Silence. John CageЧитать онлайн книгу.
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