distract from the description of vile actions and their consequences, chosen as the focus of this respond. The final call to God, calling for harsh punishment of enemies (3.64-66), is also avoided. Michel Huglo tells us that in Gallican chants based on biblical texts “there are characteristic

divergences from the Vulgate version". In fact, the responsory Conclusit not only diverges greatly from the Vulgate; the biblical text was trimmed and compressed,

and words were added where

needed to complete the sense. It seems to have been composed as a kind of “chant ‘libretto’ ”, an

expression coined by Kenneth Levy to describe the text of non-psalmic Gregorian offertories with connections to Hispanic and Milanese chant. These chant-librettos “are ‘centonizations’, which

weave together fragments of text that in the originals may be quite separate; they show a tendency to condense, to paraphrase, and even to compose new verbiage that has no scriptural basis”, in order to create an adequate vehicle for musical setting of (perhaps) a florid nature." Don Randel observed long ago that in another category of responsorial chants, the Visigothic

Psalmi, “a considerable rearrangement of the texts took place in the course of their abbreviation.

One might as well say that new texts were composed”. Jordi Pinell wrote, concerning the Visigothic Treni sung in Lent, that “the texts are heavily centonized. Besides the book of Lamentations, use is made of Job, Jeremiah and Isaiah. The complicated mosaic of biblical phrases develops on a note of complaint. This uninterrupted lament would result in unbearable monotony,

had not the art of centonization been able to avoid it. The text’s carefully crafted monotony was certainly a response to the intentions of the composer — it is probable that the author of the music himself centonized the text in accordance with his requirements —, endeavouring to

demonstrate its expressive potential by harping on a single theme: that of a dramatic, almost despairing tone"?! While conceding that centonization as a basis for textual recomposition is extremely common in Hispanic liturgical sources, Levy’s comparative research led him to propose a Gallican origin for most of these offertories, since they left a trace in Ambrosian chant and only four of them have close musical parallels in Hispanic sources.” Conclusit vias meas inimicus does not surface in the Ambrosian rite.” It does, however, appear

in Hispanic chant. It turns out that the text of our Old-Roman and Gregorian responsory is a 18 M, HUGLO, "Gallican rite”, cit. !° Kenneth Levy, “Old-Hispanic Chant in its European Context”, Actas del Congreso Internacional ‘Espana en la Musica de Occidente, Madrid: Ministerio de Cultura, 1987, vol. I, pp. 3-14 [4]. 2° Don Michael RANDEL, “Responsorial Psalmody in the Mozarabic Rite”, Etudes grégoriennes, vol. X (1969), pp. 87-

116 [94].

—

?! Jordi PINELL 1 Pons, «Repertorio del ‘Sacrificium’ (canto ofertorial del rito hispánico) para el ciclo dominical ‘de quotidiano’», Ecclesia Orans, vol. I (1984), pp. 57-111 [72]; my translation, kindly revised by Ivan Moody. ? Kenneth Levy, “Toledo, Rome, and the Legacy of Gaul", Early Music History, vol. 4 (1984), pp. 49-99; reprinted

in id., Gregorian Chant and the Carolingians, Princeton: Princeton University Press, 1998, pp. 31-81. 231 owe this information to Giacomo Baroffio (personal communication).

132

shortened version of that found in the Iberian Peninsula. It dates certainly before 732, for its incipit already appears in the Visigothic Orationale of Verona; it is, moreover, common to the two

Hispanic liturgical traditions.” It is freely based on versicles 9-12, 15, 52-53 and 58-59. The text is given below, keeping the original orthography and capitalization, but with punctuation added

(the common Hispanic-Gregorian passages are shown in italics): Conclusit vias meas inimicus.

Insidiator factus est mici, sicut leo in absconditis; semitam meam

subvertit et confregit me. Tetendit arcum suum et posuit me, quasi signum ad sagittam; replevit et inebriavit me amaritudine.

Conprehenderunt

me inimici mei sine causa, quasi avem

in

muscipula; deduxerunt in lacu mortis vitam meam, et posuerunt lapidem contra me. Vide, domine, iniquitates eorum, et iudica causam anime mee, defensor vite mee.®5 (My enemy has shut offmy ways. He is waiting to pounce on me, like a lion in his hiding

places. He has subverted my path and shattered me. He has stretched his bow and laid me low. He has made me the rarget for his arrow. He has made me drunk with bitterness. My enemies have bound me without cause like a bird in a trap. They have led my life to the pit of death and set a rock against me. See, lord, their iniquities, and for the sake of my soul judge them, oh

guardian of my life!y/é

# The Orationale now in Verona, Bibl. Capit., MS 89, was copied in Tarragona certainly before 732, and presumably before 711: cf. Louis BROU, «L'Antiphonaire wisigothique et l'Antiphonaire grégorien au début du VlIlle siècle», Anuario musical, vol. V (1950), pp. 3-10; shorter version in Higinio ANGLÉS (ed.), Arti del Congresso Internazionale

di Musica Sacra (Roma, 25-30 Maggio 1950), Tournai: Desclée, 1952, pp. 183-86. According to Dom Michael RANDEL, An Index to the Chant of tbe Mozarabic Rite, Princeton: Princeton University Press, 1973, pp. 246-47, this chant occurs in the Orationale under the form of an incipit and was written complere, with its music, only in the antiphoner León, Arch. Catedral, MS 8, fol. 155v-56r (representative of tradition A), and in Madrid, BN, ms. 10.110 (olim Toledo Cat. 35.2), fol. 101v (representative of tradition B). The León antiphoner dates from the first halfof the 10* century (L. BROU, ibid.). The Toledo codex has been dated between c. 1250 and 1325 (Anscari M. MUNDO, «La datación de los códices litárgicos visigóticos toledanos», Miscelanea en memoria de Dom Mario Férotin, 1914-1964,

Madrid-Barcelona: C.S.I.C., n.d., pp. 529-53 [530-36]). According to Jordi PINELL («El problema de las dos tradiciones del antiguo rito hispánico», Liturgia y musica mozarabes, Toledo: Instituto de Estudios VisigoticoMozarabes, 1978, pp. 3-44), tradition B was possibly established in one of Toledo” parishes, Stas. Justa y Rufina,

around 1150 by a Christian community which fled religious intolerance then growing in Morocco. 2 Both manuscripts have #ici and lacu instead of michi and lacum. The Toledo codex also has replebit, inebriabit. The León antiphoner has inebriabit, sine causam, iudica causa, anime me: cf. Louis BROU & José VIVES, Antifonario Visigôtico Mozdrabe de la Catedral de León. Edición del texto, notas e indices por —, Barcelona-Madrid: Consejo Superior de Investigaciones Científicas, 1959 [Monumenta Hispaniae Sacra, serie litürgica, Vol. V/1], p. 251. The verse used in mainstream Hispanic liturgy (tradition A) is Cogitaberunt verbum in conprehensione mea. Domine, tu nosti cogitationes eorum (They have woven a plot to seize me. Lord, you know their conspiracies). Its origin remains

unidentified, and although it recalls Lamentations, 3.60-62, the text was possibly composed anew to go together with the respond. Toledo's tradition B quotes verbatim versicle 63 and the beginning of the following one: Sessionem eorum et resurrectionem eorum vide. Ego sum psalmus eorum. Redde eis vicem domine (3.63: You see their sitting down, and their rising up; I am their song. 3.64: You will render to them a recompense, Yaweh [...]).

26 English translation kindly provided by Rip Cohen.

133

Given the early date of the Visigothic Orationale and the close historical links berween the Gallican and Old-Hispanic liturgies, the case for a non-Roman origin of the responsory is strongly reinforced. Since it is unlikely that an original Roman or Gallican text, lacking the plural subject

of deduxerunt, etc., was expanded by the Visigoths, but rather that their original text was shortened

in Gaul, it follows that the Hispanic responsory was transformed into a Gallican one; that Gregorian chant retained the Gallican version; and that it was finally transmitted to Rome, where it was reshaped in the local melodic idiom.

Liturgical data accord well with this scenery. In Rome the responsory is sung on Palm Sunday; Visigothic sources assign it ro Monday or Tuesday in Holy Week; all three possibilities occur in Gregorian manuscripts. We could suppose a primitive Roman association with Palm Sunday; but

late, random, local liturgical variation can not possibly explain the partial coincidence of Gregorian and Visigothic customs. The most plausible sequence of events is that Conclusit was an Old-

Hispanic responsory in the first place; when it was adopted in Gaul, it retained in some places the original liturgical position, while in others it was given a more prominent one (Palm Sunday). The Gregorian tradition inherited the full variety of Gallican assignments; only the most recent one,

Palm Sunday, ended up being transmitted to Rome. It remains to see whether the music confirms this hypothesis; but before we can test it, we

must arrive at a clearer understanding of the Gregorian melody.

II

The responsory presents a stable manuscript tradition as far as melodic contour is concerned, but quite a variety of modal assignment. As remarked by Karp and confirmed by the information presented in Table I below (personally gathered from the sources, collected in the CANTUS index or kindly provided to me by Ike de Loos), modes 6 and 8 have almost identical weight in the copyists preferences." In the east mode 8 predominates, while in the south and southwest mode 6 has che upper hand. Only one manuscript, to my present knowledge, assigns the chant to another mode.

27 [ke DE Loos, personal communication (22/10/1998). Id., “The Transmission of the Responsoria prolixa According to the Manuscripts of St Mary's Church Utrecht”, Tijdschrift van de Koninklijke Vereniging voor Nederlandse Musiekgeschiedenis, vol. xlix-1 (1999), pp. 5-31 [11]. 2 The CANTUS-index wrongly attributes to the MS Firenze, Arcivescovado, a 2" mode melody. Aachen, Domarchiv G 20 ends on D, but the verse adopts the eight responsorial tone, transposed a fifth above. Protus sonority is present anyway, irrespective of tonal level. According to Daniel Saulnier (personal communication, 8/10/1997), ‘A la fin du répons [...] un certain nombre de manuscrits [avec écriture sur sol] ne descendent pas plus bas que le fa, et utilisent

une formule classique du mode archaïque de ré pour conclure’.

134

Mode

6

| Provenance of MS

Present location and call number(s)

—

Toledo, Bibl. capitular, 44.2

— (Cistercian MS.)

Wien, Nationalbibl., 1799

— (Provence?)

Mdina, Cathedral Museum, A

[Aragon] Arles

Huesca, Archivo de la Catedral, 2 Paris, BN lat. 1091

Arras

Arras, Bibl. mun., 465 (893)

Barnwell (use of

Cambridge, Univ. Libr., Mm.ii.9

Sarum)

Access: (when not examined in loco or through microfilm)! CANTUS-index

facsimile ed. by Frere

Benevento

Benevento, Bibl. Cap. V.21

Braga

Braga, Arquivo da Catedral, Livros de Coro 10, 31

Cambrai

Cambrai, Bibl. mun., 38 (40)

Cluny

St. Victor-sur-Rhins, s.c.

Firenze

Firenze, Arcivescovado, s.c.

Huesca

Huesca, Archivo de la Catedral, 7

facsimile: PalMus 1/22

Gent

Gent, Univ. bibl., 15/1

De Loos

Klosterneuburg

Klosterneuburg, Aug.-Bibl.

CANTUS-index

1010/11/13/15/17

Kóln Liége?

Kéln, St. Severinus Pfarrarchiv, II A3 Durham, Chapter Library, B iii 11

De Loos

Mainz

Mainz, Dom- und Diózesanmuseum,

CANTUS-index

codex B Marseille

Paris, BN lat. 1090

Montecassino

Montecassino, Archivio della Badia,

542 Montieramey

Paris, BN lat. 796

Morimondo

Paris, BN n.a. lat. 1411

(Cistercian MS.)

?? Reference is made

facsimile ed. by Maitre

to the following facsimile editions: Paléographie musicale, II° série, vol. 1, Solesmes: Abbaye

Saint-Pierre, 1900; W. H. FRERE (ed.), Antiphonale Sarisburiense, cit.; Paléograpbie musicale, Y série, vol. 9, Solesmes: Abbaye Saint-Pierre, 1906; Paléographie Musicale, I° série, vol. 12, cit; Ismael E. de la CUESTA (ed.), Antiphonale Silense, British Library Mss. Add. 30.850, Madrid: Sociedad Espafiola de Musicologia, 1985; Ike DE Loos (ed.), Utrecht Bibliotheek der Rijksuniversiteit, MS 406 (3.].7), Ottawa: The Institute of Mediaeval Music, 1997; Claire MAITRE (ed.), Un antiphonaire cistercien pour le Temporal, XIIe siècle, Poitiers: Maison des Sciences de l'Homme, 1998; Paléographie musicale, I° série, vol. 22, Solesmes: Abbaye Saint-Pierre, 2001. Additional bibliographical references are to T. KARP, op. cit., and Karl-Werner GUMPEL, «Gregorianischer Gesang und Musica ficta: Bemerkungen

zur spanischen Musiklehre des 15. Jahrhunderts», Archiv für Musikwissenschaft 47 (1990), pp. 120-47 = "Gregorian Chant and musica ficta: New Observations from Spanish Theory of the Early Renaissance", Recerca Musicológica, vol. 6-7 (1986-1987), pp. 5-27. Mention of De Loos refers to personal communication.

135

[northern Italy]

Toledo, Bibl. capitular, 48.14

PalMus 1/9

Paris

Paris, BN lar. 15181

CANTUS-index

Pozzeveri

Lucca, Bibl. Cap.

facsimile: PalMus

[Provence]

Mdina, Cathedral Museum, B

Ripoll

Paris, BN lat. 742

Salamanca

Salamanca, Catedral, Arch. Mus. 5

Sahagün? > Celanova

Silos, Bibl. Monasterio, 9

Silos

London, BL Add. 30850

facsimile ed. by Cuesta

St. Amand

Valenciennes, Bibl. mun., 114

CANTUS-index

St. Maur-des-Fossés (Cluniac MS.)

Paris, BN lat. 12044

[southern France] (Cluniac MS.)

Solesmes, Rés. 28

601

1/9

CANTUS-index

Stuhlweissenburg

Graz, Univ, Bibl. 211

Tavèrnoles?

Toledo, Bibl. capitular, 44.1

De Loos

Tongres

Tongeren, OLV Kerk, 63

Urgell?

Barcelona, Bibl. de Catalunya, M. 39

Utrecht

Utrecht, Univ. Bibl., 406

Vallombrosa

Firenze, Bibl. Laurenziana, Conv.

[Wales] Worcester

sopp. 560 Aberystwyth, Nat. Libr., 20541 E CANTUS-index Worcester, Cathedral Chapter Library, | facsimile:

Xanten

Xanten, Stifsarchiv H 104

7

Pavia

Monza, Bibl. capit., 15/79

8

— (Franciscan MS.)

Assisi, Bibl. comunale, 693/ 694

CANTUS-index

— (Franciscan MS.)

Assisi, Arch. Catt., 5

CANTUS-index

— (Franciscan MS.)

Budapest, Univ. Libr., lat. 118

CANTUS-index

— (Franciscan MS.)

Chicago, Newberry Libr., 24

CANTUS- index

— (Franciscan MS.)

Fribourg, Bibl. Cordeliers, 2

CANTUS-index

— (Franciscan MS.)

München, St. Anna-bibl., 12° Cmm

— (Franciscan MS.)

Napoli, Bibl. naz., vi.E.20

CANTUS-index

— (Franciscan MS.)

Roma, Bibl. Ap. Var., lat. 8737

CANTUS-index

Aachen

Aachen, Domarchiv G 20

Aosta Augsburg Bamberg

Aosta, Bibl. del Sem. magg., 6 München, Bayerische Staatsbibl., Clm 4303 Bamberg, Staatsbibl. lit. 25

Einsiedeln

Einsiedeln, Stiftsbibl., 611

CANTUS-index

| Gümpel facs. ed, by de Loos:

1st layer

F 160

136

PalMus I/12

1

| CANTUS-index

CANTUS-index | CANTUS-index CANTUS-index CANTUS-index

Esztergom Havelberg

Istambul, Topkapi S. Müzesi, D. 42 Berlin, Staatsbibl. MS theol. lat. fol. 139

| CANTUS-index edition in Karp

Kirnberg

Wien, Diôzesanarchiv, C-11

CANTUS-index

Kranj

Ljubljana, Archiep. Arch., 17

CANTUS-index

Kremsmiinster

Linz, Bundesstaatliche Studienbibl.,

CANTUS-index

290 (183) Limoges (St. Martial)

Paris, BN lat. 743

Limoges (St. Martial)

Paris, BN lat. 783

Limoges

Paris, BN lat. 784

Limoges (St. Martial)

Paris, BN lat. 1085

Metz

Metz, Bibl. mun. 83

CANTUS-index

Nevers Piacenza

Paris, BN lat. 1236 Piacenza, Bib]. Capit. 65

Quedlinburg

Berlin, Staatsbibl. Preuss. Kulturbesitz,

CANTUS-index | De Loos

Mus. ms. 40047 Roma > Norcia

Roma, Bibl. Vallicelliana C.5

St. Denis

Paris BN lat. 17296

Salzburg

Vorau, Stiftsbibl., 287 (29)

CANTUS-index

Sankt-Gallen

Sankt Gallen, 390-391

facsimile: PalMus II/I

[Hartker

antiphoner] Sens

CANTUS-index

Paris BN lar. 1028

Sens

Paris, BN n.a.lat. 1535

Sens

Sens, Bibl. mun., 29

CANTUS-index Karp

Steiermark

Graz, Universitätsbibl. 29/30

CANTUS-index

Tours

Tours, Bibl. mun., 149

CANTUS-index

Utrecht

Utrecht, Univ. Bibl., 406

facs. ed. by de Loos:

Utrecht

Utrecht, Univ. bibl., 404 /7/8

De Loos

Weingarten

Stuttgart, Wiirttemb. Landesbibl. HB.L55

CANTUS-index

Karlruhe, Badische Landesbibl., Aug.

CANTUS-index

2nd layer

Zwiefalten

LX Table I. Modal classification of responsory Conclusit vias meas inimicus in surveyed sources. This is only the beginning. Hesitation between the 6" and 8° modes, as seen in Utrecht, leaves its mark also in Metz, where a respond ending on F

is given an 8"-tone verse. At Arras, the

respond ends on G, yet a 6"-tone verse follows. Many copyists who assign the responsory to the

6* mode transpose it, or part of it, a fifth above the normal pitch range, thus arriving at C-final instead of F-final (Table II).

137

Final note

Provenance of MS

Present location and call number

F

Arles

Paris, BN lat. 1091

Benevento

Benevento, Bibl. Cap. V.21

Braga

Braga, Arquivo da Catedral, Livros de Coro 10, 31

Kéln

Kóln, St. Severinus Pfarrarchiv, Il A3

Marseille

Paris, BN lat. 1090

Montieramey

Paris, BN lat. 796

[Provence]

Mdina, Cathedral Museum, B

St. Maur-des-Fossés (Cluniac MS.)

Paris, BN lat. 12044

[southern France] (Cluniac MS.)

Solesmes, Rés. 28

G

Arras

Arras, Bibl. mun., 465 (893)

C

— (Provence?)

Mdina, Cathedral Museum, A

Barnwell (use of Sarum)

Cambridge, Univ. Libr., Mm.ii.9

Cambrai

Cambrai, Bibl. mun., 38 (40)

Cluny

St. Victor-sur-Rhins, s.c.

Firenze

Firenze, Arcivescovado, s.c.

Morimondo (Cistercian MS.)

Paris, BN n.a. lat. 1411

Observations

with [E] flats added in red

starts: F to C

Pozzeveri

Lucca, Bibl. Cap.

Utrecht

Utrecht, Univ. Bibl., 406

601

Vallombrosa

Firenze, Bibl. Laurenziana, Conv. sopp.

Worcester

Worcester, Cathedral Chapter Library,

Xanten

Xanten, Stifsarchiv H 104

First layer

560 F 160

Table II. Choice of final note in G^-mode diastematic sources.

Furthermore,

when

we

begin

to compare

melodic

readings,

we

realize

that most

copyists,

irrespective of modal preference or final note, resort to transposition at one or more points,

choosing different solutions and splitting spots. In the following, I tried to synthetize the ronal behaviour of the melody according to thirty-seven diastematic manuscripts, compared against the Braga version presented earlier (Ex. 1).

138

Given that melodic reality is given by a succession of intervals, rather than the names of their boundary notes, and considering that intervals can be represented on a reticulated surface as distances berween points, all the notated versions are thought of as if coinciding in their tonal level at the beginning of the chant:

thus, a C-B-A-G or a F-E-D-C initial descending tetrachord is put at the same level as Braga’s B flat-A-GF tetrachord. The tonal level in Braga (and in every source’s incipit) is imagined as a straight horizontal line.

When

the melody is transposed in each source to a tonal level other than the incipit’s (the line

corresponding to the Braga version), this level is accordingly imagined at the distance of one to five degrees, up or down, from the base line. Seventeen transposition points are identified and numbered. The behaviour of individual manuscripts is recorded in the commentary to each transposition point; only the antiphoner from Monte Cassino and Toledo 44.2 are excluded from the commentary, because their tonal shape never departs from Braga’s. The description is cumulative, i.e., if a manuscript is said to jump a fourth at a certain

point, having jumped a second beforehand, it means that from that point onwards it is notated a fifth above the initial tonal level. For instance, Kóln begins at the C-final level, raises the word factus by a second from point 2 onwards, returns to C at 4, jumps a fifth at deduxerunt (point 7) and finally goes down a second at vitae (point 15), thus ending on F a fourth above the starting level (Ex. 3).

°/ Conclusit vias meas !/ inimicus insidiator ?/ fac- 3/-tus */ est ?/ mi- °/-hi sicut leo [...] amaritudine ?/ deduxerunt [...] lapidem #/ con- ?/-tra me !°/ Vide domine iniquitates il- !!/-lorum et / judica causam !?/ ani- '4/-mae meae defensor !5/ vitae !6/ me- !7/-ae.

Nr.

Description

0

Initial tetrachord notated between B flat and F (F-final level): Arles, Cluniac processional, Cluny, Marseille, Mdina B, Monte Cassino, Montieramey, Sens, St, Martial (783), St. Maur. Initial tetrachord notated between F and C (C-final level): Arras, Barnwell, Cambrai, Firenze, Kóln, Lucca, Mdina A, Metz, Morimondo, St. Denis, Utrecht, Vallombrosa, Worcester. Initial tetrachord notated between C and G (G-final level): Aachen, Havelberg, Limoges, Nevers, Pavia, Xanten. No clef: Aragôn, Benevento, Celanova, Huesca, Ripoll, St. Martial (743), Tavérnoles, Toledo 44.2. Nevers, which started at the G-final level, drops to F-final level. Nevers returns to the G-final level. MSS from St. Martial (743, 783) and Sens jump a third. Aachen, Aragén, Arles, Arras, Barnwell, Benevento, Cambrai, Celanova, the Cluniac processional, Cluny, Firenze, Havelberg, Huesca, Kóln, Limoges, Lucca, Metz, Montieramey, Morimondo, Pavia, Ripoll, St. Denis, St. Maur, Utrecht, Vallombrosa, Worcester and Xanten jump a second. Mdina B jumps a second. Aachen, Aragón, Arles, Arras, Barnwell, Benevento, Cambrai, Celanova, Firenze, Havelberg, Huesca, Kóln, Limoges, Lucca, Metz, Montieramey, Morimondo, Pavia, Ripoll, Sens, St. Denis, St. Martial (743, 783), Utrecht, Vallombrosa, Worcester and Xanten go down a second. Montieramey jumps a second. Ripoll goes down a second; St. Martial (743) apparently does the same. Arles jumps a second. Kéln jumps a fifth.

1 2

3 4

5 6 7

139

Barnwell, Metz and St. Martial (783) jump a second. 9

Cambrai, Mdina A, Morimondo and St. Denis jump a second.

10

Barnwell, Cambrai,

11 12

second. Ripall goes down a fourth. Marseille goes up a second. Aragón goes up a second.

the Cluniac processional, Mdina A, Metz,

Morimondo,

St. Denis and St. Maur drop a

13

Cluny goes up a fourth. Tavérnoles goes up a fourth (or may be a fifth). Aachen, Arras, Metz, St. Denis and

14 15 16 17

Xanten go up a fifth. Xanten goes down a second. Arles, Kóln, Limoges, Marseille, Montieramey and St. Martial (783) drop a second. Mdina B and Merz drop a second. Tavérnoles goes down a second. Limoges and St. Martial (783) go up a second.

Ex. 3: Shifts in the notated level of the Conclusit melody.

This situation, where overall ronal shape is sacrificed by short-range editing, is clearly anomalous. The transposition strategies observed must be the ad-hoc response to some existing problem. But this response, too, may create incoherence or other kinds of problems, whose solution will in turn

increase notational creativity. In Metz the repetendum, after the verse, is written a second above

its first presentation, while in Arles it is written a second below; this seems to have been tolerable. The partial transpositions at Cluny end up extending the chants tonal range to almost two octaves; the selected singers of the great Abbey could probably cope with this, but elsewhere, in lesser monastic

communities,

the

case

may

have

been

different.

At

Ripoll,

writing

the

section

corresponding to the repetendum, before the verse, down a fourth, seems to be an attempt to keep the ambitus under control. Aside from the layered, cumulative character of the evidence, there is a single explanation for

the wide variety of notational strategies encountered: the standard Guidonian gamut did not allow an adequate transcription of the melody; its pitch-vocabulary, as Karp concluded, must have been problematically rich. If we limit ourselves to the chant books, it will not always be easy to establish a common

ground for their disagreements, let alone identify the specific problem behind them. As Karp remarks, “the MSS present a confusing account of Conclusit vias meas”. Fortunately we can ask some theorists for help. I counted seven theoretical statements acknowledging the peculiar melodic behaviour of Conclusit, which I reproduce below in rough chronological order, from c. 1100 to

the late 15% century, with slight editing of my own to allow easier comparison. With one possible exception, the theoretical statements concerning the unusual nature of the melody are clarified and corroborated by the notated manuscript evidence. I will now comment

on them, making use of the additional data presented in the examples.

140

1. John of Afflighem [= John Cotton] (c. 1100)® Iam vero manifestum est q quod durae hominum voces et incompositae semitonia q quam maxime devitant; q qui autem flexibiles habent voces, semitoniis

plurimum 8 gaudent, eo usque ut etiam

ibi aliquotiens semitonia depromant, ubi depromenda non sunt, q quemadmodum P patet in multis q P quarti toni antiphonis

[...] Simili modo

quidam delinquunt in R/. “Conclusit vias meas”,

semitonia sonantes ubi non sunt, videlicet in illis dictionibus “inimicus insidiator”. Idem R/. plerique in fine confundunt, quia

“animae meae”, quod in mese [.a.] est incipiendum, in nete

diezeugmenon [.e.] incipiunt.

John of Afflighem criticizes those singers who place semitones where the Guidonian system does not surmise them: at inimicus insidiator, they sing a low F sharp, and at animae meae, a high F sharp. This

presupposes that the responsory begins with the descending fourth C-G and ends on the upper D, which is exactly what happens in the tradition of Aachen, as recorded in the antiphoner G.20 (Ex. 4). H

»

oun Shi

SA

ta

Ex. 4: The

end

A

Dim anime” met

of Conclusit in Aachen.

The

A.

T Id final passage,

starting at "anime", is transposed a fifth above its normal level.

The solution hinted at would be to start with the descending fourth B flat-E and finish on G, which is what happens in at least two other antiphoners, originated at Limoges and Sens (Paris,

BN lat. 783; Paris,

BN lat. 1028). The passages quoted by John are presented in Ex. 5, where a hypothetical melodic version corresponding to the earliest neumation is written at the alternative levels implied by his discussion.

Parts BN Ati da. 1028

fg

Bedawchi Dear

TEM ta

7

a dow

LI

-dd o vices

vA,

ma

LT

- m1

=

.

v

door

cari

buo

+

D

ae dato! bos

dns

Das Aa

4.

de

.

mi” mat

M

Aachen D

LA

7

me

MI

Di

Le

I 1

9832,02

120

Ex. 5: A melodic companion to Johns theoretical discussion.

3° JOHANNIS AFFLIGEMENSIS, De Musica cum Tonario, ed. J. Smits VAN WAESBERGHE, Rome: American Institute of Musicology, 1950 [Corpus Scriptorum de Musica, vol. 1], pp. 137-38. English cranslation: Hucbald, Guido and John on Music —

Three Medieval Treatises, Claude V. PALISCA (ed.) & Warren BABB (trans.), New Haven: Yale University

Press, 1978, pp. 149-50.

141

2. Theinred of Dover (mid- or late 12 century?)

Prima et quarta

e

f

|g

|a

Jh

[e

|d

Je

|f

|g

|a

|b

Je

Jd

fe

|.

e

|f

jg

la

|b

Jc

Jd

je"

|f

|g

Ja

|b

Je

|d

fe

|.11.

d

fe

|f

|g

la

|h

le

|d

le

|f

|g

ja

|b

|c

fd

|

d

le

|f

|g

|a

|b

fe

|d

[ef

|g

|a

|b

le

ld

|.12.

c

|d

le

|f

|g

|a

|h

le

jd

Je

|f

|g

la

Jb

je

|.3

c

d

le

|f

|g

|a

|b

fe

|d

^e"

|£

|g

|a

|b

Je | .13.

Duarum

[transposiciones]:

Prima [societas] vero et tercia vel communiter, omnes [ordo] diapason cum diatessaron; prima et secunda [societates], vel prima et quarta bis diapason; duas in uno octochordo varietates solo tono distantes generant, reliquis intervallis non mutatis. Unde eiusmodi cantibus ordinem » « distinguo ut hijs: "Post passionem suam", "Redime me deus Israel", “Deus exaudi", "Adorate deum", “Immutemur”, “Conclusit vias meas".

Theinred of Dover, in spite of his intimidating style, ends up being quite clear: he puts Conclusit in

the class of chants which have an octave with two mobile tones a fourth apart.” The superimpositions that, according to him, produce such a kind of octave are illustrated in Example 6 below.

The grid which precedes Theinred's explanation presents in full the possibilities generated by the superimpositon of the first and fourth scalar combinations and is therefore particularly apt, since a double octave based on low C, having two kinds of B and two kinds of E above it, allows one

to solve most, if not all the notational problems posed by the responsory, if the 6*-mode, C-final version is adopted as a basis for transcription. This corresponds to the Worcester and Sarum choice, a solution with which Theinred must have been familiar. But we will only appreciate its advantages after we have gone through other evidence. 3) THEINREDUS DOVERENSIS, Musica: Oxford, Bodleian Library, Bodley 842 (S.C. 2575), liber tercius, fol. 35v, published on-line in Thesaurus Musicarum Latinarum at http://www.music.indiana.edu/tml/12th/TDMUS3 (Accessed in 18/10/98). When this article was in press, the full critical edition by John L. SNYDER, Theinred of Dovers De legitimis ordinibus pentachordorum et tetrachordorum, Ottawa: Institute of Mediaeval Music, 2006, became available. » For a general presentation of Theinred’s work, see John SNYDER, "Non-diatonic Tones in Plainsong: Theinred of Dover versus Guido d'Arezzo", Actes du XIIe Congrès de la Société Internationale de Musicalogie, vol. 2, Strasbourg,

1986, pp. 49-67.

142

Theinred of Dover: example of bifurcated scalar constructions with double semitone relocation, using scales on C, each with two consecutive conjunet tetrachords of the same species, their superimposition generating an octave with two mobile tones a fourth apart.

Ambitus and superimpositions

Societas

Species

(combination of pentachords and tecrachords of che same species)

(relative co given

ambitus)

Diapason cum diatessaron, prima et tercia societates: C

D

E-F

G

a

C

D

E-F

G

ab

h-c

[F

G

abhc

d

c

e-f

d-e

f

dee

f]

prima (5+4+4)

3

tercia (44445)

9

prima

3

Bis diapason, prima et secunda societates: (5+4+4+5)

C C

D D

E-F E-F

G G

a a

he hec

d d

ef g e fig

a a

c h-e secunda (5454444)

[cd

effg

a

7

bhel

Bis diapason, prima et quarta societates: prima (5444445)

C C

D D

E-F E-F

G G

a he ab c

d ef d-^ f

g g

ab a-b

3

c c quarta

13

(4+4+5+5)

IG

abhc

deef

gl

Ex. 6: Theinred's octave with two mobile tones a fourth apart.

143

3. Berkeley Anonymous [= Goscalcus] (1350-1385)? Quinta coniuncta accipitur inter .G. gravem et .a. acutam, et signatur in .a. signo b, ubi dicetur fa [...]; de hac habetur exemplum in responsorio “Conclusit < ubi dicitur conclusit (Lo) > vias meas”, et in diversis aliis (Bk)/ sic de aliis (Lo)/ pluribus cantibus (Cr).

Exemplum

(Bk): see Ex. 7 below

Sexta coniuncta accipitur inter .c. et .d. acutas [...] Er incipit eius deduccio in .a. acuta [...] ut patet in exemplo “Conclusit vias meas” (Ct).

A

Fal vb ha

Cul

Conckusit

CS

t

vias

c T Tw

LS

—N

4

{ P^

La

x

id

n b

vn

Un,

JA IC]

A A LEN u.a

PA

53M

£

47

NV

=4D Ex. 7: Goscalcus example and alternative incipits in chant sources.

The author of the Berkeley treatise inaugurates here the discourse on the conjunctae, seen as a way to integrate peculiar aspects of chant practice into the post-Guidonian theoretical edifice. For long the theory of conjunctae, that is the expansion of the hexachordal system which allowed

to embrace sharpened and flattened notes so far considered irregular, was regarded as irrelevant for the understanding of good old Gregorian chant; it must merely have been, so we were told, a late attempt either to explain away the marks of corruption that polyphonic practice had left on ecclesiastical monody, or to bring the latter in line with current fashion. It is true that polyphonic

practice influenced the performance of plainchant. But in past decades it has become increasingly clear that the late Medieval and early Renaissance theorists knew very well how to distinguish the

domain of counterpoint from that of monodic chant; in their discussion they often tell us which kind of repertory they have in mind, revealing that the conjunctae were a response to the needs both of the cantor (even a conservative one) and of the polyphonic singer. 9 The Berkeley Manuscript, University of California Music Library MS. 744 (olim Phillipps 4450), ed. and trans. by Oliver B. ELLSWORTH, Lincoln, Nebraska: University of Nebraska Press, 1984 [Greek and Latin Music Theory, vol. 2], pp. 60-61. # D, PESCE, op. cit.; Karl Werner GUMPEL, «Zur Frühgeschichte der vulgärsprachlichen spanischen und katalanischen Musiktheorie», Spanische Forschungen der Gorresgesellschafi, Erste Reihe: Gesammelte Aufsitze zur Kulturgeschichte Spaniens, 24. Band, ed. Johannes VINCKE, Münster: Aschendorffsehe Verlagsbuchhandlung, 1968, pp. 257-336; id., «Gregorianischer Gesang und Musica ficta», cit., pp. 136-37, 142 = "Gregorian Chant and musica ficta”, cit.,

pp. 17, 23.

144

What the Berkeley Anonymous apparently tells us about Conclusit is, in short, that it includes the A flat, and also (ifwe take the example and manuscript Lo at face value) that it begins with a diminished fourth between the upper A flat and E. He scems to assume that the melody continues afterwards at the tonal level of F-final. Of course the diminished fourth cannot be normally written according to medieval convention, and neither has it been found so far, in the chant books

consulted. What can be found is that the incipit is written at one of three tonal levels, always with che outline of a perfect fourth with its semitone at the top, between C and G, F and C, or B flat and F (Ex. 7). Karp was so keen to conflate Goscalcus’ example with Theired’s scheme and

the testimony of practical sources that he was led to interpret the theorist as implying an initial perfect fourth between A-flat and E-flat. The manuscript Ct, in Ellworth’s edition of the treatise,

implies that the responsory could also be written in such a way as to require a high C sharp; if this applied to the incipit, a descending fourth between upper D and A would be implied. But since the example is another chant, this may be just a confusion of the copyist. The only possible traces of a diminished fourth at the start of the responsory are, for one, the unstable tonal level of the beginning relative to the following passage, and secondly, the variation in the chant sources, which seemingly hesitate between a major third and a perfect fourth at the beginning: a major third would keep the boundaries ofan initial, hypothetical diminished interval before its decomposition into tones and semitones, while a perfect fourth would keep the melodic contour of the intonation. However, each of these phenomena may be explained otherwise, and

therefore a big question mark hovers above Goscalcus observation, unless we either choose to regard this passage as corrupt, or find an alternative solution. The example is, in fact, probably erroneous, since all the diastematic sources consulted require

that the incipit be written a second above the level it is presented in the treatise. Textual corruption is a strong hypothesis, for nothing seems to corroborate the proposed placement of the A flat; the rationale for the error could have been the textual confusion between "conclusit" and a threesyllable passage starting with "con-" (such as "contra me"). However, the Mont-Renaud manuscript

and the Hartker antiphoner, from the tenth-century, suggest an alternative hypothesis: they both have a quilisma over "-clu-", where it would apparently coincide with a major third. Since the quilisma is normally associated with a minor third, a plausible solution for the inconsistency 35 The principle of tonal homogeneity accounts for the substitution of core tones for secondary tones, even when this

replacement widens the interval to sing, requiring extra energy: thus the alignment of the first note with the following tonal axis, higher by a semitone, would compensate the substitution of a fourth for a major third. Alternatively,

taking into account the fact that the first interval is a descending one, a fourth could slide down by a semitone to spare some vocal energy at the beginning (these explanatory principles are taken from the theory of melodic change expounded in Manuel Pedro FERREIRA, "Music at Cluny: The Tradition of Gregorian Chant for the Proper of the Mass. Melodic Variants and Microtonal Nuances" (Ph. D. diss., Princeton University, 1997], ProQuest 9809172, pp.

141-50). The unstable tonal level of the incipit as a whole can be a consequence of the need to accomodate first a lower semitone, and then a whole tone below the final degree.

145

is to suppose an A

flat as the upper note of the quilisma, which would then form a minor third

with the lower E This would fit Goscalcus’ remark, the neumatic evidence and the diastematic evidence regarding the intervals involving other A notes; but cannot be proved.

4. Fernand Estevan (1410)% La tercera conjuncta se signa en .e.-la-mi grave por b mol & toma su ut en .B.mol grave, asi que desimos en .e.-la-mi, fa [...] E aun se prueva por aquel responsorio del dia de rramos que se dize “Conclusit vias meas” do dize "amaritudine", por que en la primera silaba se cótiene fa e mi en e.-la-mi, estóces fazemos la en .g.-sol-re-ut grave. E pruevase en otra dicion deste mesmo responsorio do dize "mortis". E pruevase aun por otro dicio deste mesmo

responsorio do dize

“posuerunt”, por que en la primera silaba se dize fa en .e.-la-mi grave.

Braga

£d

LB

rua"

€.

F

rur NUS

Amara

ws

BC

M39,

su

Benga

.

c

ANT

-

:

Barcelona

i

I fi Te

Auer

+1 i

XT

I

-T

tos

;

1 ts

CS:

porsuce

-

runt

H

Ex. 8: Passages quoted by Estevan.

Fernand Estevan tells us that the responsory uses the E-flat on three occasions. His remark corresponds to two of six E-flats found in the Braga choirbooks, as you can see in Example 8. The passage on mortis is, together with leo, amaritudine, posuerunt and the final mee, one where there is a disagreement of contour in the larger manuscript tradition, and accordingly, the final descent does

not occur in Braga (its only significant deviation from the contour of the respond as it appears in Toledo 44.2); the corresponding passage in a Catalonian cantoral is given instead. The presence of E-flats (which could be up to seven, if Braga is taken into account: see Ex. 9) explains why so many

sources with a 6"-mode version of the responsory transpose it up a fifth, where the lower E-flat can be notated as B-flat.” This anomaly also lies behind both the suppression of the E notes at the points signaled above, and the presence of short-range internal transpositions found in many manuscripts which understandably,

for lack of a reasonable explanation, put Karp on the verge of a nervous

attack. One of these transpositions occurs in Marseille to accommodate Braga’s upper E flat on iudica. 36 Fernand ESTEVAN, Reglas de canto plano è de contrapunto è de canto de organo [ Toledo, Biblioteca Publica Provincial, R (Ms) 329], facsimile & ed. by M? Pilar ESCUDFRO Garcia, Madrid: Editorial Alpuerto/ Conservatorio Superior de Müsica de Sevilla, 1984, pp. 90-92. 37 Leo: B flat at Arras, Metz, Morimondo, Utrecht. Amaritudine: B flat at Cambrai. Mortis: B flat at Cambrai, Metz,

Morimondo, Utrecht. Posuerunt B flat at Arras, Cambrai, Metz, Morimondo, Sr. Denis, Worcester, Utrecht. Mee: B flat at Cluny.

146

ET

I

Tes TE, b

: n *

Re -

r

6

IN

2

an ti

#1 d

+ T

1

‘

aX

r 1

dede

I A TLC [2

| ZA

L

NC

ame.

2

ij

T : LV:

“i b

j*

! to- ta

Ex. 9: Other passages requiring E flat (assuming F final) in Braga. 5. Cartula de cantu plano (1350-1400)* Quarta conjuncta accipitur inter .G. grave et .a. acutam, ut apparet in responso "Conclusit vias meas” in loco qui dicitur “contra me”, post, "Vide domine”, etc. [...] Item octava conjuncta accipitur inter .g. acuta et .a. superacuta, ut apparet si vultis cantare “Conclusit vias meas"

per dyapason in loco qui dicitur "contra me". 6. Anonymous XI [> Lászlo Szalkai] (1300-1450: the treatise includes different layers, their identification and dating being a matter of dispute)? Quarta coniuncta accipitur inter .G. finale et .a. acutum, id est inter .G.-sol-re-ut et .a.-]a-mire, et signatur in .a. acuto per b molle, sic quod ibi canitur fa; ut patet in hac communione "Fidelis servus"

dicitur

[...]

Similiter

patet in hoc responsorio "Conclusit vias meas", in loco in q quo

“lapidem contra me”, et in locis aliis eiusdem responsorio. Et hoc est verum, si inicium

sumpserit in .a.-la-mi-re [...] Si autem in hoc responsorio, scilicet “Conclusit vias”, coniunctam praedictam evitare volueris, incipe ipsum in .c.-sol-fa-ut, quia praedictum responsorium est octavi toni, ergo in .c.-

sol-fa-ut incipitur et in .G.-sol-re-ut regulariter debet terminari, ut patet cuilibet subtiliter intuenti.

38 Cartula de cantu plano [Barcelona, Biblioteca de Catalunya, M. 883, fols. 70v-71v], ed. in Karl-Werner GÜMPEL, "Gregorian Chant and musica ficta", cit., pp. 24-27; also published as «Gregorianischer Gesang und Musica ficta», cit., pp. 144-47. On the date and transmission context of this small treatise, see Christian MEYER, «Un témoin de la réception méridionale des traditions d'enseignement du nord aux XIVe et XVe siécles: Barcelona,

Biblioteca de

Catalunya, M. 883», Anuario musical, 58 (2003), pp. 9-59. ?? RichardJ. WINGELL, “Anonymous XI (CS III): An Edition, Translation, and Commentary”, 3 vols. (Ph. D. diss.,

University of Southern California, 1973), I, pp. 32-33; the text of the treatise was published on-line in ZM.L. at http///www.music.indiana.edu/tml/15th/ANO11TDM.

See also Anonymous

XI,

Tractatus de Musica

Plana

et

Mensurabili, in Scriptorum de Musica Medii Aevi, novam seriem, ed. Edmond de COUSSEMAKER, Tomus III, Paris, 1869, repr. Hildesheim: Georg Olms, 1963, pp. 427-28. This passage reappears in László Szalkai's notebook of 1490, edited by Dénes BARTHA Budapest: Corvina,

(cf. D. PESCE, op. cit, pp. 83-84, 93-94; László DOBSZAY, A History of Hungarian Music,

1993, pp. 57, 221).

147

7. Seville Anonymous (c. 1480)? Orra Regla para conoscer la tercera conjunta: Todo canto que se cantare por bemol & descindiere de .ge.-sol-re-ut, o de .fe.-fa-ut, a .e.-la-mi o a .de.-sol-re, e luego tornare a bemol, tal canto se cantará por la tercera conjunta. Si descindiere de .ge.-sol-re-ut a .e.-la-mi, diremos re/la, fa; así

como hallareys en un responso de los maytines del domingo de ramos que dize “Conclusit vias meas”, que es «d»el sexto tono [...] Regla para conoscer la quinta conjunta: Todo canto que subiere de .ge.-sol-re-ut .a.-la-mi-re,

& en aquel .a.-la-mi-re toviere un punto doblado que se llama “alfa duplex intensum et remisum tonicum’,

tal canto se cantará por la quinta conjunta; así como hallareys en la dominica de

palmarum”

"in ramis

en un responsorio que dize “Conusit vias meas" en la parte que dize “contra me".

Esta conjunta se halla pocas vezes en el canto llano & aun en el canto de organo.

Brass. €t

C

A

CST contra

Paris €

ana

Wal

tantra.

BN Lat 5

AD

Lai

+83

LAT

— 5.

Ad

13296 NI

CTT

ma

cen Tr

M

i

at

Ex. 10: Passages quoted in the Carzu/z/Anon. XI/Seville Anon.

Finally, the author of the Cartula, together with Anonymous XI and the Seville Anonymous, all refer to the presence of A-flats in the 6*-mode, F-final version of Conclusit (Ex. 10). The Seville Anonymous

is the more complete, for he also speaks of low E-flats, thus confirming Theinred's

observation of a double pier (movable notes) a fourth apart. Contrary to the Berkeley Anonymous, however, the quoted A-flat passage is not the beginning of Conclusir, but rather at the words contra me." And in fact, this particular passage appears transposed in many sources in order to keep its

intervallic nature; transposition by a second allows the upper degree of the semitone to coincide with B flat (written in Aachen, Cluny, Kóln, Limoges, Montieramey, St. Martial, St. Maur and

Xanten) or F (when the melody is written at the C-final level). The copyist of antiphoner Utrecht 406 had a unique means to indicate the A flat at the fifth above, avoiding partial transposition:

he wrote a small s (semitonium) before the first E in this passage (Ex. 11).? 4° Alan D. HASTINGS (ed.), ext and Concordances of the Tratado de la Musica: MS. g.III.23, Biblioteca del Escorial, Madison, 1989: The Hispanic Seminar of Medieval Studies [Spanish Text series, nr. 52], Capítulo X, «De las conjuntas», pp. 29-35 [32-34 (fols. 32r, 33r)]. ^! Anonymous XI refers ‘other places in the same responsory'; factus is a likely candidate, if he was familiar, as he might be, with a version similar to that found in Toledo 44.2; the upper notes of the liquescence at mortis and of those

quilismas based on F are other possible locations. 42 Fol, 88v. Cf. Ike DE Loos, “Introduction”, in Utrecht Bibliotheek der Rijksuniversiteit, MS 406, cit., pp. xiv-xv.

148

Ex. 11. The passage “contra me” in the Utrecht antiphoner.

Anonymous XI tells us furthermore that the way to circumvent this anomaly is to transpose the whole responsory one tone up, transforming, in fact, a 6"-mode chant into an 8*-mode chant. The

rationale for the double modal tradition of Conclusit is thus explicitly unveiled. The main problem with this transposition is that it creates a potentially intolerable situation at inimicus insidiator, as was pointed out by John of Afflighem; the copyists solve this by postponing

the transposition

until after these words, as John would have preferred, or changing the tonal level of that passage

only. Another solution is to end the responsory on D, accommodating both E-flats and A-flats, but creating intervallic problems at the beginning and at animae meae, as John also observed.

By way of conclusion, we have discovered that the double modal tradition, the multiple transpositions and the disagreements in the tonal level of a number of passages in the responsory Conclusit can all be explained as notational responses to its peculiar melodic nature. This melody, with its strange turns, by and large survived in the performance practice until the Renaissance,

pressing the theorists to codify and integrate its rich gamut into their intellectual horizon. The

regional variety encountered does not exclude, but on the contrary, presupposes a single melodic model,

based on F, of ambiguous

modal

character.

Our

findings invalidate,

however,

Karp's

tentative reconstruction. This is not to deny that the melody can be to a large extent reconstructed, taking up Theinred of Dover's suggestion of a C scale with variable low B and variable upper E, corresponding to the mobile Es and As of the F-final version. A hypothetical edition based on the Sankt-Gallen, Mont-Renaud and Silos neumations and the diastematic sources consulted is proposed below (Ex. 12). As a melodic paradigm, it accounts for the most significant changes suffered by this chant when it was forced to fit the Guidonian diastematic grid. The evidence admits a few alternative readings, given above the staff alongside editorial suggestions. Allowance for the variability of a few neumes and notes is, in my view, a small price to pay for a clearer vision of this challenging and long misunderstood melody.

149

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Entre Jehan et Philippet, Bertaut et Estievenet en grant deduit sunt menu et souvent;

quant il sunt asamblé, de bien chanter ne se faignent noient,

mais qu'il aient avant touchiet du boin vin cler et gent. Et quant Estievenet fait le sot, il le fait si proprement, car qui ne l'aroit onques vu, il cuideroit,

qu'il le fust proprement. Lors saut Biertaus, ki fait le hors du sens; si a grant esbaniement de quatre enfans,

qui ne font pas a refuser entre la gent.

Nus hom ne puet desiervir les biens, k'Amours envoie as fins amans, qui le siervent en tous tans sanz trecherie. Dieus, que grande signerie, qui tant est douche et plaisans! Par choi je sui mult engrans de siervir sanz vilenie; se Dieu plaist, s'arai amie.

Ex. 23 Montpellier n? 294 : textes du triplum et du motetus

VI

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Montpellier 292, 270. Le motet n° 294 est une des trois compositions dans le septième fascicule

du codex Montpellier, dont la teneur est dit Chose Tassin 93. Les deux autres sont schématisées dans les figures 5 et 6; elles illustrent aussi l’intertextualité et la possibilité d’une polyphonie sémantique révélée par analyse. Dans le motet n° 292, De chanter/Bien doi/Chose Tassin (fig. 5), le verbe

chanter encadre la composition ; il se trouve au début du triplum et à la fin du motetus. Le motetus a sa division d’or (m/M) sur mon *cuer, ce qui coïncide avec le tiers de la musique ; la moitié du texte tombe sur *m'a donné, et la moitié de la musique sur *donné ; la division d'or (M/m) du texte revient sur *li volentés, et celle de la musique, sur volen*tés ; la moitié de la

deuxième partie du texte et les deux-tiers de la musique coïncident avec chan*ter. Le message émergeant du motetus semble être mon cuer m'a donné li volentés de chanter. U' examen du triplum (ex. 24) est aussi suggestive. Les divisions grammaticales du texte produisent la structure syllabique 57 + 41 + 16 ; on observe que 41 + 16 = 57, c’est-à-dire que le texte est composé de deux fois 57 syllabes, le nombre 57 étant équivalent à la section d'or (M) du total syllabique du motetus (92) et le nombre 41, au subtotal syllabique de sa section centrale. La division d'or (M/m) de la première moitié du texte revient sur mal *sentir ; le tiers de la section d'or (M) de la

musique sur sen*tir. Le milieu du texte et les deux-tiers de la section d'or (M) de la musique coincident avec *Et je sui. L'expression ses commandemens termine la section d'or (M) du texte, et le milieu de la musique tombe sur com*mandemens (aussi sur m'a *donné, dans le motetus : ses commandemens/m'a donné). La division d'or (m/M) de la seconde moitié du poème

arrive avec *sanz fausser ; précisément entre la section d'or et le dernier tiers de la musique, sur les mémes mots, on trouve encore une fois une extravagance harmonique — des sonorités paralléles de tierce et de quinte. La pénultième division grammaticale du triplum s'achéve avec le vers si sage et si plaisant ; la division d'or (m/M) de la section d'or (m) de la musique

tombe sur *sage. Les derniers mots du triplum sont amer a toutes gens. Considérant que sui peut étre interprété comme une forme du verbe sivre et que si peut assumer des valeurs différentes et méme opposées (adverbe d'intensité, ou équivalent à « ainsi », « alors », « pourtant »), le message émer-

geant de cette convergence entre la disposition du texte et de la musique se présente comme suit : mal sentir ; et je sui ses commandemens sanz fausser,

99

si sage et si plaisant : amer a toutes gens. L'auteur semble ici revendiquer

une dignité morale qui lui permet de présenter son chant et son sentement sous la lumière la plus favorable.

De chanter me vient talens par boine Amour, ki les siens fait joians; car il n'est nus, tant par ait amis grans,

que loes, k'Amors li fait son mal sentir par un regart, qu’ele li fait coisir,

ne deviegne baus et liés en tous sens. Et je sui cil, qui voel estre a ses commandemens, et du tout son plaisir voel faire sanz fausser,

k'ele me fait tant bele dame amer, si sage et si plaisant. Et tant bel set parler, qu'ele se fait amer a toutes gens.

Ex. 24 Montpellier, n? 292, texte du triplum

Le motet n? 270, Amours/L'autrier/Chose Tassin (fig. 6) présente des caractéristiques semblables : les idées-clés chanter et sans fausser occupent aussi des emplacements proportionnels importants, et sans fausser offre en plus une mutation harmonique peu usuelle. Mais, alors qu'avant la section d'or les mots mis en évidence sont lyriques, aprés ce point Dieus et les verbes garder, penser,

repentir et servir dominent.

La mutation harmonique

sur

repentirai symbolise le passage à ce niveau spirituel plus profond. La seule lecture des textes (ex. 25) n'aurait jamais suggéré ce second niveau de signification poétique. Le motetus, avec sa division d'or (M/m) sur *sade blondete, clòt ses divisions grammaticales avec joie en arai, chanterai, amerai, et

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servirai ; a*merai coincide aussi avec la division d’or (M/m) de la musique, et chante*rai avec son milieu. Le triplum a deux vers d’introduction et deux

autres d’épilogue ; le noyau du poème est divisé en trois grandes sections. Le tiers du texte tombe sur hounou*rer (aussi le dernier mot de la première section) ; la division d’or (m/M), sur cors *gent, et le milieu de la deuxième section, sur biau*té ; la section suivante finit avec l’ounour a ma dame garder. Le tiers de la musique revient sur hounou*rer, sa division d’or (m/M) sur

cors* gent, le début de la deuxième partie de deux-tiers sous gar*der. Si on examine de plus trouve que l’introduction et la première section 34 de la première partie de la deuxième section

la teneur sous de biauté, ses près la structure du texte, on totalisent 55 syllabes, contre (une proportion d’or) ; le tiers

de 55 coïncide avec *grant joie, le milieu, avec *aim, les deux-tiers, avec cla*mer, les trois-quarts, avec sans *fausser ; les divisions d’or de 34 revien-

nent sur lo*er et affer*mer 9^. En somme, les stratégies d'agencement textuel et musical définissent des messages partiellement indépendants.

Ta

Amours, dont je sui espris, me fait chanter. Bien doi estre jolis et grant joie mener, quar la riens, que plus aim et desir,

me daigne ami clamer; de cuer sans fausser L'autrier, au douz mois d'avril, main me levai; pensis a mes amours, jouer m'en alai,

la voell tout mon vivant servir et hounourer. Hé Dieus, qui verroit

dont trop m'esmai, quar ne sai, se ja joie en arai. Ne pour quant plus jolis en serai et s'en chanterai:

son cors gent, qui tant fait a loer, bien porroit dire et affermer,

que de biauté ne porroit

“Jai amé la sade blondete et amerai!”*

on son per trouver;

Ne ja de li amer ne me repentirai, mes con ses loiaus amis tous jours la servirai.

et tant set sagement parler, que nus n'i set qu'amender. Mes mesdisans, que Dieus voelle grever, me gaitent, si que je n'ios aler;

trop redout lor gengler, quar je voel l'ounour a ma dame garder. Si me dedui seulement en sa biauté remirer; je ne puis allors penser.

Ex. 25 Montpellier, n? 270, textes poétiques

102

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VI

Montpellier 256, 254. Les motets n° 256 et 254 du même fascicule du codex Montpellier ont, eux aussi, une signification plurale, décelée par l’analyse proportionnelle, et illustrent différents degrés de divergence entre la composition musicale et la structure poétique. Dans le motet n° 256, Entre Copin/Je me cuidoie/Bele Ysabelos (fig. 7), les pauses simultanées dans les voix supérieures signalent la moitié et la section d’or de la composition. Entre ces deux points, singulièrement encadrés par un même morceau mélodique dans la teneur, l’important est Dieu, représenté par une triangulation sonore ; en dehors de ce cadre, c’est l’amour humain qui domine. L’analyse des textes suggère aussi une polarité de messages : d’une part amours (triplum) et desir (motetus), de

l’autre la conscience d’une prison, de mauvaise vie/renon, leçon (triplum) et de Dieus (motetus). Dans cette dernière voix, le noyau du texte — sans intro-

duction et épilogue — est divisé en deux moitiés par le mot Dieus, mais la division d'or (M/m) de la poésie complète revient sur *desir. Dans le triplum (fig. 8), les calculs sur 125 syllabes (épilogue exclu) donnent le quart sur de mau*vaise vie et le tiers sur *renon ; la division d'or (m/M) et *Amours) coincident avec les divisions grammaticales ; Ja (M/m) et les trois-quarts tombent respectivement sur *prison division d'or (m/M) de la totalité du texte coincide avec je *ne

le milieu (sur division d'or et le*con ; la vuell. La stra-

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Tans/Annuntiantes,

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de

du motetus)

remplit la surface des textes. Si on analyse de plus prés la structure poétique du triplum (ex. 26 et fig. 9), on observe deux sections principales séparées par trois vers ; au milieu de chacune de ces sections, il y a trois vers nettement séparés des autres. Le milieu et la division d'or (M/m) du premier tercet soulignent *mon aa*ge ; ceux de la section correspondante de 147 syllabes,

loial *cuer, douz he*ritage ; ceux de la sous-section suivante, de 67 syllabes,

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m'asoua*ge et gari*son. Le milieu et la division d’or (M/m) du dernier tercet reviennent sur *l'en fait gage *mon cuer, et ceux de la correspondante section de 67 syllabes, sur *gage et *en abandon. Le message central est donc «je veux la servir toute ma vie d’adulte, je lui abandonne mon cœur en caution ; cette pensée, qu'elle suscite, me console et me donne espoir de guérison (du mal d'amour) ». Les mots mis en évidence dans le tercet central sont, par contre, mespri*son tant set sou*tilment assa*llir (division d'or

m/M, 1/2, division d'or M/m) — une complainte cachée sous la surface du texte ? Si on accepte cette interprétation, il y aurait deux niveaux de signification dans le triplum. Un troisiéme niveau peut étre encore décelé à travers le contexte musical (fig. 10): loi*al cuer, m'a*souage, et *l'en fais gage occupent des positions privilégiées, mais les mots mis en évidence entre le milieu et la division d'or (M/m) de la deuxiéme

section de la teneur sont

pri*son, mespri*son (peut-étre aussi dans le sens de mes prison), defen*dre, *cors, ne vaut un bou*ton (avec pen*ser dans le motetus). Cette partie du motet apparait ainsi, gráce à la musique, comme une réflexion mélancolique, teintée de spiritualité chrétienne, sur la réalité corporelle.

Aucun ont trouvé chant par usage,

mes a moi en doune ochoison Amours, qui resbaudist mon courage, si que m'estuet faire chancon; car amer me fait dame bele et sage et de bon renon. Et je, qui li ai fait houmage pour li servir tout mon aage de loial cuer sans penser trahison, chanterai, car de li tieng un si douz heritage, que joie n'ai se de ce non;

c'est la pensee, que mon douz mal m'asouage et fait esperer garison.

Ne pour quant seur moi puet clamer hausage

Amours et moi tout mon vivant tenir en sa prison. Ne ja pour ce ne penserai vers li mesprison; tant set soutilment assallir, k'encontre li defendre ne s'en puet on. Force de cors ne plenté de lignage ne vaut un bouton; et si li plaist de raencon rendre a son gré, sui pries et l'en fais gage ^ mon cuer, que je met du tout enabandon. Si proi merci, car autre avantage rai je ne pour moi nule autre raison.

Ex. 26 Montpellier, n° 254, texte du triplum

106

VI

(PSZ QU So adiuoyy) saruniunuuy/sui 2UOT7/ganos quo unony : OI SIMS w

A Figure 9 Texte du triplum (Montpellie r, n° 254)

VI

Vers l’Ars nova Ce jeu de niveaux de signification fournit peut-être l'explication de l'ésotérisme et aussi du succés du genre « motet » chez les intellectuels de l'époque. Une contradiction va cependant s'installer entre l'orientation platonicienne de ce jeu et l'émergence de l'aristotélisme scolastique à l’Université de Paris, avec son penchant empirique. L'influence aristotélicienne sur la théorie musicale de la seconde moitié du xml siècle est apparente dans le vocabulaire et les principes de systématisation des traités d'origine parisienne 96 ; il faut attendre le tournant du siècle pour que, avec Johannes de Grocheo, la description empirique du phénoméne musical fasse son apparition. Entre-temps, la continuité phénoménologique du motet est renforcée (un symptóme esthétique de la volonté de rapprocher la sonorité musicale de la conceptualisation de l’œuvre). L'homogénéité temporelle, par contre, apparait de plus en plus mitigée ; en effet, le système modal s’affaiblit, l'organisation rythmique des voix se différencie davantage, les variations de texture à l'intérieur d'une méme composition se radicalisent, le mètre binaire apparaît plus souvent 67. La philosophie aristotélique demande l'adéquation entre la théorie et l'objet empirique et fait éclater par conséquent une crise théorique. Finalement, avec Philippe de Vitry, la conceptualisation musicale absorbe la donnée empirique : l'adoption du contraste métrique ternaire/binaire au niveau de l'unité de temps donne le coup de gráce à l'apriorisme théologique de l'homogénéité temporelle et permet de signifier, sous le méme esprit spéculatif présidant à la théorie harmonique 8, les variations cosmiques de la mesure et de la temporalité. Des conclusions provisoires reposant sur l'examen de deux aspects du

style et du métier de compositeur peuvent ainsi étre dégagées, et une réponse peut étre donnée aux questions soulevées au début: 1) la conceptualisation numérique et proportionnelle de l'ensemble du motet n'a pas été une innovation du XIV? siècle ; 2) l'Ars nova stricto sensu

(1315-1320)

n'a pas

apporté une révolution stylistique, car la diversité de mesure et de temporalité était une réalité dans la musique francaise, aussi bien monodique que polyphonique, du xm° siècle et du début du suivant. L'Ars nova représente peut-être |’ affirmation intellectuelle d'un nouveau groupe social urbain et de son pouvoir courtisanesque ascendant (le jeune Vitry, Muris, Machaut), au détriment de la vieille école, née et barricadée

108

VI Mesure et temporalité

dans les cathédrales (Jacques de Liège) ; il nous manque encore une vraie

analyse sociologique du mouvement. De toute façon, l'Ars nova n'a pas été une simple innovation technique, une extension de l'ars vetus [notandi], car,

en rapprochant les universaux de mesure des particuliers du mouvement elle envahissait la redoute musicale du vieux platonisme en retraite et brisait le noyau intellectuel de la théorie rythmique, en méme temps qu'elle permettait de discipliner et de donner cours au plus haut niveau spéculatif, à des tendances artistiques de longue main. En somme, si on ne peut pas parler, à propos de I Ars nova, d'une révolution musicale, il faut reconnaitre qu'elle fut sa culmination théorique. Etant donné que la théorie avait le pouvoir de bouleverser ou, au contraire, légitimer l'activité et la projection intellectuelle du compositeur savant, on peut conclure que l’Ars nova, c'était un coup d'Etat.

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It seems therefore that between c. 1425-30 and c. 1435 Dufay conceived of predominantly triadic, non-quartal sonority, freed from cadential drive, as a chordal means of expressing the upmost gentleness or introspective spiritual quality; and used the conventional contrapuntal framework to render jubilant, celebratory feelings. Triads were used as plastic and static sonorities, while

quartal aggregates fulfiled dynamic and resolutive ends. Charles van den Borren's description of the fermata-marked passage in Alma redemptoris mater II, with its non-quartal beginning punc-

tuated by sub-final triads over Sumens illud ave and its contrapuntal closing section with a builtin final crescendo (division of cantus) over peccatorum miserere, comes to the mind: «Les dernières

mesures (Sumens illud ave) |...] marquent un point culminant dans l'expression de l'extase et du ravissement».?? The odd features in Nuper rosarum flores (1436) can now be explained as mirroring

Dufay's experiments during the previous decade. The triadic sonority on the word Eugenius, the pope's name, is to be understood as a static and self-sufficient chordal expression of beatitude, needing by its nature no further resolution. The triadic sonority that pervades the final Amen may conjecturally be seen as a colouring device adding spiritual flavour to a quartal and contrapuntal dynamic finale. The work appears then to mirror both concomitant and integrative conceptions, the latter being predominant; which is substantially not far from Lowinsky's own view of Nuper rosarum.

75 Charles VAN DEN BORREN,

Guillaume Dufay: son importance dans l'évolution de la musique au XVe siècle, Bruxelles,

1926, p. 189. 76 LowINsKY, 'Canon Technique...’, p. 191: «The sections for full choir must have been conceived in a mixture of simultaneous and successive procedures».

59

IX

5.5 Dufay's use of two contrastive styles to express contrastive moods in fermata-marked passages seems to disallow Charles Warren's interpretation of the fermata-sign, since extemporaneous embellishment would cancel the aesthetic effect called for by the composer. Dynamic contrapuntal drive would be obstructed and static triadic perfection would be disturbed. It is more likely that the fermata-sign would mean, as it often does when isolated, ‘all together here’, implying perhaps

a tempo ad libitum. This meaning would enable singers to enhance the aesthetic quality of given fermata passages according to their style and underlying text.

TABLE II. A chronology of style in Dufay's fermata passages Progressions Periods

Hamm's groups

Conventional

Non-quartal

Chordal

Flos florum Ave virgo

A (c. 1415 to c. 1425-30)

1

Resvelliés vous Sine nomine Gloria - Credo 4

Alma v. mater I B (c. 1425-30 velas

20] o

|

Gloria 21 -----]| ----------.

. . | Gloria - Credo 5

2b

Alhnar matrll Gloria 29

4

O beate Supremum

3

Sancti Jacobi

5

Cunctipotens

5

Spiritus et alme Rex Omnipotens

6

O proles Hispaniae

9

Ave Regina

C (c. 1435

to 1474)

60

|

^

IX Dufay in Analysis

Table II presents above a chronology of Dufay's style in fermata-marked passages according to the observations in this chapter. Three periods are distinguished: A (c. 1415 to c. 1425-30), characterized by a conventional contrapuntal approach; B (c. 1425-30 to c. 1435), in which nonquartal harmony, total disposal of the 3-3-3-5 structure, and chordal sonority are experimented with; and C (c. 1435 to 1474), marked by a conservative return to normal procedures but exhibit-

ing a superior control of ‘mutual obligation’ between the parts (while the Gloria/Credo pairs had parallel fifths between the cantus parts, neither O proles nor the Mass Ave regina allow them).

This picture is congruent with David Fallow's remarks on the evolution of Dufay's style: «[...] about 1435 [...] he began to rebuild his technique [...] was losing interest in the intense

complexity of some of his earlier motets and striving for a simpler kind of musical expression [...] The cycles of hymns, sequences and Kyrie settings that seem to date from the years immediately after 1433 correspondingly show an attempt to refine his technique, almost to return to first essentials with the most economic means [...] The composer who until then had shown the most

extraordinary range of techniques and styles in his music was now limiting himself, carefully exploring the simplest counterpoint».”” Otterbach also observed that among Dufay's rondeaux, those presenting the less conservative cadential characteristics would have been composed, according to Hamm's chronology, before 1434.7* On the other hand, this study provides objective evidence for a stylistic change in Dufay's music during the mid- and late-1420s, and traces for the first time

the origins and probable aesthetic motivations of the non-quartal and chordal styles that were to influence all subsequent fifteenth-century music.

77 David FALLOWS, sleeve notes for EMI's record Dufay by The Hilliard Ensemble, Kóln, 1987, p. 6; id., Dufay, cit.,

pp. 100, 135, 143 (see also pp. 115-117). 78 OTTERBACH, Kadenzierung und Tonalitàt..., pp. 96-97.

61

IX

Bibliography (Updated*) Aldrich 1969 = Putnam ALDRICH, ‘An Approach to the Analysis of Renaissance Music The Music Review, 30, 1969, pp. 1-21 Apel 1969 = Willi APEL, The Harvard Dictionary of Music, 2nd ed., Cambridge, Mass.,

1969 Apfel 1955 = Ernst APFEL, 'Der klangiche Satz und der freie Diskantsatz im 15. Jahrhundert' Archiv fiir Musikwissenschaft, 12, 1955, pp. 297-313 Apfel 1961 = Ernst APFEL, "Über den vierstimmigen Satz im 14. und 15. Jahrhundert’ Archiv für Musikwissenschaft, 18, 1961, pp. 34-51 Apfel 1974 = Ernst APFEL, Grundlagen einer Geschichte der Satztechnik vom 13. bis zum 16. Jahrhundert, 1, Saarbrücken, 1974 Bashour 1975 = Frederick Joseph BASHOUR, A Model for the Analysis of Structural Levels

and Tonal Movement in Compositions of the Fifteenth Century, Ph.D. diss., Yale University, 1975 Bent 1981 = Margaret BENT, 'Some Factors in the Control of Consonance and Sonority: Successive Composition and the So/us Tenor’ in International Musicological Society: Report of the Twelfth Congress, Berkeley, 1977, Kassel, 1981, pp. 625-634 Bent 1983 = Margaret BENT, ‘Resfacta and Cantare Super Librum! Journal of the American

Musicological Society, 36, 1983, pp. 371-391 Bent / Hallmark 1985 = The Works of Johannes Ciconia, ed. Margaret Bent and Anne Hallmark, Polyphonic Music of the Fouteenth Century 24, Monaco, 1985

*Bent 1998 = Margaret BENT, "I'he Grammar of Early Music: Preconditions for Analysis’ in Cristle Collins Judd, ed., Tonal Structures in Early Music, New York, 1998, pp. 15-59 *Bent 1998 = Margaret BENT, 'Music and the Early Veneto Humanists' Proceedings of the

British Academy, 101, 1998, Lectures and Memoirs, 1999, pp. 101-30 *Bent 2001 = Margaret BENT, Res facta’ in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie, 2nd ed., 29 vols., London, 2001, vol. 21, pp. 210-211

*Bent 2003 = Margaret BENT, 'Ciconia, Prosdocimus, and the Workings of Musical Grammar’ in Johannes de Ciconia, musicien de la transition, ed. Philippe Vendrix, Turnhout, 2003, pp.

65-106 Besseler 1950 = Heinrich BESSELER, Bourdon und Fauxbourdon: Studien zum Ursprung der niederländischen Musik, Leipzig, 1950 Besseler 1951-1966 = Heinrich BESSELER, ed., Guglielmi Dufay: Opera omnia, 6 vols., Corpus Mensurabilis Musicae, series I, Rome, 1951-1966

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IX Dufay in Analysis

Besseler 1962 = Heinrich BESSELER, ed., Guglielmi Dufay: Opera omnia, 6 vols., Corpus

Mensurabilis Musicae, series I, vol. iii [a]: Missarum pars altera: apparatus criticus, Rome, 1962 Blackburn 1987 = Bonnie J. BLACKBURN,

‘On Compositional Process in the Fifteenth

Century" Journal of the American Musicological Society, 40, 1987, pp. 210-284 *Blackburn 1991 = Bonnie J. BLACKBURN with Edward E. LOWINSKY and Clement A.

MILLER, eds., A Correspondence of Renaissance Musicians, Oxford, 1991 *Blackburn 1998 = BonnieJ. BLACKBURN, ‘Res facta, chose faite’ in Die Musik in Geschichte und Gegenwart, ed. Ludwig Finscher, 2nd ed., Sachteil 8, Kassel, 1998, pp. 171-176 *Blackburn 2001 = Bonnie J. BLACKBURN, "The Dispute about Harmony c. 1500 and the

Creation of a New Style’ in Théorie et analyse musicales 1450-1650: Actes du colloque international, Louvain-la-Neuve, 23-25 septembre 1999, eds. Anne-Emmanuelle Ceulemans & Bonnie J. Blackburn,

Louvain-la-Neuve: Département d'histoire de l'art et d'archéologie/Collège Erasme, 2001, pp. 1-37. Bockholdt 1960 = Rudolf BOCKHOLDT, Die frühen Messenkompositionen von Guillaume Dufay, 2 vols., Miinchner Verôffentlichungen zur Musikgeschichte V, Tutzing, 1960 Boretz 1969 = Benjamin BORETZ, 'Meta-Variations: Studies in the Foundations of Musical

Thought (I)' Perspectives of New Music, 8, 1969, pp. 1-74 Borren 1926 = Charles VAN DEN BORREN, Guillaume Dufay: son importance dans l'évolution de la musique au XVe siécle, Bruxelles, 1926

Bush 1946 = Helen E. BUSH, "The Recognition of Chordal Formation by Early Music Theorists’ The Musical Quarterly, 32, 1946, pp. 227-243 Caldwell 1984 = John CALDWELL, ‘Some Aspects of Tonal Language in Music of the Fif-

teenth and Sixteenth Centuries’ Proceedings of the Royal Musical Association, 110, 1983-1984, pp. 1-24

Carpenter 1973 = Patricia CARPENTER, "Tonal Coherence in a Motet of Dufay’ Journal of Music Theory, 17, 1973, pp. 2-65 Coussemaker

1869 = Scriptorum de musica medii aevi, novam seriem, ed. Edmond de

Coussemaker, Tomus III, Paris 1869, repr. Hildesheim, 1963 Crocker 1962 = Richard L. CROCKER, 'Discant, Counterpoint, and Harmony’ Journal of the American Musicological Society, 15, 1962, pp. 1-21 Dahlhaus 1968= Carl DAHLHAUS,

Untersuchungen über die Entstehung der harmonischen

Tonalitát, Kassel, 1968 Fallows 1987 = David FALLOWS, sleeve notes for EMI's record Dufay by The Hilliard En-

semble, Kóln, 1987 Fallows 1988 = David FALLOWS, Dufay, 2nd ed., New York, 1988

63

IX

Ferand

1957 = Ernest T. FERAND,

"What is "Res facta"?' Journal of the American

Musicological Society, 10, 1957, pp. 141-150 Ficker 1951 =, Rudolf von FICKER, ‘Zur Schópfungsgeschichte des Fauxbourdon' Acta Musicologica, 23, 1951, pp. 93-123 Fischer 1961

= Kurt von FISCHER,

‘On the Technique,

Origin, and Evolution of Italian

Trecento Music' The Musical Quarterly, 47, 1961, pp. 41-57

Fischer 1966 = Kurt von FISCHER, 'Organal and Chordal Style in Renaissance Sacred Music: New and Little-Known Sources’ in Aspects of Medieval and Renaissance Music: a Birthday Offering to Gustave Reese, ed. Jan LaRue, New York, 1966, pp. 173-182 Fox 1945 = Charles Warren Fox, 'Non-Quartal Harmony in the Renaissance’ The Musical

Quarterly, 31, 1945, pp. 33-53 Gushee 1982 = Lawrence GUSHEE, ‘Analytical Method and Compositional Process in Some Thirteenth and Fourteenth-Century Music' Forum Musicologicum, 3, 1982, pp. 165-191 Hamm

1964 = Charles E. HAMM, A Chronology of the Works of Guillaume Dufay Based on

a Study of Mensural Practice, Princeton, 1964, repr. New York, 1986

Hughes 1969 = Andrew HUGHES, 'Some Notes on the Early Fifteenth-Century Contratenor' Music & Letters, 50, 1969, pp. 376-387 Lowinsky 1946 = Edward E. Lowinsky, "The Concept of Physical and Musical Space in the Renaissance (A Preliminary Sketch)" Papers of the American Musicological Society, Annual Meeting,

1941, n. p., 1946, pp. 57-84 Lowinsky 1948 = Edward E. LOWINSKY, ‘On the Use of Scores by Sixteenth-Century Musicians' Journal of the American Musicological Society, 1, 1948, pp. 17-23 Lowinsky 1961 = Edward E. LOWINSKY, Tonality and Atonality in Sixteenth-Century Music,

Berkeley, 1961 Lowinsky 1981 = Edward E. LowiNsKy, "Canon Technique and Simultaneous Conception

in Fifteenth-Century Music: A Comparison of North and South' in Essays on the Music of}. S. Bach and Other Divers Subjects: A Tribute to Gerhard Herz, ed. Robert L. Weaver, New York, 1981, pp. 181-222

Marggraf 1966 = Wolfgang MARGGRAR

"Tonalitit und Harmonik in der franzósischen

Chanson zwischen Machaut und Dufay’ Archiv für Musikwissenschaft, 23, 1966, pp. 11-31 Meier 1952 = Bernhard MEIER, "Die Harmonik im cantus-firmus-haltigen Satz des 15.

Jahrhunderts' Archiv für Musikwissenschafi, 9, 1952, pp. 27-44 Meier 1953 = Bernhard MEIER, 'Die Handschrift Porto 714 als Quelle zur Tonartenlehre des 15. Jahrhunderts’ Musica Disciplina, 7, 1953, pp. 175-197 Mila 1972 = Massimo MILA, Guillaume Dufay I: Canzoni e Mottetti, Torino, 1972.

64

IX Dufay in Analysis

Moll 1997 = Kevin N. MOLL,, ed. and transl., Counterpoint and Compositional Process in

the Time of Dufay: Perspectives from German Musicology, New York, 1997 Nettl 1974 = Bruno NETTL, "Thoughts on Improvisation:

A Comparative Approach’ The

Musical Quarterly, 60, 1974, pp. 1-19 Netd 1986 = Bruno NETTL, ‘Improvisation, extemporization’ in New Harvard Dictionary

of Music, ed. Don Michael Randel, Cambridge, Mass., 1986, pp. 392-394 *Nosow

1997

= Robert Nosow,

'Du Fay and the Cultures of Renaissance Florence’ in

Hearing the Motet, ed. Dolores Pesce, Oxford, 1997, pp. 104-121 Otterbach 1975 = Friedemann OTTERBACH, Kadenzierung und Tonalitàt im Kantilenensatz Dufays, Freiburger Schriften zur Musikwissenschaft VII, München, Salzburg, 1975 *Owens 1997 = Jessie Ann Owens, Composers at Work: the Craft of Musical Composition, 1450-1600, New York and Oxford, 1997 Perkins 1973 = Leeman L. PERKINS, ‘Mode and Structure in the Masses of Josquin' Journal of the American Musicological Society, 26, 1973, pp. 189-239 Powers 1980 = Harold S. Powers, 'Mode' in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie, 6th ed., 20 vols., London, 1980, vol. 12, pp. 376-450 Powers 1981 = Harold S. Powers, "Tonal types and Modal Categories in Renaissance

Polyphony’ Journal of the American Musicological Society, 34, 1981, pp. 428-470 *Powers 1992 = Harold S. Powers, ‘Ts Mode Real? Pietro Aron, the Octenary System, and

Polyphony’ Basler Jahrbuch für historische Musikpraxis, 16, 1992, pp. 9-52 Randel 1971 = Don Michael RANDEL, ‘Emerging Triadic Tonality in the Fifteenth Century’ The Musical Quarterly, 57, 1971, pp. 73-86 Randel 1983 = Don Michael RANDEL, 'Dufay the Reader’ in Music and Language: Studies in the History of Music, 1, New York, 1983, pp. 38-78 Rivera 1980 = Benito V. RIVERA, German Music Theory in the Early 17th Century. The Treatises of Johannes Lippius, Ann Arbor, 1980

Seay 1975 = Johannes Tinctoris, Opera theoretica, 3 vols., ed. Albert Seay, Corpus scriptorum de musica 22, n.p., 1975

Strunk 1973 = Oliver STRUNK, Relative Sonority as a Factor in Style-Critical Analysis [1450-1550]' Studi musicali, 2, 1973, pp. 145-153, repr. in id., Essays on Music in the Western World, New York, 1974, pp. 70-78

Treitler 1965 = Leo TREITLER, "Tone System in the Secular Works of Guillaume Dufay’ Journal of the American Musicological Society, 18, 1965, pp. 131-169, 440

Skinner 1988 = Quentin SKINNER, ‘A reply to my critics’ in Meaning and Context: Quentin Skinner and His Critics, ed. James Tully, Cambridge, 1988, pp. 231-288

65

IX

Warren 1976 = Charles W. WARREN, 'Punctus Organi and Cantus Coronatus in the Music

of Dufay' in Papers Read at the Dufay Quincentenary Conference, Brooklyn College (CUNY), December 6-7, 1974, ed. Allan W. Atlas, New York, 1976, pp. 128-143, 179-181

*Wegman 1996 = Rob WEGMAN, Authorship in the Low Countries,

‘From Maker to Composer: Improvisation and Musical

1450-1500' Journal of the American Musicological Society, 49,

1996, pp. 409-479 *Wexler 1999 = Richard WEXLER, 'Simultaneous Conception and Compositional Process in the Late Fifteenth Century' in Antoine Busnoys: Method, Meaning, and Context in Late Medieval Music, ed. Paula Higgins, Oxford, 1999, pp. 389-398

66

X Proportions in Ancient and Medieval Music This paper deals with a particular mode of thought embedded in both Ancient and Medieval music theory: a mathematical bent stemming from the idea that Music, based on proportional relationships which embody Number, is an audible symbol of a God-given ontological order. This mode of thought influenced the aesthetics of the Ancients and had a crucial impact on the rationalization of musical composition in the late Middle Ages!. Reporting the ideas of ancient Greek philosophers, an anonymous secondcentury writer known as the Pseudo-Plutarch wrote: "Everything, they say, was constructed by God on the basis of musical harmony??. A similar train of thought led St. Jerome, about two hundred years later, to conclude that “The who examines] the harmony of the world and the order and concord of all creatures, sings a spiritual song"?. 'These two quotes illustrate the continuity between pagan and Christian modes of thought in the late ancient world concerning the harmonious constitution of the universe*. But these quotes also suggest that the concept of Music was then far more comprehensive, and more widely applied, than it is today. In the Ancient and Medieval world, Music was more than just intentional, organized sound, as we now tend to think; it was, above all, the theoretical knowledge of the principles illustrated by organized sound. These are proportional, mathematical principles, coextensive with those which were thought ! Written on request to be read at the IV Diderot Mathematical Forum for a nonmusicological audience, this paper does not attempt to exhaust or to redefine the subject matter; for different, complementary approaches, see Willi Apel, *Mathematics and Music in the Middle Ages", Musica e Arte Figurativa nei secoli X-XII, Todi: Accademia Tudertina, 1973, pp. 135-65, and Christian Meyer, “Mathématique et musique au Moyen Age”, Quadrivium. Musiques et Sciences,

Paris: Éditions ipmc, 1992, pp. 107-21.

Andrew Barker, Greek Musical Writings: I. The Musician and his Art, Cambridge: Cambridge University Press, 1984, pp. 248-49. Oliver Strunk, Source Reading in Music History. Antiquity and the Middle Ages, New York: W.W. Norton, 1965, p. 72. Russell À. Peck, *Number as Cosmic Language", By Things Seen: Reference and Recognition in Medieval Thought, ed. David Jeffrey, Ottawa: The University of Ottawa Press, 1979, pp. 47-80 (this essay appears also in Essays in the Numerical Analysis of Medieval Literature, ed. Caroline Eckhardt, Lewisburg: Bucknell

University Press. 1979). © Springer-Verlag Berlin Heidelberg 2002. Used by kind permission of Springer Science * Business Media.

X 2

to rule the created world; Music was therefore regarded as fit to lift the soul from sensorial experience to the contemplation of eternal, cosmic truth. According to Cassiodorus, writing in the sixth century, Mathematics, “that science which considers abstract quantity”, has four divisions: Arithmetic, Music, Geometry and Astronomy. Music “is the discipline which treats of numbers in their relation to those things which are found in sounds, such as duple, triple, quadruple, and others called relative that are similar to these”. And he continues: “The parts of music are three: Harmonics, Rhythmics, Metrics. Harmonics is the musical science which distinguishes the high and low in sounds. Rhythmics is that which inquires whether words in combination sound well or badly together. Metrics is that which by valid reasoning knows the measures of the various metres”. Music, as a scientific discipline, was thus understood to be a mathematical science which encompassed the various aspects of ordered sound, including the sound of formal speech and poetry. The instrumental piece, the modulating voice, the poetic song, all were recognized as transient, yet organized phenomena. Sound, being, in St. Augustine’s words, “an impression upon the sense", which “flows by into the past and is imprinted upon the memory"$, could only be apprehended by the intellect as abstract organization, which was identified with number, i. e. proportional conformity. This is why music could be defined as “the science of discrete, non-permanent quantity”, as Roger Bacon later put it in his Communia mathematica’.

The

Greek

Heritage

This view of Music as a theoretical discipline had already, by this time, had a long intellectual history. It had started, at least in the Western world, with Pythagoras, a philosopher who lived in the sixth century B.C. but from whom we do not have a single written line. We are nevertheless told, in no uncertain terms, by later writers, that he speculated about the correspondence between the consonant quality of some musical intervals and the simplicity and manifold mutual relations of the first four whole numbers®.

5 O. Strunk, op. cit., pp. 88-89. 6 O. Strunk, op. cit., p.93, n. 2. The idea was later taken over by St. Isidore of Seville. 7 Roger Bacon, Communia Mathematica, ed. Robert Steele, London, 1940, p. 51: Sciencia vero de quantitate discreta non-permanente est Musica. Bacon speaks often of Music in his mathematical writings, although with little originality. See also Robert Belle Burke (trans.), The Opus Majus of Roger Bacon, 1, Philadelphia, 1928, and Don Michael Randel, “Al-Farabi and the Role of Arabic Music Theory in the Latin Middle Ages”, Journal of the American Musicological Society, 29 (1976), pp. 173-88 [183-85, 187]. 8 Cf. G.S. Kirk & J. Raven, The Pre-Socratic Philosophers, Cambridge: Cambridge University Press, 1966 (Portuguese translation, Lisbon: Gulbenkian, 1979,

X Proportions in Ancient and Medieval Music

3

To illustrate, let us have a stretched string attached to a horizontal ruled scale, with a maximum vibrating lenghth of twelve units, whose sound, when pulled, we will take as reference. A vibrating portion of six units, i.e. half the maximum length, produces another sound an octave above the first. The interval of an octave can thus be identified with the proportion 1:2. A vibrating portion of four units, which corresponds to the proportion 1:3, sounds an octave and a fifth, or twelfth, above. A vibrating portion of three units, corresponding to the proportion 1:4, sounds two octaves above. We have thus three consonances related to three ratios, 1:2, 1:3, and 1:4, which are said to be multiple ratios, for the larger term is a multiple of the lesser one, which may be represented as n:zn. If we now take the numbers 1,2,3 and 4 and try to find other possible proportional, unequal combinations among them, we are left with two new ratios, 2:3 and 3:4. In both of them the larger term exceeds the smaller by one unit, illustrating the form n:n + 1. These ratios are called “epimore” or “superparticular”. We will be able to hear the interval corresponding to these ratios, selecting vibrating portions of eight against twelve units for the “hemiolic” 2:3 ratio (“hemiolic” meaning that the whole is exceeded by its half); and, again, nine against twelve units for the "epitrite" 3:4 ratio (*epitrite" meaning that the whole is exceeded by its third). We will then find, respectively, the intervals of a fifth and a fourth; both were considered consonant by the Greeks, not only on account of the interaction between their physical properties and human perception, but also because their relational use within the prevailing stylistic conditions allowed, in the absence of conventional assumptions to the contrary, the recognition of their “harmonious”, blending quality. Thus all the ratios comprised by the numbers 1,2, 3 and 4 imply, according to Pythagoras, consonant intervals. Two of them, the twelfth (1:3) and the double octave (1:4), can be decomposed into intervals of octave and fifth; the octave, the fifth and the fourth correspond to 1:2, 2:3 and 3:4, where 1:2 is not only multiple, but also superparticular as are the remaining ratios. Moreover,

the successive ratios 1:2, 2:3 and 3:4, when combined using as reference the

larger vibrating lenghth (6:8:9:12), form an octave (6:12) with a fourth and fifth inside, both when reckoned from top to bottom (e. g. 6:8:12) and from

bottom to top (12:9:6). When these same ratios are combined in sucession (3:4:6:12), they form a double octave

(3:12) with an octave down below

(6:12), a fifth above it

pp. 219-34); Andrew Barker, Greek Musical Writings, II: Harmonic and Acoustic Theory, Cambridge: Cambridge University Press, 1989, pp. 28-45; Richard L. Crocker, “Pythagorean Mathematics and Music”, in id., Studies in Medieval Music Theory and the Early Sequence, Aldershot: Variorum, 1997 (chap-

ter II).

4

^

Va

1

n

Ù

by

5,

73

!

]

d

“A

!

!

'

[

T

Lu T

T

6

8

9

t

t

I

I

k

^17

L

!

3

3/

4y

^

75

*

» I

1

0 !

4

!

!

| 12

1 !

7

y

Fig. 1.1.

(4:6) — which also provides a twelfth with the lowest sound (4:12) —, and a fourth at the top (3:4). 9

--

i

ty

79

12

!

1

!

1

I

!

' 12

^h

1

"

0 I I

1

J »

A

3

{7 !

'

4

6

!

'

!

|

t

I

35

^o^

/

A I

| 27

73

Val

y

Fig. 1.2.

The correspondence between aural judgment, which recognizes the consonant quality of intervals, and the proportional properties of the first four integers was only part of the story. Pythagoras added two observations: the fact that 1+2+3+4 equals 10 (ten being the basis of counting operations in all Indo-European peoples)”; and the fact that 10 units can be represented on a surface by 10 equidistant dots forming an equilateral triangle with four units on each side (the Pythagorean tetraktys): Although these facts may seem trivial to us, the elegance of the mathematical construct, and its explanatory aesthetic potential, help to understand why it was invested with special mystical significance. Impressed by the ® Georges Ifrah, Histoire Universelle des Chiffres, Paris: Robert Laffont, 1994, tome I, pp. 73-95. The Greeks were well aware of this fact: cf. G. Kirk & J. Raven, op. cit. (Port. trans., p. 233).

Proportions in Ancient and Medieval Music

Fig.

5

1.3.

underlying mathematical logic of consonance, Pythagoras attributed to the Universe an underlying substance which he identified with Number. In spite of all the above harmonic reasoning, the early Pythagoreans do not seem to have been concerned with the practical aspects of music. But by the time of Philolaus, who lived in the fifth century B.C., musical scales had already been derived from the consonances implied in the tetraktys. The difference between the fourth and the fifth, a whole tone (of 204 cents) represented by the proportion 8:9, was projected into the fourth in order to

determine its diatonic division’. In modern acoustics, the equal-tempered semitone has 100 cents, the tone 200 cents, the ditone or major third 400 cents, the perfect fourth 500 cents, and so on, but these intervals correspond only approximately to the “pure” intervals defined by the ratios between the vibrational frequencies of two pitches; these ratios are the same as the Pythagorean arithmetical propor-

tions!!, Let me open a parenthesis here to remind you that the basic module of Ancient Greek music, called tetrachord, is comprised in a fourth; its lower and upper limits being fixed, the two movable notes inside divided it into smaller intervals, according to the harmonic genus, which could be enhar-

monic, chromatic or diatonic (see Fig. 1.4). In the diatonic genus, the fourth could encompass two whole tones, but there was, of course, a remainder; this was identified as a semitone (of 90 cents) represented by the proportion 243:256, as can be inferred from the table of equivalences below (the ditone implies the ratio 64:81 or 192:243, the fourth, 3:4 or 192:256, therefore the difference between ditone and fourth turns out

to be 243:256). Philolaus calculated intervals suring the difference between the major third, for instance, which tones, can also be defined as the

other than the tone and semitone by measums of basic consonances. The ditone or can be construed as the addition of two difference between the sum of four fifths

10 A. Barker, Greek Musical Writings, II, Music, Oxford: Clarendon Press, 1992, 11 Cf. Mark Lindley, “Interval”, The New ed. Stanley Sadie, London: Macmillan,

pp. 36-39; Martin L. West, Ancient Greek pp. 167-68, 219-20, 235-36. Grove Dictionary of Music and Musicians, 1980, vol. 9, pp. 277-79.

movable mote 7

7

LP "

LL 7 e

"o

Bil DiATONIC

CHROMATIC

ENHARMONIC

—— HARMONIC.

GENERA

Fig. 1.4. Table

1.1. 8

64

(x32)

192

tone 9

8

72

216

9

81

243

tone

3

(x64 =)

192

fourth 4

256 192 tone 216

fourth tone 243 256

and the sum of two octaves. This can be seen in the following table, in which each column replicates the ratio 2:3, thus representing a continuous series of fifths!?: The column headed “16” represents four fifths, reached at “81” below; the double octave relative to “16” is “64”; thus, a major third is given by the proportion 64:81. Similar calculations, probably based on instrumental tuning practices by fourths and fifths, allowed Philolaus to calculate the intervals not only of the diatonic, but also of the enharmonic and chromatic tetrachords!?. Shortly after Philolaus, the Pythagorean school reached a summit in the work of Archytas, a contemporary of Plato particularly well acquainted with 1? R. Crocker, op. cit., pp. 195-96. 13 M, West, op. cit., pp. 167-68.

Proportions in Ancient and Medieval Music Table 24 3

6 9

7

1.2. 8

16

32

64

12

24

48

96

18

36

72

144

27

54

108

216

81

162

324

243

486 729

musical practice!4. The superparticular proportions which, in the tetraktys, had stopped at the number four, were allowed to play a larger role in the determination of practical scale divisions, a step no doubt encouraged by the superparticular character of the multiple proportion 1:2 and the relevance of the tone 8:9 as a tetrachordal constituent. Thus, the incomposite major third in the enharmonic genus, which we had encountered in Philolaus as a 64:81 ratio, was newly described by Archytas as a 4:5 ratio (or 64:80) equivalent to 387 cents. The proportions 5:6

(= 315 cents) and 6:7 (= 267 cents) were acknowledged as existing in the context of a pentachord; later theorists associated these minor thirds with the tetrachordal division of the chromatic genus. Finally, the ratio 7:8 (— 231 cents) came to represent the lower tone of the diatonic genus. In this way, all the superparticular proportions up to number nine were included in Archytas' harmonic scheme!: multiple

superparticular

(1:2 (1:3)

2:3

3:4)

4:5

5:6

6:7

7:8

(8:9)

(1:4) The ratio 27:28, slightly less than a third of a tone, was also proposed by Archytas as the lower interval of any tetrachord, and 35:36, roughly a quartertone, as its complement in the enharmonic genus. Other superparticular proportions, like 9:10 or 15:16, were later associated with tetrachordal divisons by several writers in the Pythagorean tradition such as Erastosthenes, Didymus and the great Ptolemy!$ (Ptolemy’s mathematical idealization of tunings known to him consists exclusively of superparticular ratios, and he even proposes a new diatonic division of the tetrachord [9:10, 10:11, 11:12] on account 14 Martin Vogel, Die Enharmonik der Griechen, 1. Teil: Tonsystem und Notation, Düsseldorf, 1963, pp. 50-57; R. Crocker, op. cit., pp. 331-33; M. West, op. cit., pp. 168, 236-38; A. Barker, Greek Musical Writings, II, pp. 39-52. 15 Cf. A. Barker, Greek Musical Writings, II, pp. 46-47. 16 M. West, op. cit., pp. 169-71, 237-40.

X 8

of the mathematical elegance of near-equal ratios in equal, superparticular excesses. He finds, however, no compelling reason to deny a consonant quality to the interval of octave plus fourth, represented by the ratio 3:8, which is

neither multiple nor superparticular)!”. Archytas was also the first to classify and explore the musical potential of proportional means. According to him, there are three means in music. One is arithmetic, the second geometric, the third harmonic. And I quote: “There is an arithmetic mean when there are three terms, proportional in that they exceed one another in the following way: the second exceeds the third by the same amount as that by which the first exceeds the second

le. g. 12:9:6 twice subtracts 3]. In this proportion it turns out that the interval between the greater terms is less, and that between the lesser terms is greater [in the given example, 12:9 gives a fourth, while 9:6 gives a fifth].” “There is a geometric mean when they are such that as the first is to the second, so is the second to the third [e. g. 12:6:3 replicates the proportion 2:1]. With these, the interval made by the greater terms is equal to that made by the lesser [in the given example, both 12:6 and 6:3 give an octave]”. Finally, there is a harmonic mean “when they are such that, by whatever fraction of itself the first term exceeds the second, the second exceeds the third by the same fraction of this latter [e. g. 12:8:6, where 12 — 8 = 12/8, and 8— 6 = 6/3]. In this proportion the interval between the greater terms is greater, and that between the lesser terms is less” [that is, 12:8 gives a fifth,

and 8:6 gives a fourth]!8. Archytas, in addition, penned mathematical demonstrations which reveal his concern with harmonics. A single theorem of his survives; it states that a superparticular ratio cannot be divided by a whole number into equal parts. It reached us in two slightly different versions. The version transmitted by Boethius, possibly closer to the original, mirrors the Greek distinction be-

tween the unity (monas) and number as originated by the unity (arithmos); it runs like this: “A superparticular ratio cannot be split exactly in half by a number proportionally interposed [ ... ]." “Let A:B be a superparticular ratio |... ]. I take the smallest integers

in that same ratio, C:D[-]E. Since C:D[+]E is the same ratio and the ratio is superparticular, the number D[+]E exceeds the number C by one of its — that is, D[+]E’s - own parts. Let this part be D. I say then that D will not be a number [i. e., a plurality of units], but unity. For if D is a number and is

part of D[+]E, the number D measures the number D[+]E, and thus it will also measure the number E. Whence it follows that it should also measure C.

Thus the number D would measure both the numbers C and D[+]E, which is 17 A. Barker, Greek Musical Writings, II, pp. 306-12; André Barbera, “The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study in Ancient Pythagoreanism", Journal of Music Theory, 28 (1984), pp. 191-224. 18 A. Barker, Greek Musical Writings, II, p. 42 (adapted).

X Proportions in Ancient and Medieval Music

9

impossible. For these are the smallest integers in the same ratio as some other numbers, the first numbers so related, and they maintain the difference of unit alone. Therefore D is unity. So the number D[+]E exceeds the number C by unity. For that reason no mean number comes between them that splits the ratio equally. It follows that between those greater numbers that maintain the same ratio as these, a mean number cannot be interposed that splits the

same ratio equally.”19 A:

B

9: 12

C:

D«E

3:143

Fig. 1.5. The significance of this theorem, which probably belonged to a now lost series of theorems, is that, the basic consonances being represented by superparticular ratios, they cannot be divided equally by rational numbers — or receive a geometric mean, which is the same. It demonstrates the need for unequal divisions of all the consonances comprised in an octave. Once this was acknowledged, Archytas showed how arithmetic and harmonic means could be used to generate proportionally integrated scales. According to Andrew Barker, “notes an octave apart are represented by terms in a geometrical progression by doubles (e. g., 6,12). If the harmonic and arithmetic means are inserted between those terms (e. g., 6,8,9,12), the new terms are the inner boundaries of the tetrachords, separated by a tone | ... ]. When harmonic and arithmetic means are placed between terms in the ratio 3:2, the ratios between means and extremes are 5:4 and 6:5. When they are placed between terms in the ratio 4:3, the resulting ratios are 7: 6 and

8:7 | ... ] Hence all the ratios underlying Archytas’ divisions [ ... ] can be constructed proportionally, by the location of means first in the octave, then in the concords generated by the first construction" 2, Surprisingly, Archytas’ divisions were not generally followed by later theorists; his methodology was, however, adopted by Plato in the Timaeus, where the philosopher, besides referring to the proportions of the world's body and to the numbers of time, explains at length the harmonic constitution of the soul of the universe through geometric progressions (1,2,4,8 and 1,3,9,27) and arithmetic and harmonic means. The Platonic harmony, which replicates, albeit in a novel way, the traditional Pythagorean divisions of Philolaus, has 19 Anicius M.L. Boethius, Fundamentals of Music, trans. Calvin M. Bower, New Haven: Yale University Press, 1989, pp. 103—5; square-bracketed additions mine. 20 A. Barker, Greek Musical Writings, II, pp. 48-49

X 10

received a great deal of attention?!; since it does not intend to describe music as practiced, we will leave it aside on this occasion. So far, we have exclusively dealt with philosophical approaches to harmonics. But there were also music teachers, practitioners with theoretical leanings, and minor musicographers who based their research on empirical data and experiment, rather than abstract philosophical constructs. These were the ones who attempted to find a lesser common denominator for musical intervals, irrespective of rational proportions;

who

conceived

instruments

meant

for acoustical research, including the monochord adopted by the followers of Pythagoras; and who ended up by creating and developing Greek musical notation. They were also, in a sense, the forerunners of the second most important musical philosopher in Ancient Greece: Aristoxenus, a brilliant

pupil of Aristotle??. Aristoxenus rejected the Pythagorean-Platonic tradition, including the representation of intervals by numerical ratios; he eschewed any attempt to justify the phenomenon of consonance and chose instead to start from continuous sound as perceived by the ear. He did not make relative pitch depend on string lengths, using instead the twin concepts of string tension and relaxation. This allowed him to deal with all musical intervals, even when these did not correspond to any rational proportion. Aristoxenus'

work

cannot

be adequately

summarized

here;

nor can we

trace its considerable impact on Greek musical theory. What is of particular interest for our present purposes is that Aristoxenus' choices were closely linked to à geometric concept of the tonal space. Intervallic quantity being treated as continuous, it was allowed to be divided freely according to perceptual or practical considerations. Philosophers, however, tended to despise practicioners; and these latter retaliated by simply ignoring philosophers. The extent to which theoretical awareness influenced Ancient Greek, Roman and Hellenistic musical practice must, in fact, remain largely moot, due to the scarcity of historical records. Variable tetrachordal divisions were no doubt in use; we can suspect that the Pythagorean-Platonic diatonic was not a very common one. Perfect fourths and fifths were important structural features in the melodies, 21 See, for instance, J. Dupuis, “Le nombre géométrique de Platon”, in id., Œuvres de Théon de Smyrne, Paris: Hachette, 1982, pp. 365-400; J.F. Mountford, “The musical scales of Plato’s Republic”, Classical Quarterly, vol. 17 (1923), pp. 125-36; Jacques Handschin, “The Timaeus Scale”, Musica disciplina, vol. IV (1950), pp.3-42; Ernest McClain, The Pythagorean Plato, New York: Nicolas Hays, 1978. Selection of texts and commentary in A. Barker, Greek Musical Writings, I, pp.124-69; II, pp.53-65. For a general presentation of Plato’s comments on music, see Warren Anderson, “Plato”, The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie, London: Macmillan, 1980, vol. 14, pp. 853-57. 22 M. West, op. cit., pp. 4-5, 167-69, 228-33; Annie Bélis, Aristoréne de Tarente et Aristote. Le Traité d'Harmonique, Paris: Klincksieck, 1986; A. Barker, Greek Musical Writings, II, pp. 119—89.

X Proportions in Ancient and Medieval Music

11

although their contour seems to have been dominated by adjacent degrees, thirds and unisons. Even the heterophonic instrumental accompaniment of song, while making use of vertical consonances, did not prefer them to other

intervals, like sevenths and tritones??. The rhythmic proportions of 1:1, 1:2, 1:3, 2:3 and 3:4 were, on the other hand, frequently encountered; sung poetry, based on the alternation of short and long syllables measured according to “feet”, implied the use of rhythmic markers, the “arsis” and the “thesis”, which, implying bodily movement, literally embodied these ratios. It would be impossible not to notice that the basic rhythmic proportions correspond, melodically, to the unison, the octave, the twelfth, the fifth and the fourth; rhythmics, metrics and harmonics were completely congruent from a mathematical point of view.

The

Latin World

It was through proportional rhythm applied to words that Ancient Greek and Roman musical theory made its entrance into Western Christian literary thought. It was at once a remarkably bold and a remarkably ambiguous debut, the one responsible being St. Augustine. This bishop, a towering figure of the late fourth-century Latin Church, wrote a voluminous treatise on Music, of which he had planned to write a second volume. What he wrote is concerned only with Rhythm. St. Augustine deals almost exclusively with literary rbythms; verbal rhythm is seen, however, as a musical phenomenon independent from Grammar: “The science of music”, he says, “to which belongs the reasoned measurement of words in themselves and their rhythm, is only concerned to see that the syllable in this or that place be shortened or lengthened according to the pattern of the proper measure. For if you put the word cano where there ought to be two long syllables and pronounce the first syllable long although it is really short, it is not a musical offence; for the lengths of the sounds reach the ear as the rhythm demands that they should. But the grammarian insists on a correction being made and directs you to substitute a word whose first syllable is long according to the authority of the ancients, whose traditions

he guards”?4, This observation is full of consequences, for three hundred years later, St. Bede would comment that some hymns of the Ambrosian type have a regular rhythmic flow, in spite of the fact that, grammatically speaking, they escape metric organization. The door was open to the imposition of freely chosen rhythms on sung texts, a possibility that the Ancient world, attached to quantitative Greek and Latin, had denied the poet-composer. 23 Cf. M. West, op. cit., chapters VI, VII, X. 24 Gregory Murray, “Gregorian Rhythm in the Gregorian Centuries. The Literary Evidence”, The Downside Review, 75 (1957), pp. 234-58; published independently by the Downside Abbey, Bath, n.d. [quote on p. 6].

12

In his musical tract, St. Augustine reveals himself as heir to the Pythagorean concept of music as sounding number. According to Robert O'Connell, for St. Augustine “the sound-embodied numbers, which delight us in measures of verse as they strike our ear, proceed in downward cascade from the

eternal numbers, which themselves proceed from God [... | The sensible and intelligible orders are [therefore] on speaking terms |... | The upward way is in the strictest sense of the term a return to the contemplative delight from

which the soul has fallen"?5, St. Augustine,

moreover,

expands

the concept

of musical

proportion

as

found in rhythm to embrace all manifestations of artistic beauty. In his words, “that which is beautiful pleases on account of number, in which, as demonstrated already, we seek equality. This can be found not only in what reaches the ears and in the movement of the bodies, but also in visible forms, of which we usually speak of beauty” ?6, Although the step taken by St. Augustine would later prove influential, he does not display in his musical treatise a direct concern with Christian, ecclesiastic practice. Indeed, only once does he refer in passing to a contemporary musical composition, and this is a hymn written by his friend, St. Ambrose of Milan. The reference is relevant, however, for he analyses the verse Deus creator omnium as being composed of four iambic feet with a total of twelve beats; in the Confessiones the analysis is more detailed: “this line”, he says, “is composed of eight syllables, short and long alternately; [...] each long

syllable has double time of each short syllable” 2’. In spite of all his strengths, the impact of St. Augustine’s thought on Christian music seems, prior to ninth-century, to have been negligible’. The same applies to Pythagorean-Platonic or Aristoxenean harmonic theory, transmitted by a few medieval authors. Between the fifth and the eighth century, the time which saw the emergence of specialized liturgical repertoires

of chant, Philosophy was not part of the daily ration of the Latin Church?9. 25 Robert J. O’Connell, Art and the Christian Intelligence in St. Augustine, Oxford: Basil Blackwell, 1978, pp. 67-68, 71. 26 De musica, VI, 12, cit. in Wladyslaw Tatarkiewicz, Historia de la Estetica, IT: La estetica medieval, Madrid: Akal, 1989, p.65 [my translation]. See also De vera religione, XXX, 35: “Since in every art what pleases is conformity, which by itself saves and embellishes everything, this conformity, in fact, requires equality and unity, be it in the semblance of the equivalent parts, be it in the proportion of the unequal ones” (ibid., p. 63). 27 G. Murray, op. cit., p.4. 28 Intellectuals could not, however, ignore St. Augustine. Cassiodorus, in the middle of sixth century, refers to St. Augustine’s teaching that “the human voice naturally has rhythmical sounds and proportioned melody in long and short syllables” (Institutiones, V, quoted in G. Murray, op. cit., p.3). 29 Joseph Dyer, “The Monastic Origins of Western Music Theory”, Cantus Planus. Papers Read at the Third Meeting (Tihany, 1988), Budapest: Hungarian Academy of Sciences, 1990, pp. 199-225.

Proportions in Ancient and Medieval Music

13

Liturgical singing was developed in clerical contexts where philosophical endeavour was generally not welcome; instrumental practice, which could provide a link with musical theory, was no more fortunate in this respect. The Psalms of the Bible were omnipresent as the basis for worship, either modestly chanted, syllabically sung, or melismatically ornamented. Music was conceived of as an emphatic proclamation of the divine Word; this public proclamation came to be more and more elaborate and ended up by requiring an extremely long and specialized training, but was never regarded as an autonomous,

abstract art.

Some musical concepts of Antiquity were assimilated, filtered through the writings of late Roman grammarians and the contributions of Cassiodorus, St. Aldhelm of Malmesbury, St. Isidore of Seville and St. Bede. The grammatical model associated with writing permitted the identification — by analogy with letters, words and periods - of melodic units, basic motives and sections; the grammatical approach to the inflexions of the voice and the corresponding vocabulary allowed for a basic analytical consciousness of relative time values and for a much more ambiguous consciousness of relative height??, As in Ancient times, a connection between the theory developed by the Greeks and liturgical practice can be discerned only in very special instances. We have seen that rhythmic alternation between short and long sounds in the proportion 1:2 was used in some hymns. The probable parallel singing in fifths or fourths of the Alleluia in the Old Roman tradition, or the fifth used as a structural interval and, sometimes, as a melodic leap in chant, are other possible instances. Our musical sources being almost entirely lacking for the earlier centuries of the Middle Ages, it is already risky to say this much. These are indeed obscure centuries, the real Dark Ages, and yet, it was then that a new Latin European identity was forged and à new musical art was born. Historically, the decades around 800 represent a turning point. The Carolingian educational and ecclesiastical policy changed the face of Western music forever. Since the time of Pepin the Short, the Franks had procured the best teachers, had multiplied the copying of books and had raised decisively the reading and writing skills of the churchmen. The adoption in the Frankish Empire of Roman liturgy and its chant necessitated a vast literary and musical effort, which eventually resulted in novel schemes of melodic clasSification and the invention of neumatic notation; this new notation recorded relative pitch contour and, at first, also the brevity or prolongation of single sounds. In Fig. 1.6a, we can see an example of early Paleofrank, "graphic" notation, where single sounds are represented by dots (isolated when long, 30 Marie-Elisabeth Duchez, “Description grammaticale et description arithmetique des phenomènes musicaux: le tournant du IXe siècle”, Miscellanea Mediaevalia, Band 13/2: Sprache und Erkenntnis im Mittelalter, Berlin, New York: Walter de Gruyter, 1981, pp. 561-79.

14 l'è

7

«n

... A NÎMAM

-

(”)

tl

4

i

A - NI-MAM

Fig.

amo

I

uu

my

DEUS

L

ME-AM :

(xe) (b)

MEUS...

SE. Gall (X-c.)

+

=||

i

(a)

us...

(n y)

—_

Eoj

FERE

ME

WV) | MEAM

—_

f.

DEUS

Jar

. ANÌ MAM

BE

eee

| Mt AM

+I 9

=

DE-US

ME -

(c) =

Moder.

US

1.6.

connected when quick): over the first syllable of animam, for instance, the notation implies quick ascending movement involving two sounds and then a third, long upper note. Figure 1.6b presents, for the same passage, an example of tenth-century St. Gall notation, representative of a “gestural” type of writing where the shapes incorporate the additional movement (extra loops and lines without melodic significance) by the hand of the choral director; note the use of horizontal strokes and letters c and ¢ to indicate the relative speed of notes. Figure 1.6c presents, for comparison, a modern transcription of the same extract, taken from the introit Ad te levavi (Paleofrank variants above); black and void note-heads stand for short and long notes,

respectively®1. The extent to which these rhythmic oppositions were conceived as proportional ratios or qualitative (approximative) distinctions has been much debated, and probably a conclusive answer will never be reached??. Alcuin, 31 This paragraph

is based

on the momentous

re-examination

by Kenneth

Levy

of the relationship between the different families of neumes (“On the Origin of Neumes”, first published in 1987), now available in his book Gregorian Chant and the Carolingians, Princeton: Princeton University Press, 1998, pp. 109-40. In the example, the Paleofrank neumes are taken from the Diisseldorf Sacramentary D.1, while the St. Gall ones derive from MSS 339 and 376 (see also Le Graduel Romain. Édition critique, IV/II, Solesmes, 1962, pp. 69-70: over [ani] mam. most sources have only two notes, both long in MSS Chartres 47 and Laon 239). The

Paleofrank variant over me/us] finds a parallel in MS Chartres 47 (cf. facsimile in Paléographie musicale, vol. XI, Solesmes, 1912). 32 A summary of the debate up to the early 1960s can be found in John Rayburn, Gregorian Chant. A History of the Controversy Concerning Its Rhythm, New

X Proportions in Ancient and Medieval Music

15

however, at the beginning of the ninth century, refers to the chant practice at Charlemagne's palace school as follows: “|The cantor] prepared the boys for the sacred chant in order that they might sing the sweet melodies clearly, and learn that music consists of prosodic feet and proportions."33 A later reference by Lupus of Ferrières, to the singing of short and long sounds in psalmody, and a passage in the ninth-century tract Scolica enchiriadis (the explanation of the expression numerose canere, illustrated by the prosodic notation of a simple antiphon) substantiate, albeit with some ambiguity,

Alcuin’s report?*. Early in the tenth-century, the remarks by the anonymous author of the Commemoratio brevis — partly echoing the Scolica enchiriadis — are particularly striking: “Breves must not be slower than is fitting for Breves; nor may Longs be distorted in erratic haste and be faster than is appropriate for Longs | ... ] All notes which are long must correspond rhythmically with those which are not long through their proper inherent durations | ... ] for the longer values consist of the shorter, and the shorter subsist in the longer, and in such a fashion that one has always twice the duration of the other,

neither more nor less | ... | for without question all music should be strictly measured in the manner of prosody. Teachers must impress this zealously upon their pupils, imparting to the children from the beginning this habit of evenness and strict measure”%. The sense of a parallel between prosodic York, 1964, repr. Westport, Conn.: Greenwood Press, 1981; and Bruno Stablein, “Theses equalistes et mensuralistes”, Encyclopédie des musiques sacrées, ed. J. Porte, vol. 2, Paris: Labergerie, 1969, pp. 80-98. The following years, however, saw the emergence of the semiological school of Eugène Cardine, which completely changed the arena. The old opposition between defenders of metrical chant and equalist chant did not altogether disappear, but a mid-way gradually became accepted, at least in practice. A bridge between the mensuralist distinction of longs and breves and the semiological acknowlegment of different rhythmical values is outlined in Manuel Pedro Ferreira, “Bases for Transcription: Gregorian Chant and the Notation of the Cantigas de Santa Maria”, in José Lépez-Calo

(coord.), Los instrumentos del Portico de la Gloria: Su reconstrucción y la másica de su tiempo, La Corufia: Fundacién Pedro Barrié de la Maza, 1993, Vol. 2, pp. 573-621. 33 Nancy Phillips, “Classical and Late Latin Sources for Ninth-Century Treatises on Music”, Music Theory and Its Sources. Antiquity and the Middle Ages, ed. André Barbera, Notre Dame (Indiana): University of Notre Dame Press, 1990,

pp. 100-35 [124]. 34

N. Phillips, op. cit., p. 125 (remark by Lupus of Ferriéres); Musica enchiriadis and Scolica enchiriadis, trans. Raymond Erickson, New Haven: Yale University Press, 1995, pp. 50-53, 69; Nancy Phillips & Michel Huglo, “Le De musica de saint Augustin et l’organisation de la durée musicale du [Xe au XIle siècles”,

Recherches Augustiniennes, XX via).

(1985), pp. 117-31 (on the antiphon Ego sum

35 Commemoratio brevis de tonis et psalmis modulandis, ed. & trans. Terence Bailey, Ottawa: The University of Ottawa Press, 1979, pp. 103, 107.

X 16

feet and ecclesiastical musical practice was still alive in the early eleventh

century, as testified by Guido of Arezzo in his treatise Micrologus*®. After a couple of generations, the Carolingian clerics were also able to start a revival of Classical learning. Some monasteries, and a few Cathedral schools, were able to rise to fame as centers of culture, without losing sight of their liturgical obligations. This allowed the emergence of a new kind of intellectual: one philosophically well read, yet attentive to his clerical, contemplative mission, which was embodied in the daily liturgy. Musical theorists from around the fifth century A.D. like Martianus Capella and Boethius, who transmitted Ancient Greek harmonics, and the roughly contemporary commentaries by Macrobius and Calcidius on Plato’s Timaeus were again read with devotion?". A new kind of music theorist was about to be born. The ninth-century music theorist devoted his best efforts to assimilating the harmonic science of the Greeks. But he was also concerned with its practical application to liturgical chant. Competing scalar systems were proposed to that end; the traditional Pythagorean-Platonic diatonic division of the octave, which in the Ancient world had never been widely used, suddenly occupied the center of the stage, and with minimal modification was adopted by many as their chief theoretical reference. The authority of Boethius, the Christian thinker in whose writings the Pythagorean octave divisions had been extensively explained, and the growing analytical awareness of melodic intervals, which resulted in diastematic notation, slowly led to the rejection of certain features of chant which were deemed incompatible with the theoretically defined scale, like modulating chromatic notes other than the B flat and the remains of soft diatonic and enharmonic microtones. The traditionalists tried to keep non-diatonic or non-Pythagorean intervals, but

eventually lost38, 36 Cf. Hucbald, Guido and John on Music — Three Medieval Treatises, trans. Warren Babb, New Haven: Yale University Press, 1978, pp. 70-73. A few commentaries: Jan W.A. Vollaerts, Rhythmic Proportions in Early Medieval Ecclesiastical Chant, 2nd edition, Leiden: E.J. Brill, 1960, pp. 168-94; Richard L. Crocker, “Musica rythmica and Musica Metrica in Antique and Medieval Theory”, in id., Studies in Medieval Music Theory and the Early Sequence, Aldershot: Variorum, 1997 (chapter IV); Nino Pirrotta, Musica tra Medioevo e Rinascimento, Torino: Einaudi, 1984, pp.3-19; Calvin M. Bower, “The Grammatical Model of Musical Understanding in the Middle Ages”, Hermeneutics and Medieval Culture, ed. P. Gallacher & H. Damico, New York: State University of New York Press, 1989,

pp. 133-45 [140 ff].

œ

37 Michel Huglo, “The Study of Ancient Sources of Music Theory in the Medieval Universities”, Music Theory and Its Sources — Antiquity and the Middle Ages, ed. André Barbera, Notre Dame, Indiana: University of Notres Dame Press, 1990, pp. 150-172. 3 Manuel Pedro Ferreira, “Music at Cluny: The Tradition of Gregorian Chant for the Proper of the Mass. Melodic Variants and Microtonal Nuances” (PhD diss.,

Princeton University, 1997) ProQuest-UMI 9809172 (1998).

X Proportions in Ancient and Medieval Music

17

At the same time, extempore polyphony (simultaneous melodic strands) associated with liturgical practice was made an object of harmonic analysis. Those practices which did not depend on the consonances acknowledged by the Greeks, like the simultaneous seconds conspicuously used in Lombardy, or the simultaneous thirds possibly current in the British Isles??, were left outside musical theory, which recognized only the fourth, the fifth and the octave as legitimate harmonic foundations for two-part singing. Passing intervals, however, were allowed, and the major second, used at the end of phrases, was sometimes defended on aesthetic grounds. Two schools of thought, in fact, emerged: one defended the rigid application of theoretical principles; another let perceptual judgment play a major role. The end-result was mixed: the major second survived as appogiatura, the major third was allowed as a passing and preparatory sonority, while the fourth lost ground, leaving the

fifth and the octave to dominate the polyphonic texture9. In the course of the eleventh-century, the pedagogic role given to the monochord, the rise of diastematic notation, the invention of the staff and of solmization completely changed the way liturgical musical would be learnt and preserved in the centuries to follow. Trained in pugna numerorum, an intellectual game which required the participants to calculate geometric, arithmetic and harmonic means*!, the younger, educated clerics could easily grasp Pythagorean-Platonic musical concepts and would no more tolerate current inconsistencies in the modal behaviour of the melodies. The transition between grammaticaly oriented musical conceptions and a systematic theoretical learning based on Greek harmonics had been completed. It is no coincidence that an Aquitanian trope to the Sanctus dating from the second half of the eleventh-century, Clangat hodie vox nostra, displays in its text an uncommon concentration of technical musical terms, as in the

verses (in translation) “High-sounding at the octave, ascending in tetrachords through discrete pitches to the high summit of its contours”. But it is also significant that the poem reached us with two melodies, of which the later one, still dating from the eleventh-century, strives to associate with the word 39 F. Alberto Gallo, *Esempli dell’ Organum dei Lumbardi nel XII secolo”, Quadrivtum, VIII (1967), 23-26; Paul J. Nixon, “Giraldus Cambrensis on Music: How Reliable Are His Historiographers?”, Proceedings of the First British-Swedish Conference on Musicology, Medieval Studies, 11-15 May 1988, ed. Ann Buckley, Stockholm: Royal Swedish Academy of Music, 1992, pp. 264-89. 40 For a summary of the evidence, with bibliography, see Manuel Pedro Ferreira, “Early Cistercian Polyphony: A Newly-Discovered Source”, in Lusitania Sacra,

v. 13-14 (2001-2002), forthcoming. 4 Wolfgang Breidert, “Arithmomachia”, Quadrivium. Musiques et Sciences, Paris: Éditions ipmc, 1992, pp. 169-78. The game was invented in the first half of the XIth century and survived until the XVIth. The mathematician Roger Bacon mentions it, which he calls Rithmimachia, in De communibus mathematice: cf. David E. Smith, “The Place of Roger Bacon in the History of Mathematics”, Roger Bacon Essays, ed. Andrew Little, Oxford, 1914, pp. 153-83 [177].

X 18

for octave, Diapason, a melodic octave; with altissona, for “high-sounding”, a leap of a fifth; and with tetracordis, a melodic motif comprehended in a tetrachord*?. Intellectual mastery of harmonics came first, but then the tentation proved irresistible to make practice conform to its conceptual frame. In the meanwhile, Arabic music and the corresponding theory, of which the most important early representative was Al-Farabi (872-950), had been transmitted to the southern, Islamic territories of the Iberian Peninsula. AlFarabi was highly indebted to the Harmonic Science of the Greeks, which he used to describe the scales known to him, having recourse both to the superparticular proportions proposed by Archytas and the tone-fractions championed by Aristoxenus. He also presented a strikingly developed rhythmic theory based on the sophisticated Arabic (Persian) tradition, which was later appropriated by the composers of the Christian Cantigas. Only a small part of Al-Farabi’s writings on music was translated into Latin in the twelfth century; in spite of some terminological misunderstanding by the translators, his Aristotelean demand that theory should conform to the observation of practice may have encouraged an empirical attitude among Western students

of Musical Science??. Late-Medieval

France

In the 1100s, St. Augustine's De musica, which had meanwhile continued to be recopied, began to receive some attention in Parisian academic circles; the number of copies slightly increased in the thirteenth-century**. Coincidence or not, it was in Paris, in the last quarter of the twelfth century, that a notational technique was developed to record proportional rhythmic flow analogous with, but completely independent from, poetic metre and even words. 42 Gunilla Iversen, “The Mirror of Music: Symbol and Reality in the Text of Clangat hodie", and Charles Atkinson, “Music and Meaning in Clangat hodie", Revista de Musicologia, XVI (1993), pp. 771-89, 790-806. 43 Rodolphe d’Erlanger, La musique arabe, vols. I-II, Paris, 1930-1935; D. Randel, op. cit.; Owen Wright, “Al-Farabi”, The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie, London: Macmillan, 1980, vol. 1, pp. 251-52; Habib Hassan Touma, “Indications of Arabian Musical Influence on the Iberian Peninsula from the 8th to the 13th Century”, Symposium Alfonso X El Sabio y la Müsica, Madrid: Sociedad Española de Musicologia, 1987, pp. 137-50; George Dimitri Sawa, Music Performance Practice in the Early Abbasid Era 132320 AH/750-932 AD, Toronto: Pontifical Institute of Mediaeval Studies, 1989; Manuel Pedro Ferreira, “Andalusian music and the Cantigas de Santa Maria”, in Stephen Parkinson (ed.), Cobras e Som. Papers from a Colloquium on the Text, Music and Manuscripts of the Cantigas de Santa Maria, Oxford: Legenda, 2000, pp. 7-19. 44 M. Huglo, “The Study of Ancient Sources", cit., pp. 167-70.

X Proportions in Ancient and Medieval Music

19

Rhythm was accepted in Parisian polyphony as an autonomous dimension of sound subjected to proportional rules and requiring the exact coordination of time intervals. Musical time was, however, still conceived of as somewhat elastic through expansion or reduction of its contents and acceleration or retention of its movement; it was only in the thirteenth-century that a fixed measuring stick was adopted, and with it, a spatial, geometric conception of

time-constructs*®. This occurred when the motet became a separate, autonomous, self-contained artifact, cultivated by scholars and intellectuals. Its internal time was measured by a single, invariable time-unit; its internal time proportions were manipulated as numbers. The rise of the motet as the most recherché of musical genres, the academic answer to the now declining trobar clus of the aristocratic elite, was the main artistic contribution of the mid-thirteenth century.

At roughly the same time, the knowledge of Euclidian geometry was raised to a new pitch. In the Elements, newly commented by Campano da Novara, arithmetic was subordinated to geometry, in the sense that geometry, dealing with the continuous, admits both rational and irrational proportions, while arithmetic, being concerned with the discrete, cannot attain the same level

of abstraction*®. This had important musical consequences. On the one hand, it freed compositional procedure from the need to conceive musical time as the successive addition of an invariable, indivisible time unit; on the other hand, Euclid presents in the Elements an irrational proportion which would be frequently used in the French motet of the thirteenth and fourteenth centuries: the so-called “extreme and mean ratio” or “golden proportion” (the latter expression is a modern coinage), which occurs when the smaller term is to the larger term in the same way as the larger

term is to the smaller plus the larger [a : b :: b : (a + b)]. In the Euclidian Elements, the extreme and mean ratio is not only defined as such but also used in connection with determination of areas and the construction of the pentagon and related solids". 45 Manuel Pedro Ferreira, “Mesure et temporalité: vers l'Ars Nova”, in La rationalisation du temps au XIIIéme siècle - Musiques et mentalités (Actes du colloque de Royaumont, 1991), Royaumont: Créaphis, 1998, pp. 65-120. 46 Fabrizio Della Seta, “Proportio. Vicende di un concetto tra Scolastica e Umanesimo", In Cantu et in Sermone - For Nino Pirrotta on His 80th Birthday,

Firenze, 1989, pp. 75-99 [79]. 47 Roger Herz-Fischler, À Mathematical History of Division in Extreme and Mean Ratio, Waterloo, Ontario: Wilfrid Laurier University Press, 1987. See also Robert Lawlor, Sacred Geometry. Philosophy and Practice, London: Thames & Hudson, 1982. The golden proportion was used in the planning of both medieval churches and books: cf. Carol Heitz; “Mathématique et Architecture”, Musica e Arte Fi-

gurativa nei secoli X-XII, Todi: Accademia Tudertina, 1973, pp. 169-93 [187-90], and Jacques Lemaire, Introduction à la Codicologie, Louvain-la-Neuve: Université Catholique de Louvain, 1989, pp. 127-34.

20

This is the only three-term proportional division which is possible with only two terms, and is self-generating, which allows it to be given teological significance. It corresponds, arithmetically, to the numerical approximation 0,61803...:1 (or 1 : 1,61803... ); rougher approximations based on integers could be obtained from the Fibonacci series, available from the early thirteenth-century onwards. In this numerical series each number equals the

sum of the two preceding ones: 1;2;3(= 1 +2); 5(= 24 3); 8(=3+5); 13(= 5 + 8); 21(= 13 +8); 34(= 13 + 21), 55(= 21 + 34), etc.; the ratio between two consecutive numbers tends to approach the golden proportion. Thus, 5/8 = 0,6250; 8/13 = 0,6154; 13/21 = 0,6190; 21/34 = 0,6176; 34/55 = 0,6182. Fibonacci himself knew of and used the extreme and mean ratio; it is characteristic of his work that he often calculated numerical approximations of it. Another important thirteenth-century mathematician, Campanus da Novara, expressed his admiration for the properties of this proportion when applied to the polihedric solids*®. Turning to the musical domain: the motet, planned as a temporal whole divided into congruous parts, tried to capture in its time organization both the traditional Pythagorean proportions and an irrational one of special symbolic value, derived from geometrical, divisive reasoning. These proportions were marked by their association with important words, formal divisions, compositional modules, remarkable intervals, rhythmic dislocations or any other feature that called attention to itself. In Fig. 1.7, à scheme corresponding to the three-part motet Entre Copin/

Je me cuidoie/ Bele Ysabelos (codex Montpellier, n? 256) shows the main structural divisions, which coincide with 1/2, the golden section, 2/3 and 3/4 of the composition. The first half is subdivided into three parts. The pauses in the upper voices and the melodic triangle in the lower, at the half-way point and the golden section of the motet, frame three statements of the word *God" which are also set out in a triangle. The hocket (a special kind of polyphonic texture with quick alternating voices) marks the proportions corresponding to the intervals of the fifth and the fourth. The last quarter of

the motet is again subdivided into three”. It must be said in passing that harmonic practice did not evolve much after 1200. Harmonic theory kept its Pythagorean-Platonic basis, although, in the twelfth century, Theired of Dover had, in glorious isolation, resusci-

tated the 4:5 proportion for the ditone (instead of 9/8 x 9/8 = 81/64). The ratios of intervals larger than the fifth, conspicuous in polyphony, were easily calculated by subtracting from the octave their reverses: octave minus major

third equals minor sixth (in modern terms, 2/1 x 64/81 = 128/81); octave minus minor third equals major sixth (2/1 x 27/32 = 54/32, equivalent to adding a tone to the fifth, 3/2 x 9/8 = 27/16); octave minus tone equals minor seventh (2/1 x 8/9 = 16/9); octave minus semitone equals major 48 R. Herz-Fischler, op. cit., pp. 136-44, 171. 49 MP. Ferreira, “Mesure et temporalité”, pp. 104—5.

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— 486/256, equivalent to adding a ditone to the

fifth, 3/2 x 81/64 — 243/128). In general, theorists, following the lead of Johannes de Garlandia (mainly

known for his innovations in the notational domain), attempted to refine the vocabulary which defined the degree of concordance, proposing intermediary categories between the obvious consonance of the octave and the obvious dissonance of the minor second; the thirds were admitted as imperfect consonances, while the status of minor and major sixth remained controversial. The fourth, which practice had definitely downgraded, retained for most authors its conventional status of consonance??, After Garlandia, the next turning-point was Philippe de Vitry, the indirect author of a treatise called Ars Nova. Vitry was a theorist-composer who, in the early-fourteenth century, reformulated musical notation and compositional technique to expand proportional manipulation of time divisions in polyphony. Praised by his contemporaries (including Petrarch), he was in touch with first-class astronomers and mathematicians like Johannes de Muris and Levi ben Gerson (Leo Hebraeus)?! . Had he not paid more attention to royal politics, public administration and an ecclesiastical career than to 50 Of. John L. Snyder, “The De legitimis ordinibus pentachordorum et tetrachordorum of Theinred of Dover" (PhD diss., Indiana University, 1982); Erich Reimer, Johannes de Garlandia: De mensurabili musica, Wiesbaden: F. Steiner, 1972; Serge Gut, “La notion de consonance chez les théoriciens du Moyen Age", Acta musicologica, 48 (1976), pp. 20-44; Michel Huglo, “La notation franconienne. An-

técédents et devenir", Cahiers de Civilisation Médiévale, XXXI (1988), pp. 123-

132 [125-26].

5! Eric Werner, “The Mathematical Foundation of Philippe de Vitri's Ars Nova”, Journal of the American Musicological Society, 9 (1956), pp. 128-32; Ars Nova Magistri Philippi de Vitriaco, ed. G. Reaney et al., n. p: American Institute of Musicology, 1964 [CSM, 8|; Ernest H. Sanders, “Vitry, Philippe de”, The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie, London: Macmillan,

1980, vol. 20, pp. 22-28.

X 22

the copying of his work, he would be nowadays as famous as the younger Guillaume de Machaut. In Vitry’s motet Firmissime/Adesto/Alleluia, about the Holy Trinity, the golden section falls, significantly, at “personis tribus”. The lower voice (Tenor) is constructed in such a way that the first statement of the melody

(color 1) occupies triple the time of the second statement (color 2), the same proportion 3:1 applying between their respective rhythmical divisions

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In the later thirteenth-century, divisive, geometric reasoning had competed with additive, numerical methodology in giving rhythmic shape to the motet not only at the overall planning stage, but also at the level of defining the shortest possible sounds to be used. By the early fourteenth-century, the geometric conception was expanded and systematized by Philippe de Vitry and his teaching first shaped into a treatise by the young Johannes de Muris,

who, following Aristotle, insisted on the continuous nature of time??. The new notational system thus developed for mensural polyphony, the Ars Nova (in the strict sense of the expression) started from basically four rhythmic categories, from larger to shorter sounds: the longa, the brevis, the semibrevis and the minima. Three different levels of mensuration were distinguished: modus, the proportional relationship between the long and the breve; tempus, between the breve and the semibreve; and prolatio, between the semibreve and the minim. At each of these levels, the longer note could be divided into two or three shorter sounds; the whole organization had, therefore, a divisive character. 52 Manuel Pedro Ferreira, “Compositional Calculation in Philippe de Vitry”, paper

presented to the XVIIIth Medieval and Renaissance Music Conference (London, 6-9 July 1990). 53 Fabrizio Della Seta, “Utrum musica tempore mensuretur continuo, an discreto. Premesse filosofiche ad una controversia del gusto musicale”, Studi musicali, XIII (1984), pp. 169-219.

1

Proportions in Ancient and Medieval Music

23

Mensuration signs were created to indicate the use of binary or ternary divisions. At the highest mensuration level, the modus, the most common signs consisted of two or three horizontal or vertical strokes, often drawn inside rectangular or quadrangular boxes, but rest signs normally sufficed, serving as indirect mensuration signs. The tempus was ternary when a full

(“perfect”) circle was drawn, binary when a broken (“imperfect”) circle took its place. The prolatio was ternary when three dots, representing minims, were put inside the circle, and binary when there were only two dots (later, the three dots were replaced by a single one, two by none). The binary and ternary divisions of brevis and semibrevis combined to give four metres, each with its time-signature. All this can be seen in Fig 1.9 below. To enhance rhythmic variety, new procedures were found to modify the proportions between time-durations; composers used colored or void notes for metric changes within a prevailing mensuration, and introduced proportional signatures, which originally replaced mensuration signs, to jump metrical levels by diminishing (or, seldom, increasing) the value of notes in certain arithmetical ratios. 4

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the time of Vitry and Machaut. At first the minim could be divided into (only) two semiminims; diminution (later indicated by special signs) allowed for the sudden halving of the rhythmical values or their reduction by two-thirds. This implied eight, twelve, eighteen or twenty-seven semiminims to a breve, but up to the late fourteenth-century, the semiminim was not universally adopted and the number nine remained a practical limit for proportional changes of

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Fig. 1.10. The proportions acknowledged in musical notation were therefore only those which involved numbers 1,2,3,4,6,8 or 9 and had a harmonic counterpart: the Pythagorean consonances 1:2 (octave), 1:3 (twelfth), 1:4 (double

octave), 2:3 (fifth) and 3:4 (fourth); the Ptolemaic consonance 3:8 (eleventh); the Pythagorean tone (8:9) and its Ptolemaic equivalent, the ninth (4:9); or, which is the same, the proportions corresponding to tone, fourth, fifth, octave and their duplicates at the octave above. All proportions which implied a contrast in excess of 1:4 (corresponding to the larger harmonic interval, the double octave) like the theoretically conceivable 1:6, 1:8, 1:9 or 2:9, were ignored. Only at the end of the fourteenth-century, with the introduction of special note shapes and later, of Arabic numerals to denote proportions, would the mensural system allow the latter proportional ratios and also those involving hitherto excluded primes, namely five (2:5, 3:5, 4:5) and seven (2:7, 3:7, 6:7). This polyrhythmic expansion, effected by a new class of professional, courtly avant-garde musicians, breached the close correspondence between the harmonic and the rhythmic dimensions of mensural polyphony. Once the step was taken to fully explore the divisive potential of the notation in order to represent à wider range of rhythmic proportions, the development of proportional signs took a path of its own; around 1430, however, a shift in

X 1

Proportions in Ancient and Medieval Music

25

aesthetic tendencies towards rhythmic clarity and fluidity led to the divorce

of this development from practical musical needs?4.

The Decline of Proportional Thinking Although the basic organization of the Ars nova mensural system was and largely remained divisive, additive ways of thinking crept in from the very beginning: for practical musicians, it was convenient to reckon rhythm from an invariable short unit of time, like the minim, while the long was too protracted to allow for easy empirical manipulation. Besides, the idea, defended by conservative theorists, that measured music was based upon number, that musical time was discreet and not continuous, did not disappear in the fourteenth century’. The tendency in late medieval mathematics to think of geometry through arithmetical concepts?6 may also have contributed to the slow erosion of the Ars nova theoretical edifice after 1400. The fifteenth century was in various ways a transitional period, marked by the emergence of chordal sonorities and the work of innovative musical theorists like Bartolomé Ramos de Pareja, who revived the harmonic proportions

4:5 (major third) and 5:6 (minor third) and their complements 5:8 (minor sixth) and 3:5 (major sixth)97. The intrincacies of time proportions and the overall planning of the whole work as a step for serious composition managed to survive well into the following century, but the increasing influence of keyboard extemporization and the new intellectual trends, which encouraged dazzling, flowing polyphony and after 1540, valued clear text delivery and emotional effect, eventually won the day. The subject of proportions, once the crux of compositional thought, receeded back to the realm of prosody and instrumental tuning. A new, secularized mental world — in a sense, still our world — was about to be born.

54 Willi Apel, The Notation of Polyphonic Music, 900-1600, 5th ed., Cambridge, Mass.: The Mediaeval Academy of America, 1953, pp. 400—435, 451-53; Richard Rastall, The Notation of Western Music. An Introduction, London: J.M. Dent, 1983, pp. 79-105; Anna Maria Busse Berger, Mensuration and Proportion Signs. Origins and Evolution, Oxford: Clarendon Press, 1993; Jason Stoessel, “Symbolic Innovation: The Notation of Jacob de Senleches”, Acta musicologica, 71 (1999), pp. 136-64. 55 Quatuor principalia musicae, cit. in A.B. Berger, op. cit., p. 45. 56 John E. Murdoch, “The Medieval Language of Proportions: Elements of the Interaction with Greek Foundations and the Development of New Mathematical Techniques”, Scientific Change. Symposium on the History of Science, London, 1964, pp. 247-71 [270]. 57 Carl Dahlhaus, Studies on the Origin of Harmonic Tonality, Princeton: Princeton University Press, 1990; Oliver Strunk, Source Reading in Music History. The Renaissance, New York: W.W. Norton, 1965, pp. 10-14.

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INDEX OF MANUSCRIPTS Arouca Antiphoner (Museu Regional de Arte Sacra) MS 25: V 268-75, plate 1, exx.1-2 Bamberg, Staatsbibliothck

Lit. 115: VI 87-91 Braga, Cathedral ms 10: 1125-6 , ex.1 ms 31: 1125 Brussels, Bibliothéque Royale 11 3828: See Souvigny Cambridge,

Fitzwilliam Museum

369: See Lewes Breviary Cambridge, University Library

Ff.i.17: UL 17, fig.4b; V 281, 292-6, 299—300, exx.8-11

Mm.ii.9: I 130, ex.2 Chansonnier Cangé (O): VI 74, 78-81, 85, exx.16-18

Cluny Gradual (Clu 1): I1 205, 208, 210-15, postscript

Noyon manuscript: IT 210 Oelenberg Antiphoner (mss 45-46): See Westmalle 12 Oclenberg Gradual (ms 47): IV 78-81, cxx.6-7 Oxford, Bodleian Library Lat. lit. d.5: See Hauterive Gradual Paris, Bibliothéque Nationale

lat. 903: See St-Yricix Gradual lat. 909: IIT 9-14, 18, 31-3, figs.1-2; V 290-1 ex.7, 298 lat. 1087: See Cluny Gradual (Clu 1) lat. 1121: TIT 31, fig.7 lat. 1139: III 17, fig.4c; V 291

lat. lat. lat. ms. ms. ms. ms.

2546: IV 78-9 3343: VIII 32 12584: II 208-9 fr. 146: VI 77 fr. 844: See Manuscrit du Roi (M) fr. 846: See Chansonnier Cangé (O) fr. 847 (P): VI 110

ms. fr. 1591

Dijon Tonary: II 213-15, postscript Escorial, Biblioteca del Monasterio, j.b.2: VI 73, 76 Hauterive Gradual: V 270, 280-86, 306 Karlsruhe,

Badische Landesbibliothek

MS 504: V 294-95, ex.9 León antiphoner (Catedral MS 8): I 153-6 Lewes Breviary: IT 209, 211 London,

British Library

Add. 18031/2: See Stavelot Missal Madrid, Biblioteca Nacional 10110: 1 153-4 Manuscrit Clairambault (X): VI 78, ex.13 Manuscrit du Roi (M): IV 75 ex.10b Manuscrit Noailles (T): VI 75, ex.9 Manuscrit R: See Paris, Bibliothéque Nationale, ms. fr.1591 Metz , Médiathéque, MS 83: IV 79

Montpellier, Bibliothéque Inter-Universitaire, Section Médecine H 159: See Dijon Tonary H 196: VI 92-107

(R): VI 73-4, 79, 110, ex.4

ms. fr. 12615: See Manuscrit Noailles (T) ms. fr. 25566, Manuscrit La Valliére (W): VI 74, 110 ms. n.a. fr. 1050: See Manuscrit Clairambault (X) n.a. lat. 2511: III 32 Rome,

Biblioteca Apostolica Vaticana

lat. 9496: III 17, fig. 4a; V 291 San Pietro B79: 1 152 Rome,

Biblioteca Casanatensc,

1907:

II 208-9 Rome, Tre Fontane: See Oelenberg Gradual Souvigny (Clu 2): II 208-9, 211 St-Yrieix Gradual: II 208—9, 211 Stavelot Missal: IT 214, ex.7 Toledo,

Catedral - Archivo y Biblioteca

Capítulares 44.2: III 32

Westmalle 12 (Oelenberg Antiphoner mss 45-46): IV 78-81, exx.1—5

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INDEX OF NAMES, WORKS AND CONCEPTS

Ad cantum letitie (2 voices, in GB-Ob, Lat.

lit. d.5): V 280-86, ex.5 Adam de la Halle: VI 82-4, fig.1 Au repairier en la douche contrée:

VI 79, ex.14 Entre Adan/Chief bien seantz/Aptatur (attributed): VI 92—6, ex.22, fig.3;

VII 89-91 Je n'ai autre retenanche: VI 79, ex.15 Puisque je sui de l'amoureuse loi: VI 81, ex.18 Qui adroit veut amours servir: VI 74, transcription 1 additive composition: IX 39-40 Ademar de Chabannes: III 13-14 Versus de Sancto Marciale LXX (Latin song): III (entire article)

Aelred of Rievaux: II 211 Aeterne regi glorie (chant):

V 274

Alcuin: X 14-15 Aldrich, Putnam: IX 45 Alfonso el Sabio (Alfonso X; Alphonse le Savant) cantiga 288: VI 73, ex. 2

cantiga 88: VI 76, ex.11 Amours/L'autrier/Chose Tassin: VI 100—103, ex.25, fig.6 Angles, Higinio: VI 70 Anonymous IV: V 291, 297, 299; VI 73-4 Anonymous

XI: I 127, 147-9

Anonymous XIII: V 301 Anonymous, Berkeley (Goscalcus): See Berkeley Anonymous Anonymous, Seville: See Seville Anonymous Anonymous of St Emmeram: V 300 Archytas: X 6-9

Aristoxenus: X 10 Ars Nova: VI 66-7, Audefroi le Bastard: Fine amours en Augustine of Hippo,

108—9; X 22-3 VI 82-4, fig.1 esperance: VI 82—5, ex.19 De musica: X 2, 11-12,

18-19 Ave, in styrpe spinosa/Ave, gloriosa/Manere: VI 88-91, exx.20-21 Ave, virgo virginum (2 voices, in GB-Ob, Lat.

lit. d.5): V 280-86, ex.6

Bacon, Roger, Communia mathematica: X 2 Barker, Andrew: X 9 Bashour, Frederick J.: IX 33 with n.17 Bede, St: X 11 Bent, Margaret: IX 35-43 Berkeley Anonymous: I 127, 144-6 Bernard of Clairvaux: IV 77 Bernardus doctor inclitus (chant): V 274 Blackburn, Bonnie: IX 36-40 with n.40 Boethius: X 8-9, 16 Boretz, Benjamin: IX 30 n.6 Brulé, Gace, Au renovel de la doçor d'esté: VI 79-81, ex.16 Caldwell, John: IX 33 Cantabo Domino (chant): II 208-9 cantare super librum: IX 35-43 Carpenter, Patricia: IX 31-3 Cartula de cantu plano (treatise): I 147-8 Cassiodorus: X 2 Catholicorum concio (2 voices, in GB-Ob, Lat. lit. d.5): V 280-86, ex.4 Charlemagne: II 213 Charles de Valois: VIII 14—16 Chord: IX Ciconia, Johannes: IX 52 Cocheril, Maur: IV 78, 80 Commemoratio brevis (treatise): X 15 concomitant composition: IX 39-40 Confessor almus claruit (chant): V 274—5 Constable, Giles: II 207 Dahlhaus, Carl: V 300 De chanter/Bien doi/Chose Tassin:

VI 99-101, ex.24, fig.5 diabolus in musica: See tritone Discantus positio vulgaris (treatise): V 296,

303 Douce playsance/Garison: VIII 16-17, 24 Dufay, Guillaume Alma redemptoris mater II: IX 50—51, ex.2 Ecclesiae militantis: TX 47 Gloria 21: IX 52-8, exx.3-5 Nuper rosarum flores: TX 31 n.8, 33,

47, 59

2

INDEX OF NAMES, WORKS AND CONCEPTS

En non Diu/Ferens: VI 92, ex.21 Enguerran de Marigny: VIII 14-16 Entre Copin/Je me cuidoie/Bele Ysabelos: VI 104—5, figs.7-8; VII 85-9, figs.1-2; X 20-21, fig.1.7 Entre Jehan/Nus hom/Chose Tassin: VI 96-9, ex.23, fig.4, transcription 2 Ernous li Vielle, Pensis, chief enclin: VI 75, ex.10 Estace de Rains, Neant plus que droiz: VI 81, ex.17 Estevan, Fernand: I 146—7 Euclid, Elements (commentary by Campano da Novara): X 19-20 Exultet celi curia (2 voices): V 269-74, 279-86, 288-9, 303-13 Fallows, David: 1X 61 Farabi, Al-: X 18 Ferand, Ernest T.: IX 35 Franco of Cologne: V 296-7 Froger, Dom Jacques: 11 214 Gaffurius, Francis: V 291—2 Gallican chant: I Gloriosus dei amicus (chant): V 274 golden section: VIII 16, 18-19, ex.3, 23 Gonçalo, frater (Gondisalvus): V 274—5 Gonçalves, Martinho: V 278 Gongalves, Pedro: V 278 Grocheio (Grocheo), Johannes de: VI 70, 108; VII 83, 85 Guido Augensis (Guido of Eu): V 77, 82 Guido d'Arezzo, Micrologus: II 214; III 15; V 290, 294-5, ex.9, 301-2 Hoc in solemnio (2 voices, in GB-Cu, Ff.i.17): V 2923, ex.8 Hourlier, Dom Jacques: Il 205, 207 Huglo, Michel: I 132; II 205, 209 Huot, Frangois: IV 78-9 intervals: V 290-303, 306-7 major second: V 290-98 perfect fourth: V 301—3 thirds and sixths: V 298—301 integrative composition: IX 39-40 Jehan de Lescurel: VI 67, 76-7 Amours,

trop vous doi cherir: VI 76-7,

ex.12 Jerome of Moravia: VI 73 Jerome, S: X 1 Johannes de Garlandia (Jean de Garlande): V 293, 296, 303; V1 68, 73; X 21

John of Afflighem (John Cotton): I 141;

V 286 Karp, Theodore: I 128-9, 140; V 294; VI 72 Ki de bons est (lai): VI 72, 84 Labaree, Robert: VI 84 Lambertus: VI 72-3, ex.5 Levy, Kenneth: I 132; II 213 Lowinsky, Edward: IX 31 n.8, 33-4, 46—7 Machaut, Guillaume de: III 19; VIII 17; IX 40 Bone pastor: VIII 17, 24 Mafalda, Princess then Queen of Castile: V 267-8, 276-9 Meier, Bernhard: IX 33 microtones: Il modes, rhythmic: VI 68, 72—6, ex.1 Moniot d'Arras: VI 82-84, fig.1 Quand voi les prés florir. VI 75, ex.10 Mozarabic rite: I Musica Enchiriadis (treatise): V 298 Ne sui pas esbahiz (chanson): VI 74, ex.6 Nicholai sollempnia (2 voices, in GB-Ob, Lat.

lit. d.5): V 280—86, 294, 306—7 non-quartal style: IX 38 number symbolism: VIII 16-23 Old Hispanic Rite: I Otterbach, Friedemann: IX 33 Petrus le Viser: VI 76 Philolaus: X 5-6 Pierre de la Croix (Petrus de Cruce): VI 104-7 Aucun on trouvé/Lonc Tans/Annuntiantes: VI 104-7, ex.26, figs.9-10 Pinell, Jordi: I 132 Plato, Timeus: X 9 Pseudo-Plutarch: X 1 Ptolemy: X 7-8 Pythagoras: X 2-5 Randel, Don: I 132; IX 30 nn.4—5, 44 Regulae de arte musica (treatise): TV 77, 82; V 286 relative sonority: IX 43-6 res facta: IX 35-43 Richart de Fournival, Chascuns qui de bien amer: VI 84 Roesner, Edward: VI 72 Sanders, Ernest: VI 86

INDEX OF NAMES, WORKS Scolica Enchiriadis (treatise): V 298; X 15 Seville Anonymous (theorist): I 148 Skinner, Quentin: IX 30 simultaneous composition: IX 34—5 St Peter of Arouca (monastery): V 267-8,

275-9 Steiner, Ruth: II 206 Strunk, Oliver: TX 43-5 successive composition: IX 34-5 temporality: VI 68, 81 ff Theinred of Dover: I 128, 142-3; V 301;

X 20-21 Thibaut de Champagne: See Thibaut de Navarre Thibaut de Navarre (Count of Champagne, King of Navarre) Au tens plain de felonie: VI 78, ex.13 Fueilee ne flour ne vaut riens en chantant: VI 73, ex.4 Pour conforte ma pesance: VI 75, ex.9 Qui plus aime plus endure: VI 81-2 Tout mi desir e tout mi grief torment: VI 74, ex.7 Tinctoris, Johannes: IX 32-3, 35-43 Liber de arte contrapuncti: IX 32, 35

with n.20, 41-2, ex.1

AND CONCEPTS

Liber de natura et proprietate tonorum: IX 32 Terminorum musicae diffinitorium: IX 35-8 Tischler, Hans: VI 70 Treitler, Leo: IX 31-3 triad: IX 44 ff tritone: VIII 14-16, ex.1 Trouvère chanson: VI 69-85 Victricem (chant): I 209

Vitry, Philippe de: VI 66—7, 87, 108-9; x 20-22 dating of his works: VIII 28-36 Firmissime/Adesto ( Vitry): VII 16, 24, ex.6; X 22, fig. 1.8 Floret/Florens (Philippe de Vitry):

VIII 14-18, exx.1-2 Petre/Lugentium: VIII 18-23, 32-6, exx.3—5 Tribum/Quoniam: VIII 16 Vos/Gratissima: VIII 24—5, ex.7 Waddell, C: IV 78—80 Werf, Hendrik van der: VI 70, 77 Zarlino, Gioseffo: TX 43-6