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In the particular case of these violin études
I start with star maps and I place a transparent sheet on them. I place
the star map at a point which is convenient for the paper. The maps I use
have blue, green, orange, yellow, red, and violet colors. I combine the
blue and green, the red and orange, the yellow and violet, then make these
colors singly or in pairs, or all three; and that gives seven different
densities. My first question to the I Ching is, “Which of those
seven possibilities (blue/green, red/orange, yellow/violet, red/orange,
blue/green with red/orange with yellow/violet) am I dealing with?”
Meanwhile
I have made a table relating the number 7 to the number 64. The number
of hexagrams in the I Ching is 64. If I divide 7 into 64 I get
9 with a remainder of 1. That means one group is a group of 10. The six
groups, 1 from 7, are groups of 9. I arrange the tables so that three groups
of 9 are the beginning of the 64 and then the group of 10 is in the middle,
then the other three groups of 9 are at the end. Then I can toss three
coins six times or I can use as I do a computer printout. A young man at
Illinois (Ed Kobrin) made a computer program for me. It makes my
work quicker than it would be if I used coins or the yarrow sticks.
The result is I quickly know which stars I am to trace. Then my next question is how many stars am I to trace? I take simply a number, 1 to 64, and then after I’ve done it, I ask, “What next am I to do?” Then when I finish enough tracings to make two pages of music—which was my decision at the beginning, to have each étude have two pages (so the violinist wouldn’t have to turn pages)—I now have a band of tracings of the stars, and it’s been designed so that it’s wide enough for me to distinguish the twelve tones. These twelve tones can appear in different octaves in the violin. My next question is which octave it is in. I put that down, then I take the papers, and I can then transcribe the stars to paper. Each one of the stars is not a single tone, it might be an aggregate, it might be two tones or it might be three or it might be legato or not and so forth. My next process was to find which passages are legato and which passages are détaché. Instead of making it even—that is to say, 1 to 32 being détaché, and 33 to 64 being legato—what I do is I ask the I Ching where the dividing point is between legato and détaché, and it might say it’s number 7, so then 1–6 would be détaché and 7–64 would be legato. And then I ask the I Ching, “For how long does that last?” and it might say for fifty-three events. After fifty-two events, I ask again. Then all the other questions that can make a tone in detached style special and different from another one are posed. I list all the possibilities and then find out which ones are operative. When I start building up intervals or triads or quatrads on the strings, I then through chance operations find out which finger is touching which note on which string. Then I call up Paul Zukofsky to ask what he can reach with which other finger which chance determines; then I catalogue his answers. I index them in a book. He thinks we will eventually publish his 3-, and 4-note chords in ways that he himself is surprised at. He is surprised at what we are learning in this work we are doing together. Rather than working from choices I work from asking questions, so that the composition is determined by the questions that are asked and you can quickly tell if your questions are radical. By radical I mean penetrating. If they are not radical, the answers aren’t. If they are basic, then what happens is something that you haven’t heard before.
John Cage
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