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COMPOSITION AS PROCESS

The following three lectures were given at Darmstadt (Germany) in September 1958. The third one, with certain revisions, is a lecture given earlier that year at Rutgers University in New Jersey, an excerpt from which was published in the Village Voice, New York City, in April 1958.

I. Changes

Having been asked by Dr. Wolfgang Steinecke, Director of the Internationale Ferienkurse für Neue Musik at Darmstadt, to discuss in particular my Music of Changes, I decided to make a lecture within the time length of the Music of Changes (each line of the text whether speech or silence requiring one second for its performance), so that whenever I would stop speaking, the corresponding part of the Music of Changes itself would be played. The music is not superimposed on the speech but is heard only in the interruptions of the speech—which, like the lengths of the paragraphs themselves, were the result of chance operations.

Note to ebook reader: what may appear to be missing lines in this section are intentional.

This is a lec-

ture on changes

that have taken

place in my com-

position means,

with particu-

lar reference

to what, a dec-

ade ago, I

termed “structure” and

“method.” By “struc-

ture” was meant the

division of

a whole into

parts; by “method,”

the note-to-note

procedure. Both

structure and meth-

od (and also

“material”—

the sounds and si-

lences of a

composition)

were, it seemed to

me then, the prop-

er concern of

the mind (as op-

posed to the heart)

(one’s ideas

of order as

opposed to one’s

spontaneous

actions); whereas

the two last

of these, namely

method and ma-

terial, to-

gether with form

(the morpholo-

gy of a con-

tinuity)

were equally

the proper con-

cern of the heart.

Composition,

then, I viewed, ten

years ago, as

an activity integrat-

ing the oppo-

sites, the ration-

al and the ir-

rational, bring-

ing about, i-

deally, a

freely moving

continui-

ty within a

strict division

of parts, the sounds,

their combina-

tion and succes-

sion being ei-

ther logical-

ly related

or arbitrar-

ily chosen.

¶The strict divi-

sion of parts, the

structure, was a

function of the

duration as-

pect of sound, since,

of all the as-

pects of sound in-

cluding frequen-

cy, amplitude,

and timbre, dur-

ation, alone,

was also a

characteris-

tic of silence.

The structure, then,

was a divi-

sion of actu-

al time by con-

ventional met-

rical means, me-

ter taken as

simply the meas-

urement of quan-

tity. ¶In the

case of the So-natas and In-terludes (which I finished in nine- teen forty-eight), only structure was organized, quite roughly for the work as a whole, exactly, however, with- in each single piece. The method was that of con- sidered impro- visation (main- ly at the pi- ano, though i- deas came to me at some mo- ments away from the instrument.

The materi-

als, the pia-

no prepara-

tions, were chosen

as one chooses

shells while walking

along a beach.

The form was as

natural as

my taste permit-

ted: so that where,

as in all of

the Sonatas and two of the Interludes, parts were to be re- peated, the for- mal concern was to make the prog- ress from the end of a section to its begin- ning seem inev- itable. ¶The structure of one of the Sona-tas, the fourth, was one hundred meas- ures of two-two time, divided into ten u- nits of ten meas- ures each. These u- nits were combined in the propor- tion three, three, two, two, to give the piece large parts, and they were subdi- vided in the same proportion to give small parts to each unit. In contrast to a structure based on the frequen- cy aspect of sound, tonali- ty, that is, this rhythmic structure was as hospi- table to non- musical sounds, noises, as it was to those of the convention- al scales and in- struments. For noth- ing about the structure was de- termined by the materials which were to oc- cur in it; it was conceived, in fact, so that it could be as well expressed by the absence of these materials as by their pres- ence. ¶In terms of the oppo- sition of free- dom and law, a piece written ten years before the Sonatas andInterludes, Con-struction in Met-al, presents the same relation- ship, but reversed: structure, method, and materi- als were all of them subjected to organi- zation. The mor- phology of the continu- ity, form, a- lone was free. Draw- ing a straight line between this sit- uation and that presented

by the later

work, the deduc-

tion might be made

that there is a

tendency in

my composi-

tion means away

from ideas

of order towards

no ideas

of order. And

though when exam-

ined the histo-

ry would probab-

ly not read as

a straight line, re-

cent works, begin-

ning with the Mu-sic of Changes, support the ac- curacy of this deduction. ¶For, in the Mu-sic of Changes, the note-to-note procedure, the method, is the function of chance operations. And the structure, though planned precise- ly as those of the Sonatasand Interludes, and more thorough- ly since it en- compassed the whole span of the com- position, was only a se- ries of numbers, three, five, six and three quarters, six and three quarters, five, three and one eighth, which became, on the one hand, the number of units within each section, and, on the other, number of meas- ures of four-four within each u- nit. At each small structural di- vision in the Music of Chan-ges, at the be- ginning, for ex- ample, and a-

gain at the fourth

and ninth measures

and so on, chance

operations

determined sta-

bility or

change of tempo.

Thus, by intro-

ducing the ac-

tion of method

into the bod-

y of the struc-

ture, and these two

opposed in terms

of order and

freedom, that struc-

ture became in-

determinate:

it was not pos-

sible to know the

total time-length

of the piece un-

til the final

chance opera-

tion, the last toss

of coins af-

fecting the rate

of tempo, had

been made. Being

indetermi-

nate, though still pres-

ent, it became

apparent that

structure was not

necessary,

even though it had

certain uses.

¶One of these u-

ses was the de-

termination

of density,

the determi-

nation, that is,

of how many

of the poten-

tially present

eight lines, each com-

posed of sounds and

silences, were

actually

to be present

within a giv-

en small structur-

al part. ¶Anoth-

er use of the

structure affect-

ed the charts of

sounds and silen-

ces, amplitudes,

durations, po-

tentially ac-

tive in the con-

tinuity.

These twenty-four

charts, eight for sounds

and silences,

eight for ampli-

tudes, eight for du-

rations, were, through-

out the course of

a single struc-

tural unit, half

of them mobile

and half of them

immobile. Mo-

bile meant that once

any of the

elements in

a chart was used

it disappeared

to be replaced

by a new one.

Immobile meant

that though an el-

ement in a

chart had been used,

it remained to

be used again.

At each unit

structural point,

a chance oper-

ation deter-

mined which of the

charts, numbers one,

three, five, and sev-

en or numbers

two, four, six, and

eight, were mobile

and which of the

charts were immo-

bile—not changing.

¶The structure, there-

fore, was in these

respects useful.

Furthermore, it

determined the

beginning and

ending of the

composition-

al process. But

this process, had

it in the end

brought about a

division of

parts the time-lengths

of which were pro-

portional to

the origi-

nal series of

numbers, would have

been extraordi-

nary. And the

presence of the

mind as a rul-

ing factor, e-

ven by such an

extraordina-

ry eventu-

ality, would

not have been es-

tablished. For what

happened came a-

bout only through

the tossing of

coins. ¶It be-

came clear, therefore,

I repeat, that

structure was not

necessary.

And, in Musicfor Piano, and subsequent pieces, indeed, structure is no longer a part of the compo- sition means. The view taken is not of an ac- tivity the purpose of which is to inte- grate the oppo- sites, but rather of an activ- ity charac- terized by process and es- sentially

purposeless. The

mind, though stripped

of its right to

control, is still

present. What does

it do, having

nothing to do?

And what happens

to a piece of

music when it

is purposeless-

ly made? ¶What hap-

pens, for instance,

to silence? That

is, how does the

mind’s perception

of it change? For-

merly, silence

was the time lapse

between sounds, use-

ful towards a va-

riety of

ends, among them

that of tasteful

arrangement, where

by separat-

ing two sounds or

two groups of sounds

their differen-

ces or rela-

tionships might re-

ceive emphasis;

or that of ex-

pressivity,

where silences

in a musi-

cal discourse might

provide pause or

punctuation;

or again, that

of architec-

ture, where the in-

troduction or

interruption

of silence might

give defini-

tion either to

a predeter-

mined structure or

to an organ-

ically de-

veloping one.

Where none of these

or other goals

is present, si-

lence becomes some-

thing else—not si-

lence at all, but

sounds, the ambi-

ent sounds. The na-

ture of these is

unpredicta-

ble and changing.

These sounds (which are

called silence on-

ly because they

do not form part

of a musi-

cal intention)

may be depen-

ded upon to

exist. The world

teems with them, and

is, in fact, at

no point free of

them. He who has

entered an an-

echoic cham-

ber, a room made

as silent as

technologi-

cally possible,

has heard there two

sounds, one high, one

low—the high the

listener’s ner-

vous system in

operation,

the low his blood

in circul-

ation. There are, dem-

onstrably, sounds

to be heard and

forever, giv-

en ears to hear.

Where these ears are

in connection

with a mind that

has nothing to

do, that mind is

free to enter

into the act

of listening,

hearing each sound

just as it is,

not as a phe-

nomenon more

or less approx-

imating a

preconception.

¶What’s the histo-

ry of the chan-

ges in my com-

position means

with particu-

lar reference

to sounds? I had

in mind when I

chose the sounds for

Construction inMetal that they should be sixteen for each player. The number six- teen was also that of the num- ber of measures of four-four in each unit of the rhythmic struc- ture. In the case of the structure this number was divided four, three, two, three, four; in the case of the materi- als the gamuts of sixteen sounds were divided into four groups of four. The plan, as preconceived, was to use four of the sounds in the first sixteen measures, intro- ducing in each succeeding struc- tural unit four more until the exposi- tion involving all sixteen and lasting through the first four units was completed. The subsequent parts, three, two, three, four, were composed

as develop-

ment of this in-

itial situ-

ation. In ac-

tuality,

this simple plan

was not real-

ized, although it

was only re-

cently that I

became fully

aware that it

was not. I had

known all along

that one of the

players used three

Japanese tem-

ple gongs rather

than four, but the

fact that only

three of these rel-

atively rare

instruments were

then availa-

ble to me, to-

gether with the

attachment I

felt towards their sound,

had convinced me

of the rightness

of this change in

number. More se-

rious, however,

it seems to

me now, was the

effect of beat-

ers: playing cow-

bells first with rub-

ber and then with

metal multi-

plied by two the

number of sounds

actually

used. Sirenlike

piano trills

which sound as one

were counted as

two. Various

other devi-

ations from the

original

plan could be dis-

covered on an-

alysis: for

instance, the ad-

dition of met-

al thundersheets

for background noise

bringing the num-

ber sixteen, for

those players who

enjoyed it

to seventeen.

One might conclude

that in compos-

ing Constructionin Metal the organiza- tion of sounds was imperfectly realized. Or he might conclude that the compos- er had not ac- tually lis- tened to the sounds he used, ¶I have already com- pared the selec- tion of the sounds for the Sona-tas and Inter-ludes to a se- lection of shells while walking a- long a beach. They are therefore a collection ex- hibiting taste. Their number was increased by use of the unacorda, this ped- al bringing a- bout altera- tions of timbre and frequency for many of the prepared keys. In terms of pitch, how- ever, there is no change from the sounds of the Con-struction. In both cases a stat- ic gamut of sounds is present- ed, no two oc- taves repeating relations. How- ever, one could hear interest- ing differen- ces between cer- tain of these sounds. On depressing a key, sometimes a single fre- quency was heard. In other cas- es depressing a key produced an interval; in still others an aggregate of pitches and timbres. Noticing the nature of this gamut led to selecting a comparable one for the String Quartet: the

inclusion there

of rigidly

scored convention-

al harmonies

is a matter

of taste, from which

a conscious con-

trol was absent.

Before writing

the Music ofChanges, two piec- es were written which also used gamuts of sounds: single sounds, doub- le sounds and oth- ers more numer- ous, some to be played simultan- eously, oth- ers successiv- ely in time. These pieces were Six-teen Dances and Concerto forPrepared Pia-no and ChamberOrchestra. The elements of the gamuts were arranged unsys- tematically in charts and the method of composition involved moves on these charts anal- agous to those used in construct- ing a magic square. Charts were al- so used for the Music of Chang-es, but in con- trast to the meth- od which involved chance opera- tions, these charts were subjected to a rational control: of the sixty-four el- ements in a square chart eight times eight (made in this way in order to interpret as sounds the co- in oracle of the Chinese Book of Changes) thirty-two were sounds, thirty-two silences. The thirty-two sounds were arranged in two squares one a- bove the other, each four by four. Whether the charts were mobile or immobile, all twelve tones were pres- ent in any four elements of a given chart, whether a line of the chart was read hori- zontally or vertically. Once this dodec- aphonic re- quirement was sat- isfied, noises and repeti- tions of tones were used with freedom.

One may conclude

from this that in

the Music ofChanges the ef- fect of the chance operations on the structure

(making very

apparent its

anachronis-

tic character)

was balanced by

a control of

the materials.

Charts remain in

the Imagi-nary LandscapeNumber IV, and in the WilliamsMix, but, due to the radios of the first piece and the librar- y of record- ed sounds of the second, and for no other rea- son, no twelve-tone control was used. The question “How do we need to cautiously pro- ceed in dual- istic terms?” was not consciously answered until the Music forPiano. In that piece notes were determined by imperfections in the paper upon which the music was writ- ten. The number of imperfec- tions was deter- mined by chance.

The origi-

nal notation

is in ink, and

the actual

steps that were tak-

en in compo-

sition have been

described in an

article in

Die Reihe. ¶Though in the Musicfor Piano I have affirmed the absence of the mind as a ruling agent from the structure and method of the composing means, its presence with regard to material is made clear on examining the sounds themselves: they are only single tones of the convention- al grand pia- no, played at the keyboard, plucked or muted on the strings, together with noises in- side or outside the piano construction. The limited na- ture of this u- niverse of pos- sibilities makes the events themselves compa- rable to the first attempts at speech of a child or the fumblings about of a blind man. The mind reappears as the agent which established the boundaries with- in which this small play took place. Some- thing more far-reach- ing is neces- sary: a com- posing of sounds within a u- niverse predi- cated upon the sounds themselves

rather than up-

on the mind which

can envisage

their coming in-

to being. ¶Sounds,

as we know, have

frequency, am-

plitude, dura-

tion, timbre, and in

a composi-

tion, an order

of succession.

Five lines repre-

senting these five

characteris-

tics may be drawn

in India ink

upon trans-

parent plastic

squares. Upon an-

other such square

a point may be

inscribed. Placing

the square with the

lines over the

square with the point,

a determi-

nation may be

made as to the

physical na-

ture of a sound

and its place with-

in a deter-

mined program sim-

ply by dropping

a perpendi-

cular from the

point to the line

and measuring

according to

any method

of measurement.

Larger points will

have the meaning

of intervals

and largest points

that of aggre-

gates. In order

to make the sev-

eral measure-

ments necessar-

y for inter-

vals and aggre-

gates, further squares

having five lines

are made and the

meaning of an-

y of the lines

is left unde-

termined, so that

a given one

refers to an-

y of the five

characteris-

tics. These squares are

square so that they

may be used in

any posi-

tion with respect

to one anoth-

er. This describes

the situa-

tion obtaining

in a recent

composition,

Variations, the composing means itself one of the eighty- four occurring in the part for piano of Concert for Pi-ano and Or-chestra. In this situation, the universe within which the action is to take place is not preconceived. Fur- thermore, as we know, sounds are e- vents in a field of possibil- ities, not on- ly at the dis- crete points conven- tions have favored. The notation of Varia-tions departs from music and im- itates the phys- ical real- ity. ¶It is now my inten- tion to relate the history of the changes with regard to duration of sounds in my com- posing means. Be- yond the fact that in the Construc-tion in Metal there was a con- trol of dura- tion patterns par- allel to that of the number of sounds chosen, nothing uncon- ventional took place. Quantities related through multiplica- tion by two or addition of one-half togeth- er with grupet- tos of three, five, seven, and nine were present. The same holds for the Sonatas andInterludes, though no rhythmic pat- terns were ration- ally controlled. In the String Quar-tet the rhythmic interest drops, movements being nearly charac- terized by the predominance of a single quantity. Not until the Mu-sic of Changes do the quantities and their no- tation change. They are there measured in space, a quar- ter note equal- ling two and one- half centime- ters. This made pos- sible the no- tation of a fraction, for ex- ample one-third of an eighth, with- out the neces- sity of no- tating the re- mainder of the fraction, the re- maining two-thirds, following the same example. This possibil- ity is di- rectly anal- ogous to the practice of cut- ting magnetic tape. In the du- ration charts of the Music ofChanges there were sixty-four el- ements, all of them durations since they were both

applicable

to sound and si-

lence (each of which

had thirty-two

elements). These

were segmented

(for example

one-half plus one-

third of an eighth

plus six-sevenths

of a quarter)

and were expres-

sible wholly

or in part. This

segmentation

was a practi-

cal measure tak-

en to avoid

the writing of

an impossi-

ble situa-

tion which might a-

rise during a

high density

structural a-

rea due to

the chance oper-

ations. ¶The same

segmentation

of durations

took place in the

Williams Mix, since a maximum of eight machines and loudspeakers had been pre-es- tablished. When the density rose from one to six- teen, it was of- ten necessar- y to express durations by their smallest parts, there being no room left on the tape for the larg- er segments. ¶Ex- act measurement and notation

of durations

is in real-

ity mental:

imaginar-

y exacti-

tude. In the case

of tape, many

circumstances

enter which ev-

er so slightly,

but nonetheless

profoundly, al-

ter the inten-

tion (even though

it was only

the carrying out

of an action

indicated

by chance oper-

ations). Some of

these circumstan-

ces are the ef-

fects of weather

upon the ma-

terial; others

follow from hu-

man frailty—

the inabil-

ity to read

a ruler and

make a cut at

a given point—

still others are

due to mechan-

ical causes,

eight machines not

running at pre-

cisely the same

speed. ¶Given these

circumstances,

one might be in-

spired towards greater

heights of dura-

tion control or

he might renounce

the need to con-

trol durations

at all. In Mu-sic for Pia-no I took the latter course. Struc- ture no longer being present, that piece took place in any length of time whatso- ever, accord- ing to the ex- igencies of an occasion. The duration of single sounds was therefore al- so left inde- terminate. The notation took the form of whole notes in space, the space suggesting but not measur- ing time. Noises were crotchets with- out stems. ¶When a performance of Music for Pi-ano involves more than one pi- anist, as it may from two to twenty, the suc- cession of sounds becomes complete- ly indeter- minate. Though each page is read from left to right con- ventionally, the combina- tion is unpre- dictable in terms of succes- sion. ¶The histo- ry of changes with reference to timbre is short. In the Construc-tion in Metal four sounds had a single timbre; while the prepared pi- ano of the Sonatas andInterludes pro- vided by its nature a klang-farbenmelo-die. This inter- est in changing timbres is evi- dent in the StringQuartet. But this matter of tim- bre, which is large- ly a question of taste, was first radically changed for me in the Imagi-nary LandscapeNumber IV. I had, I confess, never enjoyed the sound of ra- dios. This piece opened my ears

to them, and was

essentially

a giving up

of personal

taste about timbre.

I now frequent-

ly compose with

the radio

turned on, and my

friends are no long-

er embarrassed

when visiting

them I inter-

rupt their recep-

tions. Several

other kinds of

sound have been dis-

tasteful to me:

the works of Bee-

thoven, Ital-

ian bel can-to, jazz, and the vibraphone. I used Beethoven in the WilliamsMix, jazz in the Imaginar-y Landscape Num-ber V, bel can-to in the re- cent part for voice in the Concertfor Pianoand Orchestra. It remains for me to come to terms with the vib- raphone. In oth- er words, I find my taste for timbre

lacking in ne-

cessity, and

I discover

that in the pro-

portion I give

it up, I find

I hear more and

more accurate-

ly. Beethoven

now is a sur-

prise, as accept-

able to the

ear as a cow-

bell. What are the

orchestral timbres

of the Concertfor Pianoand Orchestra? It is impos- sible to pre- dict, but this may be said: they in- vite the timbres of jazz, which more than serious music has explored the possibili- ties of instru- ments. ¶With tape and music-synthe- sizers, action with the over- tone structure of sounds can be less a matter of taste and more thor- oughly an ac- tion in a field of possibil- ities. The no- tation I have described for Var-iations deals with it as such. ¶The early works have beginnings, middles, and end- ings. The later ones do not. They begin any- where, last any length of time, and involve more or fewer instru- ments and players. They are therefore not preconceived objects, and to approach them as objects is to utterly miss

the point. They are

occasions for

experience,

and this exper-

ience is not

only received

by the ears but

by the eyes too.

An ear alone

is not a be-

ing. I have no-

ticed listening

to a record

that my attention

moves to a

moving object

or a play of

light, and at a

rehearsal of

the Williams Mix last May when all eight machines were in opera- tion the atten- tion of those pres- ent was engaged by a sixty- year-old pian- o tuner who was busy tun- ing the instru- ment for the eve- ning’s concert. It becomes evi- dent that music itself is an ideal sit- uation, not a real one. The mind may be used either to ig- nore ambient sounds, pitches oth- er than the eight- y-eight, dura- tions which are not counted, timbres which are unmusi- cal or distaste- ful, and in gen- eral to con- trol and under- stand an avail- able exper- ience. Or the mind may give up its desire to improve on cre- ation and func- tion as a faith- ful receiver of experi- ence. ¶I have not yet told any stories and yet when I give a talk I gener- ally do. The subject certain- ly suggests my telling something irrelevant

but my inclin-

ation is to

tell something apt.

That reminds me:

Several years

ago I was

present at a

lecture given

by Dr. Dai-

setz Teitaro

Suzuki. He

spoke quietly

when he spoke. Some-

times, as I was

telling a friend

yesterday eve-

ning, an airplane

would pass over-

head. The lecture

was at Colum-

bia Uni-

versity and

the campus is

directly in

line with the de-

parture from La

Guardia of

planes bound for the

west. When the wea-

ther was good, the

windows were o-

pen: a plane

passing above drowned

out Dr. Dai-

setz Teitaro

Suzuki. Nev-

ertheless, he

never raised his

voice, never paused,

and never in-

formed his listen-

ers of what they

missed of the lec-

ture, and no one

ever asked him

what he had said

while the airplanes

passed above. Any-

way, he was

explaining one

day the meaning

of a Chinese

character—Yu,

I believe it

was—spending the

whole time explain-

ing it and yet

its meaning as

close as he could

get to it in

English was “un-

explainable.”

Finally he

laughed and then said,

“Isn’t it strange

that having come

all the way from

Japan I spend

my time explain-

ing to you that

which is not to

be explained?” ¶That

was not the stor-

y I was go-

ing to tell when

I first thought I

would tell one, but

it reminds me

of another.

Years ago when

I was study-

ing with Arnold

Schoenberg someone

asked him to ex-

plain his technique

of twelve-tone com-

position. His

reply was im-

mediate: “That

is none of your

business.” ¶Now

I remember

the story I

was going to

tell when I first

got the ide-

a to tell one.

I hope I can

tell it well. Sev-

eral men, three

as a matter of

fact, were out

walking one day,

and as they were

walking along

and talking one

of them noticed

another man

standing on a

hill ahead of

them. He turned to

his friends and said,

“Why do you think

that man is stand-

ing up there on

that hill?” One said,

“He must be up

there because it’s

cooler there and

he’s enjoying

the breeze.” He turned

to another

and repeated

his question, “Why

do you think that

man’s standing up

there on that hill?”

The second said,

“Since the hill is

elevated

above the rest

of the land, he

must be up there

in order to

see something in

the distance.” And

the third said, “He

must have lost his

friend and that is

why he is stand-

ing there alone

on that hill.” Af-

ter some time walk-

ing along, the

men came up the

hill and the one

who had been stand-

ing there was still

there: standing there.

They asked him to

say which one was

right concerning

his reason for

standing where he

was standing. ¶“What

reasons do you

have for my stand-

ing here?” he asked.

“We have three,” they

answered. “First, you

are standing up

here because it’s

cooler here and

you are enjoy-

ing the breeze. Second,

since the hill

is eleva-

ted above the

rest of the land,

you are up here

in order to

see something in

the distance. Third,

you have lost your

friend and that is

why you are stand-

ing here alone

on this hill. We

have walked this way;

we never meant

to climb this hill;

now we want an

answer: Which one

of us is right?”

¶The man answered,

“I just stand.” ¶When

I was studying

with Schoenberg

one day as he was

writing some

counterpoint to

show the way to

do it, he used

an eraser.

And then while he

was doing this

he said, “This end

of the pencil

is just as im-

portant as the

other end.” I

have several

times in the course

of this lecture

mentioned ink. Com-

posing, if it

is writing notes,

is then actu-

ally writing,

and the less one

thinks it’s thinking

the more it be-

comes what it is:

writing. Could mu-

sic be composed

(I do not mean

improvised) not

writing it in

pencil or ink?

The answer is

no doubt Yes and

the changes in

writing are pro-

phetic. The So-natas and In-terludes were com- posed by playing the piano, listening to differences, making a choice, roughly writing it in pencil; later this sketch

was copied, but

again in pen-

cil. Finally

an ink manuscript

was made care-

fully. The Mu-sic of Changes was composed in almost the same way. With one change: the origi- nal pencil sketch was made exac- tly, an era- ser used whenev- er necessar- y, elimin- ating the need for a neat pen- cil copy. In the case of the Imaginar-y Landscape Num-ber IV, the first step of playing the instrument was elimin- ated. The oth- ers kept. Musicfor Piano was written di- rectly in ink.

II. Indeterminacy

The excessively small type in the following pages is an attempt to emphasize the intentionally pontifical character of this lecture.

This is a lecture on composition which is indeterminate with respect to its performance. The Klavierstück XI by Karlheinz Stockhausen is an example. The Art of the Fugue by Johann Sebastian Bach is an example. In The Art of the Fugue, structure, which is the division of the whole into parts; method, which is the note-to-note procedure; and form, which is the expressive content, the morphology of the continuity, are all determined. Frequency and duration characteristics of the material are also determined. Timbre and amplitude characteristics of the material, by not being given, are indeterminate. This indeterminacy brings about the possibility of a unique overtone structure and decibel range for each performance of The Art of the Fugue. In the case of the Klavierstück XI, all the characteristics of the material are determined, and so too is the note-to-note procedure, the method. The division of the whole into parts, the structure, is determinate. The sequence of these parts, however, is indeterminate, bringing about the possibility of a unique form, which is to say a unique morphology of the continuity, a unique expressive content, for each performance.

The function of the performer, in the case of The Art of the Fugue, is comparable to that of someone filling in color where outlines are given. He may do this in an organized way which may be subjected successfully to analysis. (Transcriptions by Arnold Schoenberg and Anton Webern give examples pertinent to this century.) Or he may perform his function of colorist in a way which is not consciously organized (and therefore not subject to analysis)—either arbitrarily, feeling his way, following the dictates of his ego; or more or less unknowingly, by going inwards with reference to the structure of his mind to a point in dreams, following, as in automatic writing, the dictates of his subconscious mind; or to a point in the collective unconscious of Jungian psychoanalysis, following the inclinations of the species and doing something of more or less universal interest to human beings; or to the “deep sleep” of Indian mental practice—the Ground of Meister Eckhart—identifying there with no matter what eventuality. Or he may perform his function of colorist arbitrarily, by going outwards with reference to the structure of his mind to the point of sense perception, following his taste; or more or less unknowingly by employing some operation exterior to his mind: tables of random numbers, following the scientific interest in probability; or chance operations, identifying there with no matter what eventuality.

The function of the performer in the case of the Klavierstück XI is not that of a colorist but that of giving form, providing, that is to say, the morphology of the continuity, the expressive content. This may not be done in an organized way: for form unvitalized by spontaneity brings about the death of all the other elements of the work. Examples are provided by academic studies which copy models with respect to all their compositional elements: structure, method, material, and form. On the other hand, no matter how rigorously controlled or conventional the structure, method, and materials of a composition are, that composition will come to life if the form is not controlled but free and original. One may cite as examples the sonnets of Shakespeare and the haikus of Basho. How then in the case of the Klavierstück XI may the performer fulfill his function of giving form to the music? He must perform his function of giving form to the music in a way which is not consciously organized (and therefore not subject to analysis), either arbitrarily, feeling his way, following the dictates of his ego, or more or less unknowingly, by going inwards with reference to the structure of his mind to a point in dreams, following, as in automatic writing, the dictates of his subconscious mind; or to a point in the collective unconscious of Jungian psychoanalysis, following the inclinations of the species and doing something of more or less universal interest to human beings; or to the “deep sleep” of Indian mental practice—the Ground of Meister Eckhart—identifying there with no matter what eventuality. Or he may perform his function of giving form to the music arbitrarily, by going outwards with reference to the structure of his mind to the point of sense perception, following his taste; or more or less unknowingly by employing some operation exterior to his mind: tables of random numbers, following the scientific interest in probability; or chance operations, identifying there with no matter what eventuality.

However, due to the presence in the Klavierstück XI of the two most essentially conventional aspects of European music—that is to say, the twelve tones of the octave (the frequency characteristic of the material) and regularity of beat (affecting the element of method in the composing means), the performer—in those instances where his procedure follows any dictates at all (his feelings, his automatism, his sense of universality, his taste)—will be led to give the form aspects essentially conventional to European music. These instances will predominate over those which are unknowing where the performer wishes to act in a way consistent with the composition as written. The form aspects essentially conventional to European music are, for instance, the presentation of a whole as an object in time having a beginning, a middle, and an ending, progressive rather than static in character, which is to say possessed of a climax or climaxes and in contrast a point or points of rest.

The indeterminate aspects of the composition of the Klavierstück XI do not remove the work in its performance from the body of European musical conventions. And yet the purpose of indeterminacy would seem to be to bring about an unforseen situation. In the case of Klavierstück XI, the use of indeterminacy is in this sense unnecessary since it is ineffective. The work might as well have been written in all of its aspects determinately. It would lose, in this case, its single unconventional aspect: that of being printed on an unusually large sheet of paper which, together with an attachment that may be snapped on at several points enabling one to stretch it out flat and place it on the music rack of a piano, is put in a cardboard tube suitable for safekeeping or distribution through the mails.

This is a lecture on composition which is indeterminate with respect to its performance. The Intersection 3 by Morton Feldman is an example. The Music of Changes is not an example. In the Music of Changes, structure, which is the division of the whole into parts; method, which is the note-to-note procedure; form, which is the expressive content, the morphology of the continuity; and materials, the sounds and silences of the composition, are all determined. Though no two performances of the Music of Changes will be identical (each act is virgin, even the repeated one, to refer to René Char’s thought), two performances will resemble one another closely. Though chance operations brought about the determinations of the composition, these operations are not available in its performance. The function of the performer in the case of the Music of Changes is that of a contractor who, following an architect’s blueprint, constructs a building. That the Music of Changes was composed by means of chance operations identifies the composer with no matter what eventuality. But that its notation is in all respects determinate does not permit the performer any such identification: his work is specifically laid out before him. He is therefore not able to perform from his own center but must identify himself insofar as possible with the center of the work as written. The Music of Changes is an object more inhuman than human, since chance operations brought it into being. The fact that these things that constitute it, though only sounds, have come together to control a human being, the performer, gives the work the alarming aspect of a Frankenstein monster. This situation is of course characteristic of Western music, the masterpieces of which are its most frightening examples, which when concerned with humane communication only move over from Frankenstein monster to Dictator.