One-Footed Bride

>does anyone have the "formula" for Partch's "One-
>Footed Bride"? I have the Sethares formulas for consonance, but I'm >starting to play around with the Partch scale, and I was hoping to find >some mathematical function for the "bride" somewhere.

I'm not sure what formula Partched used, but I believe
Sethares uses the well-known algorithm from:

R. Plomp and W. J. M. Levelt, "Tonal consonance and
critical bandwidth." Journal of the Acoustical Society
of America, 38:548--560, 1965.,

which depends on the spectra involved. There is a slightly
more accurate method which also takes into account masking
effects, described in:

A. Kameoka and M. Kuriyagawa, "Consonance theory part i:
consonance of dyads." and "Consonance theory part ii:
consonance of complex tones and calculation method."
Journal of the Acoustical Society of America,
45(6):1452--1469, 1969.

I hope this helps---keep us posted!

-m
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Michael Saunders wrote:

> >does anyone have the "formula" for Partch's "One-
> >Footed Bride"? I have the Sethares formulas for consonance, but I'm
> >starting to play around with the Partch scale, and I was hoping to
> find >some mathematical function for the "bride" somewhere.
>
> I'm not sure what formula Partched used, but I believe
> Sethares uses the well-known algorithm from:

<snip>

Sethares mentioned both papers, but used his own formula that's
qualitatively the similar but simpler to calculate. I could dig it out
for you, so could he :)

I worked this stuff out a while back. I couldn't reproduce K&K's
quantitative results. I got good curves from Sethares' formula, but this
wasn't with real-world timbres.

All these measures will break down if you throw too many partials at them.
One of the important parts of Sethares' method is to simplify the
spectrum to only the most important partials. This is a subjective
process, and so may be a problem with these automatic adaptive tuners
people have in mind.

It is worth getting hold of Sethares' book to get the details and
examples. Are you the one in South Wales? If you feel like popping over
the bridge, I could lend it to you.

Partch didn't have a formula that I'm aware of, other than the odd-limit.
He drew what he thought made sense. I thought it was a bit sneaky of
Paul to veer toward a discussion of harmonic entropy ;)

Graham

--- In tuning@y..., "Michael Saunders" <michaelsaunders7@h...> wrote:

> I'm not sure what formula Partched used

He didn't use a formula -- he went by experience. The remarkable
thing is that octave-equivalent harmonic entropy is able to reproduce
his findings with remarkably few assumptions.
Harmonic_entropy@yahoogroups.com.

--- In tuning@y..., graham@m... wrote:

> Sethares mentioned both papers, but used his own formula that's
> qualitatively the similar but simpler to calculate. I could dig it
out
> for you, so could he :)

Again, Sethares, working with me, was unable to ascertain exactly how
to use his formula. And his formula fails pretty badly for chords of
three or more notes, where it fails to reproduce our observations
that otonal chords are more consonant than utonal chords.
>
> I worked this stuff out a while back. I couldn't reproduce K&K's
> quantitative results. I got good curves from Sethares' formula,
but this
> wasn't with real-world timbres.

The problem Sethares and I were finding was that, depending on the
decibel level you assumed (yes, by "amplitude" Sethares really
means "decibel level"), you can get a wildly different dissonance
curve.
>
> All these measures will break down if you throw too many partials
at them.
> One of the important parts of Sethares' method is to simplify the
> spectrum to only the most important partials.

Yes -- he justifies this in terms of masking.

> This is a subjective
> process, and so may be a problem with these automatic adaptive
tuners
> people have in mind.

Factors like vibrato, room acoustics, equipment fidelity, and of
course volume will often be more important variables than timbre for
the perception of consonance and dissonance.
>
> Partch didn't have a formula that I'm aware of, other than the odd-
limit.
> He drew what he thought made sense. I thought it was a bit sneaky
of
> Paul to veer toward a discussion of harmonic entropy ;)

I see the smiley, but I should clarify: I predicted back around '97
(see the On Harmonic Entropy webpage) that an octave-equivalent
formulation of harmonic entropy would resemble the One-Footed Bride.
It did so a lot better than I even had hoped!

Harry had a phenomenal ear. An underestimation

Paul Erlich wrote:

> --- In tuning@y..., "Michael Saunders" <michaelsaunders7@h...> wrote:
>
> > I'm not sure what formula Partched used
>
> He didn't use a formula -- he went by experience. The remarkable
> thing is that octave-equivalent harmonic entropy is able to reproduce
> his findings with remarkably few assumptions.
> Harmonic_entropy@yahoogroups.com.
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

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