Meyer's 'tonality diamond'

In an old tuning list post by Brian McLaren
http://www-math.cudenver.edu/~jstarret/post128.html

Brian wrote:

> In "History and Principles of Microtonal Keyboard Design,"
> 1985, Douglas Keislar proposes that Harry Partch might have
> gotten the idea for the tonality diamond from a book by
> Max Meyer(!) Keislar suggests that "Partch might have been
> inspired by his reading of Meyer (1929), who depicts a similar
> diamond on page 22 " of Max Meyer's 1929 book "The Musician's
> Arithmetic."
>
> Can anyone confirm or deny this?

I don't know if anyone ever responded to this, but I was
surprised to read that Keislar pointed it out, because
I noticed it as soon as I read Meyer's book!

Partch cites Meyer's book frequently in _Genesis_, so I
would not be at all surprised if he got the Tonality Diamond
idea from this diagram. I don't know enough of the details
of the evolution of Partch's theories to be sure about it,
but circumstantial evidence certainly implies a link.

Meyer's book is very hard to find, so here's the best
ASCII reproduction I can make of his diagram:

From Max F. Meyer, 1929, _The Musician's Arithmetic_, p 22:

/\
/ \
/ \
\ 7 /\
/\\ / \
/ \\ / \
/ \\ 5 /\
/\969 /\\ / \
/ \ / \\ / \
/ \/ \\ 3 /\
/\267 /\386 /\\ / \
/ \ / \ / \\ / \
/ \/ \/ \\ 1 /\
/\583 /\884 /\702 /\\ // \
/ \ / \ / \ / \\ // \
/ \/ \/ \/ \\/ \
\ 0 /\ 0 /\ 0 /\ 0 //\ /
\ / \ / \ / \ // \\ /
\/ \/ \/ \// \\/
\617 /\316 /\498 // 1 /
\ / \ / \ // \ /
\/ \/ \// \ /
\933 /\814 // 3 /
\ / \ // \ /
\/ \// \ /
\231 // 5 /
\ // \ /
\// \ /
\ 7 /
\ /
\ /

"SPANS" IN CENTS BETWEEN THE COMBINATIONS OF THE TONES
SYMBOLIZED BY 1, 3, 5, AND 7 WITHIN *ONE* OCTAVE. BEYOND
ONE OCTAVE, ADD MULTIPLES OF "1200 CT".

-monz

Joseph L. Monzo San Diego monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
| 'I had broken thru the lattice barrier...' |
| -Erv Wilson |
---------------------------------------------------

Yup, I read the Meyer book, and informed the list (back in the Mills
days) of the 90-degree rotated diamond therein. It's ironic that with
the whole 7-limit diamond in front of him, Meyer could be satisfied
with 24-tET -- the inconsistency was virtually staring him in the
face!