Scholarly discussion of the music of John Cage.

[Mark Kolmar <>]

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
M-214, Paul Creative Arts Center
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<http://unh.edu/music/>
<http://robhaskins.net>