Twentieth Century Harmony Vincent Persichetti PDF [PDF]

Zitiervorschau

TWE NTIETH-

HARMOI{Y CENTURY

TWENTIETH CET\ïTURY

HARMOÏ{Y Aryto ünãPraçnce Creanue BY VINCENT PERSICHETTI

FABER AND FABER LIMITED 3 Queen Square London

3-*

First Published in England in 1962 by Faber and Faber Limited 3 Queen Square London WCl First published in thìs edition 1978 Printed in the Uni.ted Sutes of Arnerica by Vaitr-BallouPress,lna. dll

rights resertted

ISBN 0 t71 11216 I

CONDITIONS

OF SALE

This book is sold rubject to the condition that it shall not, by any of trade or otherui.se, be lent, re-sold, hired out or otherttsisecirculated without the publisher's prior consent in any f orm of bìnding or cover otber tban tbat in which it ìs published and without a similar condition including this condition being imposeil on the subsequent purchaser

Copyright @ 196l by Vincent Pçrsiçhetti

Contents

FOREÌüORD

9

INTERVALS

I3 r3 r7 r9

CONSTRUCTION INVERSION

AND SPACING

INTERVALS

IN

CHORDS

23 25

OV.ERTONE INFLUENCE MEDIUM

2

SCALE MATERIALS

3l

MODES SYNTI{ETIC

SCALD, FORMÂTIONS

PENTATONIC

ÂND IIEXÂTONIC

CHROMATIC

SCALE

SCÂLES

3r 43 5o 6o

CHORDS BY THIRDS TRIADS SEVENTH

AND NINTH

ELEVENTHS

CHORDS

.AND THIRTEENTHS

)

3**__-

66 66 74 8z

CONTENTS

6) FIFTEENTHS

ÂND SEVENTEENTIIS

TWELVE-NOTE

4

CHORDS

85 87

CHORDS BY FOURTHS THREE-NOTO

CHORDS BY FOURTHS CHORDS BY FOURTHS

FOUR-NOTË

CHORDS BY FOT'RTITS

MULTI-NOTE

93 95 IOI

ro+

ADDED.NOTE CTïORDS

109

SIXTH

CHORDS

r09

OTHEB. âDDED-NOTE

CHORDS

III

AI'GMENTED

T2T

CHORDSBY SECONDS THREE-NOTE

CHORDS BY SECONB

l2l

MULTI-NOTE

CHORDS BY SECONDS

,25 rz6

CLUSTENS

135

POLYCHORDS T\vO

TRIADIC

THREE

UNITS

OR MORE

NON-TRIADIIC

TR,IADIC UNITS

UNITS

r37 r50

r 53 163

COMPOTINDAND MIRROR HARMONY COMPOUND MIRROR

/\ g

CONSTRUCTION

WRITINC

r6j 172

182

HARMOMC DIRECTTON PROC:RESSION CHORD CONNECTION DISSONÂNCE .í I I

Í \

PARÂLLEL

HÁRMoNy

SUCCESSIVE PERFECT FIFTHS CÂDENTTAL

DEVTCES

r8z r89 r94 r98 20r

zo6

1 0 . TIMING AND DYNAMICS

2L2

RITYTHM

2t2

PERCUSSIVE USE OF HARMONY

220

(7

CONTENTS WRITING

PANDIATONIC DYNAMICS

1t

AND RESTS

AND TRANSFORMATION 23O EMBELLISHMENT FIGURÂTION

ORNAMENTAL

EXTENSION ÂND IMITATION CHROMATIC

ALTERATION

PEDAL POINT AND OSTINATO UNISON WRITING

L2

230 235 ')t

2+r 243

KEY CENTERS I9IgL,lIv MODULATION POLYTONALITY ATONALITY SERIAL HARMONY

13

.2J zz6

248 2+8 25r .)) z6r z6z

HAR\{ONIC SYNTHESIS CO\ÍBINI\'G THE}IE

A\D

TEXTURES FORM IDEAS

INDEX OF COMPOSERS SUBJECT r\DEX

271 27r .l)

z8I 285

Foreword

Tne uusrc of the first half of the twentieth century hasproduced a harmonicpracticethat can be defined.During thesesixty years, harmonicideashavebeenin constantflux; composershavecreated new musicaldevicesand techniques.This broad paletteof materials hasfundamentalsignificancefor the presentscene,for amalgamation of the varioussound formationsand techniquesis in Process. Composershaveworked instinctively, with the ear as their guide, and have arrived at someúing of a common usageof thesematerials. Contemporarymusical resourcesinclude a wide range of materialsof the pastand present'and the availabletechniquesyield returns. abundantexpressive Works of high caliber are plentiful in the twentieth century. The rich mixture of materialsand styles is made up of many ingredients:rhythmic energy' vivid harmonic fabric, melodic color, ánd fresh linear writing. There are bold statementsand delicate momentsof fancy, and developmentalforces that embellishments, refuseto be bound by a severeformal plan. There are daringly experimentaland strongly traditional forces which bring divergent materialstogether. 9

r0)

FOREWORD

accountfor The variousharmonicdevicesdo not, in themselves, creativewriting. Only when theory and techniqueare combined with imaginationand talent do works of imponanceresult.Neverof- twentieth-century harmonic retheless,a practical knowledge_ sourcesis a requiremenìfor both performer and composer.The performeris offeredspecificinformation, and the comPoser'workablematerials Tvrentieth-Century Harrnony is not a speculativeteatise nor one proposing a personalmode of organization.Rather, it is an account of specificharmonic materialscommonly used by twentieth-century composers.Although knowledge of materialsand techniquedoesnot in itself createa personalstyle, precisionin the choice of notes and understandingof harmonic devicesare desirablein perfecting a meansof expressionand in stating a musical idea clearlv and consistentlv. This text aimsto define ihis harmonic activity and make it available to the student and young composer.A detailedstudy of the essentialharmonictechniqueof the twentieth century is presented, accordingto the practiceof contemporarycomposers.The book is for and about creativily; it presentsmusical possibilitiesto stimulate creative musical thought. Specific media are called for, but substitutionsmay. and should be made dependingupon the instrumentalistsand vocalistsavailablein the classroomor to the require originally conceivedmelody and composer.Most exercises harmony in a rhythmic frame; tempo, dynamics,and phrasingare The applicationsdo not in themselves fundamentalconsiderations. for the insupply adequatetraining, but are offered as suggestions from the literature âre not vention of further examples.Passages reproducedout of context; exact pâge locations are listed under the heading "source Material." None of the examplesrePresent râre casesor exceptionalmusicalcoincidences;they do offer rePresentativetwentieth-century harmonic methods. This text may be used in advancedharmony coursesand as a in -collegesand point of departure.in literature of music cgursesconservatones;or 1t may form the harmonic basisof a first-year composition course for both composition and noncomposition majors. The division of musical study into separatesegmentsmelody" counterpoint, harmony, rhphm, and form-is advisable

FOREWORD

(r1

only if the interdependenceof theseforces as found in the literature is maintained.Referenceis madeto contrâpuntal,formal, and orchestraldevices,for harmonic and contrapuntaÌmovementâre affectedby a work's form and medium.The way variouschordal structuresare built, the reasonsthey sound as they do, the connection of the chordsand their suitability for differing conditions, consistencyof texture, and the combining of contrastingtextuÍes mu$ be understood. Following a predeterminedpath of strict axiomsis avoided,for harmonic creativity dependsupon the relation of chord to chord in a particularcontext;any chord may progressto âny other chord, and seeminglyopposingtechniquesmay be combinedunder cerrain formal and dramatic conditions.In theoreticaldeducdonsthe emphasisis pÌacedupon creariveideasand compositionalstimulauon. Composershave,in their music,coordinatedthe variousmusical resourcesof the early part of the century. Significant creators working actively in many mediahavegiven imperusto a flourishing twentieth-century music, have given it pulse and creative health. The embryonic composerhas a technical heritage.Little can stand in his way if he possesses creative talent.

cEÂPrER

|

-

I

oNEI lntervals I

ANv rorve,can succeedany other tone, any tone can soundsimultaneouslywith any other tone or tones,and any group of tones canbe followed by any other group of tones,just asany degreeof tension or nuance can occur in any medium under any kind of stressor duration. Successfulprojection will depend upon the contextualand formal conditionsthat prevail, and upon the skill and the soul of the composer. An understandingof the harmonic processmay begin with an understandingof the melodic and harmonic intervals of sound.

CONSTRUCTION

An interval, like any other musical sound, may have different meaningsfor difrerent composers.While its physical properties âre constant,its usagechangeswith the working context to which it belongs. For centuriestheoristshave, through the scienceof acousticq 13

1 . INTERVALS

14)

observed degreesof interval tension and from this has been evolved a concept of úe relative consonant-dissonantqualities of intervals. Although this consonanr-dissonanrconcept is afiected by countless factors within any given style, and -ay vary consideiably from one âge to another, the notes of an isolated interval-whether sounded simultaneously or successively-do have a basic quality. Thb quality_is determined by the interval's o\Ãrnpanicular physical properties of sound ìr/âvesand overtones. An isolated tone, when sounded, generatesa series of overtones which form intervals that relare to each other by mathematical ratio. Generally, in the tempered scale, intervals are "onrott"rrt considered to be those formed from the lower tones of the overtone series (see Ex. l-2L), the upper overtones producing d.issonant intervals. In practice, these tone-to-tone relationships have been reduced by the use of the chromatic tempered scale from an unlimited number of intervals to twelve intervals which retain the characteristics of their counterpârrs in úe overrone series. Their textural characteristics âre as follows: perfect fifth and octave-open consonances major and minor thirds and sixths+ofr consonances minor seconds and major sevenths-sharp dissonances major seconds and minor sevenths-mild dissonances perfect fourth-consonant or dissonant tritone (augmented fourth or diminished fifth)-ambiguous, be eiúer neutral or restless

Es. 1-1 mild disonancc soÌt consonance

or

consonance dissonance

shqp dissonance

can

(1t

CONSTRUCTION

It is difficult to classify the tritone and the perfect fourth out of musical context. The tritone divides the octave at its halfway point and is the least stable of the intervals. It sounds primarily neutral in chromatic passagesand restlessin diatonic Passages.

Ex. 1-2

t

The perfect fourth soundsconsonantin dissonantsurroundingF and dissonantin consonantsurroundings.

Ex. 1-3 Andante

Intervals can follow each other in any order and may be arranged to form any pattern of tensioninterplay. For example,a seriesof intervalsmay begin with an interval of little tensionand end with an interval of great tension.The qualiry of the perfect fourth and tritone will be determinedsolelyby contexu

I . INTERVALS

16) Ex. 1-4

This is how such a tension ârangement might soundin practice.

Er. 1-Í Anthnte

Next the tension pattern is reversed; intervals of great tension move to those of relative repose. The ambiguous tritone at the end now assumesa neutral character.

Er. 1-6

Intervallic tension may be used to suit any design or function propertiesof intervalsmay of the music.The consonant-dissonant be used to support or oppose,for various expressivepurposes, other forces such as instrumental timbre, dynamics,and tempo. seemconsistentin double reedsplaying loudly. Sharp dissonances However, the sameintervalsasigned the timbre of muted strings createân entfuelydifferent effect. The feeling of one is raucous and of the other, inuospective-one givesthe impressionof intervallic tension disagreementwith other compositionalforces, and the other the impressionof agreemenl

(17

INVERSION AND SPACTNG

Ex. 1-7 Âllegro Obs.ì.

Fls,,Vns.

Lento Str. ( sord,)

As composers' attitudes and practices change, the concept of consonance and dissonancemây change. Various degrees of tension may be accepted as consonance. Consonant intervals may sound dissonant in a passage dominated by dissonanr intervals, and in harmony comprised of suongly dissonant intervals these dissonancesoften become the "consonant" norm of the musical organization

INVERSION

'When

AND

SPACING

intervals are inverted, their consonant-dissonant quality changesbecausethe spacingand register have been altered.The extent of changevarieswith the individual interval. Inverting the perfect fifth altersits basicfuncrion, this solid interval becoming an unstableperfect fourth. When sharp disonâncesare inverted, marked changesin intensity occur. The cutting minor second opensinto a widespreadingmajor seventhand thereby losessome of its sting. Inverting the tritone causesa pronounced shift in register even though no changein intervallic distancehas taken place. If intervalsare spacedmore than ân octâve âpârt, the soft consonânces(thirds and sixths) become richer; open consonances (octaves and fifths) and the consonanrperfect fourth become stronger:

1 . INTERVATS

18)

8r. 1-8

(secondsand sevenths)becomelessbiting, yet rÌore Dissonances brillianc Et. l-9

ryp Piano

,{-;

delicao

i

The tritone, neutral in chromatic progressions,becomesmoÍe ambiguousand veiled; restlessin diatonic progressions, it becomes even lessaddicted to resolution-

Ex. 1-10 ( J = s eS1, ^2Vns.= go (vcilcd)

J. fi5

, J=!ì

ë.

-^''l

7_-/ t=>

tf aresc.

.f (ress resüess)

(Ie

INTERVAI^S IN CHORDS

INTERVALS

IN

CHORDS

Two or more intervals occurring simultaneouslyform what b usually felt to be a chord. Chords may be built with equidistant intervals, Er. 1-11

mi. 2nds

ma. mi. 2nds 3rds

ma. 3rds

4úts

p. íús

IÌu. 6ús

ma. 6ths

mr. Tttrs

m& Zús

with different kinds (major, minor, etc.) of the same interval number, Ex. 1-12

ma.&mi. 2nds

ma, & mi. Tths

ma. & mi. 3rds

ma. & mi. óús

p. & aug. 4ús

p. & dnn tús

and wiú mixed intervals. En. 1-13

p.4th mi.3rd

p.4ths ma.3rd

Before a chord is set in harmonic morion the consonant-dish sonântquality of eachinterval containedin the chord should be

I . INTERVALS

N)

noted. It is only by making use of differencesin chordal values as determinedby interval characteristics that harmonictensioncan be controlled. Without this kind of freedom only a limited kind of harmonicprogressioncan be achieved,that which resultsfrom root relationshipswithin a fixed scale and key. Awarenessof intervallic tensionproducesharmonicmovementof a more flexible nature. Good part-writing is, of course,necessaryto achievesuch flexibilitv. A thiee-note chord has three intervals; observe the possible variants in consonant-dissonantcombinations. Et. 1-14

3 cons

2 cons. & I cons.& 1uild diss, 2mild" dis.

2 cons, &

1 cons., 1 mild I mild. &

t úaqpdis. & 1úarpdiss. 2úaqpdiss

A four-note chord contâinssix intervallic factors. and a fivenote chord, ten. Ex. 1-1í

3 com.r2 úarp, I neut,,lì"s.

7 cons.,2 mild, 1 sharpdiss

The quality of chordal tension affects and is affected by dynamics,medium,and spacing,but variesin different musicalcontexts. Handling theseharmonic materialsbecomessimplerif some generalclassificationof the intervallic characteristicsof chords is applied. All chords fall generally into one of two categories, those chords that contain at leastone sharp dissonanceand those Each categorymay be subdivided thar containno sharpdissonance. into those chords containins at least one tritone and those containing no tritone.

(21

INTERVALS IN CHORDS

E*. 1-16

no tritone

flo tntonê

Chords containing a tritone tend to have a restless quality, while those without tritones have stabiüty even when extremely dissonânt. The presence of a perfect fourth in a chord lends ambiguity because of this interval's abiÌity to function either as consonânce or dissonance;other intervals in the chord must determine its character, the chord being classifiableonly in its total interval context. The consonant-dissonant quality of chords containing a perfect fourth is defined by the interval formed by the bass note and the note not involved with the founh. When this interval is a mild or sharp dissonânce, the perfect fourth sounds like an open consonance; when it is a soft consonance the perfect fourth sounds miÌdly dissonant.

Ex. 1-17

sharpdis.

mild diss.

soÌt cons.

opencons.

Any kind of chord has, under "normal" conditions, its own natural doubling, such as the doubling of roots in major triads. It is possible,however, to write a chord in numerousother ways" ActuaÌly, any note may be doubled,tripled, or omitted for specific textural purposes.Doubling may be usedto enrich simple chordsn to point up characteristicpart-writing, or to strengthencertain parts of a chord. A doubledmajor third addscolor and a doubled dissonanttone increasesthe bite. Excessivecoupling (all voices doubled) producespercussive-sounding harmony. Chord membersmay be so arrangedthat specific kinds of intçryals monopolizethe musicalpâttern"

1 . INTERVALS

22) Er. 1-18 Ândantino >

#JrJ--

1'/ *::

4ths r---:-1

z--',

>

't a^Lv '/

The choseninterval may forrn sepârateinrervaÌlb strands that move in contra{F motion. E*. 1-19

ú

Spacing is an imeparablepart of the character of a tonal structure. For ordinary balance,the wide intervals are placed at the bottom of úe chord; for tautness,the wide intervalsare placedat úe top. For evenly distributed tension, all instrumenrsor voices are employedin their grateful registersand altered accordingly if specificharmonicstresses or highlightsare desired. spaced harmony Closely crowded with small intervals clears when each chord is broken into a zuccessionof intervalsin cwopart writing.

(23

OVERTONE INFLUENCE

Ex. 1-20

(a)

(b)

(a) ch. e'

But harmony that is clouded may remain so and be eÍfective; both cloudy and clear chordal materialsare essentialingredientsin musical composition.The overtone seriesis useful in measuring the aural difference.

OVERTONE

INFLUENCE

Any tone generatesa seriesof overtonesor partials that reach upward indefinitely, though not all are audible. Ex. 1-21 Overtone series

PâÍtiâls 1

,L - r te-

r

10ut2t3t4lt16 xxx

A tone has both vertical and horizontal implications; its overtones may be used simultaneously in chordal structures or consecutively in melodic lines. Some sounding bodies produce higher overtones than others. A tone produced on ân instrument capable of generating high overtones recognizable by the ear cÍIn have a quality that is resonânt and relatively dissonant becâuse of úe crowding of the upper partials. The samenote played on a medium

1 . INTERVALS

24)

having overtones that stop auraÌly with the lower or middle partiâlswill soundrelatively consonânt,but lack resonance.Such âre someof the differencesthat help give instrumentstheir individual tone qualrry. Basic harmonic materialsmay be traced to the overtone series, but only generalfacts concerningchordal structure and resonance are indicated by the paftials.A triad is formed by partials 1-3-5 (root, fifth, and third), â seventhchord by 1-3-5-7,a ninth chord by L-3-5-7-9,the whole-tonechordsby 7 to 11,chordsby fourths by 6-8-9,and the augmentedfourth chord by 6-8-11.However, deduction concerning harmonic implications of partials beyond the óth is not wholly practicablebecausethe temperedscaledoes not coincide in pitch with the 7th, llth, 13rh, and 14th partials. It is quite posible to relatemulti-note chordsby thirds to the series but the overtonesproduce limited resonance.The major triad (partials1-3-5) is clearly in tune. But the sevenrhparrialis slightly lessthan a minor third from the sixth. and if consideredâs rhe -' seventh (in chords by thirds) misinterprets the narural phenomenon.Our temperedaural thinking can include tones up to the sixth partial but beyond that point the aural perception is merely rational. The acoustician'sobservationsare useful to the composeronly if blendedwith artistic intuition. The fifth (partial 3) is a lower partial than the third (panial 5) and consequendyis more powerful; this is an important factor in understandingrelationshipsof tones, chords, and tonalities.Resonânt harmony is not formed by seekinghigher and higher overtones but by using overtonesof overtones.For example,in a C-E-G-B chord, the seventh(B) is the fifth abovethe third (F.). In this senseboú C and E are accompaniedby their fifths and therefore have strong relationshipswith theseother rones.If we wish to add an additional resonantrone, we should add not a higher, weaker overtone of C (such as Ff) but a lower and stronger overtone of an overtone (such as Gf which is partial No. 5 of E).

Ex. 1-22

#=o*

-____-#_ :g!i---------N^

__h=--ti+

No.Íof' < ^Í

rr

MEDIUM

Q'

Chordal structures are most resonantwhen the distancesbetween the membersâre somewhatsimilar to thosein the ovefione series(wide spacingin the lower registerand closespacingin the upper register).The overtoneseriessetsâ norÍn for brilliance.For maximum brilliance, let the lower tones of the chord be accompaniedby their ov/n overtones. The resonantpropenies of an instrument or of objects surrounding the performer creâte additional sonority that underpins the sound. The principle of supporting resonânceby lower sonority is occasionallyapplied to chordal structures.This color device is used primarily when the composerworks with chords in the upper registerand needsto fill in toward the bass.In lower registers,the addition of tonesis limited by the dangerof muddy progressions. Most effectivesupportingtonesare the fifth or ninth below the bottom tone of the chord becausethe fifth is a strong and resonantinterval and the ninth is a fifth below the fifth. Basses plucking the fifth or ninú below the acnral bassline cast a reflectedsheenover the harmony.

Ex. 1-23

D.B. (pizz.)

MEDIUM

The mediumto which a musicalideais given hasa direct bearing upon harmonic writing, as do intervallic texture, spacing, and are built upon the samechordal dynamics.The folÌowing passages

1 . INTERvALS

26)

progression but are conceived in completely different media and this resultsin completelydifferent kinds of harmonic settings. Chordal tension, spacing, and dynamics have changed drasticai-ly in eachversionEt. 1-24 ll'omen's voicc

Seningfor Piano a (J=

r?0)

Awarenessof timbre is essentialto good harmonic craft. eualiry of tone as definedby medium plays a functional role in harmonic movement.Music written for the piano is effective on the piano, but that wrirten for orchestragives an improper impressionwhen played on the piano. Harmonic writing should be èonceivedfor the medium employed. For example,orchesrralcolor may softenthe extremedissonance of thirteenth chords,rob the triad of its soft consonance.or alrer chordal direction. The high register of keyboard insrrumentsor the harmonicsof stringsadd brillianceto parallelharmony.clusters binding secondsmay be loosenedby the-selectionof torre, ".ir"io

(27

MEDIUM

to sound as thirds in separateorchestral choirs. Polychords are made ffansparentwhen each triad or unit within the composite structure is sounded by a separateorchestral section. Pazícato suings define uncertain passingtones in woodwind voices,and a harp may underline obscurerhyúms in lagging sffings.

SourceMaterial (red.) = a reduced score (piano, two pianos, or piano-vocal)

Two-part writing in a two-voice work: Béla Bartók,,14 Violin Duets (Boosey) Arthur Berger, Duo for Oboe and Clarinet (Peters) Pierre Boulez, Le Marteau Sans Maiue, Mvt. III (Universal) Alberto Ginastera, Duo for Flute and Oboe (Mercury) Paul Hindemith, Zwei Kanonische Duette (Schott) Arthur Flonegger, Sonatine for Two Violins (Sirène) Bohuslav 'Walter Martinu, Three Madrigals for Violin and Viola (Boosey) Piston, Duo for Viola and Cello (Associated) Francis Poulenc, Sonata for Two Clarinets (Chester) Serge Prokofiev, Sonata for Two Violins (Russe) Maurice Ravel, Sonate pour Violon et Violoncelle (Durand) Heitor Villa-Lobos, Choros No. 2 for Flute and Clarinet (Eschig)

Two-part writing in a work of more than two voices: Henk Badings, String Quartet No. 2, p. 9 (Schott) Bruno Bettinelli, Sinfonia Breve, p. 1 (Ricordi) Aaron Copland, Piano Sonata,pp.23-24 (Boosey) Hans \Ã/erner Henze, Drei Dithyramben (orchestra), p. 44 (Schott) Paul Hindemith, Organ Sonata No. l, p. 17 (Schott) Vagn Holmboe, Kammerkoncert No. 2, p. 2a (Dania) Benjamin Lees, Fantasia for Piano, p. 4 (Boosey) Peter Mennin, Five Piano Pieces,pp.2-S (C. Fischer) 'Walter Piston, Sonatafor Violin and Piano, p. 20 (Arrow) William Schuman, Symphony No. 4, p. 1 (G. Schirmer) Dmiui Shostakovich,Piano Quintet, p. 39 (Am-Rus) Igor Stravinsky, Threni (red.), pp. 5, 9, 15, 48 (Boosey) KurtWeill, Mahagonny (red.), p. 3 (Universal)

28)

1 . INTERVALS

Two-part coupled writing: Béla Rartók, Mikrokosmos, Vol. lY, p,22 (Boosey) Dmitri Kabalevsky, Piano SonaraNo. 2, p. I (Leeds) Emst Krenek, Jonny Spielt Auf, p. 4 (Universal) Robert Palmer, Piano Quarteg pp. 19-21 (G. Schirmer for S.P.A.M.) Goffredo Petrassi,Salmo IX (rèil.), p. 1 (Ricordi) Hilding Rosenberg,Piano Sonata Nõ. 3, p. ó (Nordiska) Igor Suavinsky, Le Rossignol (red.), p. 3 (Russe)

Passages fearuring specific intervals: Bela Bartók, Concerto for Orchestra, pp. 29-35 (Boosey) _,!ban_perg,Jiinf Orchester-Lieder, O-p. + (red.;, p. 2 (Universal) Niels Viggo Bentzon, Third Piano Sonata,p. 29 (Hansen) Marc Blitzstein, Regina (red.), p. 71 (Chappell) BenjaminBrittgn,-Billy Budd (red.), p. 7 (Boosey) Paul Hindemith, Madrigale, p. 65 (Schott) Arthur Honegger, Judith (rèd.), p. 110 (Salabert) Maurice Ravel, L'Heure Eqpagnole (red.), -19, p. 39 (Durand) Arnold Schoenberg, Six Little Pieces, Op. II (Universal) William Schuman,Voyage (for piano), p. Z 1G. Schirmer) Roger S_ession9, Sr1!e from "The Black Maskers," p. l0 (Marks) Dmitri Shostakovich,Symphony No. 10, pp.66aí (Leeds) Alexandre Tcherepnine, Bãgarèlìesfor Piúo, p. 2 (Heugel) Randall Thompsori, Alleluia, p. tt (E G Schiimer)

Characteristicspacing: êlg-" Coptand, Sonetafor Violin and Piano, p. 33 (Boosey) lVolfgan_g Fg{lgr, Impromptus for Orchestrâ, p. 5 (Schcitt) Alexei Haieff, Piano Concerto (red.), p. a3 (Bóosey) Karl Amadeus Flartrnann, Symphony No. 4, for Suings, p. 38 (Schott) ' Paul Hindemith, Symphonié Mathis'der Maler, p. f ("ScËott) I_gorStravins\y.Symphgny of Psalms,p. ó3 (Boõsey) Gúdo Turchi, Piccolo Concerto Norurno (orchestra), p. 20 (Ricordi)

Examplesof overtones: William Bergsma, Six Sonp, p. 6 (C. Fischer) Elüott Carter, Piano Sonata,p.27 (Music Press) Aaron Copland, Piano Variations, p. 3 (Boosey) David Diamond, Rounds for String Orchestra, p. 20 (Elkan-Vogel) Hans'W'erner Flenze,Sonataper Ãrchi, p. 27 (Schoa) Gustav Holst, The Planets,p. 113 (Boosey) Jean-LouisMartinet, Orphée,p. 19 (Heugel) Olivier Messiaen,Turangalila-Symphonie, p. ó (Durand)

(2e

MEDIUM Àrnold Schoenberg,Piano Pieces,Op. 11, p. 3 (Universal) William Schuman, [Jndertow, p. a0 (G. Schirmer) Roger Sessions,Piano Sonata No. 2, p. 16 (Marks) Igor Stravinsky,Sérénadeen La, p. 9 (Russe) Eernd Alois Zimmermann, Konfigurationen, p. a (Schott)

Applicati.ons A two- or three-line piano reduction may be used in written examples.

1. Write a phrasefor two flutes that containsseveraldissonantperfect fourths. Folìow this phrase with one that contains severalconsonant perfect fourths. 2. Write a fast and tempesflrouspassagefor two oboesemploying no sharpdissonantintervals. 3. Write a soft, lyric passageconsistingmostly of dissonantintervals. Score for two muted violins. 4. Extend the following oboe and English horn opening:

Ex. 1-25

5. Write for violin and cello a preludethat containsboth a crescendo and diminuendo of interval tension.Do not allow the dvnamic level to coincide with the intervallic tensionlevel. 6. Add a secondtrumpet part to the following trumpet line, employing a crescendoof interval tension:

30)

1 . INTERVALS

Er. 1-26

7. Construct a declamatoryphrasefor three horns using chords built by eqúdistant intervais. 8. Write a passage for three clarinetsusing only chordswith one consonant, one mild dissonant,and one sharp dissonantinteÍval. Employ a vafiety of spacings. 9. Write a passagefor string quartet using only chords of mixed intervals. 10. Write a percussive passagefor string orchestra using excessive doubling and coupling. 11. Write a scherzandopassagefor piano using similar intervals in both hands,moving in conrary motion. 12. Move three bassoonsqúckly through widely spacedconsonant chords

CEÀPTER

Tlvo

ScaleMaterials

MODES A cBxrner, ToNE to which other tones are related can establish tonality, and the manner in which these other tones are placed around the central tone produces modality. A great number of scale patterns have been used by twentieth-century composers,but seven stand apart from the others becauseof their whole-half-step order. Each has its special character, and any tone may be used as the tonic starting point.

Ex. 2-I

ionian (rnajor) Transposed to úe same tonic center for comgarisoo

2 . SCALE MATERIALS

aeolian (nat. mL)

Most of thesetwentieth-century modesbear the namesgiven them during the Middle Ages but the resemblanceis one of construcrion,trãt or"g". Ionian-isthe familiar mafor scaleand aeolian, the natural minorl locrian (infrequently used) is unmistakablebecauseof its diminishedtonic uiad. of the four remainingmodes, rwo have maior tonic and two have minor tonic triads. Lydian consistsof the major scale with the fourth scale step raised; mixolydian of the ma]or scale with the leading-tone lowered. Dorian is úe naturalminor with its sixth stepraised;and phrygian, the natural minor with the secondscalesteplowered. The distinctive flavor of theselast four modesis exploited by in which the characteristicscale employing harmonicprogressions -tone keeps the mode from becoming a *.i ú",í* often. Tiús -rlot or natural minor scale.For example,a lydian passageon D sháuld contâin a high percentageof chords that include the ton€ Gf (raisedfourth .t.p); otherwisethe lydian flavor will be lost. e s"t of chordsmay be found within the diatonic limits of each mode. As in major and minor modes,there is a definite r'elation between primary and secondaryúordal materials'1.h" pï*"ty chordsarËthe tánic, plus two dominantequivalents.Thesedouble dominantsare those maior or minpr uiads that include the char-

(33

MODES

acteristic scâle step which producesthe principal flavor of the mode.In eachmodethere lurks a diminishedtriad; this is a dificult chord becauseits diminishedfifth tends to suggestthe dominant seventhof the maior key with the samenumber of sharpsor flats asthe modein question. In the lydian mode with its characteristicfourth step (major scalewith the raisedfourth), the primary chordsare I, II, and VII and the secondaryare III, V, and VI. The diminishedtriad is IV. With the lydian on D, for example,this works out âsfollows. D lydian (characteristicflavor: 4th step):

Ex. 2-2 IUruïVV ,

|

(dim.) P*rIï

In the mixolydian mode with its characteristic seventh step (major scale with the lowered seventh) the primary chords are I, V, and VII and the secondary chords are II, IV, and VI. The diminished triad is III. D mixolydian (characteristic flavor: 7th step):

Ex. 2-3

,

(dim.)

tl

prinnry

In the dorian mode, with its characteristic sixth step (nâturâl minor scalewith the raisedsixth), the primary chordsare I, II, and IV and the secondarychordsare III, V, and VII. The diminished triad is VI. D dorian (characteristicflavor: 6th step):

2 . SCALE MATERIAIS

34)

Er. 24 IIIMIV

t

rJà.r

pÍiÍnâqf

In the phrygian modewith its characteristicsecondstep_(natural minor *itn ift" lowered second)the primary chords are I, II, and VII and the secondaryare III, IV, aãd VI. The diminishedtriad is V. D phrygian (characteristicflavor: 2nd step):

Er. 2-j

-rttention Modal chordsby úirds, other than triads,needspecial becausethe tritone present in many seventh and ninth chords impliesthe dominantieventhof a maior scale;the chord-maythen easily lose its tonic feeling and slip into a maior scale.useful seventh and ninú chords-in the modes (excepting ionian) are thoseinvolving no tritone. Phrygian seventh chords:

Er. 2-6

Phrygian ninth chords: Ex. 2-7

^-%-^

1

MODES

(3t

Triads, sevenths,and ninths progresseasily from one to another while in the samemode:

Ex. 2-8

I'trvII pdrnary

Chord succession of any kind is not iust a seriesof separareroor points but a harmonicrelationshipin which chordsmove forward. The selectionand distribution of primary and secondarychords within a given segmenrof music and the ways in which the harmonic rhphm is organized help give the music its individual sound. A singlemode is not necessarilyusedthroughout an enrire section. As working materialsfor composition the modes may be arrangedeffectively accordingto their tensionrelationships.The greâtestnumber of flats that can be appliedto a modal scaleon a particular tone will producethe "darkest" mode,the locrian. Subtracting flats (and then adding sharps)in diatonic signatureorder will produce ân arrangementof modesfrom "darkest" to "brightest.2'The dorian modeis the middle point and setsthe norm.

Er. 2-9

2 .SCALE MATERIALS

t6)

mixolydian

Within this related order â flexible set of modesis at the composer'sdisposal,and definite control of thesescaleformationswith their inherent qualitiesis possible. Although sÌiiftittg modes are effective on a stationary-key center,múch melodic referencemust be madeto the tonic if one wishesro stay within the mode; otherwisethe tonaliry will switch to major under the ionic power of the tritone. Melodic circling or chánt-like repetition of the tonic tone and frequent_cadences will help maintain the center. The following i9 a melody with a cr"r"eodo in register, dynamics, rhythm, and modal materials; the tonic center is A throughoue

Ex. 2-10 (J =ee)Clarinet

-=----> cresc.e acêel.poco n poco,

4 r A aeolian

l A mixolvdian

A doriàn

I Jl roruil

Chromatic alterations, both melodic and harmonic, are devices naturalto modalwriting.

(37

MODES Ex. 2-11

,W tenerntente

The diminished triad is a frequent subiect for chromatic alteration. This chord has a restlesstendencv becauseof its tritone and is altered to give the tritone perfect-fifth stability and resonancel the root is lowered or the diminished fifth raised. This dissonanrtextured diminished triad is found on a different scale step in each mode. In phrygian it occurs on the fifth scale step, and when altered, forms an additional dominant equivalent (three in all).

Er. 2-12

elt. dom.

alt. dom.

In locrian, the diminished uiad occurs on the tonic, but if úis diminishedtonic is alteredchromaticallvin order to avoid tritone involvementwith the key center chorá,'úe locrian flavor is lessened.Therefore the tonic of this mode is often soundedwith no fifth, or with an addednote. The useof first inversionsubduesthe tritone and the omission of the third and fifth in a total unison obliteratesie

2 . SCALE MATERIALS

38)

Ex. 2-13 (

"f no 5ú

*ddeã-notc

lst inn

It mav be observedthat since the locrian tonic triad contâins the unsiabletritone, melodic use mây be made of the chords on the first and fifth scalestepsand the tritone relationshipconsideÍed a thematiccharacteristic.

Ex. 2-14 Mârziel€ 1J=tzO;

\

is one in which a modal melody is harA pure modal passage moniied with chõrds from úe samemode and on the sametonal center.

Ex. 2-15

(Bptuyean)

Polymodaliry involves two or more diÍferent modeson the same or difierent tonal centers.The modal strandsmay be melodic or harmonic.

(J=6s1

(E aeolian)

2 Cls. 7' etpr.

,r{

J

When the samemode occurs simulrâneouslyon different ronal centers,the pâssageis polytonal and modal, but not polymodal. Ex. 2-17

When different modes occur on different tonal centers at úe sametime the passageis both polymodal and poly"tonal.

E . SCALE MATERIAIS

40) Ex. 2-18 (J=r2o)(G PhrYgtân)

(C doriaú)

A melody may move from one mode to another with a different tonal center. If a melody fluctuates through several modes the harmony may follow wíth the same or with a difierent set of modes. When the same mode is moved from one tonal center to another a modal modulation existq

Ex. 2-19

doriaa)

(A dorian)

-------i---/

(Ft dorian)

but when the modes change while the tonal center remains, modaÌ interchanges result.

(41

MODES

Ex. 2-20 Andante

3 CIs.

: (E locrian)

(E lydian)

In twentieth-century music, key signaturesare seldom used becausetonal centers and modality shift rapidly and because atonality is often present.The enharmonicchoice of spelling is determinedby the easeof readability.

Sowce Materiul -Dorian writing: Bmest Bloch, Concerto Grosso No-t+J

(Buchard)

r

(Dgrlndf "4r".TBJg:!9g*"-gjp-ç 9egg,ryqst' +[As :t.Mjlisanqerkd),p. t 1_6 arris,,fmerican-Tãllils, p. ísõlieO**Ottorino Reqpighi, Concerto Gregoriano, p. 9 (Universal) Erik Satie,Socrate (red.), p. 35 (Sirène) Jean Sibelius,Symphony No. ó, pp. 3-4 (Hansen)

'- Phrygian writing: / Ernest Bloch, Visions et Prophéties f'\ Carlos Châvez,Piano PreÌudei, p. 3 Claude Debussy,-Strrn-eUíartêt, p.

))

IldebrandoPuzettt so,,;r;;Ë f;'ëuï")Jiï.ìí o. tu (Ricordi) SymphonyNo. 5, p.4 (Musicus) Dmiui Shostakovich,

42)

2 . SCALE MATERIALS

Lydian writing: Beaiamin Britten, Seven Sonnets of Michelangelo, p. 14 (Boosey) Roy Harris, Strins Quaftet No. 3, p. 10 (Mills) Giánfrancesco Ma-lipiero,Rispetti e Strambotti' PP. 4, 8 (Chester) Darius Milhaud, Prõtée (red.), p. I (Durand) Maurice Ravel, Trois Chansons,p. 12 (Durand) Jean Sibelius, Symphony No. 4, p t+ (Breitkopf)

-*

Mixolydian writing:

, . J

Béla Bartók, Piano Concerto No. 3 (red.), p. 3 (Boosey) Beniamin Britten, SerenadeOp. 31, p. t (Boosey) Gedrse Gershwin, Preludes fõr Piúo, p. 5 (Harms)

{ ( \

\

p+'ç Ekgqt,LïFry::(#*Èril,t (Deiss)

p. 2 (Gehrmans)

Aeoüan writing: Luis Escobar,Piano SonatineNo. 2, p. 9 (Peer) Carl Orfi, Carmina Burana, p. I (Schott) Ottorino Respighi, Pines of Rome, p' 34 (Ricordi) Domingo Santa Cruz, Three Madrigals, p' 3 (Peer) Randall Thompsorq The PeaceableKingdom, p. 3a (E. C. Schirmer) Virgil Thomson, Four Saints in Three Acts (r"d.)' p. 90 (Arrow) Wiiliam Walton, Façade,p. 8l (Oxford)

eailos Chávez, Preludes for Piano, pp. 5' í-f,(G. Schirmer) Claude Debussy,Sonatafor Flute, Vìòla, and HarP, P. 11 (Durand) Klaus Egge, Symphony No. 1, p. ó (Lyche) Paul Hiíãemilh, Ludús Tonalis, p. a-(fthott) Gofiredo Petrassi,Magnificat (red.), p. 76 (Ricordi) Jean Sibeüus,Symphoãy No. 4, p. 37-(Breitkopf)

Modal interchange: Alfredo Casella,ll Peza Infantili, p. 12 (Universal) Paul Hindemith, Das Marienleben-(1948)'p' 18 (Schott) Zoltân Kodály, Sonatafor Solo Cello, p. 5 (Unive_rsal) -. Darius Milhaüd, Le Pauvre Matelot (rèd.), p. 1 (Heugel) Vincent Persichetti Piano Soaatinas,pp. 18-19 (Elkan-Vogel) Bernard Rogerg Characters frqn Hans Chriçtian Andersen, PP. 4-5 (Elkan-Vogel)

SYNTHETIC SCALE FORIVÍATIONS

(43

Ned Rorem, A Christmas Carol, pp. 3-5 (Elkan-Vogel) Igor Stravinsky, L'Histoire du Soldãt, pp. 59-ó0 (Philharmonia)

Polymodality: Béla Bartók, String Quartet No. 3, p. 10 (Boosey) Carlos Chávez, Soìratinafor Violirrand Piano' p' 4 (New M"sic) Paul Hindemith, Nobilissima Visione (ballet), p. + lSchott; Arthur Flonegger, Sept Pièces Brèves, p. 4 (Eschig) -. Olivier Messiããn,Vingt Regards (piano)' p. 18 (Durand) Darius Milhaud, Protée (red.), p. 56 (Durand) CarÌ Orff, Die Bernauerin (red.), p. 85 (Schoa) Francis Poulenc, Mouvements Perfetuels, p. 2 (Chester) Maurice Ravel, Piano Concerto in G (red.)' p. 38 (Durand) Igor Stravinsky, Oeüpus Rex (red'), p. 79 (Russe)

SYNTHETIC

SCALE FORMATIONS

Although a single tone, through its overtone series, suggests most obviouslythe maior scale,úe formation is partly rationalized. The major is only one of mâny scalescontainedin the basicrwelvetone chromaticscalethat is found in the upper region of the overtone series.Free placementof scalestepsresultsin original scale formationsbeyondthe sphereof maior and minor modes. Most original scalesâre constructedby placing any number of maior, minor, and augmentedsecondsin any order. The permutation possibilities are staggering and the mâthemâtical processhas little creative connection with composition. It is advisablethat scalesbe allowed to form as a result of the impetusof melodic or harmonic patterns;the material generatedby thematic ideasmay then be gatheredup and placedinto scaleformation. Some "original" or synthetic scalesare used more often than others.These better-known scalesoften coincidewith folk scales namedasfollow* and aresomedmes

44)

2 . SCALE MATERIALS

Ex. 2-21

(4ú mode of Double Harm.)

The synthetic seven-tone,one-octavescale, like a ma]or or minor, is made of a pair of four-note groups (tetrachords) that repeât the tonic at the eighth step. These tetrachords may be similar,asin major and Double Harmonic scales,or different, asin harmonicminor and HungarianMaior scales. The modal construction principle that produced the seven diatonic modes (dorian, phrygian, etc.) may be applied to any scale,creating multiple versions.The first modal version of any scalebeginseÍr the _tonic,the secqndon the supertoniçof that scale, etc.

STT{THETIC SCALE FORMATIONS

(4t

Ex. 2-22

Transposedto srme tonic for compar.isoo

The harmonic usefulnessof new scalesis determined by surveying their indigenous chordal materials. Each synthetic scale contains a set of chords within its own intervallic make-up. The primary chords are the tonic plus the two triads that include the scale step or steps containing the most determinable characteristic colors of the scalein question. If a maior-scale tetrachord is present the color tones are those outside the tetrachord. But if the scale contains no major-key tetrachord, the primary chords other than the tonic are those triads that are enharmonic spellings of a major or minor triad. If enharmonically spelled major or minor triads do not exist, the characteristic tone or tones are found in the notes forming augmented or diminished intervals with the tonic. The remaining triads are the secondary formations that function within the gravitation of the primary chords.

2 . SCALE MATERIALS

46)

Ex. 2-23 Original Scale characteristic rcale stepr

ru1- tott tetrachorô

III

minor

!'II maior eúarmonic

A harmonic problem is created by the fact that mosr syntheric scalesproduce one or more triads with diminished or augmented thirds and often these triads are primaries. They are usually chromatically converted into one of the four basic triads: major, minor, augrnented,or diminished. Altering the harmonic texture should not disturb the strict scale tones in the melodic writing because the burden of maintaining the flavor of the prevailing scale is placed upon the melody. The sooner the melodic voice includes all the tones of the scale,úe greater úe chance of projecting the synthetic scaleasa unit.

Er. 2-24

Further harrnonic possibiüties may be tested by considering the mirrored version of the scale. Scanning intervallic points between the original and mirrored versions reveals hidden potentialities of the scale.Fresh material such as cadential patterns, passingtextures, -and and outer-voice movement is suggested brought into focus by reflection.

(47

S]TNTHETIC SCALE FORMATIONS

Ex. 2-2í

:@l

Some scalesare reflectively identical, inversion producing exactduplicationof the original scalein retrograde.

Ex. 2-26

As in previously discussedmodal writing, the melody and harmony of a passageinvolving synthetic scalesmay stem from the samescaleoi difietent scales,and be placedon identicalor different key centers.The following passageis built of different scaleson the sametonal center:

Ex. 2-27 C HungarianMinor "

C Hungarian Maior

,

2 .SCALE MATERTALS

48)

This next passâgeis built of different scaleson different tonal centers: Ex. 2-28 go14y (J= 128 '(cg!?oa|

D HungarianMaior

,

G Oriental

New scalesmay be so built with similar or dissimilar tetrachords that the tonic is not repeâted at the first octave. When the octave is missed and the tetrachords âre continued, a two-octave scale or multi-octave scale may evolve.

Ex. 2-29

Multi-octavc

ffiì= -1-#-

Two or more tonal levels of intricate two-octave formations appearing at the same time (polymodal or polytonal) are dif6cult to project, and are best contained in music for a medium of wide color palette.

2 . SCALE MATERIALS

t0)

SourceMaterial Passages basedon syntheticscales: Féla Bartók, Sonata for Two Pianos and Percussion,p. ó5 (Boosey) Niels Viggo Benrzon,Third Piano Sonata,p. 17 (Hansen) Benjamin Britten, Turn of the Screw (red.), p. 180 (Boosey) RossLee Finney, Piano Quintet, p. 33 (U. of Mich.) Charles Griffes, The Pìeasure-Domeof Kubla Khan, -p. 14 (G. Schirmer) Lou Flarrison, Suite for Cello and Harp, p. l0 (Peer) Arthur Honegger,Symphony No. 5, p. 49 (Salabert) Alan Hovhanãís,Loísnàg Kisher, pp.'2-5 (Merion)' Olivier Messiaen,Vingt Regards (piano), p. 128 (Durand) Gofiredo Petrassi,Mà'gnific-at (red.), p. aà (Ricordi; Manuel M. Ponce, 3 Poemasde Lermontow, p. 6 (Universidad,Argentina) Maurice Ravel,Concertofor Left Hand (red.), p. 20 (Durand) Harald Saeverud,SiÌjuslâtten,p 5 (Norsk) Jean Sibelius,Symphogy No.4, p. 13 (Breitkopf) Igor Stravinsky, Fire-Bird Suite, p. 25 (Kalmús)

PENTATONIC

AND

HEXATONIC

SCALES

There âre variouskinds of basicfive-tone or pentâtonicscâles. Someof the better known are: Ex. 2-J2

The modal construction technique thât produces the seven diatonic modes produces five modes of each rype of pentatonic scale. The five modal forms of the diatonic pentatonic are as follows:

PENTATONIC AND HEXATONIC SCALES

('I

Ex. 2-33 lst modc

ü

2nd modè

3rd mode

-'C diatonic pentatonic scde

A

Trrrsposed to sarnêtonic for comparison 4th modc

5th mode

ü

^

Diatonic scales of five tones are hârmonically limited in scope becauseof the lack of semitones (when all five tones of a penratonic scale are sounded together they form â somewhat srâtic chord). It is therefore extremely dificult to achieve harmonic and melodic direction in a pure pentatonic form. When melody and harmony âre pentatonic, changing the modal versions of the pentatonic or moving from one pentatonic to another will help prevent monotony.

2 .SCALE MA,TERIALS

t2) Ex. 2-34 orgâa _

(c dieronicpenatonic)

Ândantc

lst mode

Lavish use of ornamental tones, pedal points, and frequent modal interchanges or modulations to other pentatonics will also help prevent harmonic monotony; but pure pentatonic music (nonpolymodal, etc.) is most effective when used for short spans of time. Pentatonic materials function well melodicallv or harmonically, but seldom both. Pentatonic melodies are often harmonized with foreign chords.

Ex. 2-3Í (J=12\

3lÍ*')/

One type of pentatonic scale combines well with another type on the sâme or different ke'y centers.

PENTATONIC AND HEXATONIC SCALES

(t3

Ex. 2-36 Piano Moderato

fl

:e,,rL-e '

-

t#t

atonic on B ílst mode

Diatonic pentatonicon C (5ú mode)

.._- )

Ê r'g QJr>

Str.

Orú.

Í

When the lowest note of the polychord is placed somewhere below the bassclef low F, the harmony becomesmuddy unless an open-position chord is used. (The "muddy" polychord is nevertheless a valuablestructure under appropriatedramatic conditions.)

Ex. 7-12

As a polychord is transposedupward it losesbody and resonance but gains brilliance (a). Drastic complexion changesoccur in lower registertranspositions(á) :

7 .POLYCHORDS

142)

Ex. 7-13

,f

Piano

ctesc.

A polychord may be madeup of any kind of triads.When it is constructedof major triads it is most consonantand resonant,becoming progressivelylessso asminor, rhen augmented,and finally diminishedtriads are included. The qualitiesof the twelve maiorminor (namedfrom the bottom upward) possibfitiesmay be observedwhen the upper units are addedto the bottom chord in a rising cycle of fifths beginningwith the bassnote of the bottom unit. Numbers 4, 5, 6,9, and 12 arc more useful becauseof their resonantcharacter, Ex. 7-14 oa.-mi polyúords

dÉ.f::

12t4.t678

ïÍ't 91011t2

+++

++

A minor over a major triad is richer than a major over â minor; the upper triad in the first formation receives additional supporr -from from tones of the lower chord other than the bottom tone which it is generated.

TWO TRIADIC UMTS

(143

Er. 7-1Í

Of the minor-majorpolychords,numbers1, 5, and 10havewider usebecausethey are more resonant. Ex. 7-16 mi.-ma. polychords

)^

+

.a*

+

'4-

r23456789101112

In minor-minorpolychords,the resonantnumbers1, 5, and 9 aremostfrequendyused. Ex. 7-17 -tÀ

mi.-mi. oolvchords L t +

,.tt

1234567891011t2

r*-

..

+

t-

144)

7 .POLYCHORDS

.AIl polychordscontainingât lea$ one diminishedor augmented triad are identified as chromatic polychords.The most süpple of the chromaticsare: Ex. 7-18

when the bottom chordal unit is augmentedor diminishedit is advisableto spreadthe voicesof the lower triad to avoid lowerregistercrowding. The mosr resonanrpolychordsin this caregory are: Ex. 7-19

dim.-aug.

TWO TRIADIC UMTS

(14t

The direction of polyharmony is determinedby linear movement.The counterpointof chords (counterchords)is derivedfrom a t\Mo-partlinear frame of single-tonelines. Two kinds of counterchordal techniquesserveâs a working basisfor polyharmonic writing: t\Mo-partcounterpoint used as the outer voicesof polyharmony, Ex. 7-20

Piem

xp

kgao

and two-part counterpointusedasúe roots of triads of both units making up the polyharmony. The notes of the basic tv/o-parr framework of roots move freely betweeninner and outer voices:

7 .POLYCHORDS

146)

Er. 7-2Ì

Any note of any melodicline can becomerhe roor, third, or 6fth of a major, minor, diminished,or augmentedtriad. Whether úe composerworks from the upper or lower triad, the great number of combinationsof triads that are possiblegiveshim a wide choice of textures within which the harmonic tension can fluctuate.

E*. 7-22

Str. Orch.

2

tener.

Cretc.

TWO TRIADIC UNITS

(147

Polyharmonic progressionstouch so mâny key areasthat tonaliry annnotbe securedthrough the harmonic personaliryof a prevailing scale.Tonality is establishedby the tonal implications of a predominatingmelodicline or by harmonicgravitationro a dominating chord. Resonantpolychords play the tonic role most convincingly; a wealth of invention must be savedfor the cadenceif a firm tonal center is desired.A tonality may be formed by the melody,

Ex. 7-23

or from a characteristicchord.

Ex. 7-24

3 Tpts. '

í.

Prolongedpassâges of pure polychords can result in tiring mass resonance;the richnessand thicknessstifle inner voices.Modification of the ìines by ornamenrâtionfreshensthe texture since attention is capturedby individual voice activity:

7 . POLYCHORDS

148)

Er. 7-2Í Slowly

Pi-o

"f

frò. -f,ò

-tò.

-Sò.

-çò.

-#

simitc

Unison and two-voice interruptions revitalize the polychordal texture.

Ex. 7-26 (J :132)

Violas and Gllos

í\

TWO TRIADIC UMTS

(14e

Omission of notes of either chordal unit lightens the rexrure and contributesharmonicflexibility.

Ex. 7-27

When polychords are used as architectural harmonic pillars, their dynamic conrrasrwith other types of harmony is refrêshing.

Ex. 7-28 Á,llegro

a

a

Winds

Í

?esox,

>

7 . POLYCHORDS

tt0)

SourceMaterial Polychords,two triadic units: Béla Bartók, String Quartet No. 5, p. 87 (Boosey) Peter Racine Fricker, Piano Concerto Op. 19 (red.), p. 40 (Schott) Roy Harris, SoliÌoquy and Dance,for viola and piano, p. 7 (G. Schirmer) Arihur Honegger, Symphony No. 5, p. I (Salabèrt) Charleslves, Piano SonataNo. 2, p. ó5 (Arrow) Albert Roussel,Bacchuset Ariane, p. 57 (Durand) William Schuman,Symphony for Strings, p. I (G.Schirmer) Igor Stravins$, The Rake's Progress (red.), p. 195 (Boosey)

THREE

OR MORE

TRIADIC

UNITS

Chordal units in polyharmony are often built upon different overtonesof the sameseries.There are four kinds of polychords with three or more units: thosewhoseupper units are built on the third and fifth of the botrom triad (rarely the root);

Ex. 7-29

rhosewhoseupperunits arebuilt on overtones(at any octavelevel) of the third andfifth of the bottom triad;

THREE OR MORE TRIADIC UNITS

Ex. 7-30 +

1 5th above Jú

(1t1

$*

5ú abovc3rd

thosewhoseupper units are built on overtonesof the overtonesof the third and fifth of the bottom triad;

Ex. 7-31 5ú of úc 5th of úc 5ú

and those whose upper notes are built on overtonesof the root, third, or fifth of triads other than the bottom triad.

tt2)

7 .POLYCHORDS

Multi-unit polyharmonyis so massiveand complexthat the notes of úe bottom triad must often be spreadâpârt. Someunits shouÌd be overlappedand others should have the spacebetween them widened.Doubling and coupling enlargea polychord without adding to its complexity.

E*. 7-33

Overlappingin a three-unit chord may result in a two-unit chord.

Ex. 7-34

Multi-unit polychords (usuallynot polytonal) are usedfor brief periodsof time. Their natural habitatis a climactic section,

(1t3

NON-TRIADIC LINITS

Er. 7-3Í (J:80)

Piano, ,t hands

-F

F I

çò.

E"

hr

E

rK -*

or a fast trut quiet section.

Er. 7-36 Prcsto

Ww.

I

leggicto

NON-TRIADIC

UNITS

Polychordsconsistingof seventhchord units are seldomusedin but more often in brief chordal groups that extendedpassages intensify a singÌeline or a two-paft statement'

7 .POLYCHORDS

1t4) Lr.

F ^ -

t-t t

Tl:y' J=ao)

nf

Full

cresc.mobo

B. Dr.

or asâ sforzandochord. Ex. 7-38

Somepolychordswhoseindividual unie are seventhchordscontain one or more notesin common,which makesfor a homogeneoussound; Er. 7-39 3 notcs in common

2 notes in common

t nco incommotr

(ttt

NON-TRIADIC UNITS and somehave no notesin coÍnmon.

Ex. 740 a

h]

tht


Harmonic elision brings about new relationships.Chordal relationshipsne\Ã/ro the piecemay âpp€arby omitting a chord that is expected becauseof previously estabüshedpassagesor srrong sequentialor traditionalsuccessions.

E*. 9-12 Adteio \Mwi

If a passageis thematically significant and is easily retained aurally, may be omitted or shufled in a dismembered .chords Progresslon. Ex. 9-13

1Vw. ald I tcrnPrc

CHORD CONNECTION

(18e

CHORD CONNECTION

Two inseparablefactors are involved with harmonic progression: what chord follows what chord, and how they are connected. When melodies sound together chords are formed, and when chordsfollow eachother melodicmotion is involved.Music can be primarily harmonic,melodic,or rhythmic, bur there is seldompure harmony or counterpoint for they are deeply involved with each other. Separatechord tones of any progressionhave melodic tendencies;even the most isolaredchord is full of melodic potential. Outer voicesgovern harmonicdirection and inner voicessecure the relationshipof the chords.For unrufled harmonicmotion inner voicesare moved as üttle as possibleand common tones are held. Parallelintervalslessenthe individuality of the voicesand contrary and oblique motion give the voices independence.The inherent urge of independentvoices to maintain identifiable lines can be strong enoughto ove{po\Merharmonic impulse. Smooth progressionsare but one facer of the craft. There is a danger of their becoming overly smoorh and much ingenuiqy is required to keep them fresh._Lgapingvoices,straying dissonances, escapingcommontones,modulatory twists, and chromatic daring are all part of harmonictechnique. The following deviceshelp give harmonicwriting this freshness. Inverting or transposing the interval containing common tones expandsthe registerrange:

t\

9 . HARMONIC DIRECTION

1e0) Ex. 9-14

Moving a voice to â note higher than the one just left by the voice above, or to â note lower than the note iust left by the voice below,

givesa passagea harmonic litt or drop.

A voice may be animatedby deflectingits melodic line, one more of the melody notesbeingshiftedup or down an octave. Ex. 9-16 Moderato

The registerof an enúe harmonicmâssmay be shiftedsuddenly to ânotheroctave.

CHORD CONNECTION

( 1el

Ex. 9-17

Piano I

cresc.

The range supplenes of instuments may contribute to linear flexibility. Ex. 9-18 1J.tzo;

ìÉ.

9 . HARMONIC

1e2)

DIRECTION

Melodic risesand dips may be reinforced by successive octaves, fifths, and paralielharmony. Ex. 9-19

r'G--, ü

'lteV_c í' t-i ____-_/

Piano

.Ir\_j_

A" a-

,r{

-----:.._---\

|

,/'

Eo'

Hidden fifths and octaves give coupled two-part harmony textural strengú, and thirdless harmony a freedom of movemenl

Er. 9-20

t'

(1e3

CHORD CONNECTION

The number of voicesin successive chords mây be increasedor decreased for variety in density.

Ex. 9-21 ( J= 88) Ww.

:+-

A climactic harmonicpoint may be left vacanrby rests.

Ex. 9-22

wtv and

^ ,V

cresc.moho

t + Brass

Voices may take turns soundingthe tune. When voicessharea melody in this way themâticimplicationsâre felt in the harmony. Ex. 9-23

Each voice may move chromaticallyto daringly complexchords becausewhen all voicesmove by half stepany combinationof dissonancesmay have meaning and direction. The voices containing the sharpestdissonantinterval should be well separated:

9 . HARMONIC DIRECTION

1e4) Er. 9-24

Í

feruemelte

DISSONANCE

Any combination of simultaneously sounding tones is relatively consonant if there is a more dissonantcombination in the surrounding area. An abundance of dissonancecan result in the feeìing of â consonânt textnre becausethe harmonic tension often relaxes in chords of the samevalues. The juxtaposition of chords of different values creâtes süong harmonic tension. A chord is dissonant only in relation to an over-all harmonic scheme and at times the "consonant" chord is the restless one. Because of melodic pull and chordal relationships the "consonânt" chord at (a) has a strong Ìrrge to move while the "dissonânt" chord at (b) remains unflustered.

Ex. 9-2Í

Increasing and decreasing consonance or dissonancecontributes to the shape of phrases,securescadential progressions,and articulates sectiõnal writing. Some are inherently more dissonant than otheÍs. But from the esthetic point of view the composer's ear &termines interval consonance or dissonance. Dissonance exists only where there is a norÍn of consonance implied or stated. A ninih chord may be relatively dissonant and resdessbecauseof the

DISSONANCE

(let

lessdissonantseventh and triadic material surrounding iq but the sameninth rnight be perfectly securedin consonancein a coíÌtext of ninths, elevenths,and polychords. Consonant-disonantrelationshipmay be reversedby starting and ending with a dissonantchord as the norm; consonancemay then resolveto dissonance.Extremely dissonantchords are kept in check by sequentialpatterns, overbearingmelodic lines, and characteristicmelodicintervals.A dissonantchord might represent a tonaliry and generateideasthat suggestthe form and content of a large work. A dissonantchord hasspecialusesoutsidea dissonantcontext. It sometimesends a phrasewhen used to begin the next phrase (transposed or not), Ex. 9-26 (à =e6) Tpts. rnd

or is repeated so dynamically and intensely úat the need for resolution is eradicated. In harmonic progression, each note makes its position in the chord felt as well as its position in its own melodic line. This linear force generates the harmony, conuapuntal motion, and formal design. Dissonant melodic and chordal clashes occur with less aural concern in harmony stemming from horizontal thinking-in multi-voice counterpoint (counterchords), in ornamental chords, and in reflection of some of the voices. Dissonant harmonic combinations often produce a üatonic melody.

Es. 9-27

9 . HARMONIC DIRECTION

Ie6)

This melodic writing must not be confused with artificial combinations of diatonic melody and dissonantharmony. 'When a chord is dissonant bv context it is usuallv resolved bv the movement of the voices containing the most dissonant ,orr.í. For smoothness of progression the dissonant tone resolves to the nearest note of the prevailing scale scheme.

Ex. 9-28 () =72)

ns.

The dissonânttone can resistits natural tendency to move to the neârestnote by following a scalewisemotion in the oppositedirection. If the adjacentscaletones are the samedistancefrom the dissonanttone, movementin either direction is natural.For passive non-commitmentit remainsstationary,or leapsan octave at the chord change. Ex. 9-29 +

e

A dissonanttone may evaporateby skippingto anothermember of the samechord or may freeze in parallel harmony and not The dissonanttone may skip resolveuntil the end of the passage. freely with melodicpurposein high-tensionmixed chordal forma,, rions or when suong melodic motifs overshadowthe power of the dissonanttone to resolve. The momentum of sequentialdesign Elovesdissonanttoneswithout resolution.For a suddentensionlift, the dissonanttone may resolvein another voice.

DISSONANCE

(1e7

E*. 9-30

The quality of the dissonant tone can be softened by coupüng it with consonant intervals, but doubling of the dissonant tone raises the harmonic tension. Such doubling in a simple chord enablesthat chord to function easily with complex formations.

Ex.9-31

To soften doubleddissonanttones,the voicesinvolving the dissonancemovein contrâry motion, or one of the doubledtonesmay move before the other resolves. The spacingconcern in three- and four-part harmony is often one of securingmaximum sound, but in harmony of more than four parts, doubling and spacing considerationsare directed to secur:ingvariety of texrure. Various colors and weights are obtainablethrough omissionand doubling of both dissonàntand consonant chord members.The densitv and concenrration of tonal

9 . HARMOMC DIRECTION

1e8 )

sound varies under diÍferent dramatic conditions. In an orchestral arrival of dissonant material upon a consonant climax, extensive doubling of all members of the consonant chord may be necessary to avoid loss of sound.

PARALLEL

HARMONY

When all voices in a successionof chords move in the same direction, parallel harmony occurs.Parallel harmony is found in eighteenth-centurysix-threezuccessions and in nineteenth-century diminished seventh chord successions. The term includes both strict parallelmotion in which all the chords are identical in construction, and similar motion in which the chords changeâs the voicesmove freely but in the samedirection. The direction and intervallic transpositionsmay vary and be either real or tonal.

Er. 9-32

Real parallel harmony (exact transposition) has a tendency to severconnectionswith any one key and may be used âs â meâns of enteringand Ìeavingatonality. This kind of harmony functions freely in modulatory transitionsand in thematic statementswhere tonality is meant to be obscure.Tonal parallel harmony (intervallic changesdeterminedby the scalein force) tends to preserve a modality. Parallelharmony (or chordal melody) is an expandedtextural equivalentof a melodicline; its direction is governedprimarily by melodic considerationsand its intervallic constructionby the kind of texture demandedby the dramatic form. In parallel harmony, fourths and fifths axeâsliquid asthirds and sixths, and intervals of the secondand seventhfind horizontalfreedom. Momentary parallel harmony is effective when used to accentuate a rise or fatl in a melodic line or to süp into a fresh key

PARALLEL HARMONY

(1ee

area. But extended similar morion tires quickly even úough complex chords are employed. Ways to develop the generating force of parallel harmony have become parr of the composer'i craft. Before parallel harmony becomesmonotonous one of úe following devices may be employed for a renewal of harmonic freshnessanã flow: contrary motion in one voice against the current parallel succession(a); tonal parallel motion convened to real (á);

Ex. 9-33

-à

motion of the voiceschangedro similar motion (a); the roots of parallel chords moved in the direction opposite ro the moving mass(ú);

Ex. 9-34

the direction and register changed (a); nores dropped while tlre parallelharmony is continued (á);

Ex.9-3Í

g timoroso

e . HARMONIC DIRECTION

200)

affention diverted by ornamentation and imitation (a); the octave changedin one voice (ú);

Er. 9-36 (^) G= 66)

Str. Orch.

ilf

)

::=-

the instrumentationchanged (a); different instrumentsused on differentnotes(ú); Ex. 9-37 (a) Lento (Ob.,CÌ.)

SUCCESSIVEPERFECTFIFTHS

(201

all notes raisedor dropped successivelyuntil the chord is dupli= catedat someother step. Ex. 9-38

So'pobeneptacido

Parallel harmony may be relieved by inserting fragments of nonparallel harmony, or by using two sets of parallel chords in contrary motion-the result may or may not be reflective. The chordal formation that dominates a succession of parallel chords may be broken melodically and a new set of parallel chords placed under the melodic notes of the broken chord, resulting in oblique harmony.

EÍ. 9-39

parallel added-note tertian chords

lFr I lD! | lC! | lAf I lG I

parallel chordsby 4ús

SUCCESSIVE PERFECT

FIF'THS

Unle.ss used imaginatively, successive perfect fifths become úesome; the intervallic uniformity of any combination of notes moving in parallel motion chaÌlenges a composer's inventiveness and facility. Fifths are emotionally immense, vague, and distant, or bare and dominating-they form an important harmonic in-

9 . HARMONIC DIRECTION

N2)

gredient in contemporâry composition.They are found in twopart writing, prying looseobliquemorion;

Ex. 9-40 2 Recorders

() . se). X--J----

,rf in coupledtwo-pârt writing; Er. 9-41 (J.=ss;

gp

in parallel harmony; Ex. 942

(i=

Piano $

ogüato

at the end of one sequential pattern and the beginning of the next;

SUCCESSIVEPERFECT FIFTHS

(203

Ex. 9-43 Andamc

and ât phraseioints Er. 9-44 tdi

t6

ãHo

Although perfect fifths make independenceof parts difrcult to achieve,their function in the vasttonal reserveis an important one. As part of a moving chordalbody of soundthey can be usedwithout dominating the generalrexture. The following deviceshelp push perfect fifths to rhe background. Conjunct fifths may be placedin the lower voiceswhile other parts employ conrrary or oblique motion. Es. 945

b

9 . HARMONIC DIRECTION

204)

Fifths in the upper parts becomeprominent but attention may be divertedby using rhythmically agile accompanyingpârrs. Ex. 9-46

Hn.

Chromatic fifths may be used more freely if at least one voice moves contrary to the fifths (a). Some monorony can be avoided by inserting other intervals between some of the fifths (ú).

En. 947 ( a )( J = $ )

Contrary outer pârts may be usedwith fifths in the inner parts (a). Fifths in the upper pârts are softenedby placing the third of the fifth in a lower voice (á).

SUCCESSIVEPERFECTFIFTHS

(20t

Ex. 9-48

l'Ìf*-

---\

úttpr. Va. (div.)

Skipping fifths are subduedwhen they leap to membersof the samechord (a). Florid inner voiceshelp divert the attention from fifths in the outer pans (á). Ex. 9-49 (4) (J=r16)

ttf Ha. -

9 . HARMONIC DIRECTION

206)

CADENTIAL DEVICES A cadence is an organization of melody and harmony in time, having a connotatior, ãf ,"rr. The cadencËis created harmonically through a pattern of chords, and melodically through the direction of each voice. Both are positive forces only when verified rhythmically. Cadential breathing places may occur at ends of phrases and sections and finally at the end of the piece. Under certain formal conditions, however, the final cadence may find that a prominent subject in a different key has made a bid for a new tonaliry, causing a cadence of two or more simultaneouskeys. Regardless of the complexity or inversions of the cadential chords, the two final roots will set the quality of the cadential feeling. The first chord in a two-chord cadence progresses"perfecdy" to a tonic whose root lies the interval of the existing cyclical relationship below its own.

Ex. 9-Í0

5ú rel

3rdrel.

T

m

'-T

2ndrel

-ü

T

I

The plagalequivalentsare these:

Ex. 9-í1

Íú rel'

T

TV

I

Í T

VI

I

Fvü

Any cadencewill acquire a passivequality if a dissonantton€ remârnsstaüonary.

CADENTIAL DEVICES

Qm

Ex. 9-Í2 a)

Tension and relaxation of consonanceand dissonancehelp mold cadential shapes. However, a succession of chords can produce positive cadential finality only when the underlying rhytlim confirms them. The rhythmic placement of the final chord afiects the strength of the cadence; when the last chord falls on a weak beaq repeated notes, ties, or melodic ornamentation are used to regain balance.

Ex. 9-J3

*.9*

In chromatic cadences, common rones âre avoided in order to strengthen the final tonic footing.

Ex. 9-54

#

w

The purpose of temporary cadencesis to rest briefly on a harmonic slant, thereby creating a need for harmonic, rhythmic, and melodic continuance. Deceptive cadencesare usuaÌly of this type and imply morion from one chord to anorher whose root relatiõn to the first forms an interval not characteristic of the prevailing chordal cycle. In fifth relationship, the chord of weaker i*p.ké

208)

9 . HARMONIC DIRECTION

moves to a chord whose root lies a second above its own root (a). In third relationship, root movement is up five (ú). In second relationship, root movement is up three (c).

Ex. 9-Í Í r--l

rì

Deceptive cadential progressionsare also obtained through movement to a chord outside úe establishedmodal or key realm, or by chromatic root movement. Other caclencesare created by the obliteration of all voices but one, or obliteration of all voices save a percussion note of indefinite pitch. When the final tonic establishesa positive tonality, notes mây be added freely, and if undertones are added, the tonic meaning is not disturbed. The final chord may be identical with the opening chord regardlessof tonal relationships. Cadences may include any rype of harmony: tertian, quartal, added-note, secundal, polychordal, compound, mirror, pandiatonic (Chapter 10), or twelve-note.

Ex.9-Í6

CADENTIAL DEVICES

SourceMateri.al Harmony with characteristic doubling, spacing, or omission: Aaron Copland,Piano Sonata,pp. 5,29 (Boosey) Darius Milhaud, Protée (red.), p. 8ó (Durand) Luigi Nono, Incontri for 24 Instruments, p. 14 (Scherchen) Igor Stravinsky,Mass,p. 13 (Boosey) Anton Webern, Kantate Op. 31, p. 3 (Universal)

Retrogressivewriting: Béla Bartók, Music for String Instruments, Percussion, and Celesta,p. 14 (Boosey) Alban Berg, Lyric Suite, pp.3945 (Universal) Luigi Dallapiccola, Quaderno Musicale di Annalibera (piano), n. 11 (Zerboru) Paul Hindemith, Ludus Tonalis, pp. 13-14, 57-ó0 (Associated) Olivier Messiaen,Sept Piècespour Orgue, pp. 3-4 (Leduc) Darius Milhaud, The Household Muse,p. l4 (Elkan-Vogel) Anton Webern, Variationen Op.27, p. 3 (Universal)

Real parallel harmony: Niels Viggo Bentzon, String Quartet No. 3, p. 11 (Hansen) AÌban Berg, Wozzeck (red.), p.219-22L (Universal) George Gershwin, An American in Paris, p. 48 (Harms) Karl Amadeus Hartrnann, Konzert für Bratsche mit Klavrer, p. 3 (Schott) Anaké Jolivet, Piano Concerto (red.), p. 42 (Heugel) Roger Sessions,Symphony No. 2, p. 99 (G. Schirmer) Ralph Vaughan Williams, Pastoral Symphony, p. 49 (Boosey)

210)

9 .HARMONIC DIRECTION

Tonal parallelharmony: Elüott Carter, Variations for Orchestra, p. 52 (Associated) Goffredo Petrassi,Toccata for Piano, p. 5 (Ricordi) Francis Poulenc, Les Soiréesde Nazelles (piano), p. 19 (Durand) Igor Stravinsky, Le Sacre du Printemps, p. 39 (Kalmus) Virgil Thomson, Four Saints in Three Acts (red.), p. 139 (Arrow)

Altered parallel writing: Béla Bartók, Piano Concerto No. 2 (red.), p. 38 (Boosey) Alban Berg, Lyric Suite, pp. 12,25 (Universal) John Alden Carpenter, Skyscrapers (red.), p. 39 (G. Schirmer) Frederick Delius, Requiem (red.), p. 54 (Universal) Roy Harris, Symphony No. 7, p. 89 (Associated) Maurice Ravel, L'FIeure Espagnole (red.), p. 113 (Durand) F{enri Sauguet,Concerto d'Orphée (red.), p. 38 (Heugel) Igor Stravinsky, Persephone(red.), p. 29 (Russe) Hugo Weisgall, The Tenor (red.), p. 145 (Merion)

Passages of barefifths: Georges Auric, Les Facheux (red.), p. 14 (Lerolle) Aaron Copland, Billy the Kid (ballet suite), p. t (Boosey) Manuel de Falla, Nuits dans les Jardins d'Espagne (red.), p. 17 (Eschig) Roy Harris, Symphony No. 3, p. I (G. Schirmer) Giãn Carlo Menoìti, The Uni"õ.n, the Gorgon and the Manticore (red.), p. 44 (Ricordi) William Schuman,Symphony No. 3, p. 70 (G. Schirmer)

Harmony containingp€rfect fifths: Alberto Ginastera,Piano Sonata,p. 7 (Barry) Roy Ffarris, Piano Quintet, pp. 8-9 (G. Schirmer) Bernhard l{eiden, Sonata for llorn and Piano, p. l't (Associated) Paul Hindemith, Ludus Tonalis, p. 15 (Schott) Charles lves, Piano SonataNo. 1, p. 21 (Peer) Dane Rudhyar, Three Paeansfor Piano, p. ó (New Music) William Schuman,Credendum, p. 12 (Presser) Roger Sessions,Piano Sonata No. 2, p. 8 (Marks) HaIsey Stevens, Quintet for Flute, Violir\ Viola, Cello and Piano, p. 1 (G. Schirmer for S.P.A.M.) Igor Stravinsky, Les Noces, p. 36 (Chester) $tefan Wolpe, Passacagliafoi Piano, p. 8 (New Music) Characteristic cadences: Pierre Boulez,Piano SonataNo. 2, p. 15 (Heugel) Carlos Chávez, Sinfonia India, p. 82 (G. Schirmer) Aaron Copland, Music for the Theatre, p. 67 (Boosey)

(21r

CADENTIAL DEVICES

Andrew Imbrie, Piano Sonata,p. 9 (Valley) Bruno Maderna, SerenataNo. 2 (for 11 instruments), p. 54 (Zerboni) Francis Poulenc, Mass in G maior, p. 24 (Rouart-Lerolle) Arnold Schoenberg,Erwamrng (red.), p. 47 (Universal) Gunther Schuller, Contours (small orchestra), p. 99 (Schott) Camillo Togni, Fantasia Concertante (flute and strings), p. 38 (Zerboni) Ilhan Usmanbas,String Quartet, p. 31 (Boosey) Roman Vlad, Sonatinafor Flute and Piano, p. 18 (Zerboni) Ben'Weber, Serenadefor Strings, p. 24 (Boosey)

Applications 1. Write a sustâinedpassagefor organ in which the melodic and harmonic ünes of tension are in variable relationships with the root movelïÌ€nt. 2. Write an ariosofor viola and piano (or harpsichord) in which the enúe circle of thirds is coveredby transientkeys. 3. Write a chromatic lamentation for strings where emphasisupon total melodic motion obüteratesroot feeling. 4. Shedvaryrng lights upon thematic orchestralmaterial by shifting the register severaltirnes. 5. Write an extendedsuccessionconsistingof only three chords for (AAT and Bar). four saxophones ó. Write a woodwind choralefeaturing retrogressiveprogressions. 7. Shuffie the chords of a passageso that pizzicato strings can project dismembered a progression. 8. Write a martial section for winds featuring leaping voices, straying dissonances, escapingcofilmon tones,modulatory twists, and chrornatic daring. 9. Write an abundance of dissonancefor the chamber orchestra so that a relatively consonant texture errÌerges. 10. Write an orchestral variation on a folk tune featuring various parallelharmony devices. 11. Place I great number of perfect fifths in the background of an agile dance for two pianos and brasses Write -.12. _" g-*tT or harp piece with several tempo changesand different kinds of cadences.

CIIá,PTER TEN

Timrngand Dynamics

RHYTHM

Tnnoo FoRcEsimportant to harmonic progression âre the linear motion and outline of outer voices, úe pull of harmonic or tonal centers and of the relationship of chords, and the time duration of stressed and unstressed chords. Coupled with these forces are graded tensions of texture and pitch and the rhythm created by phrasing, bowing, and tonguing indications. Harmony is always feìt in its relation to rhythmic smucture, and not until cLords .rrólrr. in a rhythmic form does harmony become wholly articulate. Harmonic rhythm is the underlying rhphm that plays a large part in controlling and stabilizing musical flow. If the harmonic changes are quick, there is an undercurrent of restlessness;if widely spaced, there is breadth. Various combinations of fluctuating melodic and harmonic rhythms give the composer a creative rhythmic potential. Tempo can be a determining factor in harmonic rhythm. Quick tempo may cause chord changes to sound like ornamental chords. Simple chords moving at a high rate of. speed may create relatively

RHYTHM

(213

complex sounds (a). Harmonic rhythm does nor move when chordsarerepeated(á). Ex. 10-1

Meter is a meâsure of rhythm. It has no rhythm of its own; it only appearsro have when rhythmic pulse coinóideswith the metric points. Strong and weak beats occur wherever the musical line placesthem, regardlessof meter.

Ex. 10-2 () =1'J2)

.f vns.I,IIva"

,

Simplerhythmsmaybecombined underonetimesignature. Ex. 10-3 ().=s6)

10 . TIMING AND DYNAMICS

2r4)

If patterns of shifted accents remain relatively consistent dte asymàeuical divisions are often indicated by compound time signaturesor dotted lines These compositemeters generte aqymmetricâl phrases. Two patterns of varying note values coinciding at occasional points will flow without a feeling of chaos. Er. 10-4 r-$-r

p Ín))i-i1 ( tr t'ílcJJÍ'í-lí

^

JJ , ) ) ),J til

r I rl

,í,ÍÍtí

Two or more rhythmic phrasesof unequallength may eachbe repeated until the return of the original combination (polyrhythm). Ex. 10-Í r

lTl

o.

)fOt

)tut.t

-T-

o.

.i..

n1.o2.l?

#

r-l

t

??

r ".?

Fl iT]

.oi...

.

el+rc,pe

iTì .

.1.

el

i-i t

o

r

F

ttll

''1e1.1.7741

'When

the pulse is irregularly but consistentlysubdivided,different time signaturesâre usedsimultaneously(polymeter). Ex. 10-6

ã)J)))tJ

i)r)li)

\ïj: â)

J ) li.

J))l)))

) [

r ll l; ,h.l) lj J_.-J-JIlll

(2rt

RHYTHM

of voicesis obtainedby using _-Completerhythmic independence different time signatureswith bar lines falling at difierent places. Et. 10-7

,=rlï

lJ. .blJ-j-tll ) lJ. .btJJ_! ) J J lJ. .b) trï;;f]T1 IJJ

Change of meter is a common meâns of achieving rhythmic variety. The fluid bar line adjusts easily and accommodates fractional meâsures.Rhythmic freedom of the bar line may result from úe demands of voial texts (prose rhythm). Musical stressis creared by pitch, intensity, color, or duration; the more factors contributing to an âccent the more complete the accent. Rhythmic pulse is most cÌearly defined when the related meÌodic, contrapuntal, and harmonic functions are emphasized. Alúough syncopation implies a dislocation of an establishedpulse, it does not necessarily oppose the meter. If the established pulse is not in accord with the merer the syncopated accents might parallel the meter.

Ex. 10-8

tuÍír_tíÍtí'| 0íÍtíf r tÉtrííf F'r'EII syncopation

Any part of a rhythmic figure may be lengthenedby a note (a), a rest (á), or a dot (c). The rhythmic rransformarionproducesametricalpatterns:

IO .TIMING AND DYNAIVÍICS

216)

Ex. 10-9 ():rr

The melodic and harmonic lines may be syncopated in opposing ways: the melodic line syncopated against harmonic pulse, harmonic rhythm syncopated against melodic pulse, or both harmonic and melodic pulse heard in comparison with a contrasting pulse o{ preceding measures.Changes of time signature may be made so ihat the syncopation falls after the bar line. Dissonant-chord syncopatiorìs urge the succeeding harmonic rhythm to move faster and consonant-chord syncopations tend to slow it down. Rhythmic forces mây sprout from the percussion line of instruments or vocal sounds of indeterminate pitches. The meÌodic and harmonic rhythms may coincide or oppose the percussion line in various ways. The following example illustrates melodic and percussiverhythm opposing the harmonic rhythm.

Ex. 10-10 ()=r20)

When one or more voices of changing notes adhereto a tinglo rhythmic pattern, isorhyúm existc

RHYTHM Er. 10-11 çJ=aa

E.H.I

í

aJ

t(str.) :>

(wïdr)

(str')

UMSON \ryRITING

(24t

or oudiningharmonicactivity with brokenchords Ex. 11-31 (J=il2)

Unison writing is effective when stating a rheme without its harmonic fabric, contrasting a single line with a chordal mass,or adding strength to a loud, full passage.Unison is also used for subsidingsound, rushing ocravesgathering power for a climax, to inuoduce â new tonal area by oudining the fresh scale,or ro project rhythmic varianrsin a reciative styIe.

SourceMaterial Unison writing: Conrad Beck, AeneasSilvius-Syrnphonie,p. 28 (Schott) Bruno Bettinelli, Fantasiafor Pianà, p. + (ÏUcorài; B^:"ji*ol!l*en,.String Quartet Nõ. 2, p. a4 (Boosey) Charles Griffes, Piano Sbnata,p. 15 (G. Schirmer) Camargo puarnien Piano Concerto No. 2 (red.), p. 3 (Associated) Roy FIarris, Piano Suite, p. a (Mills) Marcel Mihalovici, Sinforiia Partita, p. 27 (Fleugel) SergeProkofiev, Piano SonaraNo. 7, p. 2 (Leeõs) Arnold Schoenberg,String Quartet No. 4, p. 61 (G. Schirmer)

tl

246)

11 . EMBELLISHMENT AND TRANSFORMATION

Applications 1. Write a shorc piece for two flutes and two clarinets featuring nonharmonictones. 2. Harmonize the following melody (for piano) so that eachchecked note becomesa nonharmonictone.

Ex. 11-32

3. Write a woodwind passagefeaturing ornamentalchords. 4. Write a melodic line for clarinet that stemsfrom broken chords of various kinds 5. Write severalphrasesfor piano in which ornamentalfiguration is createdby chord tones. 6. Write imitative music for fwo flutes at the interval of the tritone. 7. Write music for horn and tuba with imitation in augmentation. 8. Write a pâssagefor two cellos that has imitation at a dissonantinterval. 9. Createa pyramid in brassesby employing closeimitative entrances. 10. Write â pâssagefor string orchestra using several effective cross relations. 11.Write a short piece for organ featuring harmonic alteration. 12.Write an expressiveharmonicproglessionfor stringsover or under a pedal tone in the French horn.

UNISON WRITING

(2,41

-13. Extend the following pâssagefor rwo oboes and two basoons, featuring the double pedal.

h.

11-33

14. Write melodic fragments, appropriate for use as ostinatos. 15.'Write a lively flute tune over a double-bassostinato. 16. write a string quarrer pâssagein which rwo osrinaros are used simultaneously. 17.Write a unison theme for violas or cellos 18. Increasethe intensity of a harmonically strong orchestralpassage by employing suddenunison writing.

I

-al

'"ï::ïi I K"y Centers I

TONALITY

Tno roNer- MEANTNGof an isolated chord is indefinite; it may be a crucial oÍ an ornamental chord of many keys, or it may belong to no key. When surrounded by other chords its meaning may-be restricteã to a single tonality, to t\À/o or more wavering tonalities; or if it has atonal intentions the fact can be made obvious. Tonaliry does not exist as an absolute. It is implied through harmonic articulation and through the tension and reÌaxation of chords around a tone or chord base. A panicuÌar style or period is not always limited to a predilection for a single kind of tonality. Twentiethceffury motic makes use of many degreesof tonaÌiry and employs mâny meânsfor establishingthem. In a strong tonal context, all elements of progression are subordinate tó the pull of the tonal center and a drive towards cadential realization. Traditional tonality depends upon scale and chord relationships for its organization. Usually three basic chords are needed to produce a feeling of tonality: one built upon a scale step above thã tonic, one below the tonic, and the tonic itself. Harmony with tritone gravitation is helpful in establishing the center' 248

(24e

TONALITY

by using tonesof a scaleas chordal Tonality may be established roots in varying degreesof support of úe central tonic: in balancedsupport by the subdominantand dominantto the tonic (a); in balancedsupport by the submediantand mediant (b); Ex. 12-1 (r)

(b)

aür. lni. Neep. ML

DoubleHarm. Hung. Mi. phrygrân LydianMi. locrian Me. Locrho

Neap. Ma. Symmetrical dorian

Hung. Ma Oriental ' tydian

in balancedsupportby the leadingtone and suPertonic(a); and in varying supportby scalestepsembracingthe tritone (á).

Ex. 12-2

phrygira SrryerLocrian

Neap. Mi. DoubleHarm, Enigmatic

lydian Hung. Mi Overtooe

locriatr Oricntal Eight-tone Spaniú

Orienal

19â. lydian teadinglVhole-toae

The remaining secondary scale roots decorate the three tonal pillars in each case. Music may be brought into key focus by forces other úan the tonal pull of chordal pillars. Key feeling may be created-by "tt extremely dissonantchord refusing to becomeconsonant'from a successionof simple chords resisting complex harmonic forces, from two culminating tonalities merging finally as a dominating polychord, from a group of important-tonesrecurring at decisive points,or from atonalmusicsearchingfor a key at cadentialpoints.

12 . KEY CENTERS

2t0)

Key consciousnessmay vanish temporarily only to make stonger an emerging key's return. The search for tonality or key center feeling may become a creâtive forcç in music. The tonaliry of a structure may be generated from a unifying harmonic idea from which musical gro\Mrh extends. An initial major-minor compound chord may promote polychordal writing that instigates â triâdic struggle between major and minor structures; the formal conflict may not be resolved until an obstinate melody note, corrÌmon to both triads, anchors them in a malor-minor formation quite transposed from the original chord. A work may be built tonally upon an initial harmony that falls cadentially; the final cadencemay find refuge in a group of tones far removed from the tonal implications of the first harmonic fall. A successionof chords ar an opening may, in microcosm, suggestthe tonal shapeof the enúe work. An insistent chord may establish a cenrer by resisting pressures from various tonalities.

Ex. 12-3 d.ua)

:>

t

úú

(2t1

MODULATION

Tonaliry may be established through contradictory tonal eÌements or through a streamlined drive to the tonic. In equidistant rootless harmony, âny note may be made úe tonal center through melodic insistence,spacing, or instrumentation. Music may hold its tonaliry loosely, elements of atonality being inherent from the onset. There are many degrees of key-center gravity or of keylessnessin the general area of tonaliqy or atonaliqy. At one extreme of the concept of key is tonality, the other extreme is atonality, and the point at which one ends and the other begins is indefinite. MeÌodic iines in a tonal framework can become so free that the implied harmony becomes evasively dissonant and a point reached where key feeling is lost. Partial atonality is useful in vague introductions and transition pâssages,and when preparing for a returning tonal thematic idea-

MODIJLATION

The ambiguity of any chord is such that it can be related to any of the twelve tonal centers. This is an important fâctor when modulating, â process of changing the tonal center. If a definite key change is desired, both keys should be firmly estabÌishedby at least three center affirming chords. A pivotal chord is one that is common to both keys; it is diatonic when belonging to both scale formations and chromatic when it belongs to neither, or only to one. It is not always clear ]ust which formation is the pivot chord -this only enhancesmodulatory beauty. When modulating to â permanent key, chords other than the tonic may be aimed for so that time can be made for settling into the feeling of the ne\Mtonality. A premature cadence is avoided by lumping to a distant key, then working gradually toward the desired kev. Chromatic modulation is attained by shifting an entire chord a half step in sudden parallel harmony. Abrupt modulations make the arriving tonic felt as a distant chord; to establish a firm feeling of the new key, an extended harmonic progression is necessaryin order to secure the new center. All chromatic tones are in the domain of a key when the vertical aspect g-ivesway to the hori-

12 .KEY CENTERS

2t2)

zoÍtãl movement of voices; therefore, all keys have twelve tones in common and may be reached quickly chromatically. Modulation may be realized through the semitone or orher intervals. A fresh change is felt when the modulatory interval is one other than the characteristic interval of the prévailing root progression. Modulatory changes of the third relationship are effecdve in passagesof second relationship harmony,

Ex. 12-4 A center

C

D

E

F->A mod.(3rd)

ClB

A

and changesof the secondin third relationshipharmony. Ex.

12-5

G ceirter ---'-

E center -------

Ft *Gt mod. (2nd)

Key changeshave speciallift when modulationis accompanied by an octaveleap in register. Ex. 12-6

Continuous,quickly shifting keys produce a senseof displaced tonality rather than modulation

MODULATION

Ex. 12-7

Key feeling may be gradually loosened or tightened. The gravity of a tonal center is decreased by moving a new voice through notes that give an important chord new roors.

Er. 12-8

l9dtcred(nb;

* aus. óú -(F)

A distant tonaÌity may be establishedby the reinforcemenrof the new centerby auxiliary chords,

12 .KEY CENTERS

2t4) Ex. 12-9

ë,Bq f

t&rc. ctLz^

or by the pneumatic action of violent repetitions of the neìü toÍìrc with color and spacing changes. Transient modulation is an important meansof securing variety It is lesseffectivein very dissonant in relatively consonantpassâges. harmony doesnot need,thecolor complex Chromatically passages. õf transitorv modulation. In this harmonic context, modulation is used to moïe from one section to another, rather than within a itself. progression Modulation from a single tonahqy to a polytonaliqy may be attained by moving double strands of uansient modulation in a contrâry motion of keys. A coupled tonic makes an excellent starting point.

Ex. 12-10

music

When modulating from one polytonal ârea to another, each key zone usually moves to the new zone by independent modulatory rneans; the over-all harmonic total must, however, have textural design and intelligible tension fluctuation. Distant tonal centers are reached in countless ways' but unless

(2tt

POLYTONALITY

this facile techniqueis held in careful check, harmonic growrh \rill be replacedby superficial variety.

POLYTONALITY

Polytonal writing is a procedure in which two or more keys are combined simultaneourly. If only two keys are sounded" the ryecific term bitonality may be used, but polytonality has come generally to imply the use of more than one tonal plane at the sametime. The scalesthat form the different tonic cenrersmay be intervallically identical or conrrasring, traditional or qFnrheric. Ex. 12-11 major

+

2

2

maior Hung. M,inor

=e

Hung. MiÃos.

lYdiaa

.sr t-2

phryg"tr

b+ r-!

Enigmatic

.i>

SuperLocdao

Great concern must be given the vertical factor; if tonal planes are arbiuarily combined the harmonic result will be haphazard. The music mu$ be conceived in polytonal context, not cloaked in accidental texture. Each melodic line should rerain its own individuality yet the harmonic total must have direction of flow, tension design, and textural consistenry. Although each tonal plane has its own organizational cenrer, a single over-all tonic structure is usually felt from the bass.From this basic polychordal tonic stems the polytonal texture. The following example employs C, E, and G areas at different levels, but they combine in a total harmonic sound with C functioning as the fundamental:

s

12 . KEY CENTERS

2t6) Et. 12-12

Polytonaliry, then, is a specific kind of tonal organization, a means of moving groups of voices within confined harmonic register areas.Polychordal writing is often tonal, and when each group of voiceswithin a chordal unit functions wiúin the confines of a stablescalezone,polytonaliqyoccurs. Polytonality is effective as such only when each tonal plane is kept within a clear scaleformation. Shifting of modaliry through chromaticalterationcÌoudsthe texture or simply producesmiscellaneouspolychords.For maximumclarity in the pro]ection of ditferent tonalities, one key is introduced and as the next key is becomesless added,the precedingkey, having been escablished, obvious.

Ex. 12-13

í

The scalestepsspanningthe tritone shouldbe brought into play âs soorl as possible;otherwise polponality will fail to operate. In

(2t7

POLYTONALITY

the following example,the lower F mafor strand hasno B! or E, and the upper C major strand has no F or B; the result is ambiguouslymajor.

Er. 12-14 J=120

Closelyspacedpolytonal areasbecomemuddy. The keys shouÌd be kept far enoughâpart to allow room for voice activity. Harmonic parts of three keys placed a small interval apart run into eachother. Crampedpolytonaliqyof this type is possiblebut lacks versâtility. Independentlines should not be placed at random without an understandingof polytonal construction.The fundamentalquality of polytonal texture is determinedby the key relationshipset up by the tonics. In major-key combinations,â polytonal order of tensionfrom consonantto dissonantis securedby combining fwo keys that lie a perfect 6fth, mafor ninth, major sixth, major third, major seventhapart-and so on up the cycle of fifths. The high point of resonancein the order is at the center. Ex. 12-1J j a-

Loú

1t

b-.

ma.9 rra.6 ma.3 ma.7*r9,4 ml 9 mló

Those keys that âre not closely related accordingto the circle of fifths will more easilyset âpârt the tonal key spheres.The tritone as a basisfor key coalition forms a prime polytonal relation-

12 . KEY CENTERS

2t8)

ship becauseit is the most resonantof the dissonantcombinations of keys. Polytonal combinationsof ma]or keys are: Ex. 12-16 consonâít

Similarinventory shouldbe madeof all key combinations.When minor keys are at the bottom (major or minor at the top), fewer consonantcombinationsof keys are possiblebecauseof the minor third in the lower key. When combining more than two keys, the consonant-dissonant order of resonanceis: all keys separatedby a perfect fifth, a maior ninth, a major sixth, a major third, etc.

Ex. 12-17

'When

the intervalsbetweenthe keys âre not the same,the larger interval is found between the bottom keys. When combining three or more mixed keys, the uppermostkey is governedby the resonantrelationshipto the bottom, not inner key. The resonanceof polytonality dependsupon the resonanceof the over-all tonic formation as determinedby its intervalÌic tension. The passingsecondarytextures are maneuveredaround the rnost resonantpolychords úat form the structural pillars of the particular key combination.

(2te

POLYTONALIfi E*. 12-18 Ama.

polychordalpíllars

polichordalpillars F lydiau

Fma"

These secondarytexturesoften becomethick and troublesome and are madeworkable by omissionof chord members,doubling of stronger intervals, ornamentalcoloring, unison and two-part interpolations,or by ostinatos. Polponaliry may be establishedby two or more tonal planes of harmonic writing (chordal polytonality), Ex. 12-19

or through imitative writing (horizontalpolytonality). Real canons at intervalsother than the octavecan imply polytonaliqp.Two or three lines may produce transpârentpolytonality.

Ex. 12-20

su, Trio

\canon by 4o

espr,

canonat úe uitone

12 . KEY CENTERS

Block chords againsta single contrastingkey line createsupple polytonal patterns;shifting pedalseâsethe polytonal texture.

va.(a;.i{

Well-balanced polytonaliry is secured through mirror scales (polymodality).

Er. 12-22 D lydian

I

legúo

-o--ã

(261

ATONALITY

JnJ

ATONALITY

Atonality is a term loosely applied to music in which a definite key feeling has been weakened or lost, and to music in which no key gravitation ever existed. Atonal writing is the organization of sound without key establishment by chordal root relationships; but tone combinations or âreas may form an atonal equivalent of tonality. In atonal music, relations between tones occur without reference to a diatonic scale formation. There is movement to and from characteristic intervallic formations but the central force is usually melody, and not a governing harmonic base. Atonality operâtes within â syntax that favors dissonant formations, and its organization is based upon shifting intervallic tension or an order of tones. Atonal movement is often linear but may produce vertical combinations of mixed intervals (compound harmony) that are free from the power of an overbearing tonic. When the motion of voices câusesâ constant and total dissonance,beds of sound are created upon which prominent melodic lines may lie. If chromatic chordal mixtures accumulate, formal coherence is achieved by repetition, variation, or mutation of úe chromatic sound groups. Although the harmonic factors are dependent uPon melodic relationships, these vertical structures are often manipulated as a c.ontributing element in atonal composition. The various elementsin atonal music are tightly knit by extreme motivic concentrâtion, and reference is constantly made to Previous material. There is litde regular rhythmic stamping and no

12 ' KEY CENTERS

262)

continuous chain rhythms; the rhythmic patrerns are asymmetrical and the meters irregular and often complicated. When the controÌling principle of scalar tonality is abandoned, chordal root organization of the rwelve tones ceasesto exist, and form and unity are creared by meiodic and rhythmic development. A basic order of tones, alÌ twelve or fewer, may be used as a unilying basis for a work, and formai devices evolve from the basic shape. Twelve-tone technique or composition with "rwelve notes related to one another" is primarily â conrrapuntai practice. It is essentiallya polyphonic conception with some points in common with the pre-"tonal" music of the Middle Ages. Twelve-rone writing is, therefore, mosr naturally approached in a treatise on counterpoint.

SERIAL

HARMONY

Harmony, even when secondary, is an important consideration in linear music. When harmony is regulated by a horizontal, unifying idea (twelve-tone or nor), rhe texrure may be serial; this kind of writing creates harmony of extraordinary compâctnessthrough the manifold variations of the motif relationships. Chordal formations that arise from serial linear writing have little or no function in a scalar tonal sense.Harmonic obligations arise from a chromâticism set up in harmonic areas from a characteristic series or portion of a series of tones. Logical meÌodic thinking gives the individual par$ their dtection and the ear of the composer gives them the quality of chordal movement. Some directions in serial composition point away from the specialized craft of strict "atonal" writing, where all elements are generated from a single germ cell, toward a flexible creârive process úat includes the vast musical resources of composition, both tonal and atonal. The techniques and materials of atonal music are often amalgamated with those of many types of tonal idioms; the harmonic stock includes endless possible harmonic combinations. A qynthesis of harmonic potentialities includes chord materials governed by root progressions, intervallic texture tensions, and serial

(26t

SERIAL HARMONY

devices.At any point in the formal shapea melodicgroup of notes may control harmonic texture. Any successionof any number of tones, not necessarilyall different (a), may be used in two or more voicesat once,forming harmony from horizontalmovement (b) or divided between voices, forming harmony from vertical telescoping(c).

Ex. 12-23 melodic set

ç)=ne1

4

56

:l',*.

non+erial

82

10 11

Invenim I ---------------->

tF!

2

34

Original (transpositionno. 1)

f-íã.--c

Original (tranqpositionno. 2)

ll (7)

f

12 . KEY CENTERS

264)

OrìginaÌ (uanspositionno. l)

-

senalrow extrectron

|

2 3 r

4 | 6 7 I t-------Ì-J

9'1,0 lt

9

l0ll

r

(identical notes) Inversion (transposed)

Original (transpositionno 2)

9 1011

In an extended passageor secrion of free serial music, any combination of tones may be ser up as a tonaliqy. A successionof three or more notes from the selectãd melodic ser or row of rones may be used âs a center chord (a).Atransposition of the cenrer chord erected upon its uppermosr note may form a cadential chord above the center (b); a mirror of the cenrer chord may form anorher primary chord below (c). Changing the octave pitch of one or more tones produces inversions. Inversion of the center chord may yield a new set of primary chords (d, e, and f). All other combinations of tones may form secondary harmony.

Ex. 12-24

(26t

SERIAL HARMONY

When a melodic set includesone or more identical notes,doubling of chord membersproducescolorful serial doublings.Parallel harmony may be used momentarily at points where doubling occurs.

Es. 12-2Í (J=8ob r òü.

>

1l

,Qew'

HH

In serial harmonic progression, the order of chords is often changed to increase the gravitational tendency of the chordal formations to move to the center chord.

Ex. 12-26 ccffer x

ctntet x

Transpositionof úe melodic set causesmodulatory shifting of the harmonicâreas.

Ec. 12-27

12 . KEY CENTERS

266)

When a chord from one form (original, retrograde, inversion, or retrograde inversion in any uansposition) of the melodic set is identical to a chord of another form of the set, it may be used as a pivot formation when entering new "ronal" areas. Closely related harmonic areasare those that may be found by constructing an inversion or retrograde inversion of the melodic ser starring a perfect fifth above or below the original set. Strong cadences may be formed by the primary chords (Ex. l2-2+) or by ornamenral movemenr of the parts directed toward the center chord.

Ex. 12-28 Perfect

PI.g"l

Complete (c)

(b)

Omamental (e)

+

(r) Chords may be ornamented by nonharmonic tones (a), by harmonic tones (â), or by serial tones that result from the simultaneoususe of two or more forms of the set (d).

Ex. 12-29

(267

SERIAL HARMONY

Contrasting thematic mateúl mây be built upon a new but related melodic set. The original set may be converted to another by selectingthe top notes of a seriesof telescopedchords.

Ex. 12-30 oenr9-nctmeloücsct

DFGDTFSD3CIÂB r23456789

When melodic sets employ twelve different notes, successive chords encompassthe entire twelve-tone field. A strong center or harmonic areamay result from the completion or fulfillment of úe twelve-tone set. Serial music of any type of rov/ or set constructionmust be aurally createdby melodic, harmonic, contrapuntal, rhythmic, and formal elementsof the musical structure and not alone by manipulativeprocedures.Serial technique doesnot in itself insure communication or even effective sound orthan any other.techniquedoes.When autoganization lnymore matic writing is avoided, the unifying power of serial practice allows great hannonic variery.

SourceMaterì,al Modulatory pâssages: Ernest Bloch, Piano Quintet, pp. 57-59 (G. Schirmer) Aaron Copland,The Tender Land (red.), pp.67a8 (Boosey) Ingolf Dahl, Sonata Seria for Piano, p. 14 (Presser) Jacqueslbert, Histoires for Piano, p. 3 (Leduc) Gian Carlo Menotti, The Unicorni the Gorgon and the Manticore (red.), p. 56 (Ricordi)

268)

12 . KEY CENTERS

Vincent Persichetti, Hymns and Responses for the Church Year, p. 1 (Elkan-Vogel) SergeProkofiev, SecondViolin Concerto (red.), p. 21 (Russe) Arnold Schoenberg,Gurre-Lieder (red.), p. 14ó (Universal) Harold Shapero,Sonata for Violin and Piano, p. 13 (Southern) Igor Stravinsky, Symphony in Three Movements, p. 78 (Associated)

Tonality createdby non-traditionalmeans: Peter Racine Fricker, Concerto for Piano and Orchestra (Schott) F{ansWerner Ffenze,Concerto for Piano and Orchesta (Schott) Paul Hindemith, Sonata in C for Violin and Piano (Schott) Arthur Honegger, Violin SonataNo. I (Salabert) Franco Margola, Piano Sonata 195ó (Ricordi) Francis Poulenc, Mass in G mafor (Rouart-Lerolle) Harold Shapero,Three Piano Sonatas(G. Schirmer) Igor Stravinsky, Symphonie en Ut (Schott)

Examplesof polytonality: Benjamin Britten, The Turn of the Screw (red.), p. 158 (Boosey) Alfredo Casella,ll Pezzi Infantili, p. 20 (Universãl) Manuel de Falla, Harpsichord Concerto, p. 3 (Eschig) Rodolfo Flalffter, Piano SonataNo. 2, p. 31 (Peer) Paul Hindemith, String Quartet No. 3, p. 21 (Schott) Arthur Honegger, Symphony for Suings, pp. 28-30 (Salabert) Darius Milhaud, Cinq Symphonies (petit orchesue) p. ó1 (Universal) Wallingford Riegger, New and OId (piano), p. 31 (Boosey) Igor Stravinsky, Symphoniesof Wind Instruments (red.), p. 14 (Russe) Karol Szymanowski, String Quartet Op.37, p. 19 (Universal)

Worlis with prominent atonality: Alban Berg, Wozzeck (Universal) Arthur Honegger, Pacific 231 (Senart) Charles lves, Aeschylus and Sophocles(from 19 Songs), (New Music) Carl Ruggles, Evocations for Piano (Am. Mus. Ed.) Arnold Schoenberg, Pierrot Lunaire (Universal)

Works written in free serial technique: Aaron Copland, Piano Fantasy (Boosey) Luigi Dallapiccola, Il Prigioniero (Zerboni) Irving Fine, String Quartet No. 1 (C Fischer) Wallingford Riegger, Symphony No. 3 (Associated) George Rochberg, String Quartet No. 1 (C. Fischer) Roger SessiongSymphony No. 2 (G. Schirmer) Igor Stravinsky, Agon (Boosey) Fartein Valen, Sonetto di Michelangelo (Norsk)

SERIAL HARMOÌ.{Y

(269

Applications 1. Write a woodwind pâssage whosebasictonality is E! with a stÍong titone emphasison A major. 2. Harmonize the following melody for string iluartet, preservingthe E tonal center.

Ex. 12-31 Ândantc

ú rtp.

3. Write a passagefor piano, four hands,in which an insistentchord estabÌishes a center by resistingtonal pressuresfrom various keys. 4. Composea short dancefor clarinet and piano which employsshifting tonality. 5. Write two-part counterpoint for the harpsichordwith eachpart in a different tonality. ó. Extend the following polytonal passagefor harpsichord (C mixolydian and Ef aeolian):

Ex. 12-32

12 . KEY CENTERS

270)

7. Extend the following polytonal pâssâgefor string trio (Ffi maior and F lydian):

Ex. 12^33

8. Extend úe following polytonal pâssâgefor piano (D[ and C rnajor):

Et. 12-34

9. Write a shortpianopieceasfollows: A-rwo distant---l r."u,- l-ï-,tingle

üne

LH-broken chords

õ-two closekeÏs

RH--chords LH-ostinato

A-modified repetition with coda. 10. Write an orchestral example of polytonality with agile ninth chords in the woodwinds, sustainedtriads in the horns, and an ostinato (in tenths) in the low strings and winds. 11. Write a non-serialstring-quartet exampleof atonal music. 12. Write a short piece for woodwind quintet that conains boú serial and non-serial music.

CEÂPTER TEIRTEEN

HarmonicSynthesis

COMBINING TEXTURES CoNrsrvÍpoRAnv harmonic writing b often a composite process which may involve varying placement of the norm of dissónance, choice of a single harmonic idiom or the coalition of one with anoúer, fusion of tonaìities, singlenessof sound organization or the juxtaposition of tonal and atonal aspects. The amalgamation of divergent concep,tionsof tonal formations is part of our harmonic language. Acceptance of one procedure does not necessarily mean the exclusion of others. A fugue may be written over a cântus placed under a rone row, and quartal harmony fI-T,-" lI*" blended with tertian. The vertical combination of harmonic rexrures produces polychordal and compound formations, but successive combinations entail movement from one kind of texture to another and the functioning of heterogeneous harmonic materiais side by side. A textural problem arisesfrom the manipulation of the transitional materiaÌs that lead from one type of harmony to another. The characteristic interval of one kind of harmony b contained in any other n1

272)

13 . HARMONIC

SYNTHESIS

kind of harmony and may be brought to the surface by intervallic inversion. In all textural changes,an inten'al may be featured that, when inverted, produces the characteristic interval of the new harmony. The interval of the fourth is given a prominent position in chords by thirds to allow chords by fourths ro enrer; the fifth contained in the triad is inverted to allow for oncoming fourths (a). In seventh chords the inverted fifth from the root or third may be used to introduce quartal harmony (ú). The voices of an inverted seventh chord may be arranged so that the interval of the second is emphasizedand the contextual way prepared for secundal harmony (c). In ninth chords the interval of the sevenrh from the root or third is inverted to suggestthe secundal texture of clusters or added-notechords (d).

Ex. 13-1

When moving from one rype of harmony to another the characteristic interval of the new harmony is best introduced well in advance. The doubling of a colorful tone (major third, maior seventh, or prominent nonharmonic tone) strongly suggestsoctave or unison writing that in turn makes way for foreign harmonic re-

(273

COMBINING TEXTURES

sources.The unison can becomea suppledevicefor moving from one kind of texture to another.The harmonicambiguiq' or sudden unison allows for the entranceof any texture. The versatileornâmentaltone also providestextural meânsfor entering any harmonic region. The appoggiaturaand suspensionare particularly eÍfective in preparing the intervallic texture. The melodic freedom of broken chordspermitsthe fluctuation of chordsof varying construction, Ex. 13-2

Accenting melodic tones that outline úe characteristic intervallic formation of the new âreâ creates a tonal bond between the contrasting harmonic materials.

Ex. 13-3

4,

(Pi"z)

teni*'

quâftd

-

l---------€

13 .HARMONIC SYNTHESIS

274)

The rypg of chordal formation may be changed by subtracting from a melodic morif rones that leave only the tones of the new textÌrre.

Er. 134

ct

rúr--:

Hn. 2 Bns.

.? Sn only

ouartal ----+

The equidistant chord has neither root nor power to resisrhomogeneous chordal formations and can, by chromatic motion, v/eave one harmonic fabric into another. Rough tritone relationship or prominent hidden fifths divert artention from harmonic rransformations. Sequential patteÍns can drive varied chords over many harmonic barriers. A common transitional harmonic device involving clusters is the gradual subtraction of cluster members, leaving chords that suggest the kind of harmony to follow. The reverse is no less efiective.

Ex. 13-Í

Polychords are approachedthrough coupled uiads (a), or chromatic conversion of chords (ú). Motion from polychords

(27t

THEME AND FORM IDEAS

to triads is createdby the evaporation of one triad of the polychord (c). Ex. 13-6 1J-tzo1

Full -, Orch.

(c)

Ì

Í

aí

The harmonic units of a tonal polychordal successionmay meet at a point where each progressesin a sepârâteand consistentkey zone.The polychordal progressionthen becomespolytonal. Atonality may be entered through florid writing when the individual lines are given such freedom of c{rromatic movement that the implied harmony becomesindefinite and úe feeling of key disappear*

THEME

AND

FORM

IDEAS

A melodic kernel of two or more tones may form the nucleus from which the subject matter of an enúe work is shapedand harmony derived. The compositional process is meaninglessunless

276)

13 . HARMONIC S\T{THESIS

thematic stateÍrlentsare identifiable, for continuiqy and coherence are effected through aural rerention of modfs. It is imperative that a s€nseof tempo, dynamics, and medium be part of thematic conception. Even a single tone can serveas a point of departure through dynamic and timbre implications; a pianissimo and expressivemiddle C played by a solo viola has musical impetus while a rough, staccato, and loud middle C played by three rrombones has a quite different kind of musical energy. Creative momenrum might stem from a scale formation, a series of non-scale ton€s, a chordal stmcrure, a lone tone repearing itself before finding â ne\Ãrtone from which flight can be made, the rnelodic contour formed by a complex opening chord âtrempting to shed its dissonant tones, or themes shaped by brassesanswering a loud timpani. Material might be born of creative tension caused by pattern shapes: the excitement of fast-moving voices of sopranos, the intrigue of brass figures accompanying a resounding sringsection, or the richness of strinç under a unison melody in the solo piano. Careful inventory of melodic, rhythmic, and harmonic aspects of thematic ideas must be taken, becauseas a work progressesihese elements are often used independently of each other. Not until full thematic intelligibility is realized do hidden meanings of the theme come to the surface. Thematic ideas may be purposefully enigmatic and vague, positive and complete in themselves,or musically. neutr_al,but they should be positively vague, not vaguely positive. The composer musr be fully awâre of the potentialitiés of his material so thât full advantage can be taken of ihe phenomenon of thematic uansformation. Thematic meaningfulnesscan arise only from úematic uniqy and purpose. If a themeis not nourished by its motivic consriruents it wilÌ lack significance. Form and style are inseparably related. Form is the outward eqúvalent of instinct, taste, and style, and is the manner in which kinds of materials âre presented. Divergent musical materials may be brought out of conrexr into a piece, but the successof the décision to change the prevailing milieu depends upon creative sensitivity.-ConÍlicting formal elemenrsoften result in free and imaginative forms, and the whole course of a maior work is altered. The impulse that incites the composer to deviate from the predictable must at the sametime create a feeling of inevitabiÌiqy of form.

THEME AND FORM IDEAS

(277

Associationof musical ideas is created by the melodic motif, the harmonic succession, and the rhythmic pattern; none of these three formal elementsbecomesfunctional until it is transformed by the creativemusicalprocess.It is during this growth that specific ideasfor shapingthe formal strucrure stimulatecrearivewriting: a succession of simplechordsfighting dissonantforcesmay succeed or fail; an extremelydissonantand overbearingchord refusing to becomeconsonântmay produce a distinctive harmonic progression; a succession of chords,dramaticallyplaced,may indicate the formal direction; a work may be built upon initial harmony falling cadentially; provocative formal elementsmay be inuoduced by brightening the harmony as nores get slower and darkening the harmony asnotesget fasrer;six tapedmicrotonesmay be elecuonically upset by hexachordal diapasonsthat push agitated Sprechstimmefragmentsagainstruned oriental blocks. Any tone cansucceedâny other tone, any tone can soundsimultaneouslywith any other tone or tones,and any group of tones can be followed by any other group of rones,just as any degree of tensionor nuancecân occur in any mediumunder any kind of stressor duration.Successfulprojectión will dependupon the contextual and formal conditionsthat prevail, and upon úe skill and soul of the composer.

SourceMateriul Passages containingvariouskinds of harmonic textures: Albln Berg, Violin Concerto (red.), pp.47a8 (Universal) Paul Hindemiú, Six Chansons(II), (Associated) Althgr F{onegger,Piano Concertino, pp. 1-4 (Sena*) Charleslves, Violin SonataNo. 4, p. 8 (Arrow) Michael Tippen, Suing Quartet No 3, p. I (Schott) Works

contâining

contrasting

techniques:

Béla Bartók, Piano Concerto No. 2 (Boosey) Karl Àmadeus Ffartmann, Symphony No. o'(Schott) Charles lves, Piano Sonata No. 2 (Concord), (Arrow) Vincent Persichetti, Quintet for Piano and Strings (Elkan-Vo,sel) Roman Vlad, Divertimenro for 11 Instruments (Éoosey)

13 ' HARMONIC SYNTHESIS

n8) Unique thematic idea*

Béla Bartók, String Quartet No. 4, p. 3 (Boosey) Alban Berg, Violin Concerto, p. 1 (Universal) John Cage,Amores for Prepared Piano, p. 1 (New Music) Carlos Chávez,Sinfonia India, p. 1 (G. Schirmer) Aaron Copland, Vitebsk (violin, cello and piano), p. 1 (Cos Cob) Roy Harris, Concerto for Piano, Clarinet and String Quartet, p. 39 (C,s Cob) Luigi Nono, Coro di Didone, p. 1 (Scherchen) Wailingford Riegger, Dichotoiry, p. I (New Music) Guido Turchi, Preludi e Fughetti per Pianoforte, p. 4 (Zerboni) Roman Vlad, Sonatinafor Flute and Piano, p. 2 (Zerboni) Ralph Vaughan Williarm, Symphony No. ó, p. 143 (Oxford)

Works with unique forms B€la Bartók, fti[tsic for String lrstru:ents, Percussion and Celesta (III), (Boosey) Aban Berg, Lyric Suite (III), (Universal) Luciano Berio, Cinque Variazioni per Pianoforte (Zerboni) Piere Boulez, Improvisation sur MallarrrÉ (Universal) Sylvano Bussotti, Five Piano Pieces for David Tudor (Universal) Elliott Carter, String Quartet No. 2 (Associated) Carlos Chávez, Sonatina for Violin end Piâno (New Music) Alois Hába, Suite No. 3 for Quarter-Tone Piano (Universal) Roy Harris, Symphony No 3 (G. Schirmer) Paul Hindemittr" Hin und Zurück (Schott) Charles Ives, The LJnanswered Question (Souúern) Bo Nilsson, Zwnzig Gruppen (Universal) Vincent Persichetti, Harmonium (soprano and piano), (Elkan-Vogel) Gunther Schuller, String Quartet No. 1 (ilI), (Universal) William Schuman" Symphony No ó (G. Schirmer) Karlheinz Stockhausen"Klavierstücte I-IV (Universal) Igor Suavimky, Symplroniee of Wiad kstrurnents (Russe) Edgard'Webern, Varèse, Ionisation (New Music) Five Pieces for String Quartet Op. 5 (Universal) Anton

Applications 1. Write â passagein any medium containing the following chords _ (among others) in any order a4d in any transposition

THEME AND FORM IDEAS

(27e

Ex. 13-7

2. Extend the following idea in the string orchestraand include various categoriesof harmony.

Ex. 13-8

3. Weave â passâgeof organ music through tertian, quartal, secundal, polychordal, and compound harmony. 4. Construct thematic material on the following pattern ideas: rich string harmony under a solo trumpet; fast-moving woodwinds; huge declamatorychords for two pianos;solo timpani answeredby full orchestra; string and woodwind chords surrounded by virtuoso figures in the brasses;coupled two-part writing in the band; percussiveharpnichord chordswith abbreviatedornaments;lyric polytonality in the oboe and guitar; dynamic chords in the harp with frequent two-parr interruptions in the flute and viola; a sopranovocalisewith mirror writing in the piano; clusteredbrasseswith melodic writing in the timpani and xylophone; quiet ornamentedpolychords in the organ; quartâl harrnony in the woodwind quintet with erratic harmonic rhythm; vivacious pandiatonic writing in the mixed chorus on a phrase from one of the Psalms;and a virnroso keyboard mirror for solo piano. 5. Make piano reductions of provocâtive passâgesfrom severaltwentieth-century orchestral works.

Index of Composers

Antheil, George, 222 Argento, Dominich, 74 Auric, Georges,210

BouÌez, Piete, 27, 172, 210, 278 Britten, Beniamin, 28, 42, 50,74,8t, 90, 118,172,2r9, 220,245,268 Bucchi. Valentino. 10ó Busoni,Ferruccio, ó0 Bussotti,Sylvano,278

Babbitt, Milton, 219 Badings,Henk, 27, 87 Barbei, Samuel,62, 74, 219,220,243 Cage,John, 278 Bartók, Béla, 27, 28, 42' 43,45, 50, 59' ó0' Carter, EÌÌion, 28, 172, 210, 219, 778 74, 126,150,158,180,209,270,219,222, Carpenter, John Alden, 210 225,237,277,278 CaseÌla,Alfredo, 42, 268 Beck. Conrad, 245 Châvez,Carlos,41, 42, 43, 118,210,220, Becker,John,219 222.225.278 Beeson,Jack,219 CopÌand,A,aron,27, 28, 74, 106,118,126, 118 Paul, Ben-Haim. 158, 180, 209, 210, 219, 220,225, 267, Bentzon, NieÌs Viggo, 28, 50, 209 268,278 Berg,Alban, 28, 59,63,81,85,87,90, 10ó' CorveÌÌ,Henry, 62, 733,222 133, 158,209, 2r0, 222, 241, 268, 278 Creston,Paul, 81 Berger, Arthur, 27 Bergsma,William, 28, 225 Dahl, Ingolf, 22t,267 Berio, Luciano,235,278 DaÌlapiccola, Luigi, 118, 180, 209, 2?2, Bernstein,Leonard, 90, 106 268 BettineÌli, Brrno, 27, 6f , 245 Debussy,CÌaude, 41, 42, 59, 126 Blacher, Boris, 219, 237 Delius,Frederick,210 Blackwood, EasÌey,172 Dello Joio, Norman, 243 Bìitzstein.Marc. 28 Dianrond, Davìd, 28, 222 Bloch, Ernest,41, 131,222,241,267 Donatoni. Franco.227 Blomdahl, Karl-Birger, 90, 126, 180 281

282)

INDEX OF COMPOSERS

Egge, Klaus, 42, 81 Egk, Werner, 225,235 Einem, Gottfried vorq 63 Escobar,Luis, 42 de Falla,À{anuel,210,222,268 Fine, In'ing, 222,268 Finney, RossLee, 50 Fìoyd, Carlisle,243 Former. Wolfgang, 28, 243 Foss,Lukas, 81, 243 Françaix, Jeen,219 Fricker, Peter Racine, 150,268 Gershv'in, Gecrge, 42, 81,209 Giannini, Vittorio, 90 Gielen, À,Íichael,90 Ginastera,Alberto, 27, ll8,710 Griffes, CharÌes,50, 59,245 Guarnieri, Camargo, 118,245 Hàba, Alois, 278 Haieff, Alexei, 28 Halffter, Rodoìfo, 2ó8 Flanson, Hou.ard, ó3, 22Í Harris, Roy, 41,42, 62, 81, 150,210,237, 'r4!-

)41

Lees, Benjamin, 27 Liebermann, Rolf, 90 Maderna,Bruno, 211,222,228 Malipiero, Gian-Francesco,42, 59, 87, 118 Margola, Franco, 2ó8 Martin, Frank, 7,1,118 Martinet, Jean Louis, 28 À{artinu, Bohuslav, 27 McPhee, Colin, 225 Mennin, Peter, 27, 118,219, 220 Menord, Gian Carìo, 74, 118,210,267 Messiaen,Olivier, 28, +3, 50, 157,209 Mihalovici, Marcel, 158,245 Miìhaud, Darius,42, 43,85,90,118,126, 157,r58, 180,209,225,268 Moore, Douglas,74 Nilsson, 8o,278 Nono, Luigi, 209, 220, 278 Nordoff, Pari,243 Orf, Carl, 42, 43,225

)13,

F{arrison,Lou, 50 Flartmann, Karl Amadeus,28, 180,209, 220,277 Flauberstock-Ramati,Roman, 219 Heiden, Bernard, 210 Helm, Everett. 90 FIenze,Hans Yrrcrner, 27, 28, 268 Hinc'lemith,PauÌ, 27. 28, 42, 43. 59, 60, 1 0 2 ,1 0 ó ,1 1 8 .1 5 8 .2 0 9 . 2 1 0 , 2 1 9 , ? 2 0 , 2 3 5 ,2 3 7 ,2 + 3 ,2 ó 8 ,2 7 7 ,2 7 8 lJolmboe, Vagn, 27 HoÌst, Gustav, 28, 220 Honegger,Arthur, 27,28, 43, 50, 59,62, 7 4 , 8 5 ,s / , 1 0 6 1 1 8 ,1 5 0 ,1 5 7 ,2 2 0 , 2 2 2 , ))