Composers on Mathematical Music
Subtext 6493670


. . . I am making etchings. . . .

. . . graphic work, in a sense bringing to that graphic work ways of working that came from music. And now I notice this piece (Thirty Pieces for Five Orchestras) is responding to some of the ideas I got making etchings, to bring it back into music. That’s how these metrical passages developed. I had templates which were . . . I took this size of paper, and I made a grid of 64 by 64 on it to work with the chance operations. And through chance operations I cut the piece of paper, the full size of it, into templates. Those templates, of squares and triangles and such, are so that the points of the shapes could become sounds. Or holes could be put in the shapes to produce sounds. And shapes when, through chance operations, were put on the sheets, sometimes projected off that way or this way. Well, if it came off this way (to the left) it would start one of these metrical situations going on the strong beat; and if it went off that way (to the right) it would start it off on the weak beats. And where it went off gave the pitch, because I had designed the paper to be completely sound. The reason these are so far apart is that the ledger lines of one instrument touch the ledger lines of the adjacent one. Then these will be the points inside or around the outside of the shapes and which of these possibilities you did was chance-determined, whether you were looking for the holes or the shapes themselves.

John Cage



Composers on Mathematical Music: A Subtext Poem

Other Work by John Greschak

Public Domain