Scholarly discussion of the music of John Cage.

[Andrew Culver <>]

Mark

"Did Cage ever use the changed hexagrams?”

Yes, most assuredly, at least from 1984 on. My code for IC uses the changing hex if it differs from the original hex. The same is true when using the I Ching for divination, of course.

Before 1984, when tossing by hand or using the Bell Labs printouts, I am 95% sure this was also the case. Someone with access to any used Bell Lab printouts in an archive might see affirmation of this in the way John marked off used tosses. Surely there is evidence in the literature of his works too. I marked up many of those myself in the early days (81-83), and to the best of my recollection, we would never “waste” a changed hexagram anymore than we would reuse an original hexagram if there was no changed hex.

I am no mathematician, but using the changing hex if it differs from the original definitely adds a real twist to the probabilities. This is not just pseudorandom numbers 1-64.

Speaking of pseudorandom, my C code does not just call a standard lib rand function and take the output as is. It uses a complex method of stacking and shuffling decks of pseudorandom numbers that I stumbled across in the early 80’s. The probability of repetition goes down enormously. As for the seed, it comes from the system time, which I assure cannot be the same as the last time the seed was used, by killing time for at least 1 smallest-unit-of time of the system clock  between uses.

"One of the challenges with randomness is you can be sure that occasionally a sequence does not look random at all, or produces an edge case. That is part of the fun.”

Yes, I agree totally. John, as you can image, become very sensitive to spotting the hills and valleys of chance. Me too, though less so, because I produced less constantly. 

When you use chance correctly, that is, offer up your intentions to it, while using it to produce something that you care about, you develop a sixth sense for any shift in character of the output stream. After all it is not the I Ching that stands before your fellow humans and says: This is my music. 

Chance operations used correctly and at scale will profoundly alter your understanding of yourself.

AC

On Mar 25, 2022, at 1:31 PM, Mark Kolmar <> wrote:

The 3-coin method is equivalent to a random number between 1 and 64, unless changing lines are taken into account. Based on comments on this list over the years, and books, it seems like the numbers and corresponding hexagrams would map to different possibilities. However, I have not come away with the impression that changed lines were at play. Did Cage ever use the changed hexagrams?

Yarrow stalk method has different probabilities:

9    --o--    3/16

8     -- --    7/16

7    -----    5/16

6     --x--    1/16

Yarrow stalk amounts to the same 1-64 range unless changing lines are treated in a special way.

One of the challenges with randomness is you can be sure that occasionally a sequence does not look random at all, or produces an edge case. That is part of the fun.

--Mark

On 3/23/2022 7:43 AM, Rob Haskins wrote:

">

He did use the three-coin method before working on HPSCHD, when he used the computers at Illinois to generate hexagram numbers. That iteration, however, had some flaw that he discovered while working on Empty Words. That's where the story ends for me. He may have then gone to Bell Labs (this would make some sense given the Experiments in Arts and Technology where Variations VII) was premiered. I believe David Revill teells a story that Cage hired people to toss coins for him (as well as asking friends to do it) when he was finishing Music of Changes.

I apologize if I have some of these details wrong. I'm not at home so can't consult my library.

All best,

        Rob

On Tue, Mar 22, 2022 at 10:05 PM Andrew Culver <> wrote:

David,

ic is a simulation of the three coin tossing method. Three coins, tossed six times, producing changing or unchanging broken or unbroken lines, rendering one of 64 possible original hexagrams, and possibly an additional changing hexagram also one of 64.

You can use ic, and learn more about how it works (read “How”) here: https://anarchicharmony.org/IChing/index.html

It’s the method I used before working with John, and before I “put it on the computer” (JC phrase!), i.e. when I did it by hand for my own purposes, divinational or compositional. (BTW, I consulted the I Ching about whether I should move to New York and offer to work with John, one of the more momentous questions I ever asked it. The reply was convincing.)

When I arrived (1980) he was using printouts from a program written at Bell Labs. I don’t know what method that program simulated.

Others on this list will know better than I what method he used in the early days before any computers were involved, but I always assumed (or perhaps heard in passing) that it was the three coin method.

Peace (war is obsolete)

Andrew Culver




> On Mar 22, 2022, at 5:26 PM, David Bellows <> wrote:
>
> I've been wondering if anyone knows how Cage generated his I Ching
> results. According to Wikipedia, there are many methods like the one
> coin, three coin, and yarrow stalks methods.
>
> From things I vaguely recall from reading Cage, it seems that when he
> did it manually he might have used the 3 coin method (which would have
> worked with Music of Changes.)
>
> So I'm also wondering about the software that was written for him and
> whether it just generated numbers between 1 and 64 or if it simulated
> one of the other methods like the 3 coin method.
>
> I don't know if Andrew Culver still pays attention to this list, but
> he/you might know?
>
> Thanks everyone for any ideas!
>
> Dave Bellows.
> https://www.platonicmusicengine.com

      --

Rob Haskins, D.M.A., Ph.D.

Professor and Chair, Department of Music

(he • him • his)

603-862-3987 (voicemail only)

603-862-3155 (fax)

College of Liberal Arts

University of New Hampshire
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<http://unh.edu/music/>
<http://robhaskins.net>