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