The Concept of Unity in Electronic Music

The Concept of Unity in Electronic Music Author(s): Karlheinz Stockhausen and Elaine Barkin Reviewed work(s): Source: Perspectives of New Music, Vol. 1, No. 1 (Autumn, 1962), pp. 39-48 Published by: Perspectives of New Music Stable URL: http://www.jstor.org/stable/832178 . Accessed: 20/12/2012 18:43 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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THE

CONCEPT

OF UNITY

ELECTRONIC

IN

MUSIC

(Die Einheitder musikalischen Zeit) KARLHEINZ STOCKHAUSEN

ON

SE VERAL previousoccasions, when I have been asked to explain

thecomposition of electronic music,I have describedfourcharacteristicsthatseemimportant to me forelectronic as distincomposition ofinstrumental music: guishedfromthecomposition of thecoloristic, and metric1) thecorrelation harmonic-melodic, of aspects composition rhythmic and de-composition oftimbres 2) thecomposition the characteristic differentiation 3) amongdegreesofintensity betweensoundand noise 4) theorderedrelationships oftimbre,pitch, Here,I wouldliketo discussonlythecorrelation and In duration. the it has been to regard intensity, past, customary these correlativepropertiesof sound as mutuallyindependent, as to distinct have belonging fundamentally spheres.They appeared separateas our acousticalperceptiondevelopedalong increasingly such lines. themeansemployed fortheproduction ofsound,as well Similarly, as the compositional were processitself, consequentupon this conTo generatesound-events ceptualseparation. havingsingleperceptible pitches,we used the so-calledsine tone,square-wave,or saw-tooth whichproduceperiodicoscillations. Sound-events of indegenerators, terminate wereproduced pitch,thosethatare moreor less noise-like, by meansofnoisegenerators. We variedsuchsound-ornoise-colors bymeansofelectricalfilters, withwhichone can strengthen, or suppressentirelyindiattenuate, vidualpartialsor wholefrequency-bands-the so-calledformants, or bandsofnoise-of thespectra. was controlled withtheaid ofa voltmeter, Intensity by regulating, thevoltagesrecordedon tape (wherebythespectrum itselfautomati* 39-

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PERSPECTIVES

OF NEW

MUSIC

callyvariedwiththevariationsin intensity),whereasdurationwas determined simplyby the lengthof tape on which a sound was recorded. of and manipulation in termsof the production Compositionally, to be with had dealt these individual sound, sepasound-properties as a homorately.But,on theotherhand,we perceivea sound-event ratherthan as a compositeof four separate geneousphenomenon At a properties. relativelyearly stage of my work in electronic thepossibility of equatingthis I had alreadyconsidered composition, itself.In withan analogousunityin composition unityof perception thepreparatory workformycomposition Kontakte,I found,forthe I deduced undera singlecontrol. first time,waystobringall properties can be tracedto differences of acousticperception thatall differences of soundwaves. These temporalrelations in the temporalstructure of pitch, manifestations the manydifferent enableus to distinguish their of noise: and sound-mixture, timbre,simultaneity, speed oscillation,theirparticularintervals--either equal and regularor moreor withwhichpulsations andthefrequency less irregular-their density, in intensity reachtheear. It seemedto me thatthedifferences among whenpulsationsof derivefromthelatterproperty: soundsultimately equal value followone anotherin closer temporalsuccession,the over-allintensity increases;to effect this,the densitywould,in fact, haveto be so greatthattheindividualpulseswereno longerconveyed but rather of the atmosphere as a successionof equal perturbations sound-waves:theparticlesof air agitatedby as mutuallyinterfering the initialpulseswouldthusbe reactivated pulses before by further "shaken to so and have become up,"so that speak, quiescent are, they The total in an increase over-all is of theimpression intensity. given several than rather wave complexthus appearsas a single greater smallerones. The fasterthe successionof pulses,the strongerwill be the appearanceof the resultantwave. A periodicsoundwave,suchas a simpletone,fluctuating regularly in intensity, wouldthusbe the resultof a successionof pulses that withineachperiod.The difference accelerateanddecelerate alternately of speed of the pulses in each rates slowest and fastest betweenthe of period would definethe direction its intensity(its "intensity envelope") and its amplitude.The distancebetweenperiodically thepitch. recurring equal ratesofspeedwoulddetermine Ex. 1

* 40 4

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THE

CONCEPT

OF UNITY

IN ELECTRONIC

MUSIC

If a successionof pulses of this kind were to be acceleratedso thatbetweentheperiodicrecurrences ofthehighestspeedtherewere a timeintervalof,say, 1/440 sec.,onewouldheara simpletonewith thepitchofA-440. If the rate of speed of the pulse-succession did not fluctuate regularly (

~

) but consisted instead of periods of sev-

eral unequal parts withineach equal time-span(as, for example,

so-called "color" ofa steady sound would /&\f\J\ /), the varyaccordingto thewave crests.A "period"dividedintotwo parts wouldbe represented as follows:

Ex. 2

In a moreor less noiselikesound-event theperiodswouldno longer be regular;i.e. thetimeintervalsbetweenrecurrences of equal rates of speed would not remainconstantbut would varyirregularly betweena givenfastestand slowestspeed. These extremesdetermine the limitsof a frequency band, a so-called"colorednoise"band. If the rateof speed of the pulse successionwereso widelyvariedthat thesmallestintervalbetweenpulseswereca. 1/16,000 sec., and the and everylongestca. 1/20 sec., occurringat regulartime-intervals, thingbetweentheseextremesoccurredin a highlyaperiodicfashion (in a mannerthatone mightterm"aleatoric")the resultwould be "whitenoise." For most musicians,these considerations may seem specifically relatedto acousticsratherthanto music.Actually,however, a musical is no morethan a temporalorderingof sound events, composition is a temporalorderingof just as each soundeventin a composition pulses.It is onlya questionofthepointat whichcomposition begins: in composingfor instruments whose sounds are predetermined, a not need be concerned with these On the other composer problems. hand,in electronic music,one can eithercomposeeach sounddirectly in termsof its wave succession,or, finally,each individualsound wavemaybe determined in termsofits actualvibration, by an orderof the succession of ing pulses. If, in fact,all of the experiential propertiesof sound could be tracedto a singleprincipleof ordering-suchtemporally composed successionsof pulses-compositional thoughtwouldhave to be radio 41 ?

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PERSPECTIVES

OF NEW

MUSIC

The distinction betweenthe "acousticalprearrangecallyreoriented. ment"withinthematerialand "musicalordering" usingthismaterial would now have to be discarded.The prevailingadditive,or "synthetic"compositional in whichthedifferent are procedure, properties boundtogether, would now be expandedthrougha protogenerative and moreunifiedapproach.One wouldnotproceedfromsoundpropertiesthat had alreadybeen experiencedand then allow these to determine temporalvariations;instead,one would composethe temand discovertheirresultant ofpulsesthemselves, poralarrangements soundproperties experimentally. at sucha procedure, I was Aftermyfirst, simple,attempt relatively of the theparticular abletopredictroughly orderings pulses. temporal I thenproceededto recordfixedsuccessionsof pulseson tape within a relativelylow speed range (using pulsationintervalsof between 1/16 and 16 secs.) and thenincreasedthe speed untilI arrivedat the"field"of frequencies and colorthatI desired.This was doneby withwhichthespeedofthepulsesuccesmeansof a pulsegenerator sionwas regulated hand. Thus,forexample,ifI wishedto generate by a periodicwave-thatis, a soundofconstant pitch-froma succession of pulses lastingeightsecondswhose speed variationsare fixed,I therhythmized succession1,024 wouldhaveto accelerate eight-second it ten that octaves is, transpose times, upwards,reducingits duration fromeightto 1/128 sec. In orderto sustainthispitchof 128 cps. for theoriginalsuccession128 X 10, 10 sec., I wouldhaveto re-record or 1,280 times,whichcan easilybe done by meansof a tape loop. The "color"oftheresulting soundwouldbe determined by thevariationsofspeedamongthepulsesoftheoriginalsuccession,whichare of the and accelerations nowdetermined by theperiodicduplications the wave formwithineach timespan-i.e. envelope." "intensity Withsucha compositional then,onemustproceedfrom procedure, a basic conceptof a single, unifiedmusical time;and the different per-

ceptualcategories,such as color,harmonyand melody,meterand rhythm, dynamics,and "form,"mustbe regardedas corresponding ofthisunifiedtime,as follows: to thedifferent components to periodicwaves (thatis, to 1. Harmonyand melodycorrespond of constantpitch) whoseindividualperiodsshouldnot sound-events be greaterthanca. 1/16 or lessthanca. 1/6,000sec. becausebeyond theselimitstheyare no longeraudibleas "pitches." to thewholenumber 2. The colorofharmonic spectracorresponds referto periodsof betweenca. fractions which,as "fundamentals," or noiselike 1/13,000 and ca. 1/16 sec.; the colorof nonharmonic spectra correspondsto more or less aperiodic successions of periods. S42

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THE CONCEPT OF UNITY IN ELECTRONIC MUSIC 3. Between ca. 1/30 and 1/16 sec. our perception of duration gradually changes into perceptionof meterand rhythm;i.e., periodic periods may thenbe consideredas meters,and the internalintervallic relationshipsof the distancesbetweenpulses withinany givenmeterthatwhich determinesthe tone color forperiods shorterthan ca. 1/16 sec.-may here be consideredas "rhythm." Aperiodic relationshipsof periods, which are considered "noises" in the sphere of color, correspond,when the periods are longer than ca. 1/16 sec., to aperiodic rhythmshaving no recognizable metersi.e. no recognizable periodicity (just as a deviation from simple in periodicityin the sphere of frequency--"dissonance"-corresponds, the sphereof duration,to syncopation). Although many of the new compositionshave been criticizedfor their alleged "lack of rhythm,"they may actually be considered to have "pure rhythm"without meter. This objection, moreover, is exactly analogous to that directedagainst the use of aperiodic sound waves, i.e. against "noises." 4. Meter and rhythmcorrespondto the timeintervalswhose order of magnitudeis betweenca. 1/8 and ca. 8 secs. At about 8 secs. our abilityto distinguishdurationalrelationshipsgradually breaks down. With values of greaterlengthwe are no longer able to rememberthe exact lengthsof durationsor perceivetheirproportionsas accurately as we can those thatlie betweenca. 1/8 and ca. 8 secs. "Form" in a special sense-the time relationships of longer events--correspondsto durationsof the order of magnitude of from several seconds to about 15-60 minutes (for "movements"or whole "compositions"). The transitionsand overlappingsbetween all the time spheres are quite flexible,but this is especiallyso with referenceto "form,"which is most obviously an approximation(in the literatureof music, of course, the durationsof "movements"or continuousworks vary from several minutesto ca. one hour). Perhaps I should mentionhere that each of the threelarge musical time-spheres-frequencyduration,rhythmduration,and form duration-are of approximatelyequal size: each has a compass of about seven "octaves" (where "octave" signifiesa relationof 1:2). Between the highestnote on the piano, whose fundamentalwavelengthis ca. 1/4,200 sec. and the lowest,whose wavelengthis ca. 1/27 sec., there are just over seven octaves. Below this point sound waves gradually become audible as rhythms(a good illustrationof this is the audible effectof the lowestnotes on the organ), and fromca. 1/16 sec. to ca. S43

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MUSIC

OF NEW

PERSPECTIVES

8 sec.-the span ofrhythm are again sevenoctaves, durations-there as follows: (21 -

22

23

-

4

-

25 -

26 -

2 -_.)

1/16"- 1/8" - 1/4" - 1/2" - 1" - 2" - 4" - 8".

The sphereof formduration,fromca. 8 sec. to betweenca. 900 secs. (15 minutes,the approximatetraditionaldurationof single movements of a work) and ca. 3,600 secs. also includesseven-nine as follows: octaves, - 26 ( - 21 _ 2 - 23_ 24 2 2 .) 8" - 16" - 32" - 64" - 128" - 256" - 512" - 1,024"

Thus, the totalmusicaltimesphereencompassesthe durationsbetweenca. 1/4,200sec. and ca. 900 secs.,thatis, 22 (-24) "octaves," or 22-24 progressions of 1:2. At thispointI wouldlike to demonstrate, withan examplefrom a continuous betweenthetime Kontakte, composition my overlapping of their and the sphere and ("sounds" "colors") sphere "frequencies" of"rhythms" time audible within intervals). given (individually pulses This overlapping will takeplace in thezone betweenca. 30 and ca. 6 pulses/sec.To begin with,I fed a periodicsuccessionof 16.6 filter.This successionemerged pulses/sec.intoa verynarrow-band as a soundwave of clear,recognizable pitch.Then, withinone minute's duration,I continuously variedthe frequency positionof this filterfrom40 cps to 300 cps-that is, overa span,fromlow to high, of about3 octaves-inan ascendingzigzag glissandopattern: 300 cps

40 cps

Ex. 3

are heard as variationsin the pitch These variationsin filtering fromthepulse-succession. resulting until 166 Next, I subjectedthis resultto a tenfoldacceleration, pulses/sec.soundedinsteadof 16.6 pulses/sec.;that is, one heard of 166 cps (betweenEb, and E3). a steadypitchhavinga frequency The pitchvariationbetween40 and 300 cps,heardat thefirststage, of the tone color of the 166-cps now appearsas an intensification tone(now 6 secs.induration).Becauseofthehighspeed,thispattern is no longerheardas an ascending"melodicline." * 44 *

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THE

OF UNITY

CONCEPT

IN ELECTRONIC

MUSIC

For thecontinuation ofthissound,I generateda thirty-second successionof pulseswhosespeed decreasedfrom16.6 pulses/sec.to 4 the filter pulses/sec.accordingto a zigzag pattern.Simultaneously, was continuously varieddownwardsfrom300 cps to 40 cps and thenupwardsagainto 300 cps. 300 cps

300 cps

Filter 40 cps

Frequency -- - \

Pulse

9,4

16,6/sec.

6,8 5,3

Ex. 4

4/sec.

Duringthenext45 secs.,thespeedwas lessenedfrom4 pulses/sec. to 1 pulse/sec.accordingto a patternof 4 zigzag alterations of the filterin therangebetween300 and 54 cps. After27 secs., thefilter remainedlevelat 54 cps. 45" 300 cps Filter

54 cps 4/sec. * .o

Pulse Frequency

S1/sec.

Ex. 5

In thethirdpartof the pulse successionthe speed was decreased regularlyfrom1 pulse/sec.to 1/4 pulse/sec.(within45 secs. duration); the positionof the filterremainedconstantat 54 cps forthe first15 secs., and then,suddenly,witheach individualpulse,it was variedseventimesin a fixedup-down,up-down"melodic"pattern, and thenheld constantat 44 cps. 45" Filter 54 cps

l/sec

...

44 cps

II

S0,25/sec.

6O,25/sec.

0

45 ?

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PERSPECTIVES

OF NEW

MUSIC

theresultant of Next,I connected parts,and theoveralldiminution the speed amountedto 6 octaves (from 16.6 pulses/sec.to 1/4 pulse/sec.,along withthe abovementioned pitchvariationsbetween 300 and 44 cps). (60" + 30" + 45" + 45") For thelast pulses,I graduallyalteredthefilterfeedbacktimeso that,at theend,thedurationofeachindividual pulseis increased,and the"color"becomessomewhat"metallic." At thispoint,I subjectedthetotalresultto an acceleration, which 16.6 the a from to at to tenfold acceleration amounted, beginning, to a 166 pulses/sec.,and, by virtueof the continuousalterations, 2.5-foldaccelerationat the end, so thatthe intervalsbetweenthe finalpulses amountto ca. 1.5 secs. The pitchof the finalpulses is thensteadyat 160 cps,whichis approximately thesame as thatwith whichtheeventbegan.Whereasthe acceleratedformof the original we gradas tone-color variationis heardchiefly variation, frequency uallyperceiveit again as a successionof individualpulses,as pitch, becauseofthecontinuous ofthesounds.The initialsound dissolution of 166 cps slides (in 6" + 32") about7? octavesdownwards, passof pitchmodulatesintopering throughthezone whereperception of "tonecolor"mergesintothat whereperception ceptionof rhythm, of "melody,"and thus the "color"is dissolvedinto a successionof individual"pitches." At the conclusionof thispulse succession,the intervalsbetween theindividualpulsescorrespond to 45.5 cm.,48.5 cm., 52 cm., and 57 cm. of thetape (where38.1 cm. = 1 sec.). I thenaddedthree were morepulseswitha pitchof 160 cps,betweenwhichtheintervals and 89 cm. and 140 cm. This continuedthe gradual retardation final was the third and of The lengthening protracted pulse pulses. the intoa continuous soundonceagain (by meansof overmodulating filter I madethissoundincreasfeedback).By meansofamplification fromthe and in fivestagesfiltered continuously ingly"overtone-rich" lowestto the highestportionsof the sound.As a result,within48 thenpassedoutoftherange secs.,itscolorfirstgraduallybrightened, ofaudibility, "overthetop,"as it were.

OPPOSITE

AND

OVERLEAF:

Kontakte,pp. 19 and 20 Stockhausen,

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THE

CONCEPT

OF UNITY

IN ELECTRONIC

MUSIC

Beginning 200-300 cps 450-600 cps (after8") 800-1,000 cps (after17") FILTER: 1,500-3,000 cps (after26") 5,000-10,000 cps (after35") The entireprocessof temporaltransformation, as it was applied in Kontakte,is schematically in the score betweenthe represented timecoordinates16'56.5" (highestlayer) and 18'26.5" (pp. 19-20 in the score). Most of the eventsin Kontakte,like the one in the example,werecomposedby meansofmanytemporaltransformations of pulse structures. I have already affirmed my belief that any drasticseparation betweenacousticsand musicis no longermeaningful wherecompositionincludesthesynthesis of thesoundwaves themselves. The temintoa rhythmcan, poral processby whicha sound is transformed withoutdoubt,take a musicalform.The aestheticjudgmentof the listenercan determine if theresultof thisprocessis successful,if it is significantly congruentwith the totalwork,and if it has been with and imagination. accomplished originality It is understandable in Westernmusic,wherethe that, traditional of and spheres harmony melodydominate,onlythosesound-events wereused thathaveperiodicwaves and clear,recognizable, constant "pitch."The way in whichthe laws of harmonicand melodicunion of such tones,whose harmonicsound spectraare based on wholenumberdivisionsofthesoundwavesofthefundamentals, corresponds of consonantand dissonantintervalsand preciselyto the definition theirfunction, indicatesthe necessityof excludingnoise fromthis kind of music.Similarly,in the sphereof duration,the meters,i.e. periodictimeintervals(or measures)werefilledin withrhythmsdivisionsof the meters(tone color consequently, by whole-number is to a fundamental as rhythm is to a meter)-and all ofthevariations and disruptions of the metricalperiodicity wereregulatedaccording to the definition of syncopatedand regulartimeintervalsand their function. in thesphereof form,such metricalsucCorrespondingly, cessionswereformedperiodically intounitsof 2, 4, 8, 16 measures with"irregular"(or, better,"syncopated")variantsof 3-, 5-, 7-, or 9-measureperiods.All of musicaltimewas unifiedundera common and it was unnecessary to includein thisschemetheactual principle, soundwavestructure ofinstrumental tones,sincethiswas guaranteed in advanceby the selectionand construction of instruments of fixed S47

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PERSPECTIVES

OF NEW

MUSIC

pitch.If nowadays,ontheotherhand,it has becomenecessarytotake into accountfactorssuch as thosediscussedhere,to bringall the musicundera unifiedmusicaltime,and to find spheresof electronic one generalset of laws to governeverysphereofmusicaltimeitself, music thisis simplya resultof the conditionimposedby electronic thateachsoundin a givenworkmustbe individually composed. (Translatedby Elaine Barkin)

S48

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