Q: how many tones in a tonality diamond?

> [Paul Erlich, TD 466.7]
> Kraig Grady wrote,
>
>> I saw the discussion of Partch's 43 tone scale in relations
>> to the 31 tone diamond
>
> [Paul]
> The diamond only has 29 tones, since 9/6=3/2 and 12/9=4/3.
>

That's true if you're speaking about it with 'octave'-equivalence
in effect. But Partch explicitly drew his Tonality Diamond
diagrams over the span of almost-an-'octave', with a string of
1/1s in the middle of the diamond, and with half of the rest
of the pitches in the lower 2/1 and the other half in the higher
2/1 (Partch's terminology; following the convention a few of us
here have established, it should be 1:2).

See Partch 1974, p 159, and
http://www.ixpres.com/interval/dict/tondiam.htm

Kraig is right: in this 'octave'-specific sense, the 11-limit
Tonality Diamond does indeed have 31 tones.

See my lattice of this at:
http://www.ixpres.com/interval/monzo/lattices/xl/partch11.htm

Daniel Wolf, Paul Erlich, and Brian McLaren have noted
a few inconsistencies between Partch's theories as expressed
in _Genesis_ and the techniques exhibited in his actual
compositions; in his compositions, I'd guess that sometimes
Partch had 'octave'-equivalency in mind, at other times he
had 'octave'-specifity in mind. Any score citations backing
either of these up would be appreciated.

BTW,

> [Jon Szanto, TD 465.5]
> If nothing else, he [Partch] was pretty clear in his
> determination. While the theoretical underpinnings may
> have been delineated in Delusion (back in 1949 and the
> later edition in 1974), the years of _actual composition_
> may have pointed him to *his* best use of the tonality
> diamond / JI resources he had set up, <...snip>

Jon, don't you mean _Genesis_ here and not _Delusion_?
The dates you give correspond to the book, and as far as
I knew, _Delusion of the Fury_ was composed entirely in
the late 1960s.

And what's the correct reference date for the 1st edition
of _Genesis_? The Preface is dated 1947 by Partch, but
the copyright is 1949. I think I had previously (always?)
seen it referred to as 'Partch 1947', but Jon uses 1949 here.
...???

REFERENCES
----------

Partch, Harry. 1974. _Genesis of a Music_.
2nd edition. Da Capo Press, New York.

(The Tonality Diamond also apprears in the 1st edition.)

-monz

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

Joe,

>Jon, don't you mean _Genesis_ here and not _Delusion_?
>The dates you give correspond to the book, and as far as
>I knew, _Delusion of the Fury_ was composed entirely in
>the late 1960s.

Yes, a far-too-befuddled brain. Most obviously, I mean "Genesis of a Music".

>And what's the correct reference date for the 1st edition
>of _Genesis_? The Preface is dated 1947 by Partch, but
>the copyright is 1949. I think I had previously (always?)
>seen it referred to as 'Partch 1947', but Jon uses 1949 here.
>...???

Well, most reference dates should point to the *publication* date, so that
would be 1949 (University of Wisconsin Press).

By the way, this business about the tonality diamond having either 29 or 31
tones is a bit semantical: Partch clearly labels the two 'notes' that are
duplicated in the diamond, leading to 29 'discrete' pitches, but for
logical, compositional and, not least, visual sense 31 is a path that makes
just as much sense to follow.

See? No Y2K problems to speak of. Stupid humans...
Jon
`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`
Jonathan M. Szanto : Corporeal Meadows - Harry Partch, online.
jszanto@adnc.com : http://www.corporeal.com/
`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`

From Daniel Wolf:

>Although the tones in the diagonal row of 1/1, 5/5, 3/3, 7/7,
>9/9, 11/11 share the same frequency, Partch uses them as different tones
>_functionally_. This is not facetious or clever: the distinct functional
>identities of these tones were important enough to Partch that he used a
>lot of extra hardwood to carve redundant tones in the middle row of the
>diamond marimba!

Absolutely. Staring me in the face and I didn't think to include that
'facet'. Not to make Partch the exemplar, but I've always been fascinated
by the ability of the Diamond Marimba to be a physical, music-producing
resource that corresponds to the underlying theories. Are there any other
examples, from other composers, that exhibit this one-to-one functionality
(serendipity?).

Best,
Jon

`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`
Jonathan M. Szanto : Corporeal Meadows - Harry Partch, online.
jszanto@adnc.com : http://www.corporeal.com/
`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`

>Not to make Partch the exemplar, but I've always been fascinated
>by the ability of the Diamond Marimba to be a physical, music-producing
>resource that corresponds to the underlying theories. Are there any other
>examples, from other composers, that exhibit this one-to-one functionality
>(serendipity?).

The 22-tone keyboard mapping in my paper is an example. The "Decatonic
Waltz" I performed at the Microthon falls right out of it.