Silence. John Cage

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