Composers on Mathematical Music
Subtext 7162291


. . . When the serial principle was first applied to all the components of sound, we were thrown bodily, or rather headlong, into a cauldron of figures, recklessly mixing mathematics and elementary arithmetic; the theory of permutations used in serial music is not a very complex scientific concept; one need only reread Pascal to be convinced of this, and to realise that our systems and calculations are summed up in quite modest theories, whose scope is limited to a definite object. Moreover, by dint of ‘preorganisation’ and ‘precontrol’ of the material, total absurdity was let loose; numerous distribution-tables necessitated almost as many correction-tables, and hence a ballistics of notes; to produce valid results, everything had to be rectified! In fact the basic ‘magic squares’ were related to an ideal material (‘My overcoat also became an ideal’—Rimbaud: Ma Bohème), without any thought of contingencies—donkey work—of any kind: rhythmic organisation disregarded realisable metric relationships, structures of timbres scorned the registers and dynamics of instruments, dynamic principles paid no heed to balance, groups of pitches were unrelated to harmonic considerations or to the limits of tessitura. Each system, carefully worked out in its own terms, could only cohabit with the others through a miraculous coincidence. The works of this period also show an extreme inflexibility in all their aspects; elements in the ‘magic squares’ which the composer, with his magic wand, forgot at the birth of the work, react violently against the foreign and hostile order forced upon them; they get their own revenge: the work does not achieve any conclusively coherent organisation; it sounds bad and its aggressiveness is not always intentional.

Enslaved in such a yoke it was difficult not to feel oneself at the mercy of the law of large numbers: in the last resort, any choice had only a relative importance, simply amounting to cutting a slice of chance. This procedure might be seen as a take-over by numbers; the composer fled from his own responsibility, relying on a numerical organisation which was quite incapable of choice and decision; at the same time he felt bullied by such an organisation in that it forced him to depend on a crippling absurdity.

What could be the reaction to this extreme situation? There were exactly two possibilities: either to break out of the system by expecting no more of numbers than what they could give—that is to say, very little—or to avoid the difficulties by debauchery, seeking justification in what were, after all, pretty banal psychological and parapsychological considerations. The second way was obviously the more tempting, for it demanded only a minimum of effort and imagination.

Pierre Boulez



Composers on Mathematical Music: A Subtext Poem

Other Work by John Greschak

Public Domain