Silence. John Cage

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