RE: [crazy_music] Re: Does the "Partch system" exist anywhere in software?

Well, going from 7 unit amplitude partials to 11 unit amplitude partials got
me some more consonances, including 10/7! I renamed the files and added
gridlines to the 11-partial plot. 10/9, 9/8 and 8/7 now take their rightful
place between 1/1 and 7/6, 7/5 and 10/7 are both represented now with
roughly equal dissonance scores, 11/9 is there, looking slightly less
dissonant than its neighbor 6/5, and quite a few more of the 43 degrees of
the Partch scale are now located at consonances.

As to the differences between these curves and the harmonic entropy curves,
my conjecture is that for purely harmonic spectra, aside from the fact that
the consonances in the HE curves are round rather than pointed, for most
practical purposes the curves will be the same if one tweaks the parameters
correctly. I personally prefer the pointed consonances to the rounded ones.

Incidentally, when I used partials with amplitudes equal to 1/n rather than
1, the curves were nowhere near as dramatic. Since the Sethares theory is
supposedly based on psychoacoustics, I question whether the "average
untrained ear" perceives consonance and dissonance the way the harmonic
entropy curve and the unit-amplitude Sethares curve show, or more the way
the 1/n scaled amplitude curve shows.

Clearly we musical folk can hear these things, but can our more naive
listeners? The relative smoothness of the curve for harmonic sounds with
descending-amplitude partials might explain why the masses have little
trouble enjoying 12-TET music on conventional instruments, despite the
theory that says the equal tempered major third, for example, is "woefully
out of tune". I'm going to plot the two curves on the same graph and upload
the picture a little later.

One other note: I haven't said much about Xenakis in this discussion, and
his theories and techniques share equal footing with those of Partch in this
work. In passing, though, I would like to note that there is a section in
_Formalized Music_ about the evolution of music from the Ancient Greek
tetrachords that I think is highly relevant. I doubt if there is anything in
it that the folks here haven't already seen, but it was one of the things
that triggered my interest in combining Xenakis and Partch.
--
M. Edward (Ed) Borasky, Chief Scientist, Borasky Research
http://www.borasky-research.net http://www.aracnet.com/~znmeb
mailto:znmeb@... mailto:znmeb@...

If there's nothing to astrology, how come so many famous men were born on
holidays?

> -----Original Message-----
> From: monz [mailto:joemonz@...]

> You should be aware that Sethares's goal is to find tuning systems which
> harmonize specific timbres. Thus, his curve has an otonal bias.
> Partch's does not - it is strictly a dyadic interval measure, which
> exhibits the dualistic (otonal/utonal) properties that are fundamental
> to Partch's theories.

Well, as the title of Sethares' book is _Tuning, Timbre, Spectrum, Scale_, I
think his goals are somewhat broader than that, and indeed, broader than
mine at the moment. My goal is to produce a piece and the tools to create
the piece. I don't see the "otonal bias" in the Sethares curves. The bias I
*do* see there is that the Sethares equations depend, as does the underlying
theory, on the absolute frequencies at which the notes are played. The
harmonic entropy curves, IIRC, are purely based on ratios. My curves were
generated with 1/1 equal to Partch's G 392. Since my piece will use the
Partch scale, I intend to use purely harmonic timbres to maximize the
consonances, and it will probably be centered at G392. And I certainly
intend to use both Otonalities and Utonalities.

> IMO, the harmonic entropy curve is much closer to what you're trying
> to do. Sethares's curves are implemented with larger collections
> of pitches in mind (triads, tetrads, pentads, hexads, etc.).

My intention is to use all of these (although there is only one hexad in
each tonality).

> BTW, as you should be aware, I'm interested in implementing a
> number of Partch's theoretical procedures in JustMusic. I just
> posted something to that group last week about creating a window
> to display his "Field of Attraction":
> /justmusic/topicId_unknown.html#144

Once I get my code working and my piece in construction, I'll contribute it
to JustMusic. It will most likely be in C, since "sfront" is written in C
and creates output files in C and Derive can write C code. The Field Of
Attraction is one element I will be using.

> ----- Original Message -----
> From: M. Edward Borasky <znmeb@...>
> To: <crazy_music@yahoogroups.com>
> Sent: Sunday, June 17, 2001 1:07 PM
> Subject: RE: [crazy_music] Re: Does the "Partch system" exist anywhere in
software?
>
>
> Well, going from 7 unit amplitude partials to 11 unit amplitude partials
got
> me some more consonances, including 10/7! I renamed the files and added
> gridlines to the 11-partial plot. 10/9, 9/8 and 8/7 now take their
rightful
> place between 1/1 and 7/6, 7/5 and 10/7 are both represented now with
> roughly equal dissonance scores, 11/9 is there, looking slightly less
> dissonant than its neighbor 6/5, and quite a few more of the 43 degrees of
> the Partch scale are now located at consonances.

OK, that made me realize another aspect of what you are doing.
You were clearing thinking before in terms of *odd*-limit, yes?
(or maybe prime-limit?)

But Partch's curve is based on *integer*-limit, I suppose with some
qualification based on odd- or prime-limit (?).

So expanding your limit to 11 (whether integer-, odd-, or prime-)
automatically included all numbers under 11, thus you got those
"octave" complements.

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

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--- In crazy_music@y..., "M. Edward Borasky" <znmeb@a...> wrote:

/crazy_music/topicId_145.html#164

> Well, going from 7 unit amplitude partials to 11 unit amplitude
partials got
> me some more consonances, including 10/7! I renamed the files and
added
> gridlines to the 11-partial plot. 10/9, 9/8 and 8/7 now take their
rightful
> place between 1/1 and 7/6, 7/5 and 10/7 are both represented now
with
> roughly equal dissonance scores, 11/9 is there, looking slightly
less
> dissonant than its neighbor 6/5, and quite a few more of the 43
degrees of
> the Partch scale are now located at consonances.
>
> As to the differences between these curves and the harmonic entropy
curves,
> my conjecture is that for purely harmonic spectra, aside from the
fact that
> the consonances in the HE curves are round rather than pointed, for
most
> practical purposes the curves will be the same if one tweaks the
parameters
> correctly. I personally prefer the pointed consonances to the
rounded ones.
>

Hello Ed...

I believe there is some discussion of the harmonic entropy curves as
they relate to Partch's "One Footed Bride" in Paul Erlich's recent
paper, "The Forms of Tonality..."

You may be interested in contacting Paul about it...

_______ _______ _______
Joseph Pehrson