An Annotated English Translation of Harmonielehre of Rudolf Louis and Ludwig Thuille

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WASHINGTON UNIVERSITY Department of Music

Dissertation Committee: Roland Jordan, Chairman Harold Blumenfeld Orland Johnson Ti 1ford Brooks AN ANNOTATED ENGLISH TRANSLATION OF HARMONIELEHRE OF RUDOLF LOUIS AND LUDWIG THUILLE by

Richard Isadore Schwartz

A dissertation presented to the Graduate School of Arts and Sciences of Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

August, 1982 Saint Louis, Missouri

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©

copyright by Richard Isadore Schwartz 1982

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() TABLE OF CONTENTS Translator's Preface •••

iv

Translator's Introduction

•

•

•

•

VI i

Translation of HARMONIELEHRE MOTTO

....

• • • • • • • • • • • •

2

FOREWORD TO THE FIRST EDITION FROM THE FOREWORD TO THE SECOND EDITION

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. ... .

6

FROM THE FOREWORD TO THE THIRD EDITION

7

FOREWORD TO THE FOURTH EDITION ••

8

TABLE OF CONTENTS

9

...

TAB.LE OF ASSIGNMENTS •

16

PRELIMINARY CONCEPTS ••

18

FIRST PART: THE DIATONIC •

23

SECOND PART: THE CHROMATIC AND ENHARMONIC

. . 257

APPENDICES: EXAMPLES OF THE CHROMATIC AND ENHARMONIC IN MUSIC LITERATURE ••••••••••••• II Ill

CONCERNING THE PROHIBITION OF PARALLELS •

• 465

CONCERNING CHURCH MODES ANO THE EXOTIC

• 478

Translator's Bibliography • • • • • • • • • •

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••• 428

• • 511

iii

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.Translator's Preface The translation of the Harmonielehre of Rudolf Louis (1870-1914) and Ludwig Thuille (1861-1907) provides English speaking musicians with a major pedagogical work in music theory.

This treatment of the

concepts of tonal harmony based firmly upon the theory of chord functions transcends most current English and Ameri.can textbooks •. The care and precision with which chromatic and enharmonic harmony are presented are of particular interest since both are often poorly discussed in the current literature. The book appeared in ten editions between 1907 and 1933.

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It was

necessary, therefore, to determine which edition, if any, was the most representative of the authors 1 achi eve.'11ent. to be the

ob~ious

The

fou_rth edition

prove~

choice--as will be documented in the introduction.

Other than ignoring the frequent use of italics, the translator has altered nothing in the structure of the book.

In some cases common

English terms are substituted for literal translations of the German, while in other cases footnotes correlate the vocabularies. This project would have been many individuals.

impossib~e

without the contribution of

Of particular importance to me was Mr. Wallace Klein.

He introduced me initially to the German language and provided me with an unquenchable thirst for knowledge.

I wish to thank Professor Richard

Rei ten of the Language Department of Vi rg in i a State Uni vers i ty for his assistance in proofreading the original draft, Professor Harold

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Blumenfeld of Washington University whose knowledge of both music theory iv

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and the many inflections of the German language was

v~tal

to the com-

pletion of this dissertation, and my advisor, Professor Roland Jordan whose teaching and guidance throughout this project has been an invaluable source of intellectual stimulation.

To Lois Guschke I give my

thanks for the many hours spent typing the working draft, and to Doris Suits, typist extraordinaire, I offer my gratitude for her unique sense of humor and encouragement given in completion of the final product. Of all those connected with this paper, the one who has made the most sacrifices is my wife, Iris.

Her love and understanding will

always be my source of strength and confidence. To my parents I owe my greatest debt of gratitude.

In their

contributions to my life and education they have always gone beyond the call of duty.

To them this dissertation is dedicated.

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Trans1ator 1 s Introduction Hugo Riemann (1849-1919), considered as the father of modern musicology, praises

~he

Harmonielehre of Louis and Thuille in his

review of 1907 as "one of the most interesting phenomena of music theory !n recent decades 11 • 1 Riemann's admiration of the "consistency and 1ogic of the arguments" in the book with its "unsurpassed analytic examinations and excellent musical examples" and !ts lack of "dogmatic prohibitions and sane ti ons 11 seems to have been shared by others, for the text appeared in ten editions between 1907 and 1933. Ludwig Thuille lived to see the first edition type set, but died shortly before publication.

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Although Louis supervised 1ater editions,

Thuille 1 s influence dominates the technical and pedagogical aspects of the work.

While the

s~cond

edition of 1908 is an exact reprint of the

first, the third (1910) includes an introductory chapter on "Preliminary Concepts of Harmonic Theory" and reverses the order of ideas in the chapter on "Triad lnversions, 11 such that the theory of the suspension and passing sixth chord and stx-four chord is presented after the discussion co"cerning their application as genuine triadic inversions. The text was improved and new examples including those from the music of Thui 1le were added..

The edition concludes with a complete 1 ist of

Thuille 1 s compositions.

1

Hugo Riemann,

11

Eine neue Harmoi1ielehre, 11 S~ddeutsche Honatshefte

4(1907):1:499-501.

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vi

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The fourth edition (1913) which appears here in translation includes Louis' improvements in the text and the addition of a few examples.

Louis writes in the foreword that he feels certain the

Harmonielehre had proven itself to be a necessary addition to music pedagogy.

A supplementary workbook, compendium, and book of so;utions

to the assignments in both the Harmonielehre and the workbook were also published.

Ruclolf Louis died in November, 1914, shortly after the pub-

lication of this edition.

Five subsequent editions (1914, 1917, 1920,

1924, and 1927) are exact reprints of the fourth.

Walter Courvoisier

(1875-1931) began to produce a revised tenth edition in 1930. felt that practical music and theory had progressed

bey~nd

Courvoisier

the scope

of previous editions. 2 To complete such a task he requested the assistance of three colleagues--Dr. Richard G1 schrey, Gustav Geierhaus, and Dr. Karl Blessinger--all professors at the Staddlichen Akadamie hen. II der Ton k unst •1n Hunc

The edition appeared in 1933--after the

untimely death of Walter Courvoisier.

The tenth and last edition,

like its predecessors, is based upon functional harmony and includes changes in the text and examples.

The edition, however, devotes more

time to diatonic harmony and includes the more modern symbols of b11, bVI , #1 V , #11 , and bl V.

T, D, and S (tonic, dominant, and subdominant)

are used consistently throughout the text, rather than conventional step theory symbols.

Most of the musical examples are by the editors.

Of those remaining, only a few are by contemporary composers.

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In many

2 Rudolf Louis and Ludwig Thuille, Harmonielehre, 10th ed. Ed., Walter Courvoisier at al. (Stuttgart: Ernst Klett, 1933), p. ix. vii

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ways, the tenth edition is the least

i~teresting

and important.

The success of this textbook is proven by the number of editions. Originally intended for classroom use at the KHnigliche Husikschule in Munich, it became a major source of information on harmonic thought3 and was used for many years in Germany4 and Austria for the instruction of harmonic theory. Of the many scholars who studied the Harmonielehre, the most wellknown are Paul Pisk (1893lstel {1880-1948).

), Ernst Bloch {1885-1977), and Edgar

Among the lesser-known are Hugo Reichenberger {1873-

1938), Ernst Boehe (1888-1938), Walter Braunfels {1882-1954), Paul von Klenau {1883-1946), Felix von Rath {1886-1905), Fritz Neff {18731904), and Julius-Weissmann (1879-1950).

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Primarily influenced by Reimann, the authors maintain the impertance of tonic, dominant, and subdominant of any given harmonic formation.

func~ions

and the consonance

Like Riemann, Louis and Thuille believe

that the only consonant formations are major and minor triads, as well as their derived intervals.5

The authors also believe that the acoustical

consonance of intervals within a chord formation does not determine

3 Oskar Kaul, "Ludwig Thuille," Musik in die Geschichte und Ge enwart, eds. Friedrich Blume et al., 1 vols. Kassel: Barenreiter, 1949= 1968), 13 : 379 • 4 E. Knoflach, "Vcm G~nsbacher bis Pembauer-Ti roler Mus iker im 19. Jahrhuntlert, 11 Oesterreichische Musikzeitschrift, 25(1970):704. 5 Hugo Riemann, Hugo Riemann's Theory of Harmony: A Study of Book Ill b Hu o William C. Mickelsen and Histor of Music Theor Riemann, trans. and ed. William c. Mickelsen Lincoln: University of Nebraska Press, 1977), p. 31.

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its harmonic consonance.

The type of triad, however, is the determining

The perfect fifth, for example, is consonant because it is a

factor.

component of either a major or a minor triad.

These triads, on the

other hand, are not consonant as a result of their construction out of acoustically consonant intervals such as the fifth, fourth, and third. Dissonance, according to Riemann, results from the conflict between 1) tonic and subdominant, 2) tonic and dominant, or 3) subdominant and dominant--for example, a dominant seventh chord which combines dominant and subdominant components.

Formations also dissonant to Riemann are

those combining major and minor modalities--for example, a fully diminished v117 chord since it combines the dominant and minor subdominant triads.

A formation is dissonant to Louis and Thuille simply if

it is neither a major triad nor a minor one.

Riemann, Louis and Thuille,

however, describe special cases in which formations appear to be con6 sonant, but are dissonant due to the musical context. The II 1 chord, for example, can be conceived as a dominant triad with omitted fifth and added sixth or as a Ill triad in first inversion.

Such a chord

sounds consonant in itself, but can be dissonant in terms of conception.

Riemann called such harmonies

11

pseudo-consonances, 11 but Louis

and Thuil le suggest the term "conceptual dissonances" since they are dis~onant

only in interpretation.

In addition to the philosophy of Hugo Riemann, Johann Wolfgang von Goethe's concept of "Primordial Phenomenon116 also influenced the authors.

Goethe believed that phenomena perceived in experience are

those which can be empirically classified.

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Such classification, however,

6 Johann Wolfgang von Goethe, S~nmtliche Werke, 6 vols. (Philadelphia: F. W. Thomas, 1856), 6:120. ix

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certain essential conditions under which

phenomer.~

can occur.

Some

phenomena are governed by a higher law which cannot be intellectually expressed Jn words or hypotheses, but can only be intuitively comprehended.

Such phenomena are called

supersedes them.

11

primordia1 11 because nothing

According to Louis and Thuille consonance is a

"primordial phenomenon" for consonance can be intuitively perceived by the musician and does not need any further clarification "unless one departs from the realm of pure empiricism to stand upon the wavering ground of acoustical or psychological speculatton. 117 Although the authors thoroughly agree with Riemann's functional theory, they do not discuss his theory of undertones or his theory or harmonic duality.

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These theories are generally unaccepted today.

The authors' choice of chord symbols derived from step theory differs from Riemann's.

This departure from Riemann's elaborate system of

symbols is probably for pedagogical reasons. felt that the simpler the for their

clarific~tion,

symbo~s

The authors must have

were, the less time would be needed

and the more time would be available to explore

the; theory of chord functions, conceptua I d f ssonances, and functioning roots. Two valid concepts neglected in the publication are secondary dominants and monotonality.

The authors mention the existence of

secondary function, but do not extend the idea or

di~cuss

the overall

7 Page 70, footnote, my translation.

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harmonic implications of secondary dominants.

The authors also fail to

deal with a problem that Arnold Schoenberg (1874-1951) and Heinrich Schenker (1868-1935) attempt to solve--monotonality, i.e., the relationship of secondary keys within the overall harmonic structure. Schoenberg creates a theory of regions that fixes relationships between the tonic key of a work and all secondary tonalities.

Schenker dissolves

secondary tona1ities in a system that presents a work as a single unified

Gestalt-~reducing

harmonic content to primary voice-leading.

The Harmonielehre includes approaches that are not found in modern textbooks in English.

The use of major-minor which simplifies the

inclusion of minor subdominant harmony in major, treatment of extended passing formations, interpolated chords (often secondary dominant constructions) and the idea of implied pedalpoint are all of value in the analysis of late 19th and early 20th century music. References are made in the Harmonielehre to numerous theorists other than Riemann. They include August Ambros, Salomon de Caus, Edward

,

Fetis, Moritz Hauptmann, Adolf Marx, Max Reger, Dent, Francois-Joseph s Jean-Jacques Rousseau, S. Sechter, G. Weber, Zarlino, K. Zelter, and the psycho-acoustician Karl Stumpf. Musical examples are chosen from the works of many major composers-beginning with

Montever~i

and including examples from the early 20th

century by R. Strauss, Bruckner, Thuille, Courvoisier, and others.

Of

all the examples in the Harmonielehre, only one is by a French composer (Cesar Franck),8 but none are by Russian composers, 'Felix Mendelssohn,

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8 See page 131, my translation. xi

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~ustav

Mahler, or Arnold Schoenberg--although passing references are

made to Claude Debussy9 and Camille Saint-Sa~ns.10 The authors are not very partial to the music of French and Russian composers since "[their] attempts ••• to obtain a new mode from this so-called whole-tone row are in fact to be understood as amateurish, childish amusements. 1111

The authors• reasons for omitting Mahler's music, how-

ever, are probably quite different.

Rudolf Louis believed Mahler's

compositions tc be repulsive:

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If Mahler's music would speak Yiddish, it would be perhaps unintelligible to me. But it is repulsive to me because it!.£!!. Jewish. 'This is to say that it speaks musical German, but with an accent, with an inflection, and above all, with the gestures of an eastern, all too eastern Jew. So, even to those whom it does not offend directly, it can not possibly communicate anything. One does not have to be repelled by Mahler's artistic personality in order to realize the complete emptiness and vacuity of an art in which the spasm of an impotent mock-Titanism reduces itself to a frank gratification of common seamstress-like sentimentality.12 Louis expressed these be 1i efs "even at the risk of being associated with a faction whose views and tendencies [he] finds foolish and cruel •111 3 While Schoenberg's early works may well have been unfamiliar to the authors, the exclusion of Mendelssohn's music--combined with the passage quoted above--suggests the possibility that social currents totally unrelated to music may have influenced their choice of examples.

9 See page 492, below. lO See page 492, below.

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11 See page 415, below. 12 Rudolf Louis, Die deutsche Musik der Geqenwart (Munich: G. MUller, 1909), cited in Nicholas Slonimsky, ed., Lexicon of Musical Invective (Seattle and London: University of Washington Press, 1965), p. 121. l3 Ibid., p. 182. xi i

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Nonetheless, as translator, I have developed the highest respect for the authors and their theoretical principles. In the final analysis, the Hannonie1ehre is a most valuable padagogical text since it is both theoretical and practical.

It represents

the state of the art in German music pedagogy at the turn of the century.

Solid and well-structured, the publication is still more thorough

and comprehensive than many current texts--particularly with respect to chapters on chromatic and enharmonic harmony.

With revision and

extension, the work could become a major source of information on tonal harmony.

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xiii

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Biographical Sketches Ludwig

Thuille~

the youngest son of Johann, a music retailer,

was born on November 30, 1861, in Bozen, Tirol. trained on the piano by hfs father.

Ludwig was first

After his parents• death he tra-

vel led to KremsmUnster in 18'/2 to study violin, piano and organ.

In

1876 Thuille married the widow of conductor and composer Matth~us Nagiller.

They travelled together to Innsbruck where Thuille received

a general education and studied theory and keyboard with Joseph Pembauer. Later he studied theory, organ, and composition with Joseph Rheinberger and piano with Karl BMrmann at the KHnigliche Musikschule in Munich.

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In 1883 Thuille began teaching piano and theory at the Kgnigliche Musikschule and in 1888 he was promoted to full professor. replaced Rheinberger as Professor of

Cc~~osition

Thuille

in 1893 and remained

in this position until his death on February 5, 1907. Thuille 1 s accomplishments as a teacher were first rewarded in 1883 when he received a grant from

t~e

Frankfurt-am-Mainz Mozart Foundation.

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As a testimony to his stature, many awards were named in his honor. Among them are the Prinzregent Luitpoldpreis, the Ludwigs-Medaille ftlr Kunst und Wissenschaft, and the Ludwig Thuille Grant awarded by the Berlin Akademie der KUnste. Rudolf Louis was born on January 30, 1870, in Schwetzingen, Germany, and died November 15, 1914, in Munich.

His grandfather, Daniel, was a

highly respected teacher of philosophy and had a great influence on

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Rudolf.

After graduating from the Heidelberger Mittelschule he served

in the military in Heidelberg.

In 1889 he began studying Philosophy

in Geneva, but later in Vienna he became interested in music, and graduated from the University of Vienna with a thesis on conflict in music.

L":,;;!is continued to st:.Jdy composition with Friedrich Klose and

conducting

~rith

Felix Mottl in Karlsruhe.

In 1897 he travelled to

Munich and succeeded H. Porges as music critic for the Hllnchner Neusten Nachrichteno

In Munich Louis developed a close friendship with Thuille,

and fn 1907 both men published the first edition of the Harmonielehre.

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/ xv

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MOTTO Nothing appearing to us in experience can be discussed or expressed in an absolute manner, but always carries a limiting condition, such that we may not call black, black and white, white--even though they may appear to be so. Thus every attempt, be it what it may and regardless of what it manifest, bears within itself a secret enemy which limits and renders uncertain everything that the attempt, a potiori, shows. This is the reason why one does not get very far through teaching and instruction; only he who takes action--the artist who grasps the Truth and knows how to bring it to fruition--is decisive.

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Goethe

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2

(_) FOREWORD TO THE FIRST EDITION The present book owes its creation to a need of which the authors became increasingly aware from year to year during the course of their teaching.

The conviction that this need not only for a practical theory

of harmony but also for one which satisf_i_es mOdern requiref!1ents was not an isolated need, but rather, a general one gave the authors the courage to publish their work. Our Theory of Harmony attempts to be both a practical and theoretical textbook.

In this respect, it is differerit from all purely scientific

treatments of the subject dealing only with the theoretical aspect of harmony and ignoring its practical side.

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The present Theory of Harmony

also differs from those methods which teach harmony only in a mechanical manner by means of rote learning.

Such methods which defy any rational

justification or derivation are based on the assumption that no theory in the true sense of the word is needed at all. Our Theory of Harmony contributes to the education of the budding musician in two ways.

On the one hand, the textbook provides theory and,

as such, teaches the essence and meaning of harmonic relationships.

On

the other hand, it provides technique and teaches the practical application of harmony as a means of artistic expression. It was the fate of the older textbooks to neglect the theoretical side of harmony in favor of the instruction of technical skill.

One

can understand to a certain degree, however, why these practical textbooks displayed an aversion to all types of theorizing if one considers

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that harmonic theory until now was mainly concerned with harmonic speculation, i.e., a dogmatic and uncriticai kind of theorizing.

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3 Practically speaking, such theorizing was actually val id only in a few cases and therefore was tota 1ly use less due to its lack of "respect for the facts. 11 This respect makes it impossible for the human imagination to replace reality with arbitrary philosophical hypotheses.

Such

harmonic speculation does not describe reality, but is involved with the creation of bound' ess fantasies.. .. .... As a result, we weie especially careful to assune a strictly empirical standpoint and to maintain it vigorously. of harmony, as we conceive it, is the

analy~is

The point of departure of phenomena heard by the

musician of our time and culture not only in terms of chords but also In terrns of their connections. This analysis is to be done in the most accurate and most exhaustive manner possible, uninfluenced by any kind of theoretical prejudice. The d.eclarations of ac·tual musical perception and interpretation provides empirical data.

The most complete and simple comprehensive

descripti·on of empirical data (see Hans Cornelius, Psychology as an Empirical Science, page iii) Is the true task of the theoretical side of harmonic theory.

This description acquires a rational characteristic,

i.e., it becomes explanation and definition precisely because it behaves in a comprehensive manner.

Such description therefore makes possible a

mastery of the infinite phenomena of reality by the methodical means of derivation, i.e., correlation.

By discovering similarities, finding

analogies, and grouping, identifying, separating, and combining phenomena having a common characteristic, this description can be reduced to a rel.atively smal 1 number of ·simple formulas. ~

The descrip-

also succeeds in explaining an immense number of concrete facts

through only a few basic paradigmatic facts {Goethe's Primordial

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4 Phenomena).

These basic facts can also be derived in reverse, from the

concrete facts themselves.

We were careful, however, not to let this

process of simplification degenerate into a falsification of the facts. On the other hand. it is impossible for reality not to be altered once it has been affected by theory.

It is also impossible for theory accur-

ately to describe reality because of the nature of the relationship between the subject and object.

The characteristic power of our intel-

lect is its ability to conceive of the specific in terms of the general, and the general in terms of the specific.

Even the smallest phenomenon,

however, is essentially an individual and unique entity.

It immediately

ceases to exist as such if we ascribe to it a general concept. degree then, all theorizing is a problematic undertaking.

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To this

We wished to

acknowledge our awareness of this problem by proclaiming Goethe's words as the motto of our Theory of Harmony. A few additional comments about the practical side of our Theory of Harmony are needed to complete these brief remarks concerning our interpretation of its theoretical side. In contrast with most older textbooks, we have placed more emphasis on the theoretical side of harmonic theory and have especially tried to cite and accurately analyze many examples from music literature in order to achieve a more vivid understanding of harmonic relationships in a concrete musical art work.

We must, however, not neglect the other side of

teaching harmonic theory, i.e., imparting proficiency in harmonizing a simple setting.

The instruction of harmonic theory must satisfy two

contrasting requirements.

On the one hand, our book must fulfil 1 modern

needs and discard the obsolete system of rules contradicted by the modern free development of musical perceptions and formations.

On the other

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hand, we must not let the entire theory of voice-leading and harmonic realization become ruled by anarchy and unrestraint. We believed that we could achieve a balance between these two contrasting requirements by recognizing that one may never say principle not only true of politics but also of music. nothing which is forbidden. The conclusion

~r~wn

11

never 11--a

There is actually

Anything is possible in the hands of a master.

from this undeniable fact, however, is not that the

exceptions should be discarded because of the rules, but rather that the system of rules must be rationalized in order to be able to affirm their validity and justify exceptions without contradiction.

If we ask not only

why a given rule was formulated, but also what requirements of musical perception and understanding are satisfied by following such a rule, it becomes apparent that the traditions of the past can be maintained in most cases with only a few modifications. only if

11

do 1 s 11 and

11

This tradition can be maintained

don 1 ts 11 are not considered to be absolute, but are

formulated hypothetically rather than categorically. ·Although we may believe that we are at the 11apex of our time" with respect to our theoretical formulations and practical instruction, a certain conservatism can be noticed in our treatment of the pedagogical questions in our Theory of Harmony.

We consider this conservatism to be

completely justified since it puts in perspective the effort of writing a modern theory of harmony and expresses the idea that in art the subject of'the theoretician is always the result of the efforts of the practitioner.

Nothing productive was ever achieved, however, when the two

exchanged roles.

In such a case, the stimulus for progress came not

from the reflection of the thinker but from the living instinct of the creative genius.

Munich.

January, 1907.

The Authors.

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THE FOREWORD TO THE SECOND EDITION

It is most unexpected and surprising for me to be in the position of

~urrently

writing a preface to the second edition of this book only

a little more than a year since its first appearance. r· •

me great satisfaction. cerning the death of perhaps would not

I am nevertheless struck with deep sorrow con-

Lu~wig

h~ve

This has given

Thui11e, without whom this Harmonie1ehre

emerged and in any case would not have become

what it is. Our book was completely set in type

but was not yet published when

Ludwig Thuille suffered sudden death at the age of forty-five on Fe~ruary

5, 1907.

Like a bolt of lightning out of the blue, this unexpec-

ted catastrophe struck the relatives and friends of a man who was always revered as the very model of inexhaustible vitality. the least expected his approaching end.

No one In

I was granted the good fortune

of personal contact with ThuilJe and realized the tremendous loss we all feJt at the untimely death of this great artist and splendid human being.

Even those not closely associated with Thuille can somewhat

sense the significance that this loss has had for me, not only from a purely personal viewpoint, but also in terms of his contribution to this book as its co-author. Munich.

Early 1908.

Rudolf Louis. /

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FROM THE FOREWORD TO THE THIRD_ EDITION Three and one-half years after the first appearance of nielehre a third edition has become necessary.

our~­

The form given to this

edition may well serve as the final version of our method.

It differs

from the second edition since it includes the changes originally made in the student edition (Grundriss der Harmonielehre by Rudolf Louis, Stuttgart, Carl Gr'.1ninger, first appearing in 1908), i.e., the addition of an introductory chapter treating the preliminary concepts of harmony and the change of the order of ideas in the chapter on triad inversion. In particular, the theory of suspension and passing sixth chords and six-four chords is presented in this edition before the discussion of

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the practical application of sixth ehords and six-four chords as genuine triadic inversions. As a result of both my experience and my colleagues' experience in using this text,

have also chosen to make an unusually large number

of small improvements in not only the text, but also the examples, and to increase the number of examples for the purpose of illustration. These additional examples are taken especially from the most recent music literature, for example Strauss• Elektra, etc. Finally, every admirer of Ludwig Thuille--i.e., certainly anyone utilizing this book--wfll consider the complete list of compositions published by the prematurely departed master a valuable addition to this text. Riedering.

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August 1910.

Rudolf Louis.

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FOREWORD TO THE FOURTH EDITION The fourth edition of this book ts an exact reprint 9f the third with the exceptior. of only a few improvements and additions. one-half years after the appearance of the third has already become necessary.

editio~,

Two and

a new edition

This gives me the assurance that our

Harmonielehre, as it stands, has proven itself to be a necessary addition to this area of instruction. Both a workbook supplementing the practical part of the textbook and an answer-book have rece,ntly been published.

The answer-book

contains solutions not only to the assignments in the textbook but

~lso

to those in the workbook. These two supplementary books complete our publications related to the Harmonielehre.

Everything has been done to render our method as

useful as possible, even in terms of self-instruction. Munich.

March 1913.

Rudolf Louis.

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9

(_) TABLE OF CONTENTS PRELIMINARY CONCEPTS:

What is Harmonic Theory? Dissonance.

Consonance and

Major and Minor Triad. Relationship of

Theory of Intervals.

17

Triads FIRST PART: THE DIATONIC CHAPTER I.

§ 1.

The Primary Triads of the Key

Preliminaries. Arrangement of the Major Key into

23

its Three Primary Triads §2.

Characteristics of the Mutual Relationships of the

26

Three Primary Triads Connection of Primary Triads.

Four-Voice Setting

Various Forms and Positions of the Triads Types of Voice-Mov~nto

30

32

Voice-Leading__ !\u,es.

Connection of the Tonic with Both of its 34

Dominants

§6.

Progression from the Subdominant to the Dominant. 36

Para 1lel Unisons and Octaves

§ 7.

Parallel Fifths.

§ 8.

Arrangement of the Minor Key into its Three Primary

Antipara'flels.

Liberties

Triads

§9. CHAPTER II. (

§lo.

The Three Types of Minor Scales

39

45

47

Sixth Chords and Six-Four Chords Derivation of Sixth Chords and Six-Four Chords through the Inversion of Triads • • • • •

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51

10

Application of Sixth Chords and Six-Four Chords as Triad Inversions ••

§ 12.

Non-Harmonic Tones.

53

Auxi 1 iary Tones.

Suspensions.

Derivation of Sixth Chords and Six-Four Chords through S'uspens ions • ~13.

............

62

Effective Dissonances and Conceptual Dissonances (Pseudo-Consonances)

§14.

65

Derivation of Sixth Chords and Six-Four Chords through Auxiliary Tones and Passing Tones •

§15.

Consonant Chord and Consonant Interval.

67

The Sixth

and Fourth as Consonance and Dissonance • •

(

)

§16.

69

Application of Six-Four Chords and Sixth Chords as

-'

Suspension Format ions

..............

72

§17. Application of Six-Four Chords and Sixth Chords as Passing Format ions CHAPTER Ill.

..........

82

The Dominant Seventh Chord and Dominant Ninth Chord

§18. Formation of the Dominant Seventh Chord. Resolution of the Seventh.

Various Positions and Inversions

of the Dominant Seventh Chord ••

§19.

Preparation of the Dominant Seventh.

90 Voice-Leading

Rules for the Introduction and Continuation of the Dominant Seventh

Chord~

Irregular Resolution

of the Leading-Tone and the Dominant Seventh

§20.

96

Practical Application of the Dominant Seventh Chord and its Inversions.

Perfect and Imperfect

Authentic Cadence •

....... .....

• •• 103

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11 .

(_ / . - ....

~,,

§21.

The

Formation of the Dominant Ninth Chord.

110

Dissonance of the Ninth • • • • • • §22.

The Various Positions and Inversions of the Dominant Ninth Chord.

114

Secondary Harmonies in Major

Clil\PTER IV.

§ 23.

The Second Scale Degree tn Major

122

§24.

The Thi rd Sea le Degree in Major •

131

§25.

The Sixth Scale Degree in Major •

§26.

The Seventh Scale Degree in Major

§27.

The Tonic and Subdominant Seventh Chords in Major. Sequences.

(

Its Preparation and Resolution

..

.• .. . ~

... ........

Summary •

142

148

Secondary Harmonies in Minor

CHAPTER V.

§30.

..... The Third and Sixth Scale Degree in Minor . . . . The Seventh S~le Degree in Minor • . . • . . . .

§31.

The Tonic and Subdominant Seventh Chord in Minor.

§28. The Second Scale Degree in §29.

136

Sequences. CHAPTER VI.

Mi~or

161 164 169

175

Summary •

Expanding the Concept of Tonality

§ 32. The Natural (Aeolian) and Dorian Minor

.......

181

§33. The Chords of Aeolian and Dorian Minor. Application of Aeolian Minor. Use of Dorian Minor.

Sunmary Sunrnary •

..

....

Major-Minor and its Use ••• CHAPTER VII.

§ 36.

186 191

194

Incidental Harmonic Formations

Review and Expansion of the Concept of the Suspension and its Application

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200

()

12 Various Types of Suspensions and their Resolutions

208

The Passing Tone ••

222

4

•••

Auxiliary To:ie and Anticipation CHAPTER VIII.

227

Diatonic Modulation

§40. The Nature and Different Types of Modulation. Modulation by Means of Diatonic Substitution • §41.

Overview of Diatonic Substitution Possibilities

§42.

Consonant Triads as Means of Diatonic Modulation

§43.

Inversions of Consonant Triads and Dissonant Chords

...

..... ... •

as Means of Diatonic Modulation

237

240 243

250

SECOND PART: THE CHROMATIC AND ENHARMONIC

(

CHAPTER I.

Chromatic Progression The Nature and Concept of Chromatic Progression The Cross-Relation

... .... ..... . . . .

257

261

CHAPTER II. Altered Chords §46.

The Nature and Purpose of Alteration. Raising the Subdominant

§47.

Chromatically

. ....

The Diminished Third and Augmented Sixth.

267 Chords

with Augmented Sixth • • • • •

§48.

Resolution of the Augmented Sixth. Diminished Third.

272 Chords with

The Diminished Seventh Chord

with the Chromatically Raised Fifth. Sea Jes • • • • • • • • • • •

(

§49.

Gypsy

. . . .. .. . . ..

277

Chromatically Raising the Second Scale Degree. Possibility of Further Upward Alteration •

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283

13

§ so.

Lowering the Second Scale Degree

286

§51.

Neapolitan Sixth Chord •

291

§s2.

Lowering the Subdominant in Minor.

Combination of

Several Alterations in One Chord ••• CHAPTER Ill.

§ 53.

.....

Chromaticism as a Means of Modulation

Concept of Chromatic Modulation.

The Change of Mode

of the Consonant Triad •

309

~54.

Further Chromatic Alteration of the Consonant Triad.

316

.§ 55.

Chromatic Altera·t ion of Dissonant Chords

320

§56.

Continuation • • • • • • • • • • • • • • •

326

CHAPTER IV.

Chromatic Auxiliary Tones, Suspensions and Passing Tones.

(

Further Types of Incidental Harmonic

Format ions

§ 57.

The Chromatic Formation of Auxi.liary Tone!i. Su.spensions and Passing Tones

. 337

§ 58.

Orthography of the Chromatic Sea le

§59.

The Concurrence of Chromatically Different Tones Belonging to the Same Scale Degree • • • • •

§'60.

Interpolated Chords. in

a Chromatic

CHAPTER V. \

\

§64·

341

346

Succession of Similar Harmonies

Passage ••

352

...

Peda 1 Po int

(

299

360

Rules for the Use of Pedal Point. Sustained Voices •

364

S yncopa i: ion.

371

Ooubie Harmonies

Enharmonic Modulation Enharmonic Change and Enharmonic Reinterpretation. Modulation by Enharmonic Change

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376

§ 65.

Enharmonic Reinterpretation of the Diminished • 381

Seventh Chord ,. • • • • • • • • • • • • •

§ 66.

Enharmonic Reinterpretation of the Augmented Triad •• 386

§67.

Enharmonic Reinterpretation of the Augmented SixFour Chord

§68.

• • • 390

Further Enharmonic Reinterpretation

CHAPTER VI.

((

• • • • • •

• • 395

Summary

§69.

Combining Consonant Triads with Each Other (Table) •• 403

§70.

Concerning the Third Relation •••

• 407

§71. §72.

Concerning the Whole Tone Row •••

• 413

Combining the Dominant Seventh Chord with Consonant Triads (Table)

'

§73.

. . . . . . . . . . . . . . . . • 417

The Diminished Seventh Chord in its Relation to the Consonant Triad and the Dominant Seventh Chord • 423

(Tab le) • APPEND IX I:

Examples of the Chromatic and Enharmonic in Music Literature

. . . . . . . . . . . . . . . . . . •• 428

APPEND IX I I :

Concerning the Prohibition of Parallels •

APPENDIX 111:

Concerning Church Modes and the Exotic

. . . •• 465

(

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478

15

TABLE OF ASSIGNMENTS 1.

Presentation of All Major Keys (Triads of the Tonic, Dominant, Subdom inant) • • • • • • •

2.

...........

26

Four-Voice Realization of Major and Minor Triads in Different Position--i.e., in Close. Open, Octave 9 34

Third and Fifth Position

3. Connecting the Tonic to its Two Dominants •

36

4. Eight Short Melodic Passages in Major (in the Soprano) with the Exclusive Application of the Triads of I, IV, V (in Root Position). All Passages are to be Harmonized in Four Voices •

43

5. The Same as Number 1, but in Minor

..........

47

6. Six Melodic Passages in Minor. as in Number 4 •

49

7. Formation of the Sixth Chord and Six-Four Chord

52

8. Sixteen Figured and Unfigured Basses and Sopranos to be Harmonized in Four Voices with the Application of I 9, IV• and V in Root Posit ion and in lnvers ions

9.

.....

57

Fifteen Assignments to be Completed in the Same Manner as Number 8 with the Application of Suspension Sixth Chords and Six-Four Chords

10.

............... ..

78

Eight Assignments Appearing in the Same Hanner as Number 8 with the AppUcation of Suspension and Passing Sixth

86

Chords and Six-Four Chords • • • • • • •

(

~ominant

Seventh Chords (V7,

V~,

vj,

V~)

11.

Formation of

12.

Twelve Figured and Unfigured Basses and Sopranos for the

95

Application of Dominant Seventh Chords and their Inversions ••

............ ..

• • • • • 108

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16 13.

Six Assignments Involving the Dominant Ninth Chords and their Inversions

14.

""

. . . . . . . . . . . . . . . • 119

Thirteen Assignments for the Application of Secondary Triads and Secondary Seventh Chords Appearing in Root Position as well as in their Inversion - in Major •

15.

...

• 157

Twelve Assignments for the Same Applications as in Number 14, • 178

but in Minor • • • • • • • • • • • • • I

16.

Fourteen Assignments for the Application of the Harmonies of Aeolian Minor, Dorian Minor, and Major-Minor • • • • • • • 196

(\

17.

Fifteen Assignments for the Application of Suspensions

18.

Twelve Assignments for the Application of Passing Diatonic Voice-Movement •••

...

.....

217

• • • 231 244

19.

Diatonic Modulations

20.

Twenty-Four Assignments for the Application of Altered Chords in Minor, Major, and Major-Minor

21.

•• 305 • 331

a) Chromatic Modulation •• b) Twenty-Three Assignments with Chromatic Digressions

22.

332

Twelve Assignments for the Application of Chromatic Passing Movement • • • • • • • • • • • • • •

•• 354

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17

PRELIMIW\RY CONCEPTS Simultaneous sounds (chords) are the basic elements of harmonic

1.

Harmonic theory ts the study (i.e., description and explanation)

theory.

of chords, their formation and juxtaposition, their mutual relationship, and the ma1111er and way of their succession ("progress ion").

It teaches

us to understand and apply chords. 2. All conceivable musical chords are either consonant or dissonant.

A chord is consonant if its components blend into a tonal iden-

tity that gives us the impression that the tones belong together, go well with each other, and are compatible with each other.

On the

other hand, we speak of a chord as dissonant if the simultaneous tones

(·

do not sound

11

united11 but

11

divergent11 •

Tiley quarrel with each other,

so to speak, creating the impression that one tone wishes to displace the other.

3. There are only two types of consonant chords: 1.

The major triad

II 2..

and

The minor triad

Every chord which is not a major or minor triad (or constructed in the same way or from the same tones) is a dissonant chord. 4.

We are able to determfoe chord type by differentiating the

pitches of its structural components.

( \

for such differentiation .

A fixed measurement is needed

The distance between two tones, the interval,

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()

18

is this f txed measurement.

The criterion for measuring the interval

yields the seven tone (diatonic) basic scale: 3.

~~)

•1.

""'2.

ti

.3.

22

4.

?2

s

ea

s

5.

6.

1•

8.

= 1.

Latin nunbers are used for the designation of intervals correspondin g to the individual scale degrees.

The intervals are accordingly named

as fo 1lows:

(

.

...

From the first to the first degree:

Unison

From the first to the second degree:

Second

From the first to the third degree:

Thi rd

From the first to the fourth deg;ee:

Fourth

From the first to the fifth degree:

Fifth

From the first to the sixth degree:

Sixth

From the first to the seventh degree:

Seventh

From the first to the eighth degree:

Octave

The ninth degree corresponds again to the second, the tenth to the third, etc., such that the intervallic relationship and designation are similarly repeated in the higher octave, although in certain ctrcumstances it ts necessary to designate these intervals exceeding the octave with specia 1 names.

(

The intervals are then cal led:

From the first to the ninth degree:

Ninth

From the first to the tenth degree:

Tenth

From the first to the eleventh degree:

Eleventh

From the first to the twelfth degree:

Twelfth

From the first to the thirteenth degree: Thirteenth

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(

19 \

.

s.

Inversio n of Interval s - An interval is inverted if either the

upper pitch is displace d an octave lower, or the lower pitch is displace d an octave higher. a) Third lnversio n:Sixth

b) Unison lnversio n:Octave

??all

illn 3

By means of inversio n, the unison becomes an octave, the second a seventh, the third a sixth, the fourth a fifth, the fifth a fourth, the sixth a third, the seventh a second, and the octave a unison. The sun of the nunbers correspo nding to the original interval and its inversio n is equivale nt to 9. 1 2 3 4 5 6 7 8 +s 1 6 s 4 a 2 1

9 9 9 9 9 9 9 9

6.

Just as all tones which are not present tn the basic scale can

be obtained by chromat ic alterati on (raising or lowering tones in this basic scale), so can all interval s be derived from the interval lic relation ships also presente d in the basic scale.

The interval of a

third for example is represen ted not only by c to e, but also by the b interval s between any altered c and any altered e, for example c-e ,

c#-eb,

c-e!I,

etc.

In this way there are differen t types of thirds,

seconds, sixths, etc.

Charact eristic adjectiv es are needed to differen -

tiate between these subcateg ories, i.e., interval s appearin g to be dif~ ferent but actually belongin g to the same scale degree.

(

Such adjectiv es

are perfect, major, minor, augmented, and diminish ed.

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20

The following table gives a summary of all intervals that generally occur in harmonic relationships:

2. Second

1. Unison

~-J,,

.... .. I• II •

perfect

aug.

t&1 • po • minor 5. Fifth Pi

iS'

• •dim. perfect

aug.

aug.

dim.

dim. perfect 6. Six th

aug.

.. ffi4.. I .. ..Gd

8.

·dim.

lw

fa&

aug.

t--11 @=-4?# I fb : • I• • · • aug.

;;ii,.. P9 I

•

Q

major

minor

minor

dim.

7. Seventh

(

•

s

ma ior

Eb

I

l7ii

3. Third

major

8. Octave

sfl

minor major

I•

?2

I

•

?2

ttr@ •

= £ 3¥110= J> -t 11 Tenor

2

(

2

3 The movement V - IV is not one of these natural and autonomous combir1ations of primary harmonies. It can be clearly seen that al 1 progressions of primary triads are in some sense cadential movements, except this progression V - IV. The subdominant, however, whenever it follows the dominant does, not have the power to function as a momentary resting poir1t or even as a point of relaxation within the harmonic progression.

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31

(

Although these ranges are useful most of the time, one should not be meticulously bound to them particularly if the practice exercises have a pronounced instrumental character. The beginner, especially one who is trained on the piano. will have a tendGncy to hear and perceive each chord as an inseparable complex, an unanalyzable entity, i.e., a mass of sound which could be better judged only in relatfon to its overall timbre, but not with respect to its particular formation. the outset.

This tendency must be counteracted from

According to harmonic theory (in contrast to contrapuntal

theory) simultaneous sounds· are actually ready-made entities or 11

chords 11 •

From a practical point of view, however, the goal of harmonic

theory as the preliminary step to counterpoint is the study and realiza-

(.

tion of polyphonic settings.

The interpretation of chords as ready-

made complexes is only an abstraction, or an i 1lus ior., so to speak. Chords are not ready-made entities but :n truth are newly formed wherever and whenever they appear _in polyphonic settings. movement and interaction of the individual voices.

They result from the Therefore in per-

forming and evaluating chord combinations we must never limit ourselves to regarding chord progressions as ready-made entities in themselves. One must constantly realize that each voice has a relative independence and individuality.

The movement of each voice as well as its relation-

ship to the movement of the other voices is of the greatest

importa~ce.

It must be mentioned that it is not important that a G major triad follows an F major triad.

However, it is important how the second

triad is reached from the first, ha.-1 the individual voices move and the manner in which the resulting intervals are related to each other.

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32 If in polyphonic setting the individu al voices are consider ed to be relative ly independ ent, even though they are closely related to each other by belonging to the same chord, it is advisab le for the student to imagine his exercise s actually performed by four differen t people, four singing voices, or four instrune nts, and even have it performed as such whenever possible .

While completi ng the exercise s in this book the

student should always first consider which chord is to be used with each harmonic change.

By doing this, the progress ion of the bass is obtained .

The student should then consider into which note of the chosen chord each If the upper voice is given,

one of the other three voices must move.

the student should consider into which note of the chosen chord each

c

one of the other two voices must move.

At the same time the student

should be certain of the intended vo ice-movemen-t';·---

S4.

A four-voi ce chord is produced by doubling one chord tone.

With

~

primary triads doubling should be done first with the root, and then with the fifth.

As a rule, doubling the

thi~d

of a triad is to be

avoided if this tone function s as a leading- tone.

In particul ar, the

third of the dominant as a subsemitonium modi, i.e., ascendin g leadingtone to the tonic, is never to be doubled in settings of four or less voice parts.

(See page38 f.for the reason for this prohibit ion.)

It is frequen tly necessar y to omit a tone of a triad. obviousl y never occur with the root.

This can

If the root is anitted the triad

itseif would no longer exist and something entirety differen t would take its place. The fifth, however, can be omitted, because the resultin g interval of a third is capable of function ing as a perfectl y sufficie nt represen tative of the triad.

A triad without the third is also possible , but

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()

~

33 it sounds rather empty, its basic character being missing.

It remains

Uhcartain whether the open fifth should act as a substitute for a major triad or a minor one. The third of a triad is omitted only if this empty and ambiguous effect is desired.

(Recall, for example, the opening bars of Beethoven 1 s

Ninth Symphony, the opening of the Overture to the Flying Dutchman, the end of the first movement of Liszt's

~and

of Bruckner's Ninth

Symphony, etc.) Ancient music theory did not recognize the consonance of the major and minor third.

This resulted in the traditional distinction of perfect

consonances (un Ison, octave, fifth, fourth) and imperfect consonances

(.:

(major and minor thirds, major and minor sixths).

The alleged "imper-

fection 11 of the consonant third prevented masters of this older church music from

en~!ng

a composition with the complete triad.

We therefore

associate the specific effect of cadences containing an open fifth with the idea of the archaic church.

The archaic sounding church style of

modern times (Liszt, C~cilianer) frequently utilizes this effect. A chord may have different positions, i.e., different ways of grouping the individual voices.

We call these positions close and open.

With

the former, the voices seem to be pushed very close to each other, such that no other tone of the same chord can be found between two neighboring voices.

With the latter, the individual voic·as are placed further away

from each other than with the former.

A chord is also in close position

even if the bass is far away from the tenor as long as the upper voices

(

are in close position.

A four-voice chord is in mixed position if two

voices are in close position and two in open position.

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()

· It is advisable for reasons of timbre not to let the distance between two neighboring voices become too wide.

The interval between

the soprano and alto should never exceed a tenth. and the interval between the two inner voices should not exceed an octave.

The distance between

the bass and tenor, however, can exceed the interval between the soprano and alto. The tonic, third, or fifth of the triad can be in the upper voice.

(

Accordingly , we can differentia te the octave, third, and fifth positions of chords.

In the example above (14a and 14c) the C major triad is in

octave position, in 14b and d in third position, and in 14e, f, and g fifth position. The root on the other hand must always be in the bass unless we wish to create a formation other than a triad (in the true and narrow sense of the word) (see page 51ff.}. Assignment No. 2:

The student is to write the major and minor triads

in various positions in four voices, i.e., in close position, open position, octave position, third, and fifth position.

§ 5.

In every chord progression at least one voice must progress, i.e.,

change to another tone.

Voices can ascend or descend by means of either

a step or leap.

(

A threefold relationship is possible between two voices in all of these types of progression s.

Both voices can either move in the same

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( I

35

. )

direction (similar motion, motus rectus), or one voice may ascend while the other descends (contrary motion, motus contrarius), or one voice may move, while the other remains on the same tone (oblique motion, motus ob 1lquus). 15. .

Similar motion

1.

b.

II.

d.

C.

t~. ? F1qkp1Ffi l~I Contrary motion

2.

..J

biJ

f'

c.

b.

L

ct

~ 1@¢Jtd ~I~

J

ti

3. Oblique motion b.

L

1~ g ;J 1411 ~

(

C.

J

13

11

F r 1;

Parallel motion is produced if the intervallic distance between two voices in similar motion remains the same (as in examples 15 12 and 15 lb ). Antiparallel motion is produced if two voices move in contrary motion as is shown in 152d. Two successive chords will either have one (or several) tone(s)_ .in common with each other, or the second chord will consist of tones not yet contained in the first.

Since the relationship between two chords becomes

evident through their common tones, it is advisable always to retain all possible common' tones in the same voice in a given chord progression ( 11

1eave them alone").

Chords are combined in this manner only if other

melodic considerations do not come into pla_y, i.e., they are combined as (

such to show their mutual re.lationship within the chord pro_gression in

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the most obvious manner. Just as the mutual relationship of two given chords is emphasized, so too is their melodic relationship emphasized by allowing the moving voices to proceed to the closest available tone of the second chord by step or by a minimal leap.

The effect of a close connection of successive

chords will be essentially heightened if progressions by half-steps (leading-tone movements) are applied whenever possible. The third of the dominant especially demands resolution to the tontc--a requisite which can only occasionally be avoided in cases of sufficient motivation (see pages 43 and 99ff .) Assignment No. 3:

The student Is to connect the primary triads of

various major keys in different positions--triads which have one tone in comnon, i.e., I - V - I and I - IV - I. ~6.

The solution to the preceding assignment will demonstrate that

connecting these fifth-related triads offers no further difficulties.

The

attempt to combine two triads not directly related, such as the subdominant with the dominant, is something entirely different and gives rise to several important observations. If the progression IV - V is performed in the following manner:

alt voices would proceed uniformly in similar motion, such that the mutual intervallic relationships remain the same as they were prior to the

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(_)

37 progression. An exact duplicate in precisely the same position follows the first major triad. If two voices in perfect unison proceed by step or leap in the same direct ion to another uni son, so-ca 1 led "para 1le1 un isons 11 are created.

rt

17·a ?h

II

?? ::5!'-

31 I ; a ::1:1

It is easy to comprehend that the two voices do not move differently, but rather in exactly the same manner, such that we are actually not dealing at all with two-voice motion but only with a single doubled vo.ice.

Par-

allel unisons are absolutely incorrect wherever several voices move independently-- that is to say, in every polyphonic setting (see page 32).

The ·reason for this is that when

two

voices move in parallel

unisons and merge into one voice, one of the voices loses its independence and no longer functions as a vocal "individual" but becomes a doubled voice part functioning merely as a reinforced sound.

Precisely at the

moment that two voices progress in unison in a four-voice setting,

four voices no longer actually exist. A three-voice setting appears in its stead, thus contradicting the very concept of four-voice setting. Consonance of the perfect octave is so strong that two tones an octave apart give us the impression of being identical.

(

Although c 1 is

actually a different tone than c, we speak of both· tones as being different

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38

positions of one and the same tone.

A result of this octave equivalency

is that parallel octaves, i.e., progressions of one perfect octave to another in similar motion, are to be considered exactly the same as parallel unisons and are to be avoided in true polyphonic settings. Tones having a strongly pronounced leading-tone characteristic are especially prominent precisely because of their tendency to stand out strongly from within any chord.

Their Inherent tendency to demand resolu-

tion automatically draws attention to itself.

The reason for this is

precisely that every leading-tone is a sensitive tone, especially if it is a descending leading-tone (11 note sensible" in French). 4 Its doubling has little justification. One must also realize that doubling a leadingtone, i.e., a tone having a strong tendency to progress In a completely defined manner, constantly creates the danger of parallel unisons or parallel octaves.

The third of the dominant, therefore, is never to be

doubled in settings of four or less voices. If two voices proceed from an interval other than a unison (or octave) to a unison (or octave) in similar motion, so-called octaves) are created.

1

11

hidden 11 unisons (or

'0pen 11 parallels of this kind are created if a

unison or octave is the interval from which both voices proceed. a. Op.en 19 • 1

&1

dnfa ~

11

P#

b. Hidden 11

#f111

t:; t# 11

11

The reason given for the prohibition of parallel unisons and parallel octaves needs at least one modification in order to be valid also for progressions of hidden unisons and hidden octaves.

(

Different movements

4 [According to the authors, a leading-tone can ascend or descend depending upon whether it is an upper half-step auxiliary or lower halfstep auxiliary.]

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39

are actually created by each voice of a

11

hidden

11

parallel, but they do

Their point of origin is different and

have two elements in common.

their direction and destination are the same.

Both voices are similar

to two travelers who begin their journey from different places, meet along the way, and travel the rest of their journey together.

In certain

cases their movements can be so similar that the effect of the movement can be much like that of parallel octaves or parallel unisons.

The

attempt to describe such cases more accurately appears in Appendix II. For the time being, however, it is sufficient for the teacher to make the student aware of the characteristica lly empty impression of such ~~rallels.

An ear thus educated will rather quickly succeed in deter-

mining which hidden unisons and hidden octaves are acceptable and which

(;

ones are not.

Our first assignments do not offer the student much oppor-

tunity to create decisively inferior progressions, but it

~ould

be better

for the beginner to risk a questionable hidden octave or un,ison just once than to create

progressio~s

containing unnatural forced voice-leading by

too cautiousiy avoiding all hidden parallels. ~

7. Let us now attempt to avoid parallel octaves which can occur in

progressions from the subdominant to the dominant by means of the utilization of contrary motion:

20.

A satisfactory result is not yet achieved in this manner.

(

Two kinds

of parallels remain even after the parallel octaves are eliminatedo The bass and soprano proceed from a perfect fifth to a perfect fifth

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40

creating parallel fifths.

The bass and alto proceed from a major third

to a major third resu 1ting in para 1le1 major thirds. Accardi ng to the old rule, progressions i.n parallel fifths are considered just as faulty as those in parallel octaves, and the progression in parallel major thirds is questionable at least.

What was said, however, about hidden

octaves must also be said about parallel fi.fths and parallel thirds, i.e., these progressions are definitely to be questioned only in certain cases, but by no means in all situations.

The reason for for-

bidding parallel thirds and fifths is not as obvious as that given for the faultiness of parallel octaves.

We are dealing here with a rather

ccmplex problem, which is treatedmore thoroughly in Appendix 11. For our present practical purposes the following comments will

(.

suffice.

If two basic harmonies (for example two primary triads) having

no c011111on tones follow each other in independent harmonic movements, one should be very careful to avoid the easily occurring impression of an uncon~ected

and unrelated juxtaposition of the two chords.

This impres-

sion occurs particularly if the position (the mutual interval relationships of the voices) of the second chord is exactly the same as that of the first.

The less the second chord resembles the first with regard to

the arrangement of the voices--i.e., the fewer parallel movements from one chord to another--the more this impression disappears. a.

b.

c.

d.

21.

(

The faulty progression 21a is not improved much in 21b, and even 21c is still rather ugly.

Only when the parallel major thirds are also eliminated

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41

by means of contrary motion, as in 21d, does the juxtaposition of the The close connection previously

two triads become a harmonious fusion.

missing is produced by the three upper voices proceeding in contrary motion to the bass. Accordingly, with diatonic stepwise succession of diatonic triads we must especially avoid parallel fifths produced by the root and fifth of the second chord being in the same respective voices in which they appeared in the first chord.

Such parallel fifths are completely pro-

hibited if it is a question of the piogression of two primary triads as with IV - V, the only progression in our first assignments threatening the danger of stepwise parallel fifths.

A similar but less restrictive

rule applies to parallel thirds produced between the root and third of two major triads progressing stepwise.

Moreover, it is the teacher's

task to make the student aware of the unpleasant sound of distinct parallel fifths and gradually to refine the ear and arouse its sensitivity to the questionable character of such progressions. Hidden octaves and hidden fifths are regarded in the same manner. The tatter are produced by two voices progressing in similar motion from an interval different than a perfect fifth to an interval of a perfect fifth. Parallel Fifths

Hidden Fifths

Today the prohibition of hidden fifths is observed less strictly than that governing hidden octaves.

(

There is hardly any reason to search

for the unpleasant effect of hidden fifths if the chords are connected with good voice-leading and in a fluid manner.

It is advisable therefore

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

(,S F' I r r JIF' s FI r J r IJ. j r

J J I J. J5 JIJ J J 83

12.

Soprano; Open position

13.

Soprano; Open position

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62 14.

tbih "f2 r f I r J 15.

._ 16.

Soprano; Open position

JI J r FItr"F r I f2

r rIr

rIr

r r I II ?)

Soprano; Open position in the beginning

J J. )'

JI J F F r hrl r

r·

r

IF

EFEf@

J J. J' J I J J 1 . If

Soprano; Close position in the beginning

- I tt=e' FU r Eflt CJ I r r I EM kt ~$1n a: fl±Etrt rlqg r IF

( § 12.

· In order· to understand the other type of application of sixth

chords and six-four chords--bein g partially or totally different from triad inversions-- the nature and concept of so-called non-harmonic tones must be understood. Its very name signifies what is meant by a non-harmonic tone.

It

is a tone foreign to the harmony of a chord, does not fit into it and, therefore, clashes with it.

A non-harmonic tone is a dissonance char-

acteristica lly appearing within a chord formation as a foreign element, but not as an element belonging to the chord--in particular, the tone inmediately adjacent to a chord tone. (

I

The tone a second above or

below the chord tone can be introduced into the chord as a non-harmonic

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l)

63 dissonant component.

Thus we obtain the auxiliary tone (in the broad-

est sense of the word)--i.e., a non-harmonic tone temporarily replacing the chord tone immediately adjacent to it.

The auxiliary remains in

this position, and not in its own, untii it resolves, i.e., until the chord tone returns to its proper place and displaces the previous auxiliary. The auxiliary tone appears either on an accented part of the measure--and therefore is a suspension--or on an unaccented part of the measure as an auxiliary tone in the narrow sense of the word.

If

we imagine the entrance of the third of the dominant triad delayed

in the progression I - V,

( C:I

V

such that the alto in the second measure does not immediately take a b but still retains the c of the previous measure and only proceeds to a different tone later, a suspension is obtained.

aa C: I

(

V

I

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64

(_/

A dissonant formation is created. by a foreign tone. the root.

It is a triadic harmony disturbed

The foreign tone in example 38 is the fourth above

It is tied over from the previous triad and temporarily

appears, so to speak, as an upper auxiliary tone to the third of the dominant triad.

The dissonance is resolved when the non-harmonic

suspension proceeds to the chord tone which was previously omitted. If the soprano--and not the alto--is

u~~d

in the formation of

a suspension, as shown in the above connection of I ar.d V triads, the sixth chord g-b-e is produced.

39,

( C:I

V

This sixth chord has nothing at all to do with the inversion of the minor triad e-g-b, but rather is to be considered as a suspension formation in precisely the same manner that the

11

f ive-four chord 11 was in example 38.

The soprano and alto could also s im i 1ar1y create a format ion of a double suspension.

The result is a suspension six-four chord.

40.

C: I

V

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(_)

A chord formation consisting of tones of the tonic triad, therefore, could be interpreted not in the sense of a tonic triad (as its Inversion), but in the sense of a dominant triad (as a suspension to it). ~13.

Of all the possibilities of suspension formations, there are

special cases in which apparently consonant chords occur--particularly sixth chords and six-four chords--and do not differ in appearance from the inversions of consonant triads.

These formations by themselves are

entirely consonant, but are actually interpreted as dissonances due to the musical context.

The triad in question must be related to a func-

tioning root which is dissonant with one or more of its components. H. Riemann named such dissonant harmonies "pseudo-consonances". Their consonance is expressed only in terms of their outward appearance

(

and, therefore, is only illusory.

We would like to suggest the term

"conceptual dissonance" as a far moro descriptive expression of their peculiar character. We are actually dealing with chords always consonant when taken out of' musical context, but which are applied occasionally in· a way which invites their interpretation as harmonic dissonances. When conceptual dissonances actually do occur, the difference between purely acoustical hearing and musical (11 harmonic11 ) hearing is revealed in the most obvious manner.

It is possible, therefore, to speak

of a contrast between acoustic and harmonic (conceptual) dissonances. Acoustic dissonances are always heard as such, while harmonic dissonances in the physical-psychological sense are considered entirely consonant even though they are perceived as dissonances by the musician (and partly also by the psycho-acoustician). Acoustically, dissonance is definitely

(

present, but harmonic dissonance is dormant, so to speak, and only

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66

(/

conceptual--existing in and for the consciousness, but not in terms of its physical appearance.

The characteristic effect of conceptual

dissonances is due to the fact that they are essentially both consonant and dissonant at the same time.

The outer (physical) ear hears them

as consonances, while the inner (intellectual) ear, without a doubt hears them as dissonances. The introduction of the suspension Is possible in two ways: either it is prepared or unprepared (free). The suspension is prepared if the non-harmonic tone existed in the previous chord in the same voice, such that it could be tied over to the new chord.

The suspension is

unprepared if this is not the case; it can be either completely unprepared3 or only half-unprepared, i.e., partially prepared. '

(:

The suspension

is completely unprepared if the tone did not appear in the previous chord at all, and half-unprepared if it appeared in only one of the other voices.

Introductions of unprepared suspensions can result without

harshness if the suspension chord appears in the fonn of a conceptual di ssona nee. a. Prepared

b. Completely unprepared

c. Halfunprepared

41.

C: IV

/

V a: IV · 1

C: IV V

a: V I

C: I

V

3 [Louis and Thuille differentiate the completely unprepared suspension from the appoggiatura, even though their appearance Is exactly the same.]

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( .

67 ._:.'

In the second part of example 41b the subdominant seems to follow the dominant in the key of a minor. This progr ession contr adicts our earli er statem ent (see page 11) that the dominant resis ts progr ession to the subdominant.

The progr ession V - IV - I, there fore, is not

actua lly prese nt at all, but rathe r the progr ession V - I. The six-fo ur chord a-d-f is not the invers ion of the subdominant triad d-f-a , but a suspe nsion of the fourth and sixth to the tonic triad a-e-e .

§ 14.

The auxil fary tone on the weak part of the beat-- auxi 1iary

tone in the narrow sense --is introd uced eithe r by step or leap. In the first ease, the given voice leaves a chord tone by step, proceeds to an upper or lower auxil iary, and then return s to its point of depar ture. L

c.

b.

42. C: I · -

a: I

C:V

-

-

In" the second case, the voice leaps from a given chord tone to the upper or lower auxil iary of anoth er chord tone, and then resolv es to the tone to which the auxil iary belon gs. L

* 43.

*

J C:

(

c.

C: I

a: I

J -

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C.

68 The simultaneous occurrence of two auxiliary tones in the same formation Examples 42b, 42c, 43a, and

is shown in examples 42b, 43b, and 43c.

43b reveal how conceptually dissonant sixth chords and six-four chords are formed as a result of auxiliaries. Another type of non-harmonic tone is created by filling in the leap between two tones in the same voice with a change of harmony {or merely with a change of position or inversion of one and the same harmony).

The passing formation is created in this way; and tones filling

in the leap are called passing tones {see example 44). L

IV C: I c.

IV

I

-

lV

II

.J. C: I

-

C: I

The derivation of a passing sixth chord is illustrated in example 44b, and that of a passing six-four chord in example 44c. It is just as characteristic for the suspension to occur with an accent as it is for the passing tone to occur naturally without an accent, i.e., a passing tone usually occurs on a weak part of the beat {see page 224f). The passing tone has the property of being unaccented in common with the genuine auxi 1 iary tone.

This is not the case, however, if the

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69

\(_.: , '

latter has the character of a suspension.

The passing tone introduced

by step from one chord tone to another is similar to the auxiliary tone

proceeding by step in the same manner. theorists, including

s.

This similarity convinced many

Sechter, to ascribe the general concept of

passing tones to stepwise introduced auxiliary tones.

Such auxiliary

tones are known as so-called "returning passing tones"--certainly somewhat in conflict with the meaning of the word. On page 67 it was discussed how a suspension formation could create the apparent continuation from the dominant to the subdominant.

A pass-

ing tone is also capable of producing the same phenomenon, as shown in 6 example 44b. A passing sixth chord appears between the I and IV chords as a result of the passing tones in the tenor and bass.

(

This sixth

chord would be totally misinterpreted if it were conceived as an inversion of the dominant triad.

Here we are not dealing with two harmonic

movements (I - V - IV), but only with a single movement (I - IV). The theory of non-harmonic tones in this section was discussed only as much as it seemed absolutely necessary to comprehend the derivation of sixth chords and six-four chords.

For more information see page

200ff. ~15.

Correct interpretation of the essence and application of

chord formations ordinarily considered triad inversions is facilitated by understanding that there are basically only two kinds of harmonic consonances: the major triad and the minor triad.

If a given chord

appears to consist of tones of a consonant triad, but is different from such a triad in terms of the arrangement of its tones, such that the

(

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70

(.1

intervals of a fourth or sixth (calculated from the bass},4 occur, we cannot be certain whether such a chord, harmonically speaking, is to be considered a consonant formation or a dissonant one.

The sixth and the

fourth are--in and for themselves--nothing other than unquestionably consonant Intervals: they are consonant only inasmuch as--and as long as --they are interpreted as inversions of the third or fifth.

The reason

for this is that the consonance of a given interval is not the primary factor for determining harmonic consonance.

The consonance of the given

chord (the type of triad), however, is such a factor.

The perfect octave,

perfect fifth, and major and minor third are consonant intervais for the musician because they are components of major and minor triads.

The con-

sonance of a major and minor triad, however, is not governed by the triad's

(:

construction out of "consonant intervals 11 .5

4 See page 51 for the explanation of the harmonic significance of the lowest voice.

(

5 This interpretation is confirmed by the fact that there exists a chord which consists of intervals consonant with each other--at least within the tempered system--and yet perceived as a most piercing _. dissonance. This chord is the augmented triad--c-e-g# for example. This particular triad consists of two major thirds (c-e and e-g#), and its two outer tones are related by an augmented fifth (c-g#)--enharmonica 1 ly the same as a minor sixth (c-ab). One would not have been surprised that this chord is perceived as a sharp dissonance--in spite of its construction out of genuinely consonant intervals--if one had considered that the reason for its dissonance is simply that it is neither a major triad nor a minor triad. (See, for example, Stumpf, Consonanz und Di ssonanz, page 103ff .• ) The point of departure for the acoust i ca 1 concept of consonance and dissonan·ce is the interval. The only proper point of departure for the concept of harmonic (11musica1 11 ) consonance and dissonance is the triad. This latter concept is to be sharply differentiated from the acoustical concept, although both are still closely related. Consonance of major and minor triads is a "primordial phenomenon" in Goethe's sense. (See Goethe, Farbenlehre, Didakt ischer Teil ~ 175.) This phenomenon is an overriding empirical fact, and can be deduced from nothing higher unless one departs from the realm of pure empiricism to stand upon the wavering ground of acoustical or psychological speculation (see also Stumpf, "Consonanz and Concordanz, 11 Zeitschrift fUr Psycholoqie, volume 58).

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71 ·l··.,....' .,

Harmonic context always determines whether the intervals of the fourth and sixth in a given situation are to be considered as inverted intervals--and therefore consonant--or as auxiliary tones (suspensions or passing tones)--and therefore dissonant. An essential difference between these intervals can be discovered if they are compared with respect to their dual nature.

The sixth Is .more easily interpreted as

an interval of inversion than as a dissonance, while the fourth is more easily interpreted as a dissonance than as an inversion of a consonant interval.

This becomes evident if we examine the intervals individually.

If a major or minor sixth appears by itself, it is heard simply as an inversion of a minor or major third and, therefore, as an unquestionably consonant interval.

(

A different interpretation of the sixth--

perhaps as a suspension to the fifth--might be forced upon our senses depending upon the context in which the sixth occurs.

Such an interpre-

tation occurs only if we, for some reason, do not accept the first interpretation.

Our consonant interpretation of the sixth is what

lawyers call eraesumtioiuris;, i.e., the sixth is to be considered consonant until the "opposite is proven, 11 so to

~peak.

The situation is entirely different with the perfect fourth.

If

this interval is heard by itself, it is not first considered to be an inversion of the interval of a fifth, but rather a suspension to the (major or mi.nor) third.

Harmonically speaking, we presume the fourth to

be a dissonance, and yield to the consonant interpretation {as an inverted interval) only if the context forces us to do so. The old controversy concerning the consonance or dissonance of the

(

fourth is therefore resolved beyond the shadow of doubt.

Acoustically

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72 speaking, the fourth is a consonance--in fact, an exclusive consonance. This acoustical concept, however, does not have any influence on the musician at all.

Harmonically speaking, the fourth can be not only a

consonance but also a dissonance--dep ending upon whether it is interpreted as an inversion of the perfect fifth or as an upper auxiliary to the major or minor third (or even as the lower auxiliary to the perfect fourth).

The characteristic musical effect of the fourth is due to the

fact that it can be interpreted as an auxiliary tone, i.e., especially in the case of the open fourth.

The old counterpoint rule--i.e.; the

perfect fourth is to be treated as a dissonance in a rigorous twovoice setting--is a result of this particular interpretation.6

(

§16.

The difference between the immediate interpretations of the

sixth and the fourth has an influence on the interpretation and application of two chords containing these intervals as characteristic components: the sixth chord and six-four chord.

The sixth chord is

most frequently applied as a chord inversion and less frequently as a conceptual dissonance.

(

6 The reasons for the difference between the consonant and dissonant interpretations of the fourth and sixth will not be discussed. Perhaps it should be at least briefly mentioned that there seems to be yet another criterion for determining the consonance and d·issonance of any given interval. This criterion is not considered to be a primary one but rather a secondary one which, in certain cases, is certainly not unimportant. This criterion is the degree of pleasantness of intervals, i.e., their 11 euphony11 • The existence of th is er i ter ion can be proven by the fact that an interval sounds more consonant, the more pleasant it is to the ear. The perfect fourth usually sounds consonant and at the very least is considered to be pleasant. In any case, the fourth is less pleasing to the ear than either the major or minor sixth. This is perhaps the reason that it is difficult to interpret the fourth as a consonance.

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73 The situation is the opposite with the six-four chord: it occurs constantly as a conceptual dissonance (suspension or passing chord), but the possibility of applying the chord as a distinct and pure chord inversion is relatively quite limited. Six-four chord and sixth chord as a suspension chord. The application of

a) The six-four chord as a suspension chord; the cadentia1

if chord

is especially important with respect to the

conceptually dissonant application of chords normally considered as 6 triad inversions. The 1 chord occurs very frequently at cadences and

4

is essentially nothing other than a suspension formation.

Its fourth

and sixth are not inversions of the fifth and third of the tonic triad,

(

but rather a double suspension to the third and fifth of the dominant triad.

This formation delays the expected entrance of dominant harmony

and appears naturally between the subdominant and dominant in the authentic cadence.

This type of close is cadentially very powerful

because the effect of this deiay heightens the tension.

The cadential

six-four chord allows an equal fulfillment of two apparently incompatible requirements: 1) the emphasis on the entrance of the dominant by means of an accent, and 2) the introduction of both the tonic on the strong part of the measure--necess ary for a metrically perfect cadential effect --and the dominant on the weak part of the measure. b.

a.

45.

(

C: I

IV

V (I)

a: I

IV

V (I)

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( -.:

74

.;

The following rules for applying the six-four chord in a cadence are the direct result of the chord's capacity as a suspension formati on: 1•

6 The 1 chord always appears on an accented part of the measure

4

and is resolved to an unaccented part of the measure. 2.

The bass of the 1! chord remains stationary until it subse-

quently resolves to dominant harmony.

3. The tone best suited for doubling is the bass of the i.e., the functioning root.

it chord,

The fourth and sixth, however, as dissonant

tones remain undoubled as a rule in a four-voice setting. 4.

·(·'' .

.

The fourth and sixth most naturally resolve stepwise downward

to their respective tones of the dominant triad. If we interpret the cadential six-four chord as a suspension formation to the dominant chord, this does not mean that its tones are not, in fact, those of the tonic triad.

Harmonically speaking,

however, these tones are not related to the functioning root of tonic harmony, but rather to that of dominant harmony.7

The characteristic

effect of this six-four chord is due to the fact that it is a combination of both tonic and dominant in one and the same formation.

Inter-

preted as such, this chord can be·appi'ied l'nuch more freely than if it were interpreted only as a chord of suspension, i.e., as a chord whose derivation is conceived in the same manner as a suspension.

c·

7 Every six-four chord applied in this manner is in fact what H. Riemann wanted to change into a minor triad--a triad with the fifth as the functioning root. ~]

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75

(_: The interpretation of 1! as a tonic inverston--or at least the

possibility of such--is only secondary to its interpretation as dominant harmony.

The fo 11 owing free reso 1ut ions of accented six-four chords

are perfectly unobjectionable. b.

L

46.

C: lV

V (I

1

V]

IV

V

fl

c:.

VJ

1

d.

IV

V (I

-

1

VJ

a: IV

V [I

Complete absence of resolution to the dominant, however, occurs occasionally in a less restricted style--for example, in the first movement of Beethoven's Ninth Symphony, measure 34f.

Such a phenomenon

is conceivable if we realize that the accented six-four chord does have two possible interpretations. Suspensions of the fourth and sixth over a tonic pitch produce a conceptually dissonant subdominant six-four chord in the same way that the same suspensions over the dominant create a conceptually dissonant tonic six-four chord. b.

L

47.

( C: V

I [IV

IJ

a: V

I (IV

11

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76 If the dominant precedes the tonic as in example 47, an imaginary progress from the dominant to the subdominant does occur (see pages 2·7, 67, and 69).

The double suspension to the tonic appears to be an

inversion of the subdominant triad.

This six-four chord combines the

effect of both subdominant and tonic in the same way that the six-four chord above the dominant combines the effect of the tonic with that of the dominant. In major this same double suspension over the subdominant tone creates an effectively dissonant

v11f

and major sixth (as shown in 48a).

chord with an augmented fourth

Possible application of such a six-

four chord is somewhat limited because the descending movement of its fourth (b in measure 1) conflicts with the leading-tone tendency of the seventh scale degree.

In minor, on the other hand, with the intro-

duction of the natural (unraised) seventh scale degree, the six-four chord in question is a conceptual dissonance (48b). b.

L

48.

C: I

JV

a: I

JV

v

The cadential (conceptually dissonant) s·ix-four chord is normally interpreted as a harmony which must resolve to the dominant chord.

Its

application, therefore, as an accented six-four chord of any scale degree other than the fifth degree requires a certain amount of caution.

We

are inclined to hear the bass of any given six-four chord as a dominant, (

i.e., the bass will be changed into a dominant even if it is not one.

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(_)

77 The characteristic charm of the suspension of the fourth and sixth above the subdominant in minor (example 48b, measure 2) is due to the fact that a resolution to the D major triad--the dominant in G--is expected. The chord which does appear, however, is only a subdominant in a minor. Its appearance is justified by means of its continuation.

The six-four

chord can be applied occasionally, such that only its fourth is interpreted as a suspension.

In this case the chord resolves to a sixth

chord--a pure triadic inversion.

(See, for example, Schubert, German

Dances, op. 33, No. 2 in D major.) b.

The sixth chord as a suspension chord. A suspension sixth

chord does not occur as frequently as--and is not as important as--a

(

suspension six-four chord.

Such a sixth chord is treated in exactly

the same manner as the suspension six-four chord. part of the measure and resolves on a weak part. same, as a rule, unt i1 the chord resolves. the bass (functioning root).

It occurs on a strong The bass remains the

The best tone to doui:)le· is

Doubling the third is also possible--but

not with v6 in major, v6 in minor, or 1v 6 in minor.

It is impossible

to double the third in the v6 chord in major because of its leadingtone capacity; doubling this tone in minor certainly requires some caution also because of its leading-tone capacity.

The sixth, as a rule,

is treated as a suspension dissonance, i.e., it is resolved downward and is not doubled in a four-voice setting. Conceptually dissonant form3tions are not created by suspensions of the fourth and sixth above the subdominant in major.

(

Furthermore,

such formations are not created by suspensions of the sixth above the

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(_:

78 dominant and subdominant in minor.

Effective dissonances, however, do

result--namely the v6 chord with a major third and minor sixth (49a), and the 1v6 chord with a minor third and major sixth (49b).

a.

b.

49.

a:lV

V

I

IV

Statements concerning the freer treatment of cadential six-four chords (see page 74f.) are also valid for suspension sixth chords appearing in

(

the form of conceptual dissonances. ~

(For more information see the

Theory of Inversions of Secondary Triads in chapters 4 and 5.) Assignment No. 9:

The following basses are either fig_ured or

unfigured and are to be realized in four voices in the manner cited on page 57ff.

The upper voices are to be harmonized in four voices.

Create

suspension sixth chords and six-four chords as frequently as possible.

I. a.

c.

)>.

50.~~tblf.Ml~ C: I

I

2.a

tb ~ (

V -

V -

b.

,J JI:

a: I -

IV -

IV -

c.

NB'

IV -

IV -

! J--t~9f$*=t~] I

V -

V -

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79

() N.B.~

A stepwise descending leading-tone is impossible in minor

because of the resulting movement of an augmented second. the

~fnor

Therefore,

seventh (the seventh scale degree of the natural minor scale)

must be applied in the formation of the cadential six-four chord constructed on the subdominant in minor. Special mention should be made that suspensions in this assignment are obviously to be the result of sixth chords and six-four chords. This is also true of the passing-tones in assignment 10. 51. (5)

~ ~~

1. Bass; Close position 65 43

6

r (I 61

(·

a.

6 5 '6

I

61

6 5

e~~-~·

65 43

6

Ie

65 43 6

I

&s

65

I J 1==i ~

· 2. Bass; Close position 6

6

#

6

65 6

®e=" r I r#hFd r r I r

65 4 6

#

65 43 6

6565 4#

#-

r Ir· MI r· r I r J Erl

3. Bass; Close position

4. Bass; Close position

(

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

80

5.

Bass; Close position

6.

Bass; Close position

7. Soprano; Close position

8.

I~,¢),

Soprano; Close position in the beginning

t!Q JI r

r:

Ed#'!. J

J JI r J

,J

J±tJ J

L:J:a I; .D

I JJ

9. Soprano; Close position FP=#~1e-r .-:

PI ..

f©'n Qr J

, mr e r a

'

1

JIJ Jl 10.

0

j

j

il il 1

a e1 j

IE

Soprano;

Close position

19'v2 i l J JI J J JI J J rl r iE&ratH tfVV~ r r t:J Ir· I

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

81

(_)

15.

11.

Soprano; Close position

12.

Soprano; Close position

13.

Soprano; Close position

14.

Soprano; Close position

Soprano; Close position in the beginning

•rrni"t N.B.

(

:

r a1u r WY-" r rlr

1$',~. ct J tjA

J)

;6*1

J) 41J J

&

1

"f1¥M

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82

()

N.B.

See page 78, example

so2c

for a clarification of the appli-

cation of the tone b in c# minor. ~17.

a)

The six-four chord and sixth chord as passing chords. The six-four chord as a passing cho,r.s!.

Every six-four chord

is either a suspension, passing, or auxiliary formation.

This is not

true, however, if the bass changes with a stationary triadic harmony. In such a case the six-four chord is a pure triadic inversion. ·rhe effect and treatment of an accented six-four chord is like that of a suspension, and the effect and treatment of an unaccented six-four chord like that of a passing-tone (or auxiliary tone) formation.

Therefore,

if a new harmony is introduced with an unaccented six-four chord, the

(_;

latter must always be considered as a passing or auxiliary formation. The cadential six-four chord is introduced with an accent either at the beginning of a measure or within the measure itself. six-four chord,

ha~ever,

The passing

occurs as a rule on an unaccented part of the

measure, and less frequently on a strong part of the measure

provi~ed

the chord appears within a longer passing formation (see the concept of II

i rregu la r passing chords" on page 223f f.) •

Such a chord occurs on.1 y

infrequently on the beginning of a measure if the measure is a weak element within a higher order metric complex, and assumes the same weak position within the complex that the passing tone does within the measure. The decisive factor for recognizing and applying the passing six-four chord is always the absence of an accent since an accent would call attention to the introduction of the chord.

(

It is easy to realize that special rules usually provided for the

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83 application of the unaccented six-four chord are unnecessary If the chord is considered as a passing formation, i.e., not an independent chord, but rather a connecting link between two harmonies.

Every passing

formation (see page 68) occurs either between two different harmonies or between two different positions (or inversions) of one and the same harmony.

It is even possible for a passing formation to occur between

a chord and its exact duplicate--even with respect to its position and form of inversion.

In this case the concept of auxiliary chords (as

with example 52f) is to be ascribed to these passing chords.

It is

characteristic for the passing six-four chord to connect two different forms of the same harmony.

In such a case a functioning root change is

not introduced with the six-four chord.

r

The following statement must be considered the rule for the strict

~·

treatment of unaccented passing six-four chords: all voice movements leading to and following the six-four chord must occur

such that all

tones of the six-four chord function as pure passing tones or auxiliary tones, I.e., as tones not belonging to the preceding or subsequent chord. The following typical situations are to be distinguished: 1.

The six-four chord occurs over a stationary bass, as shown in

2.

The bass proceeds to and leaves the six-four chord by step,

52a.

i.e., either continuing in the same direction (52b, c, d, e) or returning to the original tone (52f). 3.

The bass leaps to the six-four chord and leaves by step, as

shown in 52g.

In this particular example the c in the bass must be

/

(

considered as the upper auxiliary to the third (b) of the root (G).

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. (

84

.! /

4.

The bass of the six-four chord is reached either by step or

leap, but is left only by means of a leap (52h).

The bass is actually

a passing tone (or auxiliary tone) progressing by leap.

Strictly speak-

ing, such a tone requires subse"'ent resolution. N.B.!

The first and second situation occur much more frequently

. than the third or fourth.

a. .

c.

b.

d.

r·

52.

.J

.J

~

C: V-

e.

a: I g.

f.

-

-C:IVh.

..... a: IV-- V

I

-

-

C: V- -

Since the possibility of interpretir.g the

IV- [I -

IV)

suspe~sion

six-four chord

(see page 74) and passing six-four chord as chord inversions is always secondary to their possible interpretation as conceptual dissonances, their upper voices can resolve in an unrestricted manner in a free setting.

They can descend by step as passing tones (or auxiliary tones)

without subsequent resolution--or merely with a partial resolution to another voice as shown in 52d and e.

(

It is not wise, however, to apply

this liberty to the movement of the bass.

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85 b.

The sixth chord as a passing chord.

The passing six-four chord

can be applied more freely as a conceptual dissonance than as a chord inversion.

If a sixth chord has a definite passing character, it can

be applied more freely, i.e., as a type of independent chord inversion.

It Is always much easier to interpret the sixth chord as a passing chord than it is to interpret the six-four chord as a passing chord.

The

exclusive interpretation of the sixth chord as a passing chord, however, is generally necessary only if its interpretation as a chord inversion 6 would create an unnatura 1 progress ion such as V - 1v • Therefci·e, the sixth chord built on the pitch a in __example 53c must be considered a passing formation, in the broad sense of the word--i.e., as an inter8 polated chord in spite of the ascending bass.

(

Louis calls such interpolated chords "passing triads" on page 18f. in Aufgaben fUr den Unterricht in der Harmonielehre, Stuttgart, 1910, First Part. The progression V - IV is very possible as a passing formation, but is unsatisfying as an independent chord progression.

The question-

able character of two sixth chords progressing in fifths or fourths also completely disappears if the second sixth chord is introduced and continued

such that it could be understood as a passing or auxiliary

format ion~

8 See, moreover, the concept of the 11 Fux aux i 1ia ry tone" (page 229f.) for explanation of the progression of the bass in 53c. See also the concept of the anticipation (page 228f.) in explanation of the progression of the alto and tenor.

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86

til . ~·'

53.

C: IV -

V

v

or: IV V

C: V -

-

I C: V -

-

In example 54 the movement of the bass of the second sixth chord and that of the soprano of both sixth chords have somewhat the character of auxiliary tones to core.

(.·.· 54. C:l

As·sfgnment No. 10:

(V

I]

a: I

(IV

V

VJ

Passing sixth chords and particula rly passing

six-four chords are to be applied in the following phrases.

Suspensio n

sixth chords (and six-four chords) apparentl y occur frequently , but are of only secondary importanc e to their applicatio n as passing chords.

(

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87 55.

Bass; Close position

1.

6 (8) 4 3

~.-. tP'r' I II F I r

. 2.

~

(5) 6 4 .

a·

I 46

8

6

6 46

4

J Jl I r' Ir J J Ir 5

8 s 4 3

e·J I r JI J.,

Bass; Close position

et

8 4

6

6

I

G-

I

65

6

I

6

I

64

10,, e r r r I r r rIr 1M c: Ir '" J I r r 1-fPr JI J Jj

3.

Bass; Close position in the beginning

(5)

p= e J I f2 r J I:J 11

1

4.

5.

tlJi~ •! r (

J J IJ. r I e f' I e r r I t2 J I I 0

Bass; Close position

Soprano; Close position (in

r· v1r

J 1cat

H~nde1 1 s

style)

rr1F' s r1aa r r 1

. . r f21r F rl 1' 0

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

I

J Jig I

88 6.

tj;e J

Soprano; Close position

N.B. #2

; I J r f I I!' I J J FI

r J I J J J I J. I J. I

7. Soprano; Close position N.B. #3

t&} ., rIt r r I r r t r-1 r r J1r

J -J I J J JI

(: 8.

it - V -

Soprano; Close position

N.B. #1: In measures 7-8 the progression is 146 - IV 6 - IV I.

1v6 and IV are auxiliary formations interpolated between

two six-four chords.

These six-four chords are suspension chords over

the harmony of the dominant. N. B. #2: I n measures 12-13 the progression is V 16 - IV.

The

if chord and the first

I~

- IV -

IV chord are passing formations

6 between V and 1 •

(

IV, etc.

it - 16 -

N.Bo #3: In measures 2-3 the progression is I - 1v 6 The and 16 chords are most easily interpreted as chord

if

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inversions~ and the

1v

6 as an auxiliary formation.

In this particular

progression , therefore, these chords are interpretad i.n a manner which conflicts with their usual interpretati on!

-.,

'('1\_.

'

(

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90 CHAPTER 111 Dominant Seventh Chord and Dominant Ninth Chord

§ 18.

The dominant seventh chord is formed by adding the subdominant

tone to the harmony of the dominant as a foreign component.

The simultaneous existence of the dominant and subdominant in the same chord formation functions as a dissonance, i.e., as a conflict between two incompatible tonal elements of which one must yield to the other.

(

The dominant--represented by a complete triad--is much stronger than the single tone of the subdominant.

The v7 chord, therefore, is usually

understood as dominant harmony disturbed by a foreign tone.

The result

of this interpretation is that the dominant triad ts recognized as the consonant component and the seventh as the dissonant component.

The

need toresolvethe v7 chord, i.e., to resolve the tonal conflict existing within the chord, is clearly expressed by the need to resolve the seventh.

The consonance of the V triad is maintained, such that its

tones retain their complete freedom of movement even as components of the v7 chord.

The tone of the subdominant (the dominant seventh),

however, is to be displaced.

A distinct progression forces 'the domi-

nant tone upon the dissonant subdomlnant tone. It is also certainly conceivable that the seventh in a v7 chord,

(

i.e., the tone of the subdominant, could be interpreted as the functioning

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(/

91 root of the harmony.

In such a case the root, third, and fifth would

be foreign components yielding to the seventh, i.e., the entire complex would be a suspension chord (or passing chord) which must resolve to the subdominant.

57. C:l

IV

a: I

lV

-

C: IV

'a: IV

d.

v

Concerning the case in which both dominant and subdominant interpretations simultaneously exist in the same v7 ch~rd, see page 101f. Usually, however, the v7 chord is not understood in the sense of a subdominant, but rather in the sense of a dominant, i.e., the seventh requires resolution, but not the root, third, or fifth.· The natural resolution of the seventh is stepwise downward. A resolution of the dominant seventh chord to

.3

chord other than

the tonic is not conceivable if we only take into consideration primary harmonies within the key.

The following irregular resolutions of the

dominant seventh, however, are possible: /

1.

The seventh proceeds by step upward to the fifth of the tonic.

\

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(_

92 2.

The seventh proceeds by leap upward or downward to the tonic

itself. The second case occurs less frequently than the first.

The reason I

for this is that the concept of the auxiliary tone (in the broadest sense of the wora) under1i2s every distinct dissonance, i.e., the neighboring relationship between the consonant and dissonant tone in a major or minor triad Is clearly expressed in terms of the stepwise progression of the dissonant tone. It is not very clear, however, why the downward resolution of the dominant seventh is perceived as a far more natura 1 progress ion than the upward resolution. undeniable fact.

(

Various reasons have been provided for this One of them is that the traditional downward resolu•

tion of the dominant seventh in major produces a leading-tone movement. Upward resolution, however, results in the fifth above the tonic--a tone already existing in the v7 chord itself.

Parallel fifths can

easily result from the simultaneous upward movement of the seventh and the leading-tone.

Downward resolution of the minor seventh is perceived

as a natural progression.

This tone can resolve in a different manner

only with certain precautions.

The reason seems to be that the minor

seventh is the inversion of the second.

The tendency of the major

second to resolve to the {major or minor) third is clearly expressed in terms of the dissonance of the former.

The interval of a second is

actually heard as a disturbed consonance of a third, a would-be third, or as an interval which is in the process of becoming a third.

(

If the

latter results from a second, the appearance of the dissonance of the

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~;

93 second is heard as a delay, i.e., a suspension formation.

Expectation

for resolution inherent in the interval of a second is very distinct (as it is with every dissonance).

In this case, resolution to the

third is expected. If the major second is a suspension (or passing tone) to the third, its inversion--the minor seventh--must be most easily understood as a suspension to the sixth (or a passing tone to the sixth). even if the seventh does not occur as a

s~spension

rather as a component of an independent chord.

This applies

dissonance, but

The reason is that the

sixth must be the natural resolution of the seventh.

The sixth created

by the upper tone of the interval of a seventh proceeding downward by

(_

step (as the "dissonant tone"). Of the tones comprising the v7 chord, the root and fifth can be doubled.

The third and seventh, however, cannot be doubled in settings

of four or less voices because of their distinct resolution tendency The fifth of the v7 chord--and occasionally even the

(see page 38f).

third--can be omittedft A 7 is written under the bass to indicate a seventh chord in thoroughbass notation.

Fou~

positions are to be differentiated with

the v7 chord: octave position, third position, fifth position, and seventh position. a. Octave position

(

b. Third position

c. Fifth

d. Seventh

position

position

58.

C: V

1: V

C: V

a; V

C: V

a: V

C: V

a: V

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(i These positions represent the seventh chord in its primary form or basic Gestalt, i.e., a seventh chord in the true and narrow sense of the word.

If, however, the third, fifth, or seventh of this chord

is transferred to the bass, the following three inversions are formed:

·-·-··-J.•....T_he six-five chord.

This chord can appear in third, fifth,

or sixth position and is designated in thoroughbass notation with a in the bass.

~

Its fifth is dissonant with the functioning root.

a. Third b. Fifth c. Sixth ·position position position

59.

1(··. ''.,_

I

e

The octave position of the six-five chord· is impossible.

This is a basic

rule! 2.

The four-three chord.

notation with a

j

This chord is designated in thoroughbass

in the bass and can occur in third, fifth, sixth

and octave position.

Its third is dissonant with the functioning

root.

a. Third b. Fourth c. Sixth d. Octave position position position position

60.

(

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(:

95

3. The four-two chord.

This chord is designated in thoroughbass

notation with a 2 in the bass and can occur in second, fourth, or sixth position.

Its bass tone is dissonant with the functioning root. a. Second b. Fourth c. Sixth pns!tion position position

61.

The octave position of the four-two chord is impossible as an inversion of the

(

11

genuine11 seventh chord.9 Th is is a basic rule~

Assignment No. 11:

It is advisable for the student to construct

and recognize the v7 chord and its inversions. To this end, we offer various suggestions: 1.

The student is to form the v7 chord in all major and minor

keys of the circle of fifths and circle of fourths.

This will demon-

strate that the v7 chord (and V triad) is the same in major as it is in each respective parallel minor. 2.

The teacher is to place the figures

7, ~·

j.

and 2 below the

basses and allow such basses to be harmonized with appropriate chords.

3.

The student is to write the seventh chord, six-five chord,

four-three chord, and four-two chord in various keys.

Consideration

should also be given to various inversions and positions of the chord.

(

9 A 11 genuine11 seventh chord is to be understood as a seventh chord whose root is the functioning root of the harmony.

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(_.

96 ~19.

The introd uction of the dominant sevent h can be either prepar ed

or unprep ared.

In the first c~se the sevent h existe d in the previo us

chord, and in the second case the sevent h is introdu ced freely , i.e., it is not a tone common to either chord. The prepar ation of the sevent

h

can appear either in the same voice (62a) or in anothe r voice (62b).

-

••

b•

62.

(:

If the introd uction of the dominant sevent h is free, the root will most often be prepar ed in the same voice (63a), but can be prepar ed in anothe r voice (63b). 10

..

b.

63.

The sevent h is most easily introd uced if either itself or the root is prepar ed in the same voice. Freque ntly the sevent h occurs in passin g (64) while the root is prepar ed in the same voice.

(

I

lO ·[The root in example 63b sounds as if it were prepar ed in the alto and does not reinfo rce the autho r's statem ent very well.]

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(.I

97

64.

If both the

seven~h

and root are unprepar ed {or prepared only in one

of the other voices), both tones are best introduc ed in contrary motion. Not so smooth:

65.

It is possible for the seventh and its root to be absent from the chord precedin g the v7 chord if we are dealing with the applicat ion of secondar y harmonie s. The third and seventh of the V'7 chord have prescrib ed resoluti ons. The former proceeds as a leading- tone stepwise upward to the tonic, and the lstter as a dissonan ce proceedi ng stepwise downward to the third above the tonic.

The root and fifth of the v7 chord, however, progress

freely, i.e., they can be continue d at will.

The root of the seventh

chord (i.e., the dominant) in the progress ion v7 - I most naturall y either remains on the same tone or leaps a fifth downward (or fourth (

upward) to the tonic--a s a bass movement.

The leap of a third downward

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98 to the third above the tonic is possible only with the simultaneous upward resolution of the seventh to the fifth above the tonic. this case the leap functions as a type of the dominant seventh.

11

In

substitute11 resolution of

The unmotivated doubling of the third of a

primary triad, however, always sounds unpleasant--especially in major= Nevertheless, the worst type of hidden octaves result from a similar motion of both the seventh and another voice to the same tone. hidden.octaves are to be avoided

u~der

Such

all circumstances {see page

46Sf .). The fifth of the v7 chord most naturally proceeds stepwise downward to the tonic.

It proceeds less frequently stepwise upward to the third This is a basic

above the tonic, as shown in 669.

(.

·.

rule~

The leap of

a fourth upward (or fifth downward) to the fifth above the tonic must This movement cannot occur if the dominant

be melodically motivated.

leaps to the tonic because of the resulting antiparallel fifths.

Such

movement occurs less frequently with the resolution of the v7 chord in its basic Gestalt than with that of its inversions, as shown in 66h. Incorrect

..

b.

c.

d.

e.

66.

Impossible ·~

(see Liszt , Pret udes) g.

h.

(

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()

99 In 66g doubling the third of the tonic

t~iad

is melodically moti-

vated by the passing movement in the soprano and bass. Irregular resolutions of basically restricted tones of the v7 chord, i.e., third and seventh, occur as follows: a) The leading-tone progresses by leap downward to the fifth of the tonic triad.

This liberty was already applied to the resolution

of the dominant triad provided the fifth of the tonic triad in the irregular resolution is less offensive with the v7 chord than with the V triad because the v7 chord is more closely related to the tonic triad than the dominant triad is (see page 107).

The indispensable prerequi-

site for the free application of this particular liberty is that the ;(: -

.. .

leading-tone must be in an inner voice.

In the progression V to I the

downward leap of the leading-tone is more feasible if the bass leaps a fourth upward since similar motion is avoided (67a).

The downward

leap of the leading-tone (for example, in cadences of Bach Chorales) frequently occurs with the similar motion of the bass, i.e., fifth downward (67b).

••

b•

67.

In our more recent art music this leap of the leading-tone occurs infrequently as a melodic movement (in the upper voice).

This leap,

however, is more characteristic of specific types of regional and

(

exotic folk music.

Such a leap does not come into consideration as a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

100

bass movement with the progression V - I.

(This is a basic rule!

See

also page 104.) b) The leading-tone proceeds stepwise downward.

ihis movement is

possible with the progression V - I only if the sixth scale degree is applied as a non-harmonic tone (passing tone or suspension tone).

This

sixth degree belongs neither to the dominant nor to the tonic as a chord component. T~e!efore,

This tone must subsequentlr resolve stepwise downward. we are actually dealing with nothing other than a modification

of the leap of the leading-tone a third downward.

This movement is pos-

sible for the upper voice in the manner shown below.

(

'..

68.

~&1 €):

;

~"-

I

,.

I i==r

:µs1 r I ~·

e

~~ p .g.

)@tLEf

FD JI

c) The leading-tone leaps a fourth upward to the third of the tonic.

This leap does not occur very frequently and is possible only

if it is melodically justified.

Such a leap occurs less frequently with

the v7 chord than with the V triad because this leap--with the regular resolution of the seventh--results in a doubled third.

In Bach Chorales

the tenor frequently leaps a fourth upward to the third above the tonic if the cadence is executed with the V triad in fifth position (69a). This

progressio~

occurs frequently in an outer voice only if the voice

in question subsequently proceeds stepwise downward. The tonic third in this case is very similar to an auxiliary tone to the fifth of the dominant (69b and c).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

101

.b:A a.

·

b.

c.

;;l_J 1-l=H 'l ----It-rJ rJ ·!be· 1J '~ r4 1r·a·n4,g . -- ir· · :=ir· · ~1 J 1. l. .

u

~~1?1n~~ A: I IV V -

I

C: V - -

· Pl

I

a:· V (IJ

d) The seventh_ procee ds stepwi se upward to the fifth of the tonic. This compa rativel y freque nt resolu tion can occur easi1y if the root of · the v7 chord accept s the substi tute resolu tion of the sevent h by means · of a 1eap of a third downward, as shown in 70a and 70b.

(

With a statio nary root, however, the need for the natura l resolu tion of the sevent h will be much strong er if the sevent h and root appear in adjace nt voices as an interva 1 of a second (or sevent h) as shown in 70c or 70da The resolu tion in 70d, strict ly speaki ng, is possib le only if it appear s within a passin g movement. e) The sevent h leaps a fourth upward or fifth downward to the tonic. This very free progre ssion unders tandab ly occurs only in rare instan ces. The reason is that the dominant sevent h in this case no longer has any relatio nship to the dominant as its root, but is treate d as if it actual ly were the root (subdo minan t!).

The remaining tones of the

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()

102

chord. however, are not of secondary importance to this subdominant pitch,

The dominant seventh chord is interprete d neither purely in

the sense of the dominant nor purely in the sense of the subdomina nt. Both interpreta tions, on the other hand, coexist.

Root. third, and

fifth are interprete d as components of the V triad and are treated as such.

The seventh is interprete d as the root of the IV chord and

is continued as such. The resolution of V~ to the tonic triad--fre quently occurring in

irregular resolution .

Bach always creates this type of resolution if

it is impossible to continue to the tonic sixth chord because the

(

vocal part itself proceeds to the third above the tonic. 71.

J.

s.

da nun

c: W

Bach. St. John Passion.

Ju • das zu slch ge • nom·men hat-te die Schat

V (IVI)

The six-four chord resolution of the on page 431--take n from the sixth piece of ~--only

No. 2

vi chord

cited in example 4a

Schu~~nn 1 s

Bildern aus dem

appears to belong to this type of resolution .

( I

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

(,'

103 If the dominant seventh is not in the bass, it can leap to the tonic without much harshness, i.e., if the leap is melodically motivated.

The seventh in stepwise

mo~ion

will always originate from the

1·oot and possess somewhat the qua 1 ity of a downward leaping passing tone or auxi 1 iary tone. 72.

a.

Beethoven, Op. 10, No. 1, Finale

,

f fil=t

d.

I•

a a1 f If B:V

( b.

I

Sgambati, .Str.ing Quartet. Op. 17, First Movement

1

J_

I

§ 20.

The instructor who wishes to teach· his student a we11-defined

principle will do well to establish from the outset that the dominant seventh, as a rule, resolves downward by step.

(

Upward resolution by

step can be permitted only in well motivated cases.

The downward

leap of the seventh, however, is never permissible.

Therefore, in

practice, the following progressions of the v7 chord and its inversions

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

1o4 a re

p~s s i b 1e: 11 1) v7 can continue to the tonic triad

oi

tonic six-four chord.

It can proceed to the tonic sixth chord only with irregular resolution of the seventh.

-

73.

..

'

Incorrect

2) Regular resolution of the V~ chord is to the tonic triad. Very rarely does if: resolve to the !~-sin~e t~e leading-~one leaps downward!

The downward leaping leading-tone can be completely justi-

fied in this case actually only by means of subsequent resolution. to

V~

1: is entirely possible only if the if chord appears as a formation

(passing chord or suspension chord) interpolated between two different 6 4· positions of the dominant chord, as shown in 74c between v and v2 • 5

..

. b.

c.

74.

/

I

11 It is obvious that various positions and inversions of the v7 chord can always follow each other. Any limitation in the freedom of movement of the leading-tone and seventh does not occur if the inversions of the v7 change over a stationary functioning root. These two tones, however, normally progress in a well defined manner. The V~ chord is

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105 3)

The fifth of the dominant

prog~esses

tonic itself or to the third above the tonic. tonic sixth

chor~ can follow the vj chord.

naturally either to the Both the tonic triad and

In this last case, offensive

doublings of the third of the tonic triad must be avoided, i.e., it is wise to place the seventh in the tenor (75b) or to move it upward to the fifth above the tonic (75c).

Such doubling should be avoided

unless it occurs melodically in a voice not adjacent to the bass, for example by means of a passing movement as shown in 75d.

A leap from

the bass of a vj chord to the fifth of the tonic in the progression vj -

if is conceivable only as an embellishment of the regular step-

wise movement to the tonic or to its third, i.e., with a subsequent resolution as in 75e.

••

b.

c.

cl.

e.

75.

4) Finally, the progression of the V~ chord is governed by the demand for stepwise downward resolution of the dominant seventh. V~ proceeds almost without exception to 16 • (Concerning the doubling of the tonic-third,see the preceding section 3.)

(

the only exception to this since the subsequent resolution of the dominant seventh--appearing in the bass--is expected to be to the third above the tonic. This is true even if the resolution of dominant harmony is not from the V~ chord itself but rather from a different inversion form of the v7 chord.

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(

.

106

\ ../

a.

c.

b.

76~

Nevertheles~..,

it is not c001.pwtel'{_

J!JIP..O_?_~!or -~i_:_o_~~~~==d·-~o·-·'t

provided the progression occurs only in passing.

(In 76c, the g in

the alto functions to some degree as a "sustained voice11 --see page 360.) The resolution of v7 to the subdominan t--like that of the V chord to the subdominain t--is only illusory as a rule, i.e., such resolution results from a suspension formation or passing

forw~ticn.

In this

case the do1J.ble suspension of the fourth and sixth above the tonic creates the illusion of the tv 6 chord. The subdominant appearing

4

between the two forms of dominant harmony with a stationary functioning root is an interpolated chord or an incidental formation foreign to the root of the dominant (see pages 139 and 419ff.).

77.

C:V

I (IV)

V -

(IV)

-

I a: V

I -

(IV)

V--

llVJ

(

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107

The progression V - I is a more decisive cadence with the application of the v7 chord than with only that of the V triad.

The reason

is that the dissonance of the seventh--pressing downward to the third of the tonic--makes the relationship between v7 and I even closer than the one between V and I.

The interval of a tritone between the leading-

tone and seventh is the truly characteristic component of v7 harmony! The tendency of the v7 chord to resolve to I is even more distinct and compelling than that of the V triad.

The authentic cadence appears

in its most perfect form if the following conditions are fulfilled: 1.

The authentic cadence is harmonically perfect if the I triad

in root position follows the v7 chord.

The descent of the bass a fifth

functions more decisively than does the ascent of the bass a fourth. 2.

e

The authentic cadence is melodically perfect if the upper

voice proceeds to the tonic, i.e., usually ascending or descending by step.

3. The authentic cadence is metrically perfect if the cadential chord occurs on the accented part of the measure. The V -

progression is a so-called "imperfect" cadence if these

conditions are not fulfilled.

(

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108

(_) 1. Perfect cadence

2. Imperfect cadence

78.

Assignment No. 12: Complete each exercise in four voices in the manner indicated.

79. 1. Bass; Close position in the beginning

·(

'

4 3

(5)

6 5 6 65 6 7 4 3 5 43 6 p·-~

6

6 6 46 . 4

@WfrFrl F' r I F 1-GY [$44 r 2.

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121

65

676

(5)43 a

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I

I?

3.

s:

Bass;

# a

~!ose

fr

7

I r J Id

position

76

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i 19 r F tt'

...

6

FI

e

:1 3

65

64§

43 6

JI J

rr I t'

I

6~

J Rd

Bass; Close position in the beginning

(3)

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p=Qvp, er If"

t

Ir r

@tr·

rIr

LJI J J JQLJ 43£)~

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t~

109

)

4.

Bass; Close position· .

N.B.!

(6} .

12•M " r 1t r 1f r I r r I r aIr rl-r r r J oo 1

v•

5.~

w• v& w:

1

1

Bass; Open ··posit ion ········ · -·· ........... .

.

---·· ···-·---·- ··-- __ ..,_.

(8)

r @2F~bJ IJ r=ttr JJJ J Af&*& al@I

12=~ I

6. (8)

1?!%fer Fir rl

Bass; Open position

r FJ r· 7.

FI

r Qibf¥J r 9 °l

Soprano; Close position

r e ri e r HFJkPt1lt=f=FM f&i r r FI Ir r r I J=;;t-1 J J JI &;ii J J J. I £&1 ·= r r

1

0

~,~ .u

OJ

J -Jl:: J~8.

r- -r I:

I

n :

Soprano; Close position in the beginning

(

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····--·-···

··-···-

·-· ·-

l

".

110

i

-er

9.

I r=t r I r

Soprano; Close position

rIr

J J IJ J IJ J 1vi it .

10.

Soprano; Close position in the beginning

11.

Soprano; Close position in the beginning

tbffl ·t rI r r r I r er I r 12.

r r1¢if J r r Ir Et l J J J LJ If

Soprano; Mixed position in the beginning

f$¥ er p IJ J J Ir r ti N.B.!

Jd¥£1 ~ J 1J I

d

Ir r r I J. r I r jJ I * II

Example 4, measure 3: 1v6 is an interpolated chord (freely

treated passing chord).

Measures 2 and 3 are to be clearly understood

as dominant harmony (with fas the root). ~ 21.

A v9 chord is obtained if we add not only the subdominant

itself, but also its third to the harmony of the V triad.

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111

80.

fb=v I) IV C: V

J@til) IV=g

a-e.

,.;

a: I . b VI u-: V

VI

IV

a:I

V

b VI.

B: V

b

I

e:-: V

VI

IV

V

I

V

I

I

E :V

d. a-C.

a: I C: VI

a: I

I

i, l a: V

V

IV

.V

From minor to major a-0.

VI IV

VI

a: I I Ci: II

a-0.

V

a: I I G: II

V

VI

D: II

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249

a-A.

V A: I

lV

a: I

a: I V E: I e: IV

a: I e: IV

a-fil=.

I IV

v

8:1

a-f.

a: I

e:.IV

b:

b:

I

. a: I C: VI

IV~

I fil't': IV

V

J!

f~:

I

I f:V

VI

V

IV

b a-B.

( IV V

v

lV

1

I

V

a-lib.

~ ~ I,fl[====== ~IE4J I 1J

a: I

b VI

b:

vab:

1:1

1v

H-¥=·11;====== v

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(J

250

§43.

b.

Inversions of consonant triads.

If the minor sixth chord

is interpreted as a subdominant substitute (II), the functioning root of the harmony is the bass, i.e., the subdominant.

For this reason the

ear will have a certain inclination to interpret the minor sixth chord as a II chord, especially if the bass is doubled and the sixth is situated in the upper voice.

The chord's significance as a means of

modulation is a result of its interpretation.

a: VII

(

I G: II

v

Concerning the same interpretation of the major sixth chord-the so-called Neopolitan sixth chord--refer to section 51. Application of the accented six-four chord as a suspension to the V triad has become so stereotyped that the accented six-four chord is normally interpreted as a suspension.

If it is introduced on a

strong part of the measure on a scale degree other than the dominant, the chord usually produces a modulation to the key in which its bass tone is the dominant.

(

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251

C:

V

f:

fl]

v

C: I

[II]

O:V

(\ a: I

(IV)

G:V

a: V

(Ill)

F: V

It is not necessar y to make special mention that the bass of a six-four chord is always to be doubled if it is to be applied in this type of modulat ion. 2.

Dissonan t chord as a means of modulat ion.

To assess the

signific ance of any given dissonan t chord as a means of modulati on, the musician must realize that certain types of dissonan t formatio ns have a definite stereoty ped tonal function . four chord has such a function .

(

11

The applicat ion of the six-

These types of dissonan ces are called

charact eristic11 since they have a specific harmonic relation ship,

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(>

252 i.e., the chord in which they appear has a definite tonal relationship. The most characteristic of all dissonances is the minor seventh added to the major triad.

This seventh changes the chord into a dominant

harmony and is interpreted as a dominant seventh.

Both

c~neeptions--

i.e., the major triad with a minor seventh and dominant function--are so closely associated with each other in cur musical consciousness that they can no longer be separated.

Although g-b-d-f is conceivable

as a diatonic formation in d minor and (if necessary) even in a minor, the introduction of this chord always creates the impression of C major (or c minor).

For all practical purposes v7 is diatonically

unambiguous and, therefore, is not very possible as a genuine means of modulation. Even in situations like the following,

(_

' b.

L

~~~~s~

Ei-==r+r

210. { C: I

V d: IV(r) vn

II

V

C: I

V

fll

I d:Vll I

it is easier to accept an implied chromatic progression than to reinterpret the v7 as a subdominant seventh chord with a major third (see page 192).

v7 can indirectly result in a modulation if it resolves

to a six-four chord. This phenomenon is discussed on page 250f. The major sixth added to a major or minor triad is only of secondary importance as a characteristic dissonance. This sixth is characteristic for the subdominant in the same way that the minor seventh is for

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253 The difference between these dissonances is that the

the dominant.

minor seventh added to the major triad clearly demands a dominant interpretation, while the added major sixth only suggests the subdominant and in no way excludes other interpretations.

Therefore, chords

characterized by this major sixth can also be very well applied in a substitution modulation, in fact extremely well if they are reinterpreted as subdominant harmonies.

In the form of a six-five chord the

subdominant meaning of these harmonies is very strong, but very weak in the form of a four-three chord, and even weaker in the form of a seventh chord.

This is particularly true of the half-diminished

seventh chord which occurs as easliy in major on Vii (as a dominant substitute) as it does in the relative minor on II (as a subdominant substitute.

The interpretation of d-f-ab-c either as EbVll (= V) or

as ell (= IV) depends not only upon the form of its inversion, but also upon the placement of its seventh, i.e., whether it lies in the upper voice, one of the inner voices, or in the bass.

If this chord

is interpreted as EbVll (= V), the seventh of the chord is the dominant ninth.

If the seventh lies in the upper voice, this chord is

easily interpr~ted as VII in Eb.

Furthermore, if the seventh lies in

an inner voice, it is more difficult to have this particular interpretation; and if it lies in the bass, such an interpretation is almost impossible. The diminished triad with or without a minor seventh can usually be considered as a 11 (= IV) chord in a minor key, or as a VI I (= V) chord in either major or minor.

(

The most obvious interpretation of the

first inversion of a diminished triad is that of a subdominant.

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Its

(_:;

254

interpretati on as a dominant substitute wi11 most easily occur if the triad appears in root position, but both interpretati ons are equally valid for the six-four chord--provi ded these two inversions are . feasible in a particular four-voice setting. The major triad with a major seventh is not important as a means of modulation since it is not as effective as the application of the triad without the seventh.

(.

1~~~~ a: VII

[Ill) f:V

I

The dim i n"is hed seventh chord is d ia ton i ca 11 y unambiguous and is incapable of tonal reinterpreta tion.

Six-four chord resolutions of

the dominant seventh chord and diminished seventh chord can result, however, in a modulation {example 211).

Tu conclude this chapter, only a few examples of diatonic

modula~

tion through reinterpreta tion are provided below, i.e., only with the application of triad inversions and dissonant chords.

(

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

255

(_\

C-0.

C-F.

212.

ll(IV) ll(IV) V VI

C: I F: V

I IC: I O:IVVll(V) I

V

IV

C-g.

C-a.

(i C: I

C: I

Vll(V)

IO(g):IV Vll(V)g:I ll(IV) V

(a: Ill) a:ll(IV) V

C-f.

-I i C: I f:

(

v

c: IV I

ll(IV>

V

C: I f: V

P;t; i r !fll : IV

V

'

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

(

256 )

~·

a-d.

a: I d: V llllV) V

a-g.

-

a: I I O(g):ll(IV) V g:Vl{I) ll(iV) V

11-P.

--

r·

(

Pf~

.a: I II C: VI Vll(V) I 11(1\i) V

a: I (Ill)

f: Ill

v

VI ll(IV)

I

v -

(

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

l

(

.-

'{j

257 .

;

SECOND PART THE CHROMATIC AND ENHARMONIC CHAPTER I Chromatfc Progression

§44.

The basic scale--upon which our entire tonal system is based

--encompasses the interval of an octave in seven stepwise movements, such that a half-step movement in each case appears after two or three whole-step movements--or in short, two half-steps exist to complement five whole-steps. scale degree

(

3.

...

5.

6.

7.

8. (

t@ J. J J

J

J

J

J

JI

L

213.

2.

whole whole I.

2.

half 3.

whole whol.e whole

...

5.

6.

1.)

half-step 7.

Older theory obtained the other modes from this basic scale·-representing pure major--by changing the second, third, fourth, fifth, sixth, or seventh tone of tbe basic scale into the root of each respective new scale.

This older theory also arrived at the various keys by transposing·

the basic scale itself and by transposing to other scale degrees the new scales obtained by means of root displacement.

Scales of the seven

(authentic) church modes (see page 482ff.) and those of their transposi-

c

tions result from these operations.

Only such tones or movements of

tones are called diatonic, in the original and narrowest sense of the word, as occur within these seven modes.

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258

Our modern music kn

Iab:: -0

I

~iio Pf

3. a-b-(0).

IF '---' I 4='J a: I

etc.

Vl~=f~:Vll ~: l=b (0): V

1

II etc.

FLrr 4 ~' ~

1

11: I

Vll=r": VII (~II . b: v

(

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

385

Modulatory cadences can be even more effective if the entrance of the V triad or v7 chord is delayed by interpolating a six-four chord.

If

six-four chord resolutions of the diminished seventh chord in addition to those In the transition

fr~«

minor to major are taken into consider-

ation, the following possible modulatio.ns are the result: 2

(

Modulations of this kind are somewhat different than diatonic and chromatic resolutions of the diminished seventh chord only in terms of interpretation and spelling.

(

2 [F minor, cb minor, ab minor, and d minor are also possible.]

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386

(.'

T~a

diminished seventh chord, therefore--diatonically, chromatically,

and enharmonically--allows modulations to occur from the key of a minor (A major) to the following keys: b minor (B major), c minor (C major), d minor (D major), eb minor (Eb major), f minor. (F major),

(f#

t#

minor

major), and ab minor (Ab major). Concerning Beethoven's preference for the diminished seventh chord

as a means of modulation check the following source: Th.

v.

Frimmel,

See also example 40 in this text.

Beethoven - Studien II, page 58f.

The diminished triad (as a VII) is nothing other than a component of the diminished seventh chord and can naturally be enharmonically reinterpreted in a similar manner.

The diminished triad as a Vll,.how-

ever, can be enharmonically reinterpreted in two ways.

(·

It is diatonically

ambiguous and has a total of four different interpretations.

a21.

~

I

!:

a: II (IV) f#=:

C (cj: VII

~ 66.

1: : 'vii

t

' : eb: VII

The augmented triad is somewhat analogous to the diminished

seventh chord because it is constructed in thirds--i.e., the former in major thirds and the latter in minor thirds.

It synrnetrically encom-

passes an octave from its root to the octave above the root.

322.

t~

ij9FJI .•

h·

..

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(

-) /

The interval between the root and third is the same as the interval between the third and fifth--a major third.

A diminished fourth exists

between the fifth and octave and is enharmonically identical to the major third.

The diminished seventh chord has three enharmonic iein-

terpretations in contrast to the augmented triad which has only two because either its third or fifth can be interpreted as the root.

In

this respect the diminished triad is considered to be the same as the augmented triad and becomes an incomplete diminished seventh chord by means of enharmonic reinterpretation&

The augmented triad, however, is

exactly the same as the diminished seventh chord because it remains the same even after reinterpretation.

~= !: !::

(·

f: Ill c..: Ill a: Ill A: V f; V Db: V

The augmented triad is applied more frequently as an altered chord in major (V triad with augmented fifth) than as a diatonic chord in minor (Ill= dominant substitute)--see page 284f.

Through enharmonic

reinterpretation, therefore, the augmented triad provides the means to reach two major keys situated a third higher and lower than the original key.

It is not completely impossible, however, to interpret the chord

as a diatonic formation in minor and consequently apply it to an enharmonic modulation.

It is evident that the same augmented triad occurs not

only in a given minor key (on the third scale degree), but also in the (

major (as an altered V triad): for example e-. V

In

ter • ra

pax

ho-

. Ab I (V)

~V ............------------------~--

The fact that resolutions of the v7 chords in both excerpts result

(

in six-four chords certainly indicates that an enharmonic reinterpretation

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

(

402 ..

is to be accepted.

i"he root and th I rd of the seven th chord are changed

into auxiliary tones and proceed downward respectively to the fifth and root of the following

t~iad.

The entire excerpt from Klose 1 s Mass

(340b) can also be interpreted as a free passing movement over the root F {bb : V).

This root remains until the appearance of v7 harmony.

(:

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403

CHAPTER VI Comprehensiv~

§ 69.

Summary

To achieve a completely exhaustive insight into the multi-

facited chromatic and enharmonic relationships existing between individua1 chords, it is advisable to investigate various possibilities systematically, i.e., to investigate whether--and in what manner--a given chord could be connected with another.

If diatonic relation-

ships are also taken into consideration, an almost complete table of all possible chord

co~nections

could be obtained.

In the following section consonant triads, v7 chords, and diminished seventh chords are examined.

The following questions, therefore, must

be asked:

c

1) What type of major triad can fo 1low another major triad?

2) What type of minor triad can fo 1 low another minor triad?

3) What type of major triad can fo 11ow a minor triad? and

finally,

4) What type of minor triad can follow a major triad? The summary illustrates that any consonant triad can be reached from any other consonant triad in some_ manner, assuming_ on.l_y that enharmonically identical formations are considered to be absolutely the same--i.e., within our modern tonal system.

Progressions in the table

are always conceived, such that the first triad in each case is considered as the tonic.

Numerals for scale degrees below the staff do

not exhaust possibilities of modulation or digression, but rather represent only the more important and more obvious one.

(

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

404

{.'

Possibilities of connecting consonant triads 1.

From major to major

c c:_o.

e-a.'

C: I

P: V

(II (lV))

c~o

.

c-A .

C: I v C: I c""': V C:I 0c:VI. E : IV I 0: IV I A;;: I Db:V

b

Eb: IV

A :I

C-B~

C-A.

·~f~~ t=~~b~ NI · C: I 0: IV

(

(II)

v

C: I

d:

v

I t: re ti J [mC:: VIII (IV) IV)I C:a: IllI

M ll(IVi

\

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

405

() C-9:

J~r-fim~

1

_µggfu:JW@@

d: VII

2. ~

C-c .

C-c.

(:

Z:f!=@f

C: I g,; IV B~

II

V

b

C-f.

C-e.

fltJ

11 ; #JI ;

1431 i l9ij tj I

O:IV

P:VI

IV C: I I

111 · C: I I f: V

VI

C: I t•: I

I C: I gb : V

VII]

If: V

Clf: IV

C-a· .

C-a.

111/

f~: V

H -

C-g.

C-gb.

C-g ,

C-F':

rp 'rP rllr rP

C: I A: Ill C: I · 11 C: I b~ !V C: I 0 : VI e: VI a: IV cit: I

B:D

8: II (IV) I

From major to minor C-e..

C-d.

·=~' i

{

VI C: I e: VI.

C-b~ N B. ! 0

-

C: I d: IV f: II ·(IV)

C-b.

IC:! : ;I: ;::2:: ::: C: I E:lll: Y C: I

c: VI

V

C: I f: V

i

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

418 b.

a: I E

·:v

a: I e:,IV

v

a-D'.

a: I 0: II

a-f".

Mino•

a: I F: ill ·

I!-.: I Ob :.V

N.B.t

·-~'.

a:'J . O~:V

a~ I Ab::V

a-D

v

v

'· .

~:

I F'f:·V

a-E',

a: I

. V ·.

a-ff'.

( a: I B: V . a: I 8: V

N.

B.:

a: I C: VI

V

:: I c1f: V

Notice that an A major triad is the "basic form" of the

Neapolit an sixth chord in the key of G# major.

This is precisel y the

reason that the chromat ic transitio n from a:I to Ab:v; is question able. The g (in the bass) 4 is better understo od as f## because in this form it is an ascendin g leading- tone.

4 [The "No ta Bene! 11 s hou 1d have been p 1aced over the next two chords in order to avoid confusio n.]

(

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419 2.

From a

v7

chord to a consonant triad [350] a. Major

b

o•-A. o•-A.

o•-D.

(.··.

C: V

lnmediate modu 1at ion

b .

0'-E.

N.B. #2

I C: V C: V · I C:V ['Ill] C:V Eb:. b: IV f~: V . D: II (IV) D: V - · ·

0'-E..

I

'F II

0'-P.

N.B.

i i II 2

C: V

a: V

#~

.

Q•-f"'. ·

# II h ·J I j jiij¥H

[C: V IV] F: llCJV) I

C: V b: IV

V

(

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420

(,.;

b. Minor

b

,,,_...

0'-a..

O'-b~

0'-L

N.B. #5

_i

V(l)C:V a17:V

C:Vd(D) ;,IV

0'-b..

~

0'-c.

::J .

IF~_. JS

l?=

c f; ;{,

11

Fii

d

.

C:V f:IV

0'-d.

a 4 u; & ii

N.B. #6

11

F' . J

c: V

II

r nr r 11

C:V A:Jll(V) C:V -

O'-eb. N.B. #7

N.B. #1

0'-cif.

rJ:

l(VI) c: V

C: ·y d'": VDCV+WI) I

C:V

0'-e.

0'-f. N. B. #8

b~ W C: V III C: V

w1 ,

r

r

II II

a: V 0 7-f":

W C: V fil: VII (V)

G7-e~ either the Bbmajor triad is interp reted as an inter-

polate d chord (passin g chord) or the v7 chord is reinte rprete d, such that the f ceases to be a dominant sevent h requir ing resolu tion. See also page 400f. N.B. #2

(

G7-o:

the chrom atic altera tion of the dominant sevent h is

possib le only if a subseq uent resolu tion of the sevent h occurs in the same voice or in anothe r voice as a substi tute resolu tion. If subsequent resolu tion of the sevent h does not occur, the tone is to be enharm onical ly reinte rprete d.

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()

421 N.B. #3

G7-F:

the subdominant triad can follow the v7 chord if the

former is interpreted as an interpolated chord (passing, suspension, or auxiliary chord} or if the

latte~

is reinterpreted, such that

b-d-f-g is considered a II chord in F major (a six-five chord constructed on the raised subdominant).

This chord always possesses a certain vio-

lent character--except if it resolves to a six-four chord.

In such a

case the F major triad first appears only as a suspension to the C major triad or seventh chord.

An aesthetically well-justified and very

effective application of this progression can be found in Hans Pfitzner's Die Rose vom Liebensgarten (page 6 of the piano reduction} in which the G major tonic follows the v7 chord in D major (A7}.

(

N.B. #4 G7-g:

this progression occurs indeed only in passing!

N.B. #5

the seventh requires subsequent resolution or the

G7-b:

v7 chord requires reinterpretation as a suspension formation to the B major triad. N.B. #6 G7-d:

if g-d-b-f is actually a v7 chord and continues as

such, subsequent resolution of F is necessary.

In our example the d

minor triad is a passing formation over the G functioning root. N.B. #7

G7-eb:

see page 428, example la.

Concerning these two

examples refer to the concept of the "deceptive pause" on page 139. N.B. #8 G7·f: refer to the progression G7-F above.

(

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422

From a v7 chord to a v7 chord

3.

[351]

N.B. #1

N.B. #2

0'-8' N B,. #3 0

tc::::::::::::::::c: C: V

C: V

C: V

b

C: V.--E : I C: V-1111) C: V B:ll(IV)(Vl)c:V (VJ) d:lV V [Eb: VJ [c: VJ I B:ll(IV) [I) · cft: V D·b : V E: V

N.B. #4

C:Y.f:VC:V _. C:V C;V~ :VG;Va:V·C:V .C:V b: IVf :V D:ll(IY)[I] P:ll(IV)[l]b:IV

a:v

G7-G#7:

N.B. #1

.

ebv

V

this progressio n is possible only in a chromatic

passing movemen t--i.e., with enharmonic reinterpr etation. N.B. #2

G7-a7:

this progressio n occurs in passing with subsequen t

resolution of the dominant seventh.

Otherwise , g-b-d-f is reinterpr e-

ted as g-cb-d-f (suspensio n to ab-bb-d-f ). N.B. #3

G7-e7:

upward alteration of the dominant seventh is indeed

possible only in passing. reinterpre ted. N.B. #3

(

Otherwise , this seventh must be enharmon ically

See page 393.

G7-F7: b-d-f-g is a six-five chord constructe d on the

altered subdominant in F major.

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()

423

~73.

The result of our systema tic investig ation of the v7 chord is the same as it was with the consonan t triad: any v7 chord can be reached I

from any major and minor triad, and converse ly, any m;: ~ .,... • a: IV

--

-...

mi ch

+u•

v.

(

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

450

nicht,

du llebst, du

liebst

mi ch nicht.

--------

J

l lb:V

26.

a: IV -

v

The beginning of the excerpt is especially informative because

the imprecise spelling conceals the true harmonic context.

c

The section

beginning with the words ''was blUht mir" is an exact transposition (one half-step higher) of the first four measures.

Schubert spelled

the chords correctly in the transposed section, but not so in the first four measures (probably to avoid too many accidentals).

It would be

wise, therefore, to carefully examine the second section.

The first

harmony is the dominant in·c major. The diminished seventh chord f-b-d-ab is also to be interpreted in the sense of a dominant in C major, but is related to the root F (CIV).

It is resolved, such that

the subdominant in C major becomes a dominant in bb minor.

The first

temporary--and subsequently definitive--return to a minor is achieved through the enharmonic equivalency of the dominant seventh chord f-a-c-eb (bbV) with the augmented six-four chord f-a-c-cfl (alV).

(

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.-

451

(_)

27.

R. Wagner, Tristan, Piano reduction, page 135

11: ll(IV) b: IV

( .::: II (!V}

27.

VllCV)) E: lll(V)

v

First, a remark should be made about the spelling.

in the first measure is interpreted as f-a-b-,jl (=all).

The chord

It resolves

to the chromatically altered chord e#·g-b-d (blV) and not to the chord e-rJl-b-d (aV)Q

E#·g-b-d finds tonal resolution in measure 7.

It con-

tinues to B major--appearing to be the same as the dominant in E major. A parenthesis, so to speak, exists between measures 2 and 7: e#-g-b-d is enharmonica11y reinterpreted as f-g-b-d (cV) with the f sustained as a pedal point.

CVI occurs next as a passing chromatic chord.

Cl I

is followed by the ab minor triad which is heard in the sense of c minor (eb is a suspension to d).

At the same time, however, this chord (as

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(

452 '

' .. /

Jl-b-d# substitu ting for f#·b-di') already anticipa tes the dominant in E major. 28.

_/\_» It..

Chopin, B minor Etude, op. 25

... ,J

~ :I•

p;o..oiii

~-·

•

,....

-•

J

-4

u

h~

-

_t~ .....

P~J

_l_

1_

:"!!!:

-IT

V =

v

g: IV

This half-ste p descendi ng sequence is made possible by means of the enharmonic identity of the

( '~

v7

chord in

JI

minor with the augmented

six-four chord in the key existing one half-ste p lower. '

29.

11 II R. Wagner, Die Gotterdam merung

v

c: V

29.

(

cb.

~b: ll(IV) -

c: V - - -

Eb: ll(IV)

The b in the v7 chord g-b-d-f is enharmo nically changed into

The chord, therefor e, can be related to F major (II in Eb major).

F-b-eb-a b can be related to the dominant in c minor (with the eb being

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453

(_,-, a suspension to d), and its enharmonic change can be subsequently introduced with reinterpretation. 30.

R. Wagner, Tristan, Piano reduction, page

~42

1" A: Vll(V)-__,_ _ __ Eb: Vll(V) Ab: I V - - - - -

30.

Chord #1 in the second measure--first appearing as cJl-tll-d-f

(AVll)--becomes the dominant substitute in Eb major through enharmonic reinterpretation (ab-c-d-f), i.e., a subdominant in Ab major. 31.

d:

1

J

by

•"'

J

P3'

d:I

31.

Schubert, Piano Sonata in a minor

JJ

113 l>p

5

!

v

i

£1 ..g

&

0

s t:ejdJ

f: I

v

The dominant ninth chord ind minor--a-c#-e-g-bb--is reinter-

preted as a suspension formation to the 16 chord in F.

This is made

possible by the enharmonic change of c# into db.

(

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(_

454

} ·'

32.

R. Strauss, Ein Heldenleben, miniature score, page 51

~,a~~~µljJ

1tf

M'F:. 0. : I F: ll(IV)

32.

V Q

(f: VI) : V

The tonic triad in Gb .major is interpreted as a triadic form

of the Neapolitan sixth chord in F. key of G major is the result.

(

ffijgJ

A digression to F major within the

The sixth of the Neapolitan chord--gb--

in the upper voice is enharmonically changed into f# and becomes the lower half-step auxiliary to the fifth of the dominant in F major. 33.

R. Strauss, Also Sprach Zarathustra

~-

r

~

j_

~~

.. -u

.,@.

I

:K

~

""

]

l -"-

.-Ii~

j

c: IV

::!;

f:

v

IV

(VII)

::!;

~

..........

(II

b~ V

r"""'

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

455

(.

33. To acquire an insight into the actually very simple harmonic context of this only apparently complicated excerptp it should be noticed that measure 1 appears over the F functioning root, measure 2 over C, measure 3 over F, measure 4 over C, and measures 5 and 6 over F.

The subdominant in c minor occurs in measuie 1 and proceeds to the

tonic.

Between these harmonies appears the passing chord fb-ab-b-d.

Downward alteration of the fifth in the diminished seventh chord cVI I is interpreted in the sense of the subdominant and as such is enharmonical ly the same as the dominant in A major!

A formation sounding the

same as cVll also appears in the second half of measure 3 except that e actually appears in the bass--not eb.

(

This tone is to be understood

either as an anticipation of the third above the next root (C) or as a downward ieap i ng aux i 1 i ary tone.

It wou 1d not be entire 1y impciss i b le

to interpret e-ab-b-d as e-