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The Shapingof usicallements

R M N D R U S S E L Lnd LLEN TRUBITT

n ivers i ty o f awai i

S HIRMER OOKSA Division of Macmillan Inc.ew York

Maxwell Macmillan CanadaCanadaMaxwell Macmillan Internationalew York Oxford Singapore Sydney

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Copyright 1992 bySchir mer Books A Division of Macmillan Inc.All rights reserved. No part of this book may bereproduced or transmitted in any form or by anymeans electronic or mechanical includingphotocopying recording or by any informationstorage and retrieval system without permission inwriting from the Publisher.Schirmer BooksA Division of Macmillan Inc.866 Third Avenue New York N Y 10022Maxwell Macmillan Canada Inc.1200 Eglin ton Avenue East Suite 200Don Mills Ontario M3C 3N1Macmillan Inc. is part of the Maxwell Communication Group of Companies

Library of Congress Catalog Card Number: 91-245Printed in the United States of Americaprinting number1 2 3 4 5 6 7 8 9 10Libraryof ongress Cataloging in Publication DataRussell Armand. 1932

The Shaping of Musical Elements / ArmandRussell and Allen Trubitt.

p cm.Includes index.

ISBN 0-02-872120-91 Music Theory.I Trubitt Allen R II Title.

MT6 R963S5 1991781 dc20 91-245CIP

MNThe paper used in this publication meets theminimum requirements of American NationalStandard for Information Sciences Permanence ofPaper for Printed Library Materials. ANSI 239.48-1984.

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1

Preface xPolyphonic Techniques

Tonal Polyphony 2Tonal Counterpoint 2The Style of the Period of CommonPractice 2

Counterpoint in the Style of the Periodof Common Practice 3Analyze the Given Melody 4Write the Second Voice 5Imitation 7Polyphonic Sequences 8

The Two Essential Features 8Writing Polyphonic Sequences 1Invertible Counterpoint

Basic Principles of InvertibleCounterpoint 11Writing Invertible Counterpoint 14Analysis of Inverted Counterpoint 17Summary 18

2 Fugue and Fugal Movements 9Exposition 2

The Subject 2The Answer 21Counterpoint Appearing with theAnswer 23Codetta 24The Second Statement of theSubject 25Continuation and Completion of theExposition 25Analytical Method 28The Central Portion 29

Restatement 29Episode 29Stretto and Coda 3

Fugue Analysis 31Summary of Sections 34Key Areas 35Contrapuntal Devices 36Melodic Treatment 37

Forms 37Applications of the Fugue Concept 38Summary 39

3 Applications of Polyphonic Techniques 4Music Employing a Cantus Firmus 41Polyphonic Music Employing a MotivicEmphasis 5

Overall Pitch Organization 5Melody 5Texture 53Form 55Tension 65Interpretation 66Summary 66

4 The Evolving Subdominant and SupertonicChords 8Augmented Sixth Chords 69

Three Types of Augmented SixthChords 7Harmonic Doubling 73Progressions 73Voice Leading 74Less Common Treatment 76Harmonic Tension and Augmented SixtChords 84

The Neapolitan Sixth Chord 86Normal Treatment 87Less Common Treatment 88The Neapolitan Sixth and HarmonicTension 92

iii

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Harmonic Analysis 92The Concept of Normalcy 93The Three Aspects of HarmonicAnalysis 93Interrelating the Three Aspects ofHarmonic Analysis 95

Summary 965 The Evolving Dominant Chord 97

The Augmented Dominant Chord 98Normal Treatment 98Enharmonic Spellings 100Nonharmonic Tones 102Tension 103

The Dominant Chord with LoweredFifth 103Normal Treatment 103Less Common Treatment 105Tension 106

The Dominant Ninth Chord 106Normal Treatment 106Ambiguous Ninths and NonharmonicTones 109Inversions 110

The Dominant Thirteenth Chord 112Normal Treatment 112Ambiguous Thirteenths andNonharmonic Tones 113Less Common Treatment 114Tension with the Dominant Ninth andThirteenth Chords 115

Writing a Four Voice Accompanimentfor a Given Melody 115Summary 116

B Less Common Chord ProgressionsExpansion of the Normal

117

v

ProgreSSion 118Secondary Augmented SixthChords 118Unstereotyped Chromatic Chords in theNormal ProgreSSion 121

Nonfunctional Harmony 123Diatonic Nonfunctional Harmony 123Chromatic NonfunctionalHarmony 125

CONTENTS

Decorative Chords 131Passing and Neighbor Chords 132Appoggiatura Chords 133Other Decorative Chords 134

Harmonic Tension 138Summary 140

7 Chromatic and Remote Modulation 141

s

9

Chromatic Pivot Chords 142Diminished Sevenths as PivotChords 142The Neapolitan Sixth as a PivotChord 147Augmented Sixths as Pivot Chords 149

Direct Modulation and VoiceLeading 150Tonal Instability 152

Transient Modulations 152Tonal Ambiguity 157Tonal Regions 163

Harmonic Tension 163Harmonic Analysis 165

Normalcy in Chord Analysis 165Normalcy in Key Identification 166Combining Criteria for Normalcy 167Tonal Coherence 169

Aspects of the Analysis 169Criteria for Coherence 170Summary 177

Writing for Instruments 178Fundamental Considerations

Instrumental Groupings 179Transposition 179Instrumental Table 181Applications 185

Score Reading 185Writing for InstrumentalEnsembles 191Summary 195

Writing Vocal Music 196Text Setting 197

Rhythm 197Vocal Melodies 200

179

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Keyboard Accompaniments 201Accompanimental Techniques 202Textural Relationships 203

Songs and Form 208Forms Used for Songs 208Relationship of Text and Form 208Introductions Interludes andCoda 209Song Analysis 209Application in Choral Writing 213

Summary 214D Variation Forms 215

Sectional Variations 216Characteristics 216Analysis 218

Continuous Variations 227Pitch and Rhythmic Organization 228Melody 228Harmony and Form 8

Application of VariationTechniques 231Tension in Variation Forms 234Summary 235

11 Sonata Forms 236

12

Sonata-Allegro Form 237Exposition 245Development 247Introduction 249Coda 251

Structural Organization 252Tension 253Sonatina Form 253Sonata-Allegro Form in theConcerto 257Summary 259

Rondo Forms 260Simple Rondo Forms 261Sonata-Rondo Forms 264Structural Analysis 271Tension 272Summary 272

CONTENTS

13

14

Analysis and Interpretation 273Factors in Analysis 274

Analytical Approach 274Form 275Tension 276Levels of Inquiry 276Interpretation 281Summary 282

Impressionistic Harmony 283Scales 284Chord Progressions 286

Harmonic Analysis 288Melody and Harmony inImpressionism 289Types of Chords 291

General Treatment of Triads andSeventh Chords 292Higher Tertian Structures 293Added-tone Chords 298Other Nontertian Harmonies 301

Harmonic Tension 305Summary 306

5 Melody Texture and Form in ImpressionisticMusic 307Melody 308

Motives 308Emergent Tones 310Texture 310

Alternating Textural Roles 312Intermittent TexturalComponents 312Timbre 316DynamicS 319Form 319

Phrases and Cadences 319Higher Structural Levels 320Larger Forms 322Summary 326

v

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16 Tonal Music in the Twentieth Century:Part I 3 7Types of Tonal Organization 329

Variable Pitch Complement: FreeTonality 329Regulated Pitch Complements 332Tonal Centers 336Rhythmic Organization 337Metric Devices 337Nonmetric Rhythm 347Melody 348Harmony 350Interval Emphasis 355Texture 355

Varieties of Coupling 356Register Changes 359Rhythmic Density 362Emphasis on Texture 364Timbre and Dynamics 364Unity and Variety 366Summary 366

17 Tonal Music in the Twentieth Century:

v

Part 2 368Phrases and Cadences 369

Rhythmic Considerations 369Melodic Considerations 372Harmonic Considerations 376Textural and TimbralConsiderations 377Structural Relationships 382Forms 383

Smaller Forms 383Arch Form 384Sonata Allegro Form 386Variations 387Rondo Form 387Fugue 388Tension 388Stylistic Analysis 390

Pitch Organization 390Rhythmic Organization 390Melody 390Harmony 390Texture 391Timbre 391

CONTENTS

1B

19

Dynamics 391Form 391Tension 391Summary 391

Pitch Sets 393Pitch Class Sets 395

Normal Form 396Designation of Sets 397Interval Classes 398Inversions of Sets 398The Prime Form 399Interval Vectors 4Analysis of Pitch Sets 401Cell Technique 4 8Analysis of Pitch Sets with OtherFactors 413Form 416Tension 419Writing Free Atonality 423Summary 424

Serial Techniques 4 5The Forms of the Series 426Application of Serial Concepts in theMusical Context 429Subset Structuring 433Combinatoriality 436Sources Sets 438Exploring Relationships betweenDifferent Series 439Other Types of Serialism 440Analysis 441Summary 442

2 0 Finale: Recent Trends 444Recent Trends toward GreaterDiversification 445Post Webern Tendencies 445Aleatoric Techniques 448Recent Notational Symbols 449

Pitch 450Repetition or Improvisation 451

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Recent Trends toward GreaterUnification 452Texture oriented Music 457Minimalism 461

Eclectic Styles 463orm 463

Tension 464Electronic Music 469

Analog Techniques 469Computer Music 47Summary 47

Appendix A Review 474Sample Analysis 478

Appendix B Guide to AnalyticalSymbols 48Glossary 484Index 489

CONTENTS v

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S ~ v e r l interrelat.ed concerns h.ave been influential in giving this volumeIts final form. FIrst, the ordenng of the chapters reflects the historicaldevelopment of music since the seventeenth century. The early chapterson polyphony emphasize Baroque models though Classic and Romantic exam-ples have been included where possible), then the chapters on chromatic har-mony and the larger forms emphasize the Classic and Romantic eras, and in thefinal chapters the focus shifts to the Impressionists and composers of the twentiethcentury. Hence this volume can be divided into two parts, with chapters 1 13 deal-ing with the music of the common practice period, and chapters 14 20 coveringthe transition into this century and continuing up to the presentAnother concern that has had a formative impact on this text is our desire to givethe student a broadly based, systematic procedure to use in analysis. The varioustheoretical elements of music are dealt with in systematic order, with the hope thatconsistency of approach will benefit the student engaging in analysis. Our method,which we call an integrating analysis is presented fully in chapter 13, by whichpoint the student has the basic technical background needed for the analysis oftraditional tonal music. The elements of an integrating analysis are, in order: pitchand rhythm conceived in broad terms), followed by melody, harmony, texture,timbre, and dynamics. The reason for placing these elements in this particular or-der is partly logical and partly to insure that no contributing factor will be over-looked in the analytical process. After these areas have been examined in more orless depth depending on the purpose of the analysis), the ami.lysis focuses on twosynthesizing considerations: form and tension. The analysis thus moves from thegeneral to the particular and back to the general.The final concern of the authors has been to relate theoretical studies to perfor-mance as closely as possible. This is reflected in the numerous discussions of ten-sion, the rise and fall of which is of primary concern to the performer.

t is unlikely that one would use volume 2 of this text without having gonethrough volume 1 but for those who do, and for those who would like to surveysome of the materials covered in volume 1 the appendix of volume 2 containssummary material including lists of terms and symbols, a chart of normal progres-sions, a sample analysis, and a glossary.Prior to publication the two volumes of this text were tested for several years inmusic theory classes at the University of Hawaii at Manoa. The authors wish to ex-press their gratitude for the numerous corrections and suggestions made by ourstudents and by the following colleagues: Professors Gary Danchenka, E. TakeoKudo, R. Neil McKay and Byron K. Yasui.

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TermsIntroduced inhis hapter

olyphonicTechniqueston l polyphonyton l

coun te rpo in tper iod o f

co m m o npr c t i ce

polyphonicsequence

invert ib lecoun te rpo in t

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P OlYPhOnyafter 1600 was based on the principles of tonality combinedwith techniques of counterpoint such as imitation invertiblecounterpoint, and polyphonic sequences. The study of two-voicecounterpoint and imitation that was begun in the first volume will now beextended and will come to include polyphonic sequences and invertiblecounterpoint.

TON L POLYPHONY

tonal polyphony

tonalcounte rpoint

Before 1600 musicians used a polyphonic style that was based on the system ofdiatonic modes; after that date, however, the modal system was gradually replacedby the present system of major and minor keys. The development of the majorminor system together with advances in harmony brought tonal music and tonalpolyphony into prominence. The tonal system assumed a dominant role that itmaintained until the end of the Romantic era, around 1900.

onal ounterpoints tonality emerged there also arose a contrapuntal style of writing, which remained the model for polyphonic texture until well into the nineteenth century.Stylistically, tonal counterpoint combines tonality with contrapuntal techniques,most of which had been used before 1600 in modal music. It retains wide applica

bility even today; hence it is used as the model for present-day study.

The Style of the Per iod of omm on Pract iceperiod of Tonal counterpoint was developed during theperiodof ommonpractice the pe-common pract ice riod between 1600 and 1900 in which composers in the Western world shared a

more or less common musical style. Using the major-minor system of keys, thisstyle included modulations and harmony with stereotyped, normal progressions. It will be advantageous to review the chart of normal progression that appeared in volume 1 (see table 1-1).

CH PTER ONE olyphonic Techniques

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n major keys

group 5 group 4 group 3 group 2 group 1iii vi ii Vvii

n minor keys

group 6 group 5 group 4 group 3 group 2 group 1VII III VI iio Vv iv viio

T B LE 1 The normal progression of chords

In addition to chord progressions, cadence patterns and many other facets ofmusic became normalized during the period of common practice. A commonvocabulary of familiar patterns provided the listener with clear tonality, that iswith tonal or key orientation, throughout a piece of music.

ilil i O U N T E R P O I N T IN THE STYLE O THE PERIODO F C O M M O N PR CT ICE

We began a studyof basic counterpoint in volume 1 where it was shown that har-mony is a coordinating element that enables us to combine independent melo-dies, each with its own contour, direction, and rhythm. We shall now review thisinformation in preparation for the study of polyphonic techniques. Our discus-sion will center on the procedure for writing a contrapuntal line with a given so-prano. This procedure, which is illustrated using the melody shown in example I-I, consists of two stages: 1) an analysis of the given melody with which thecounterpoint will be written and (2) the actual writing of the counterpoint.

E X M P L E 1 1 Melody

CH PTER ONE Polyphonic Techniques

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4

nalyze the Given MeladyIn order to write tonal counterpoint, it is necessary to have an analytical under-standing of both the harmonic implications and the melodic structure of the givenline.

Step I Harmonic nalysisFirst, identify the harmonic implications of the given line. Your decisions at thispoint maybe tentative, subject to later adjustment. Usually preferable is a relativelysimple harmonic background, with few altered chords and an emphasis on thosechords lying close to the tonic in the chart of normal progressions (in the lower-numbered chord groups). Rather short harmonic cycles are also preferable, aslonger progressions may create unwanted restrictions on melodic flow. If theanalysiS shows ambiguous moments, you should make tentative decisions, whichare subject to later revision as the added melodies begin to take shape. Normalprogressions are expected, of course, as is a moderately placed harmonic rhythm.Keeping the harmonic analysis rather basic, labeling primarily harmonies on thestrong beats will allow greater freedom for melodic activity as voices are added(see ex. 1-2 .

EXAMPLE 1 2 Basic h rmonic analysis of given melody

C: ii v v

Step 2 Melodic nalysisIdentify the more prominent chord tones in the given melody. These are usuallyemergent tones (see Guide to Analytical Symbols in the Appendix). In simpletextures one emergent tone per measure is suffiCient, but more may be needed,depending on the pace and contour of the melody and its harmonic implications.In locating these emergent tones, identify tones that will be significant in buildingsonorities with the added voices. The duration and metric location of these toneswill be very important. In example 1-3 the emergent tones are indicated with up-ward arrows.


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E X A M P L E 1 3 Location of emergent tones in given melody

c: ii v v

W ri te the econd Voice

tep I Sketch PitchesMake a sketch of the important pitches of the next most important line (after themelody) which is in this case, the bass. As the new voices are added the moresalient lines will be determined first, and the less salient parts will make any necessary accommodations as the texture becomes thicker. (See m rg nt ton s inGuide to Analytical Symbols. ) Using stemless note heads, plot the importanttones that are to be set against the emergent tones of the given melody. The exactrhythm will be determined later; our purpose now is to develop the overall shape

of the second-most salient line. Although there are many examples in the literature in which the second line moves obliquely or parallel with the first, contrarymotion will assure greater independence of the parts. Note the emphasis on theharmonic intervals of the third and sixth. These intervals are most useful in representing a chord in fewer than four voices. At this stage in the process, when locating the emergent tones, one seeks a balance between linear and vertical considerations. We must consider good voice leading, and since the part be ing dded is thebass line, we must pay attention to the chord inversion that will be formed. Example 1-4 shows a sketch with these factors taken into account.

E X A M P L E 14 Sketch of important tones of the second voice

c 16 ii v 16 v

CH PTER ONE Polyphonic Techniques 5

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tep 2 Sketch RhythmThe next step is to plan the rhythmic features of the second line. Several factorsmust be taken into account:1. The resultant rhythm, that is the rhythmic pattern that is formed by thetwo voices sounding simultaneously, is given first consideration. Rhythmically weak or dead areas should be avoided. Usually a rather constant

rhythmic flow is desirable, such that the attacks of the tones of the two linesare relatively evenly spaced. Gaps in the rhythmic activity that arise at thispoint may be filled later by the third part, but it is usually best to limit theresponsibilities of the third voice, in order to preserve the salience of thesecond line.2. When salient lines occur Simultaneously the agogic accents often occur atdifferent times. If the agogic accents coincide too often, the contrapuntaleffect will be weakened. (See gogic ccent in Guide to Analytical Symbols. )3. The second line may stress unity with the first line and borrow motives fromit or it may be differentiated and introduce one or two new motives of itsown. Example 1-5 illustrates a moderately differentiated line.

EXAMPLE 15 Sketch of the rhythm of the second voiceI

c: r ii v r vi u i r r r U r

tep 3 Complete the SecondVoiceHaving determined the most important pitches to be used and the broad rhythmicoutline of the second part, you may complete the line by choosing nd placingnon-emergent pitches. The contour must remain correct in its details, that is itmust avoid forbidden parallels, allow leading tones to resolve, nd so on. The basic sonority will be consonant, but nonharmonic tones, particularly passing andneighbor tones, will appear. Suspensions may also be used with good effect, butappoggiaturas and escape tones should be used sparingly lest they obscure theharmony. The chord representation should be clear, and non-emergent chordtones may become quite prominent in the course of completing the second voice.In example 1-6 the completed bass is given, with rhythm and all pitches specified.The selection of harmonic intervals shows some preference for thirds and Sixths,but less than in the earlier sketch.


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IM ITATION

EXAMPLE 1 6 Second voice completed\ I F9 J ..r--- I

f I I ~

I -: r ii v r v

The procedure for composing imitative counterpoint in two parts waspresentedin volume 1 and will be reviewed here. The plan consistsof three steps, i llustratedin example 1 7. You may now follow procedures for writing counte rpoint that aredetailed earlier in this chapter. Steps 2 and 3 above are applied to succeeding portions of each voice if the imitation is to be continued: See (2) and 3) in example 17.

EXAMPLE 1 7 Two-voice imitative counterpoint\ 3) I '---...

....@ 2).I -D: r vii r

CD The given subject, the leader, appears in the first voiceup to the pointwhere the second (answering) voice enters. A harmonic analysis is included.

@ The second voice, the follower, is written at the chosen intervaland delay,and a harmonic analysis is included.@ The counterpointof the leader is completed, using new material.


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POLYPHON IC SEBUENCES

polyphonisequen e

I

\ I

I IW1J '; 1I

B

A motive or passage that is restated immediately in the same voice at a differentpitch level is called a melodic sequence. When the sequencing process is extendedto include all voices of a polyphonic passage it is termed apolyphonic sequence.The voices of a polyphonic sequence need not have the same motives.

The Two Essential Features

The leg is the element of a sequence that is restated at different pitch levels. A normal, unmodified polyphonic sequence consists of two or more voices simultaneously employing sequences that possess the same essential features, that is, thesame pattern of pitch-level change and legs of the same length. Note how the pattern of pitch-level change is described for the polyphonic sequence shown in example 1-8. The length of each leg is also indicated.

EXAMPLE 1 9 J. S. Bach: Well Tempered Clavier I, Prelude 20 BWV 889polyphonic sequence: descending by seconds; I-bar leg

I I

I III I.b..

The LegThe leg is shorter than a phrase- typically two bars at the longest, and a metricallysimple division of a measure at the shortest. Example 1-8 illustrates a one-measureleg, and example 1-9 shows one polyphonic sequence with a leg of one-half of abar and a second sequence with a leg of one beat. Special care must be taken inidentifying the first and last legs of a sequence, as different voices may take up orabandon the sequential pattern, or leg, at different times. Melodic sequences inindividual lines become polyphonic sequences when all voices present participate in stating the sequential pattern. Often the polyphonic sequence will begin ata metrically weak point, as in example 1-8. In example 1-9, a motive taken from thefirst sequence descending sixth with tied sixteenth notes and descending step)provides the basis for a second sequence using shorter legs.


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fI

til

:

EXAMPLE 1 9 Bach: Clavierilbung Partita II, Sinfoniapolyphonic sequence: descending by fifths;2-beat leg polyphonic sequence: descending byseconds; I beat leg

~ . f - ~ r--..

Il)

.f - I

~ ~ ~ q eqT ~~ )l J I

In order for a passage to be considered a sequence, of course, its leg must appear at least twice. However, a sequence is usuallynot used more than three times.Both sequences in example 1-10end before the third legs are completed.

The attern ofPitch Level ChangeA sequence maybe diatonic as in ex. I-lOa in C major)or modulating. A sequenceis modulating if its pitch-level change involves alterationsof the scale and tonic orat least suggests temporary tonics through secondary dominantsand such as inex. I-lOb in D major). Examples I-lOa and I-lOb illustrate polyphonic sequencesin three voices. These passages are typical in that they maintain the sequential pattern in all three voices until the third leg, in which the voices abandon the patternat different times.

EXAMPLE 1 1 0

B Bach: Sinfonia No.8polyphonic sequence: ascending by seconds; 2-beat leg

I

b Bach: Sinfonia No.3 polyphonic sequence: descending by seconds; 2-beat legI I


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1 0

Writ ing olyphonic SequencesThe procedure for writing a contrapuntal sequence in two voices can be organized into four steps:1. Give the subject to the first voice ex. 1-11). This establishes the intervallicpattern of the first leg and the length of all legs of the sequence.

EXAMPLE 11 First leg in one voice

2. Repeat the leg in the first voice at anew pitch level ex. 1-12). This establishes the interval of descent or ascent. As in example 1-12, it is common fora sequence to complete two legs and begin a third.

EXAMPLE 1 12 First leg nd continu tion

3 Assess the harmonic implications of the subject. With this harmony in mind,add a second contrapuntal voice to the first leg ex. 1-13).

EXAMPLE 1 13 Addition of second voice to the first leg

G: I-

IV

4 Continue the counterpointof the second voice with the later legs of the sequence ex. 1-14).At this point you should check the melodic nd harmoniccontinuityof the voices; some revisions maybe necessary to assure a smoothtransition from leg to leg.

CH PTER ONE PolyphoniC Techniques

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E X A M P L E 1 14 Polyphonic sequence in two voices

G: 16 IV iii vi6 ii

In example 1 15 the passage is continued to complete the harmonic cycle ndthe analysis of the sequence is added.

E X A M P L E 1 1 5 Polyphonic sequence continued to c dencepolyphonic sequence: descending by seconds; 2-beat leg

lu I I- ....- -JG: 16 IV viio6 iii vi6 ii V 16I N V E R T I B L E C O U N T E R P O I N T

invert iblecounte rpoint

Invertible counterpoint simultaneously satisfies two principles: variety nd unity.

Basic Principles of nvert ib le Count er po i n tInvertible counterpoint also called contrapuntal inversion refers to the potentialfor exchanging voices within the vertical space of a polyphonic texture: Materialthat was originally lower in the texture can at some later pOint be placed higherand the corresponding music that was originally above can be placed in the lowervoice. The term is used whenever the restatement of material in the lower voice isexchanged with an upper voice; a th ird voice may be present but is not necessarilyinvolved in the inversion process. The exchange of parts may occur at any point in

CH PTER ONE Polyphonic Techniques 1 1

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2

the music following their initial appearance. Sometimes the inversion occurs immediately after the initial statement, while at other times the inversion appearsmuch later. However, the term invertible counterpoint is also applied to passageswritten so that any of three, four, or even five contrapuntal lines may be placed inthe bass. If the music of two voices is treated as invertible counterpOint, it is calleddouble counterpoint ; if three voices, triple counterpoint ; nd so forth.

nversion at the OctaveThis is the most common type of inversion, and it illustrates the principle of intervallic inversion: Unisons became octaves, thirds became sixths, et cetera, as shownin example 1 16. Inversion in which these intervallic changes take place is calledinversion at the octave.

EXAMPLE S. Inversion at the octave

ci -f : M II 3These intervals: I 2 3 5 6 7 8Invert to become: 8 7 6 5 3 2 1

- - - - - 1l 09: i

If polyphonic lines are inverted so that these changes in intervals come about, itis said to be inversion at the octave also. In example 1-17 the principle of inversion has been applied to two polyphonic lines. Compare the bracketed portions ofmeasures 3 and 4 with the corresponding portions of measures 5 nd 6. Notice thatthe voices have exchanged positions and that the intervals between the voiceshave become inverted according to the relations shown in example 1 16. Becauseinversion at the Single, double, or triple octave is Virtually the same, all three areoften referred to as inversion at the octave.

nversion at Other IntervalsInversion may also occur at intervals other than the octave. Inversion at the tenthand twelfth is found infrequently. The chart in example 1-18a applies to inversionat the tenth, and example 1-18b illustrates inversion at the twelfth.

CH PTER ONE PolyphOniC Techniques

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EXAMPLE 1 17 Bach: Invention No 15 -- T

contrapuntal inversion at the octave. See mm. 3-4

EXAMPLE 11

a Inversion at the tenth

Invertedintervals3) 2) 8 7 6 5 4 310 9

1 2 3 4 5 6 7 8 9 10 or 1 2 3 4 5 6 7 810 9 8 7 6 5 4 3 2 1 3 2 8 7 6 5 4 3

b Haydn: Mass No 12 Contrapuntal Inversion at the twelfth1.

\ I I I

II . .:

2 \ I -

contrapun tal inversion at the twelfth See mm. 1-2 in ex. bl

C H PT ER ON E PolyphoniC Techniques 1 3

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1 4

A careful scrutiny of the charts in examples 1-16 and 1-18a, showing each interval and its inversion, will reveal why inversion at the octave is so useful. In doublecounterpoint at the octave, most consonances remain consonances-that isthirds become Sixths, and unisons become octaves. One feature of double counterpoint at the tenth is that parallel sixths become parallel fifths.

EXAMPLE 1 19 Parallel sixths inverted at the octave tenth and twelfthOriginal passage1\ n - - 1 n

Inverted at the octave at the tenth at the twelfth1\

- 'U ' -

Wri t ing nvertible CounterpointIn writing invertible counterpoint we will limit ourselves to the octave as the interval of inversion. The procedure to be followed is based on that used in writingtonal counterpoint.

nalyze the GivenMelody1 armonic nalysisSelect chords for the given melodic line, to which a lower part will be added later.Choose a relatively slow harmonic rhythm in order to keep the listener s attentionfocused on the melodic lines. You must take care to choose chords that, wheninverted, will not produce an unwanted second inversion. For instance, a rootposition IV chord (E-flat in the bass) in the first measure of example 1-20 wouldinvert to become V ~ (B-flat in the bass). As explained in previous study, triads insecond inversion are treated in very limited ways, so the inverted version mustconform to such correct treatment.

EXAMPLE 1 20 Given melody with basic harmonization

Bh: Il r

V7


UUR

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2 Melodic AnalysisIdentify the more prominent chord tones in the melody. These tones are typicallyemergent tones. In example 1 21 the emergent tones are circled.

rite the econdVoice1 Sketch the econdVoiceWithin the chosen harmonic framework, select the emergent tones for the addedpart. These tones are shown as stemless note heads in the bass in example 1 21.Certain intervals require special care. For instance, if a soprano note is harmonized so as to be the fifth of a triad, then under inversion it will become the bassnote of a second-inversion chord, which must be handled correctly. Ofcourse successive fourths in any passage would invert to become parallel fifths. Notice inexample 1 21 that the original chords sketched in example 1-20 have been kept,although their inversions sometimes differ.

EXAMPLE 21 Sketch of the important tones of the second voiceI

I

Bb: 16

T

y43

2 Complete the econd VoiceThe second voice is completed using rhythms that are complementary to the firstpart. Attention to the resultant rhythm should prevent dead spots, or unintendedconflicts with the meter. Agogic accents in the two parts may coincide at strongmetric pOints, but too frequent coincidence will weaken the independence of theadded part. s example 1 22 shows, additional pitches are selected to provide melodic interest a salient line) and correct harmony and voice leading.

EXAMPLE 1 22 Second voice completedI I I

I

IBb: 16

I


I

1 5

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1 6

nvert th PassageThis passage can e inverted by moving the material of the upper voice down afifteenth (two octaves) into the bass voice and the lower material into the uppervoice, as shown in example 1-23.

EXAMPLE 1 23 Inversion at the fifteenth of example 122\ I

I ~ I,......,

I .....B ~ V ~ r

The original distance between the voices is an important factor in writing invertible counterpoint. If the given voices move as far as say an octave or fartherapart, then the contrapuntal inversion at the octave is impossible: The upper partwill not become the lower. Example 1-24a would require inversion at the fifteenthfor a real exchange of parts to occur. In example 1-24b the parts are not exchangedafter the first beat of measure 1.

EXAMPLE 1 24 Inversion at the octave without exchange of parts

Since the intervals available for invertible counterpoint are somewhat limited,the two parts to be inverted may taken by themselves, produce correct but notnecessarily very appealing or harmonically rich results. Combinations of chordroot and third are preferred, and doubled roots are used sparingly. Rememberthat other voices may e present to fill out the harmony.


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I

II

Analysis of Inverted CounterpointIdentifying a passage in invertible counterpoint is simplest, of course, when thepassage is followed immediately by its inversion. When there is a great deal ofintervening material, one must be quite alert to notice a recurrence of a particularmelodic line in combination with the same counterpoint with which it appearedearlier. The difficulties of recognizing an inversion may be compounded by thepassage's recurrence in a different key. To determine the interval of contrapuntalinversion, locate a particular interval in the original passage and the corresponding interval in the inverted passage. Add these intervals, and subtract 1 from thesum: The result will be the interval of inversion. In example 1-25 note that in measure 2 a tenth becomes a sixth: 10 6 = 16 and 16 - 1 = 15 the interval ofinversion.

EXAMPLE 1 25

B.

Mozart: Requiem, K. 626, Kyrie. Contrapuntal inversion atthe octave

original interval =10fI ~ = = = = -@ I I ~ '

1.: .I r 1 . . . . .= f

inverted interval=6b fI . .I I \ . - ..I \

I:I iiiiOiiiiiiii - -

contrapuntal inversion at the octave. See mm. 2-4

Subtracting 1 is necessary because our system of naming intervals counts the unison as one, even though the distance between its pitches is zero.When analyzing passages in invertible counterpoint, keep these points in mind:1. Locate the beginning and ending by comparing the original and invertedmaterial. Enclose both passages in brackets.2. Indicate the device and the interval of inversion above the second bracket,and give the measure numbers for the original passage: inversion at theoctave; see measures 2-4.

One final point: The devices and techniques discussed in this chapter are notmutually exclusive. They may be combined in various ways-for example, sequence and imitation, inversion and sequence, imitation and inversion.


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UMMARY

8

The development of the major-minor system together with advances in harmonybrought tonal music and tonal polyphony into prominence around 1600, at thebeginning of what is now called the per iod o common practice.The preceding chapter deals with the analysis and writing of polyphonic devices in tonal counterpoint, including imitation, polyphonic sequences, and invertible counterpoint. Each of these techniques is useful s a means of achieving abalance of unity and variety in the music. The procedures for composing withthese techniques call for a melodic and harmonic analysis of the initial material.This is followed by an incremental completion of the contrapuntal voice, takingcare to avoid dead spots in the rhythmic flow and unwanted parallel motion between the voices, and maintaining a desirable level of interrelationship betweenthe voices. While agogic accents occasionally occur simultaneously in one, two, orthree voices, too frequent coincidence of these accents will weaken the independence of parts that is at the heart of the polyphonic texture.

CHAPTER ONE Polyph nic Techniques

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,.-.. - -,

TermsIn t roduced nThis Chap te r

ugue andugalMovementsf uguesubjectfugal exposi t ionhead o f a fugue

subject )answe rreal answe rt ona l answe rcoun te rsub jec tcode t tacen t ra l por t i on

r i torne l lot r ea tmen t

res ta temen tepisodefa lse en t rys t r e t t ocodar i torne l lo f o rmfuga tofughe t ta

CH PTER TWO ugue and ugal Movements 9

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fuguesubjectfugel exposit ion

A fugue is a polyphonic work or portion of a work that presents one ormore initial melodic themes, called subjects in a systematic way knownasfugal exposition and then restates the subject one or more times. Amore specific definition of the term is not very useful, as differing characteristicsmay be found in works by various composers. It is often suggested that the termrefers to a technique, and not a specific form. Generally two parts can be identifiedwithin any fugue: 1) an exposition and 2) a central portion. Although the termfugue was first used during the Renaissance, it is the Baroque fugue particularlyof Bach and Handel) that today is considered typical. The Baroque era extendedfrom about 1600 to 1750.

2E X P O S I T I O N

head of a fuguesubject

2

A fugue is written for a specificnumber ofvoices or parts, usually from two to five.The voices enter in succession, each stating the subject in imitation of the preced-ing voice. This general description may be indistinguishable from descriptions ofround or canon; but the imitation in fugues is ofa highly specialized sort, as amorecareful examination of the fugal subject and other components of the expositionwill reveal.

The SubjectFugue subjects normally are quite distinctive and make a strong impression thatgives them a clear identity throughout the work. This identity is necessary in thecontextof complex contrapuntal textures that characteristically pervade the fugue.The subject may be as brief as two beats or as long as several measures. Often thesubject opens with a striking figure that sets it apart from the remainder of thesubject, as in example 2-1. This opening figure is known as the he dof the subject.

EXAMPLE 2

a. J S Bach: Well Tempered Clavier I Fugue 7 BWV 852

~ '1, e r J J J J j qf] I r r Fb Bach: Well Tempered Clavier I Fugue 11 BWV 856

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nswer

real nswer

ton l nswer

The Answe r

Immediately after the opening voice completes its statement of the subject, a second voice enters with the same material. This imitation is known as the answerand it is usually transposed up a PS; that is the imitation is at the 5th above or 4thbelow). n answer in which every tone of the subject is transposed exactly up a PSor down a P4 is called a real answer Normally the subject appears in the tonic keyand the answer in the dominant key see ex. 2-2).

EXAMPLE

s Bach: Well-Tempered Clavier I Fugue 4 BWV 849subject answer r oo IIr

b Bach: Well-Tempered Clavier I Fugue 1 BWV 846subject answer

e t J J J raJ? I ;1)5J]11 t no E fci I tfJrrr6Each of the real answers in example 2-2 by itself, appears to be in the key of thedominant. When answering certain subjects composers use a modif ied type of imitation known as the ton l answer In example 2-3 notice that each answer imitateslike a real answer most of the time; however, one or more tones of the subject areanswered at the P4 above or the PS below. The tonal answer is most often foundwith subjects that either 1) begin on the fifth scale degree, 2) skip from the firstto the fifth scale degree, or 3) modulate. Subjects that emphasize the first and fifthscale degrees present the tonic key in its strongest light; the tonal answer also emphasizes these tones, at least initially, and thus reaffirms the tonic and the overalltonality. The reasons and techniques for writing tonal answers are quite complex,

as these were developed in the Renaissance period and altered over the centuries.We will not undertake a full discussion of this topiC here. For the present we shallfocus on the means for identifying a tonal answer, and leave the writing of tonalanswers to a more detailed study of counterpoint. In example 2-3 the notes circledin each tonal answer are those that deviate from an exact transposition of the subject.

CH PTER TW O Fugue and Fugal Movements 2

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EXAMPLE 2 3 Bach Well Tempered Clavier I sele ted fugue subjects andanswersNo. 2 BWV 847): subject n Ianswer

No 7 BWV 852): subject

answer

No 8 BWV 853): subject

answer

No. 13 BWV 858): subject

answer

No. 18 BWV 863): subject

answer

CH PTER TWO Fugue and ugal Movements

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Count er po in t ppear ing wi th t h e A n s w e r

cauntersubject

As the second voice states the answer the first voice provides a contrapuntal ac-companiment. This accompanimental material may not be particularly significantin the later development of the fugue or it may become very important. If it consistently appears with the subject as a kind of associate or partner melody then it isknown as a countersubject When a countersubject is used it is usually written ininvertible counterpoint with the subject so that it may appear above or below thesubject. Note the ways in which the countersubjects are used in examples 2-4a and2-4b.

E X A MP L E 2 4

B . Bach: Well Tempered Clavier I Fugue 11 BWV 856,answer

\ 5II ... .fI . . ....... . . . . fL:\

-subject -countersubJect

I - 10,countersubjectI q ..... --. j r [ I~ ~ ~ ~ . . . . ... I h '. f l ... 6. fJ 1 J -I : -

II . ..\ r I l I I l.. T T .; r ~ . ~ -r r I

rI . .--.rb. Bach: Well Tempered Clavier I Fugue 7 BWV 852

r subject r ,countersubject\ , - ,-, .,. -....I ; ==:::I::::j IiiiiiiiiIiiiii...-:

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t

4

EXAMPLE 2 4b continued)

subject.J

In example 2-4a the music of the alto in the lower staff) in measures 5 7 is founda P4 higher in the soprano in measures 10-12. In measures 5 7 the alto has thecountersubject while the soprano has the answer; in measures 10-12 the sopranohas the countersubject while the bass has the subject. Each voice enters with thesubject or answer and then presents the countersubject with the entrance of thenext voice.

In example 2-4b the countersubject appears in the soprano in measures 3 4and in the alto in measures 6-7. Ifone compares the details of the countersubjectin these two statements it becomes apparent that the countersubject includes onlythe last eight notes of the soprano in measure 3 and the alto in measure 6 and thefirst nine notes of the soprano in measure 4 and the alto in measure 7.

adet ta

One can determine the exact length of the subject by observing how much of thematerial of the opening statement is used in succeeding presentations and howconSistently it is used. The subject may not include the material immediately preceding the entry of the answer. One might expect to find a comparable delay before the entry of the third voice; but whereas the subject prepares the entry of theanswer by moving toward or even modulating into the key of the dominant, theanswer does not always end with a ready approach to the tonic especially before


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cade t t ethe entry of the third voice). A passage delaying the entrance of the third voice iscalled a codett or bridge and usually modulates back to the tonic key. In manycases it consists of a continuation of the motives already used in the subject, theanswer, or the counterpoint accompanying the answer. Notice that in each of theprevious examples (exx. 2-4a and b) a one-bar codetta provides this transition inpreparation for the entry of the third voice, which thus seems to arrive late.

The Second S t a t e m e n t of t h e Subjec tIn most fugues the first, third, and i th (etc.) voice entries present the subject,while the even-numbered entries present the answer. On rare occasions, however, one finds a fugue in which the subject is followed by two successive answers.The vocal terminology SATB is normally used to identify the entries of a fugue.This terminology is employed even when the ranges involved do not correspondto vocal capabilities. The differences between the registers used by a subject andits answer do, however, make it logical to follow a subject in the soprano or tenorwith an answer in the alto or bass, and vice versa. In most cases the third voice willenter an octave above or below the first entry. s the third voice states the subject,the second voice will proceed with the countersubject (if there is one) or othercontrapuntal material. Concurrently, the first voice may move to other material,but it also may present a second countersubject. One can determine whether asecond countersubject has been used only by looking ahead in the fugue to see ifthe material in question appears regularly in association with the subject.The terminology for describing the structure of fugues varies. The term doublefugu is especially problematic. This term sometimes denotes a fugue with a regularly recurring countersubject, which is viewed as a second double) subject. Insome fugues the countersubject-or second subject-always appears with thesubject, even in its initial statement. The effect of the opening, then, is one of twovoice counterpoint, in contrast to the monophoniC opening that characterizesmost fugues. Example 2-5 presents the opening of a well-known fugue of this type.

ont inuat ion nd omple t ion of the Exposit ionEach voice of the fugue enters in turn with the subject or answer. When all voiceshave thus presented the subject or answer the exposition is complete. The exposition in example 2-4b ends on the downbeat of measure 8 and the central portionbegins immediately thereafter. Occasionally, as in example 2-6 one finds a fuguein which the initial presentation of the subject in all voices is followed by a relatively brief passage leading to a strong cadence. In such cases, the cadence marksthe close of the fugal exposition.


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EXAMPLE 2 6 Mozart: Requiem K 626 Kyrie\ Allegro

\ f

Chri-ste e - Ie - \

f .I r ..... =

Ky - ri - e e - Ie - i -son e - Ie -II Allegro

I @J j r r r b.L.. I- I II ,: ,,,I V .. I l i# =i II 11 . - ........=:=\ f =

IKy - ri - e e - Ie - i - son, e - Ie -

\ -H...

- i - son\ f

r r -Chri-ste e - Ie -

.---. ..... =- i - son e - Ie - i -son Ky - ri -

fI I I J I,,@J ~ t . r .u UdS,... ..;.J I q :.Lr r r r - ~ 1 ' r - r 1 ' Ll L r 666[- I :

-J

6 CHAPTER TWO Fugue and Fugal Movements

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IIIt

flIt

IIIt

:

\

t :

EXAMPLE 26 . continued

.- - -- i - son, e - e - i - son, e - e -f

I R ... - -Ky - ri - e e - e - i - son e -- I- i-son, e - e - i - son

~ -e e - Ie - i - son, e - e - i-son Chri-ste e - e -i"""" =I I I J J I I I -. .

L b:J I r I I I r r rhTI r J; hJ - n J J tJ I i.. - .... I

EXAMPLE 26 . Bach: Well Tempered lavier II, Fugue 9, WV 854

II

Grave J = 60\ II fl a 4

:

r rJI

0

I I I

10

r r r r r -lI J I I

J

CHAPTER TWO Fugue and FugalMovements

I IJ II J nJ orJ. J J J; l

7

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2B

If on the other hand, the passage leading to a strong cadence is extensive, thenit is usually best to assume that the exposition is complete when the last enteringvoice has stated the subject or answer. In rare cases the number of voices mayfluctuate. The number ofvoices in the exposition may gradually increase, but thishappens in a flexible way that does not obscure the structure of the exposition. Inexample 2-7 the presentation of a three-voice fugue is regular until measure 11,after which the number of voices varies between two and four.

EXAMPLE 27 Bach: Sonata in C for violin solo, BWV 1005, Fugue

nalytical MethodThe following graphic approach can be used to diagram the presentation of material by the various voices. Figure 2-1 shows an analysis of examples 2-4a and 2-4b.Sections are labeled at the top of the graph; in each example here only the exposition is diagramed, and its codetta is labeled in parentheses the bracket beneaththe label marks the duration of the codetta). Each barline is marked, and the firstand every fifth measure is numbered. Voices are graphed in the order of theirranges, high to low, and capital letters indicate the principal material employed: Sfollowed by a dashed line denotes the subject; A followed by a dashed line denotesthe answer; and CS followed by a solid line denotes the countersubject. ther material is shown with a jagged line. Such material may include counterpoint that ismotivically related to the subject, answer, or countersubject, or it may be new material. Keys are indicated if they are in effect for at least two measures and confirmed by a clear cadence. Transient keys are shown in parentheses.


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B Bach: Well Tempered Clavier I Fugue 11 WV 856 b Bach: Well Tempered Clavier I Fugue 7 WV 85Sections: ExpositionMeasures: 1

codetta)----I10

Sections: Exposition codetta)----Measures: 1 5

Material Uop. A ----------------\ l \csin Alto S----------VV\lcs \ f \ / \NV

Voices: Bass S--------------Material U P

in AltoVoices: BassS ---------VVVVVVVVV

A \ IV NVVS -----------

H : B ~ : ) H : )I (Bk)(H:eys: F: I c: F: I Keys:

F IGURE 2 1 Analyses of examples 2-4a and 2-4b

T H E C E N T R A L P O R T I O N

central por t ionritornellot r ea tmentresta tementepisode

If the exposition of the fugue seems highly formalized, the central portion is muchless so. We can make two very broad generalizations that will be true of the centralportion of most fugues: 1) The pattern of key succession describes a tonal archsimilar to that found in binary forms; this arch consists of the establishment of thetonic key, a departure into various related keys, and a return to the tonic. 2) Melodically the fugue uses a ritornello treatment or returning treatment in whichthe subject or answer clearly returns in the central portion as restatements andalternates with episode passages that are less directly related to the principalsubject.

R e s t a t e m e n tRestatements of the subject occur in various tonic-related keys and thus form themidsection of the tonal arch. Whereas the exposition of the fugue presents a pattern of alternation between tonic and dominant keys, the central portion exploresother rela ted keys. Usually the restatement is simply a transposit ion of the subject,but it may also involve other kinds of modification, such as melodic inversion, augmentation, or diminution.

pisodeAn episode is a passage in which no complete statement of the subject or answerappears such statements are confined to the restatement passages). The episodenormally explores motivic material derived from the subject, answer, countersub-ject, or other material from the exposition, and serves to develop these motives. Its

CHAPTER TW O Fugue and Fugal Movements 9

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f lse entry

s t r e t t o

1\ I

l I I I_:

5 J .I JI

motivic exploration can take the forms that we studied earlier-sequence inversion, augmentation or diminution-as well as other types of modification.Sometimes a composer, relying on the listener s expectations for alternatingepisodes and restatements, presents ajalse entry. In a false entry, the subject oranswer head is presented as if to begin a restatement, but the voice then departsfrom the expected material and the passage thus assumes an episodic role.

S t r e t t a and CadaIn restatements after the exposition, the subject may be answered with the samedelay in imitation as was used in the initial statement, or it may be answered with ashortened delay. A restatement of the subject involving shortened delay in imitation is called stretto, Compare the four-bar delay between the subject and answerin example 2-4a with the two-bar delay between the three statements (in soprano,alto, and bass) of the subject in example 2-8.

EXAMPLE 2B Bach: Well Tempered Clavier I Fugue 11, BWV 847J .J .J ] J I I I J j .I J lr-subjeet

r-subjeetlHl Jl 1l J] IHl i - . . .I l I.I i ~ f ~a :

--sub eet101\ ' '

I . .- f ~ q r ~ r i r b::l ~ r i iI : .

I I T r

3 CH PTER TW O Fugue and Fugal Movements

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I

jj

cod

The effect of stretto is more intense in fugues where the delay is shorter than thatshown in example 2-8. Not all fugue subjects lend themselves to stretto, however.One might guess that, in the fugue shown in example 2-8 Bach worked out thevarious stretto possibilities very thoroughly, and perhaps immediately after hecomposed the subject.

The central portion of the fugue usually concludes with a return to the tonic keyfor the final restatement s) of the subject. This is the typical treatment, but thereare several ways in which a fugue might deviate from this norm. In some instances,departures from the tonic are so few that the conclusive effect of a returning tonickey is weakened, and in rarer instances, there may be no restatement of the subjectafter the return to the tonic key.

Any material that follows the return to the tonic and the final restatement iscalled a coda Various contrapuntal devices may appear in the coda, as is true ofthe episodes; pedal points are particularly common.

FUGUE ANALYS IS

The Mozart fugue given in example 2-9 contains several of the features discussedabove. Its central port ion contains two episodes and two restatement sections.Figure 2-2 graphically summarizes the points annota ted in the score ex. 2-9).Locations of contrapuntal devices are indicated by particular numbers, each ofwhich is explained below the chart. Examples of special melodic treatment areSimilarly flagged with letters that are explained below the figure.

EXAMPLE 2 9 Mozart: Fugue for Piano, K 154Exposition answer soprano)

\ I I 5 I I I I II r r 1r I 1 I I W rrrr ru 1r r I TIL lJ rrrr.subject alto)

codetta\ I ~ J-----... I 1 1 1 I - '1 10 l 1 - r ......

- ltD 1 ---------I rr i r 1 r r i r r { ' r I ' -- L: [ af:Isubject bass)imitation: seventh below, 2-beat delaypolyphonic sequence: descending by seconds, I-bar leg

CHAPTER TWO Fugue and Fugal Movements 31

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\ I

:

\ III .

\ I

@J

:

3

EXAMPLE 2 S continued)

Central Portionepisode 1 (uses subject head)

I , ,

contrapuntal inversion at the octave polyphonic sequence: descent by thirds I-bar leg(soprano and bass); see m. 5motives from codetta (see mm. 7-9)

1 1 ' r1J 20 1___ I I I I J I Ir r . l..J,...J I l_ [J .J I l -.L, lJ J I

I I I I I .- __ 12---'I I I I r I I 1 , ,imitation: seventh below, 2-beat delay

polyphonic sequence: descent by seconds,I-bar legI r7i .... I ..... I l l 25.'1 - VI I rh .a p. I )J J ~ f.

I -estatement group 1 subject (soprano)r--- I I I I I I.I r r [ I I I r r I I r

-h .. ' .. *' * *' ~ ~ . . t _ *subject (alto) -

subject in melodic inversion (bass)

CHAPTER TW O ugue and ugal Movements

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II ,I

-. I :

,I ..I .

1\tI :

50,I ..I :

EXAMPLE 2 9 continued)

, 35 1 ' '1 1 1 - 1 _ I II 11 I I I I r I I I '1 1

f . . . f h .subject n melodic inversIOn (alto)

answer (bass)I i 1 1 r '1 1 - ..., 40I 1 I L Ur t

.'contrapuntal inversion at the octave I I(alto and bass); see m. 4

last tone of subject 1 octave lower (soprano)

answer (alto):notes 3 through 7 lowered 1 step

.. .....,1 J...-' r r

I

restatement group 2subject (soprano)t 3 th h 7 a sed 1 stepo es roug r I

/L r r r r-- ranswer (bass)

r q ~ I

1

] ]V

r Ib.

subject in melodic inversion(soprano)1 ,.jiU I tr

1 It I ' r 1 _ ..Istretto: soprano (in melodicinversion) and alto,imitation at unison, I-bardelayepisode 2

45...... ....

1P rl JI l n rJI 1

stretto: soprano and bass (in melodic inversion and augmentation), no delay:notes 3 through 7 (bass) raised 1 stepI ~ . . . . .

r I I I '1 1 1 r I U J '1r j r u- .l Jsubject (alto)

CH PTER TWO Fugue and ugal Movements

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Sections:

Measures:Material

inVoices: U

oP AltoBass

Keys:Devices:MeiodicTreatment:

Sections:

Measures:

Exposition

5

g:12

3 35

(codetta)

1

(Bk) (g:)3

40

Central PortionEpisode 1

15

(Bk) d:4

ab

2

56

Epis. 2 Restatements(group 2)

45 50Material UOP S -------------\I\IVVV\s ------------in Alto VVVV\ VV S ------------ VVV \ A ---------lVVVVVVVV\s --------------Voices: Bass IVV S ------------\J\IV\/VA------------NVVV\ V\ VA --------------------------------Keys:Devices:MeiodicTreatment:

4

g:

c

(c:) (g:)7 8 9

d e f g h

F IGUR 2 2 Summary of fugue annotations (ex. 2-9)

Sum mar y o f Sect ionsThe Mozart fugue can be divided into the following sections.

ExpositionCentral Portion

episode 1restatement group 1episode 2restatement group 2

measures 1-13measures 14-54measures 14-25measures 26-44measures 45-46measures 47-54

CHAPTER lW Fugue and Fugal Movements

25

Restatements(group 1)

g:

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Episodes and restatements divide the central portion of the fugue into segments ofirregular length. The first episode is especially long and begins with a polyphonicsequence that links it to the last bar of the exposition (m. 13). Episode 2 is particularly brief and more loosely structured.

Key r easThe exposition is presented in the tonic key of G minor, with brief excursions toB-flat major. The central portion of the fugue emphasizes the keyofD minor in thefirst episode, but the tonic key of G minor returns with the first group of restatements. The tonic key persists thereafter, except for a suggestion ofCminor beforeand dur ing the very brief second episode.

ont rapunta l DevicesNumbers appearing in the row Devices (fig. 2-2) have the following meanings.ing meanings.1. Imitation: measures 7-9 (soprano, alto), at seventh below, 2-beat delay(occurs in the exposition: codetta).2 Polyphonic sequence: measures 7-9 descending by seconds, I-bar leg(exposition: codetta).3 Inverted counterpoint: measure 12 (see m 5), at the octave (soprano, bass).4 Polyphonic sequence: measures 13-15, descending by thirds, I-bar leg(episode 1).5 Imitation: measures 19-21 (alto, bass), at the seventh below, 2-beat delay(episode 1).6 Polyphonic sequence: measures 20-21, descending by seconds, I-bar leg(episode 1).7 Inverted counterpoint: measure 38 (see m 4), at the octave (alto, bass)(restatement group 1).8 Stretto: measures 41-44, modified imitation (soprano, alto) with melodicinversion (soprano), I-bar delay (restatement group 2).9. Stretto: measures 47-52, modified imitation (soprano, bass) with melodicinversion and augmentation (bass), at the octave above, no delay; also (bassand alto) at the fifth above, 3-bar delay (restatement group 2).


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3 6

elodic TreatmentThe letters in the row Melodic Treatment (fig. 2-2) have the following meanings.a. Measures 13-15: episode 1 uses the head of the subject.b. Measures 19-21: episode 1 uses motives from the codetta (mm. 7-9 and

motives presented in the counterpoint of the exposition (with the answer,m. 5).c. Measures 32-34: restatement of subject (bass) with melodic inversion.d. Measures 35-37: restatement of subject (alto) with melodic inversion.e. Measures 41-43: restatementof subject (soprano) with melodic inversionand the last tone an octave lower.f. Measures 42-44: modified restatement of answer (alto) with notes 3-7 low

ered 1 step.g. Measures 45-47: episode 2 uses motives from the counterpoint of the exposition (m. 11 and m. 5).h. Measures 47-49: modified restatement of subject (soprano) with notes 3-7raised 1 step.i Measures 47-52: modified restatement of answer (bass) with melodic inversion and notes 3-7 raised 1 step.j. Measures 50-52: modified restatement of subject (alto) with melodic inversion.

We can make a few general observations about this subject and answer. Thesubject and answer are tonally unstable and include several altered chords (inmm. 2 and 5). Both subject and answer are modified frequently. The subject ischaracterized by the initial leap of a descending fourth (tonic to dominant tones),and the answer by the leap ofa fifth (dominant to tonic tones); hence, this is a tonalanswer (see ex. 2-10).

EXAMPLE 2 10 Forms of the subject and answer presented in example 2-9B S subject): m. 1

b A answer): m. 4

CH PTER TW O Fugue and Fugal Movements

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FORMS

EXAMPLE 2 10 continued)

c S nverted: m. 32

d S inverted and modified (last note one octave lower): m. 41

e S modified (notes 3-7 one step higher): m. 47

f A modified (notes 3-7 lowered one step): m. 42

g A inverted, augmented, and modified (notes 3-7 one step higher): m. 47

The material in the final two bars (ex. 2-9, mm. 53-54) seems devoted to thecadential formula, which indicates that it is not a separate coda but rather an extension of the restatement passage preceding it.

iU l l i i il l E

The procedures used in the fugue became stereotyped somewhat after the Baroque period. Although the pattern of a regular exposition followed by a cleaalternation of restatements and episodes may be found in many fugues, there arealso examples in the literature that do not fit this mold. The stereotyped patternsometimes referred to as the school fugue, must be viewed in terms of customary and typical, not standard or required.


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ritorn l lo form

There are fugues that have no episodes, but consist of a continuous stream ofrestatements (an example of this type is Bach's Well Tempered Clavier I Fugue 1).Sometimes, as in example 2-9 the tonal arch of a fugue may be altered by itsspending much more time in the tonic key than in later departures. ne may evenfind a fugue with two arches: the tonic returns well befo re the end, thisis followedby further excursions to other keys, and then the tonic key is reestablished.Evidence of this sort indicates that the fugue is not a form in the sense of asectional scheme or plan. It is better understood as aprocedure involving specifictextural treatment. A fugue is often divided into two or three main sections suchthat the principal internal cadences of the movement occur within the central portion. The overall design of the typical fugue shares with other kinds of Baroquemusic the returning or ritornello treatment. Ritornelloform consists of statements, called ritornello statements, in which earl ier-used material returns at leastonce in a nontonic key, and at least once more in the tonic key. Episodes containing either related or contrasting material appear betweensome of these ritornellostatements. In fugues the ritornello statements are termed restatements.Not all fugues use even this very general plan, so abroad conception of the termfugue is necessary to avoid endless contradictions. In many Baroque suites thegigue movement is a fugue in binary form. The fugue shown in example2-9 appears to be divided into two large sections, as is implied by the restatements andthe return of the tonic key in measure 26.

P P L I C T I O N S O F T H E F U G U E C O N C E P T

fugatofughet ta

8

Entire movements maybe devoted to the fugal procedure without the termfugueappearing in the title. Larger choral works frequently include fugues. In Handel 'sMessiah No. 25 And with His Stripes We Are Healed, and No. 28, He Trusted inGod, are fugues. In Bach's Magnificat, No.9, Sicut erat, is an accompanied fuguein which additional supportive material appears Simultaneously with the fugalprocedures.

Sometimes a fugue comprises a portion of a movement. The overture of theBaroque period often consisted of a slow introduction followed by a fugal allegro.The term fugal is used in a general way to describe portions of works that aremore than just contrapuntal or imitative, but exhibit other characteristics of thefugue as well. The term applies even when the treatment occurs within a relativelysmall part of a larger movement, or when the fugal sections are interspersed withhomophoniC passages.An interesting example of the latter usage is the last movement ofMozart's String Quartet, K 387.

There are other terms that refer to fugal concepts. The termfug to refers to afugal exposit ion occurring in a piece that is not a fugue overall. Such passages appear in both choral and instrumental works. Afughetta is a small fugue. It is diminutive in scale and may contain the conventional elementsof the fugue, or the central portion may appear shorteneddue to an absence of episodic passages.


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S U M M R Y2 2

A fugue is a polyphonic work, or portion of a work, that presents one or moreinitial melodic themes, called subjects, in a systematic way known as a fugal expo-sition, and then restates the subject s) one or more times. Generally two large for-mal sections can be identified: 1) the exposition, and 2) the central portion. Sev-eral concepts are associated with the exposition; these include the subject, answer,countersubject, and codetta. The central por tion of the fugue typically containsepisodes and restatements of the subject and may also contain stretto. A coda maybe appended to the close of a fugue. In the organization of a fugue, melodic andmotivic relationships, contrapuntal devices, and key relationships are important.

CH PTER TWO ugue and ugal Movements 9

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Pages 40 through 473 are available in the full version.Please seewww.shapingmusic.comfor information on obtaining this book.

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eview

7

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O e following outline may e useful for reviewing the concepts presentedin volume 1I Musical elements

A Pitch organization overall): scales, keys, modesB Rhythmic organization overall): tempos, meterC Melody: melodic rhythm, contourD HarmonyE TextureF TimbreG DynamicsH FormI Tension

II MelodyA Agogic accents: arsis, thesis, subordinate agogic patternsB Emergent tones: prominence from rhythm or contourC Motives

1 Motivic developmenta reappearance: recurrence, repetitionb changes in pitch levelc melodic sequence, legsd modified reappearance: inversion, retrogression, alteredcontour, altered rhythm, fragmentation, diminution, aug-

mentation2 Motivic analysis use of letters, brackets)

D Melodic cadences1 Conclusive2 Inconclusive

III. HarmonyA Chord typesB Normal progression

1 Chord groupsiatonic chordsn major keys

group 7 group 6 group 5 group 4 group 3iii vi ii

17

PPENDIX A

group 2 groupv

1

7 5

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in minor keys

VII III VI iio V

v i7 iv viio

Secondary domin nt chordsin major keys

V7 iii V7lvi V7 ii V NV7 N

in minor keys

V7 I11 V71VI V7 iv V7N

Secondary leading tone chordsin major keys

vU07 iii viio71vi viio7 ii viio7Nviio71N

in minor keys

viio71VI1 viio7 I11 viio71VI viio7 iv viio7N

orrowed chordsin major keys

bIll bVI ii viio7iv

in minor keys

ii IN

7 6 PPENDIX

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r - ~ - . - ,

2. Harmonic cyclesC. Nonharmonic tones: passing tone, neighbor tone, appoggiatura, escapetone, suspension, retardation, anticipation, double neighbor group,pedal pointD. Harmonic rhythm: durations, agogic patterns in harmonic rhythmE Harmonization

1. Chord tones, nonharmonic implications2. Chord progression3. Harmonic rhythmF. Part writing1. Ranges, spacing, doubling, omission2. Inversions3. Voice leading: resolutions, relative motion

G. Altered chords1. Borrowed chordsa. Changes in chord quality iiO, iv)b. Changes in roots \, III, VI)2. Secondary dominants

a. Chord qualitiesb. Root movementc. Role in normal progressiond. Irregular progressions and resolutions

3. Secondary leading-tone chordsa. Chord qualitiesb. Root movementc Role in normal progressiond. Irregular progressionsG. Harmonic cadences: perfect and imperfect authentic, half, deceptive,

plagalIV. Tonality

A Determination of keys1. Pitch complement and scale2. Harmonic implications cadences and progressions)

B. Modulation1. Common chord pivot chord) modulation2. Direct modulation

C. Key cyclesV Texture

A Basic types: monophony, homophony, polyphonyB. Basic components melodiC roles)

1. Salient lineS salient line2. Recessive line

R = recessive line3R = three recessive linesvR variable num er of recessive lines3. Implied lines

PPENDIX A

S) implied salient lineR) = implied recessive linev)R = variable num er of implied lines

7 7

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C Relationships between components1. Melodic doubling

Sx or Rx (also Sx2 or Rx2) line doubled in octavesSx3 or Rx3 = line doubled in three octaves

2. Couplinga. Partial (rhythmic only)[ 3R or

fR three recessive lines,R coupled rhythmicallyR

b. Full coupling (rhythmic and in contour)T 2R two recessive lines, fully coupled

3. HeterophonyT 2R two recessive lines in heterophony

VI. FormA Sectional or structural analysis (downward arrows)

1. Level-1 phrases: length, cadences, arrows2. Higher levels: groupings of units, slashes on arrows, cadential relationships, uni t relationships

B. Forms: binary, ternary, bar, other sectional forms (three-part and fourpart, etc.)C Tension analysis (upward arrows)

1. Phrase crest: upward arrow2. Higher-level crests: slashes on upward arrows

lit ISAMPLE ANALYSIS

7B

A sample analysis of a short piece is given below, to allow you to review many ofthe analytical concepts discussed in volume 1. The music can be found in example9-15. Also refer to that example to see howupward and downward arrows are usedin this text, and relate that example to the following diagram of the sectional structure.

mm: 1 5 9 12 17 21 25 29 33 36 40 45Form

Phrases:a a b a b c c' d e f f

Sections:Intro A B Coda

Keys:D: f : e: G: D:

PPENDIX A

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c---

---.

The work uses a two-part form, AB with an introduction and coda. There areeleven phrases. The unit relationships are: a a ba c c de f f The keys used are allclosely related to the tonic, D major.Unity in rhythm and texture is achieved through the accompaniment pattern.Each of the two main sections is also unified by the melodic ideas revealed in theunit relationships of the phrases, in the melodic figures of cadential patterns (firstin mm. 8 16 and 24; and then in mm. 19-20 and 35-36), and in the cadentialharmonic progressions in measures 19-20 and 35-36. n interlocking phrase isfound in measure 12 and an overlapping phrase is seen in measure 36.Several other concepts are illustrated in the harmonic treatment:

..6D: 5

.. 65

Nonharmonic tones:passing tones: measures 1,2,8,28,29,30,31,43appoggiaturas: measures 18 45anticipations: measures 16,45suspensions: measures 4 8 13retardations: measures 10 24

Diatonic seventh chords:V7 and inversions: measures 14 16 19,21,23,35,37,39,41,44ii7 and inversions: measures 3 7 21 23 25 27 34, 37, 41

Borrowed chord:G: viio;: measure 32

Secondary dominants: measures 38, 42 43Sample harmonic analysis: measures 37-45

V7 vi5/v iIY

Y7 y6 vi5/vi Y7/V

Y7

Y7

APPENDIX

16

7 9

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BD

Secondary leading-tone chords: measures 11, 32Common chord modulations: measures 12,24,28Sample harmonic analysis: measures 10-13D: I IV V viio7/V I {f : IIIDirect modulation: measure 21Ambiguity of key: measures 28-34 D or G?)Texture:

Introductions[2R

Heterophony:

AandBs[vR

Codas s s[3R 2R vR~

v43

Between piano soprano line) and voice: throughout, except for measures 32-33 and passages without voiceBetween piano tenor line) and voice: measures 9-10,17-18,32-33

PPENDIX

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Guide tonalyticalSymbols

4B

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I

t rUctural AnalyeleFirst-level unit ph rase

Interlocking phrases ----- ------- .1

Volume 1, Chapter 3

Volume 1, Chapter 3

I ~ r J I JJ 331 J J I j jJ ~ J I J JI R r I ~IIOverlapping phrases - - - - - - - - - - -

\

:

Higher-level units

-;9 -

b st-leve l unit ends lI

Rhythmic and Melcdlc Anelyale

~ s_ - - - - - , -f r I

I nd-level unit startsIJ lI st-level un it ends lt I1J J I J JII J J IJ

Agogic accents Metric accents Emergent tones

Volume 1 Chapter 21.....

I

I

Volume 1 Chapter 21lI st-level unit startsIJ3rd-leve l unit endsII~ 10I J J I J J J J IJ tII

Volume 1 Chapter 2

( ) t . st tII j rrr j rrr I r J J J Ir J r II

se PPENDIX B

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Tenelon AnelyslsCrests of phrase at first level Volume 1, Chapter 3

~ ~I irst-level crestI ~J I IJ I;

Crests of higher-level units Volume 1 Chapter 24I i rst-level cresdJ 3 J BilIJ J 4 c t l f O ~ a t ~ r U H I J H J J J II econd-level crest I

Er I fJ JJ O 1 ~ r J 1 3 3 n 1J J r u 1I i I I I Lf I ourth-level cresd~ ~ eve r s ~ 15 i Ir g r ct 1r r rr iE: l reG 1E rErr 1f r 1 1

20

Textural Analysis

a

~ I ~ l e v e l cresd ~J IJ I;

s s[ ~ or [ 3R

A PP N D IX B

S[ RX22R

Js

[ ~

Volume 1 Chap te 15

S[ 3R[ 2Rxv

4 8

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4 B 4

A D D E D T D N E C H D R D: A chord consistingof a triad plus at least one additional diatonic orchromatic tone other than the seventh; mostcommon are added seconds and sixths.AGDGIC ACCENT: The psychologicalemphasis that accrues to a tone that is precededby one or more shorter tones.AGDGIC PATTERN: A group of durationsending with the longest and including all thepreceding shorte r durations. The last tone iscalled the thesis; the shorter note s) is termedthe arsis Agogic patterns within an arsis arecalledsubordinate agogic patterns.ALTERED CHDRD: A chord containing atone not in the prevailing diatonic scale.ALTERNATE PRDGRESSION: Aprogression that does not appear on the chartof normal progressions but occurs with suchfrequency that it cannot be consideredirregular; examples include N-I, V-vi, vi-V,and iii-NoANSWER: The initial imitation of the subjectin a fugue. When the imitation is consistently atthe i th above or fourth below or octavetranspositions of these) the answer is calledreal, and an answer that departs from this istermed tonal. With more than two voices theanswer is usually given to the even-numberedvoices, and the subject to the odd-numberedvoices.A S Y MME T R IC A L METER Meter in whichthe number of beats is not divisible by two orthree. Sometimes termed irregular meter.ATONALITY: Absence of tonality, implyingthat a tonal center has not been established.The two principal types of atonality arefreeatonality for which pitch-class se t analysis wasdesigned, and serial atonality for which thetwelve tone system was designed.

AUGMENTATION: The appearance of amotive with the note values increased by aspecific amount, often doubled.A U G ME N T E D S IX T H CHORDS: Chordsthat contain the interval of an augmented sixth,usually formed by the lowered sixth degreediatonic 6 n a minor key) in the bass and theraised fourth degree in an upper voice. Themost common augmented sixth chords are:Italian sixth chord, It6 iv6 with a raised root ina minor key); German sixth chord, r ~ i v ~with a raised root in a minor key, or doublyaugmented as ii j with raised root and third);and French sixth chord, Frj iijwith a raisedthird in a minor key). A dominant chord withlowered i th also contains an augmented sixthin any inversions other than the first.B A S S O OSTINATO: See ostinato.BIMODALITY: Simultaneous use of twodifferent diatonic modes, usually with the sametonic.BITONALITY See polytonality.BORROWED CHORDS: Chords that containtones borrowed from another mode; forexample, in a major key a chord that uses oneor more tones found in the parallel minor keysuch as the minor iv chord.C H A N G IN G METER Relatively frequentchanges in meter, often within phrases. Alsocalledmixe meter.C H R O MA T IC P IV O T CHORD A pivot chordthat is an altered chord within one or both ofthe keys involved in the modulation.C O D E T TA A brief passage that concludes asection or larger passage. The term is usuallyapplied to internal portions of a composition,rather than endings.

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COMBINATORIALITV. The property of atwelve tone series in which the first hexachordof an original form of the series contains thesame tones as the second hexachord of at leastone retrograde inversion or one inverted formof the series. If it has one such relationship andnot the other, it is called semicombinatorial. Ifthe series has such a relationship with at leastone form of both the inverted nd theretrograde inversion of the series it is termedall combinatorial.COUNTERSUB JECT The counterpointaccompanying the answer of a fugue, andsuccessive statements of the subject or answer.COUPLING Two or more Simultaneouslysounding parts with identical rhythm with orwithout identical melodic contour. Thecoupling may be partial, or rhythmic, meaningthe lines have identical rhythms; or thecoupling may be full, in which case the lineshave identical rhythm and contour . The linesmay be an intervallic distance apart except theunison or one or more octaves, in which casesthe device is termed doublingC R E S T O F T E N S I O N . The point in a phraseor higher structural unit at which the tensionreaches its highest level and the release oftension begins.DERIVED SERIES Twelve tone series thatuses the same pitch class set for subsets withinthe series.DIMINUTION. The rhythmiC relationshipbetween a motive and its reappearance withnote values systematically shortened, usually byhalf the value.D O M I N A N T A U G M E N T E D . A dominantchord in which the fifth has been raised suchthat the triad is augmented.D O M I N A N T WITH LOWERED FIFTH Adominant chord in which the fifth has beenlowered such the triad has a major third and adiminished fifth Such a chord usually includesa seventh.D V A D S . Two tones forming a melodic orharmonic interval.EMERGE NT TONE. A melodic tone thatachieves special prominence through itsrhythmic location, duration, contour, or otherfeature.

GLOSS RY

EPISODE. In a fugue, a passage in the centralportion in which the subject or answer does notappear. Usually includes motivic material fromthe exposi tion and often employs contrapuntaldevices. In ritornello form, a passage betweenstatements of the ritornello theme.EXPOSIT ION. In a sonata-allegro, sonatina,or sonata-rondo form, the initial section, inwhich the main themes are presented. In afugue, the initial section, in which the subject oranswer appears initially in all the voices.FIRSTL V L UNIT A phrase that serves asthe basic unit of musical form. The analyticalmethod used in this text indicates the pointbetween phrases by a downward arrow withsingle slashes.F O R M A L UNIT. A unit of musical structure.The smallest such unit is the phrase. Phrasescombine to form periods, which group to formever larger units, allowing the creation of hugemusical works. Each unit is set off by the endingcadence) of the preceding unit. Sometimescalled structural unit.FREE ATONALITV. See atonality.FREE TONALITV. See tonality.FRENCH S IXTH CHORD. See augmentedsixth chords.G E R M A N SIXTH CHORD. See augmentedsixth chords.G R O U N D BASS. See ostinato.HARBINGER CHORD. In a modulation, thefirst chord that is clearly not in the original keyThis harbinger signals the approach of the keyH A R MO N I C CVCLE A chord progressionextending from one appearance of the tonicchord excluding tonic six-four chords) to thenext. It includes one or more interveningchords.HETEROPHONV. The simultaneoussounding of two or more differing versions ofessentially the same melody.H E X A C H O R D . A set of six tones that mayappear harmonically and/or melodically.Particularly important in twelve tone serialtechnique.

4 B 5

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8 6

INTERVAL CLASS. n interval, its inversion,all compound versions of these, and allenharmonic versions.INVERS ION TWELVE TONE SERIESJ. Theform of a twelve tone series in which theoriginal pitch relationships the prime form)are reversed in direction, up or down, startingwith the first pitch.INVERTIBLE COUNTERPOINT.polyphonic passage that maybe presented withthe bass material used in an upper voice andthe material from an upper voice changed tothe bass.IRREGULAR METRIC GROUPINGS. Metersin which the secondary accents create groups ofmore than one size, usually combinations oftwo- and three-beat groups.ITALIAN SIXTH CHORD. See augmentedsixth chords.KEY CYCLE. A series of key changes thatbegins with a particular tonic key and returns tothat keyLINKING TONES. A series of melodic tonesin a variation that retains order similar oridentical to that in the theme, thereby linkingthe melodic experiences th rough thissimilarity. Additional tones may appear aroundthe linking tones, the rhythms may vary, and theassociated harmony m yor may not varyMELODIC DOUBLING. The reinforcementof a melodic line by another voice orinstrument sounding the same melody inunison or octaves.MELODIC INVERSION. The reappearanceof a melodic line with the directionsreversed - those intervals that at first wereascending are later heard descending, and viceversa.MIXED METERS. See changing meter.NEAPOLITAN SIXTH CHORD. n alteredchord that is a first-inversion major triad on thelowered supertonic.NONFUNCT IONAL HARMONYharmonic progress ion that deviates conSistentlyfrom normal progression.

GLOSS RY

NORMAL PROGRESSION. A progressionthat has been traditionally used so often that itcan be considered normal and expected. Suchprogressions are reflected in the chart ofnormal progressions. Harmony that usespredominantly normal progressions is said tobe functional.OSTINATO. A musical idea that is repeatedwithout change in the same part. n ostinatocan be rhythmiC, melodiC, or harmonic. Abassoostinato or groun bass is an ostinato in thelowest voice, and may be used as the mainunifying basis for variations.PALINDROME. A musical unit in which theelements or relationships are the same forwardand backward.PANDIATONICISM Diatonic music thatdoes not use functional harmony and oftenemphasizes melodic independence.PANTONALITV. The treatment of all twelvetones with equal emphasis, so as to avoidestablishing a tonal center.PARALLELISM. Parallel movement ofintervals or chords going beyond the treatmentof the period of common practice.PENTATONIC SCALE. A scale consisting offive tones.PERMUTATION. The appearance, inrearranged order, of a group of successivetones.PITCH CLASS. Agroup of pitchesrepresented by a letter name that includes thatpitch in all octaves and all enharmonic forms.PLANING. See parallelism.POLYCHORD. A single ch ord that consists oftwo or more clearly identifiable chords. Themost common polychord consists of twochords, and is called a bichordPOLVTONALITV. The simultaneous use ofmore than one tonality. When two tonalities areused it is termed bitonalityPRIME SERIES. The original form of atwelve tone series.GUARTAL CHORDS. Chords that appear tobe constructed by stacking fourths.

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QUASI CADENCE: A cadence effect createdby any of various elements, such as contour orrhythm, but not reflected in the harmony.QUINTAL CHDRDS: Chords that appear tobe constructed by stacking fifths.RECAPITULATIDN: The return of a sectionof music heard earlier, usually the first part of apiece returning toward the end.RETRANSIT IDN: A passage that precedesthe return of the main theme or section. Itusually involves a change of key between thesurrounding sections. In sonata-allegro andsonatina forms the term may refer to a brief,clearly defined passage preceding therecapitulation or preceding a repeat of theexposition. In forms such as the ternary androndo forms, the term is applied to passagespreceding a return of the main theme orsection.RETRDGRADE INVERSIDN: The form of atwelve tone series in which the pitchrelationships of the inversion of the series aretaken in reverse order.RETRDGRADE SERIES The form of atwelve tone series in which the original pitchrelationships are taken in reverse order.SALIENT LINE A melodic l ine that capturesthe primary attention of the listener.S E C D N D A R Y D D M I N A N T : A chord (otherthanV that has been altered to have therelationship of dominant to a chord that is nottonic; for example, the dominant of thesuper tonic chord, Viii.S E C U N D A L C H D R D S : Chords that appearto be constructed by stacking seconds.SEQUENCE: Repeated statements of arelatively brief musical passage at progressivelychanging pitch levels. The initial passage is lessthan a phrase in length and typically can befrom one or two beats to two measures inlength. If the sequence is in only one voice it iscalled a melodic sequence If it is in all voic

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