Yahoo Tuning Groups Ultimate Backup tuning Partch question

I had a question about the Partch tonality diamond, but apparently
nobody got around to it or saw it...

I am assuming that Partch's Tonality Diamond in the Diamond
Marimba is exactly the same pitch set-up as illustrated in _Genesis_,
correct?

So then, I was wondering why Prent Rodgers put the 11 limit "Numerary
Nexes" on the very RIM of the Diamond Marimba on his Java applet. He
has the ascending limits go towards the RIM of the instrument -- both
numerators and denominators.

That's different from the way Partch shows the ratios in his book.

Is there a reason that Rodgers would do this and, if so, what would
be the musical advantages?

Or... is the Partch ORIGINAL set-up superior musically??

Thanks!

________ __ _________
Joseph Pehrson

🔗Jon Szanto <JSZANTO@ADNC.COM>

Joe,

--- In tuning@y..., jpehrson@r... wrote:
> I had a question about the Partch tonality diamond, but apparently
> nobody got around to it or saw it...
> So then, I was wondering why Prent Rodgers put the 11
> limit "Numerary Nexes" on the very RIM of the Diamond Marimba on
> his Java applet.

Did you write Prent and ask him about it? Any of us would just be
guessing at his intent, and since Partch did it in a vacuum (there
weren't any pre-existing Diamond Marimbas) I don't know that he would
have viewed it as superior.

When he built the DM, he originally thought that it would be useful
for demonstrating his Tonality Diamond; as it turned out, the layout
was much more 'musical' (my term) then he might have imagined, as can
be witnessed in the wide variety of use the instrument achieved in
his music for the next 20 years (built in 1946).

See what Prent has to say, I'd be curious too!

Cheers,
Jon

🔗jpehrson@rcn.com

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_25331.html#25339

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Or... is the Partch ORIGINAL set-up superior musically??
>
> Partch's original set-up has this great advantage: pitches go up as
> one moves from left to right. In fact, Monz had a great webpage
> illustrating this beautifully . . . one of Monz's many "lost"
> webpages.
>
> Prent's set-up has the identities in order: 1,3,5,7,9,11. So it's
> more appealing mathematically but perhaps less appealing musically.

That was also *my* guess! Playing around with the applet, I didn't
find it as satisfying as the couple of times I've been actually able
to play the Diamond Marimba. (Dean Drummond is exceptionally nice in
this regard... he actually lets people play the thing...)

It seemed *much* more musical in the Partch configuration...

I wish I could be *linked* to the Monz page!! Does it have sound
too?? I hope so...

_________ ________ _______
Joseph Pehrson

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, June 18, 2001 1:15 PM
> Subject: [tuning] Re: Partch question
>
>
> --- In tuning@y..., jpehrson@r... wrote:
>
> > Or... is the Partch ORIGINAL set-up superior musically??
>
> Partch's original set-up has this great advantage: pitches go up as
> one moves from left to right. In fact, Monz had a great webpage
> illustrating this beautifully . . . one of Monz's many "lost"
> webpages.

Hmmm... I'm mystified. I don't remember this at all.

Paul, you have a good memory... tell me more about this
page, and I can probably find it. Maybe a bit of text
to search for...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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🔗Paul Erlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, June 18, 2001 3:08 PM
> Subject: [tuning] Re: Partch question
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > Hmmm... I'm mystified. I don't remember this at all.
> >
> > Paul, you have a good memory... tell me more about this
> > page, and I can probably find it.
>
> It was the Tonality Diamond, displayed in Marimba form, except that
> the positions were slightly distorted . . . so that position on the
> left-right axis represented pitch-height _exactly_ . . . it was at
> least a year ago . . .

Oh, now I'm certain I know what you're referring to... but AFAIK
I never made a webpage about this (did I? ... well, I did now!).

I probably showed it to you (Paul) when I visited you in
February 1999. A black-and-white version is in my book now,
but not in the early copy you have.

I've added a color graphic of it to the bottom of my Dictionary
"tonality diamond" entry:
http://www.ixpres.com/interval/dict/tondiam.htm

It's an idea I had for a keyboard instrument, back around 1993.
The buttons of the keyboard are arranged in a diamond, and
the 50-cent boundaries between the 12-EDO scale are used to
paint a pattern on the background similar to the usual Halberstadt
pattern of black and white piano keys.

The pitches of a 19-odd-limit tonality diamond are laid out in
Partch's diamond format, but arranged so that the otonal and
utonal decads form ascending and descending scales, respectively.
The red lines are otonal and the blue lines are utonal. The
proportions of the scales are thus 16:17:18:19:(20=10):11:12:13:14:15.

And (close to what Paul states) the horizontal axis represents
pitch-height exactly, so that a vertical column of buttons,
viewed against the background of either a white or black "key",
gives a precise view of all the different versions of any given
12-EDO pitch-class.

For example, looking down the row of buttons over the black
"C#/Db key" next to "middle-C", from top to bottom, one can see:

15/14 = the 15-odentity of 8/7-otonality and
the 7-udentity of 15/8-utonality,

14/13 = the 7-odentity of 16/13-otonality and
the 13-udentity of 7/4-utonality,

13/12 = the 13-odentity of 4/3-otonality and
the 3-udentity of 13/8-utonality,

12/11 = the 3-odentity of 16/11-otonality and
the 11-udentity of 3/2-utonality,

20/19 = the 5-odentity of 32/19-otonality and
the 19-udentity of 5/4-utonality,

19/18 = the 19-odentity of 16/9-otonality and
the 9-udentity of 19/16-utonality,

18/17 = the 9-odentity of 32/17-otonality and
the 17-udentity of 9/8-utonality, and

17/16 = the 17-odentity of 1/1-otonality and
the 1-identity of 17/16-utonality,

and finally, if we look over at the lone C#/Db in
the lower 2:1 ("octave") of the keyboard, we see:

16/15 = the 1-odentity of 16/15-otonality and
the 15-udentity of 1/1-utonality.

This gives a nice graphical presentation of all the
different pitches falling between 0.50 and 1.50 Semitones
(or 50 and 150 cents), which would have the following
values in my 72-EDO-based HEWM notation, C = n^0 ,
with the following meaning for accidentals:

^ + 1/4-tone
> + 1/6-tone
+ + 1/12-tone
0
- - 1/12-tone
< - 1/6-tone
v - 1/4-tone

Semitones ratio HEWM prime-factor prime-factor vector
3 5 7 11 13 17 19

0.89 20/19 Db- 5^1 19^-1 | 0 1 0 0 0 0 -1|
0.94 19/18 C# 3^-2 19^1 |-2 0 0 0 0 0 1|
0.99 18/17 C# 3^2 17^-1 | 2 0 0 0 0 -1 0|
1.05 17/16 Db 17^-1 | 0 0 0 0 0 -1 0|
1.12 16/15 Db+ 3^-1 5^-1 |-1 -1 0 0 0 0 0|
1.19 15/14 C#+ 3^1 5^1 7^-1 | 1 1 -1 0 0 0 0|
1.28 14/13 Db> 7^1 13^-1 | 0 0 1 0 -1 0 0|
1.39 13/12 Db> 3^-1 13^1 |-1 0 0 0 1 0 0|
1.51 12/11 Dv 3^1 11^-1 | 1 0 0 -1 0 0 0|

And so on for all the other "black and white keys".
The only "key" or pitch-class having only one pitch
is C = n^0.

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