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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Get your free @... address at http://mail.yahoo.com

--- 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