Partch's Bride

Michael Saunders asked about the relationship between
Partch's one footed bride and dissonance curves:

I havent actually done it, but I'll bet you could get very close
to the one footed bride using the sensory dissonance methods.
While some people dont like the fact that the method
is dependent on the details of the spectrum of the sound, one
advantage is that by using different spectra you can shape
the curve in many ways. In this case, you pretty clearly want to
use a harmonic spectrum, but you are left with a number of degrees
of freedom as regards the amplitudes of the partials, and the
pitch of the fundamental.

Of course, theres the matter that Partch was plotting consonance,
whereas sensory dissonance (as with Plomp and Levelt and Helmholtz) is the inverse,
but basically if you look at Partch's curve, he has peaks of consonance
where partials coincide. This is qualitatively
what you expect from sensory dissonance, except that you must invert
the "peaks of consonance" into "valleys of dissonance".

Which brings up an interesting question: what timbres was Partch listening
to when he was drawing these curves? From the look of the curve, clearly
something with many strong harmonics... maybe his reed organ?
It is also very possible that Partch drew these curves not from a single
listening to a single instrument, but as an integration of his experiences
with a variety of sounds over a length of time. If it is this latter,
then its less likely that a single dissonance curve will capture all the
detail. Does anyone know?

Bill Sethares

Although Harry knew people who were into electronics, and he owned some very good hi-fi equipment, I don't believe he ever had any test equipment, such as an audio oscillator. Playing back a single frequency of a sine wave on tape versus varying the frequency of the oscillator, as it were, live at the same time, either mixed through the same amplifier and loudspeaker or through another channel, would allow an investigation by listening for beats. Or you could use two oscillators. Beware because these may have a certain amount of drift, as may a tape machine. Checking with a frequency counter may help, but this also could drift, or not have a fine enough readout, such as only the nearest 1 Hz. Still, even without great precision, you could draw a good graph. Just don't expect to be able to detect differences of a few cents. Whether you use sine waves or other waveforms may make a difference. The choice of what octave to use may also matter. The oscillator scale is more expanded at lower frequencies, but a frequency counter (most oscillators have markings that aren't very accurate) good to the nearest Hz, for example, will have more Hz per octave at higher frequencies. Obviously, the octave between 20 and 40 Hz has only 20Hz, not enough to work with a 43 tone to the octave scale! If you use other waveforms with harmonics, be aware that some of the harmonics may fall above the upper limit of your range of hearing. Also, when using electronic equipment, be aware that some intermodulation distortion may be introduced, in addition to any sum and difference tones that you may hear.
If you read Harry's brief comments in "Genesis of a Music" about the possibilities of electronic instruments, it seems clear that he had no experience with them. This was largely because they were unaffordable to him, or came on the market too late in his life, rather than any clear aversion to them or philosophical preference for acoustic instruments, apart from being less "corporeal".
My impression is that Harry was much more concerned with composing and performing real music than with doing psychoacoustic investigations. After "Genesis" was published, he didn't even seem very interested or involved with scale theory or discussions about it. Not only was he a musician seduced into carpentry, he was a writer seduced into arithmetic and mathematics.
>>> SETHARES@ECESERV0.ECE.WISC.EDU 05/29/01 12:13PM >>>

Michael Saunders asked about the relationship between
Partch's one footed bride and dissonance curves:

I havent actually done it, but I'll bet you could get very close
to the one footed bride using the sensory dissonance methods.
While some people dont like the fact that the method
is dependent on the details of the spectrum of the sound, one
advantage is that by using different spectra you can shape
the curve in many ways. In this case, you pretty clearly want to
use a harmonic spectrum, but you are left with a number of degrees
of freedom as regards the amplitudes of the partials, and the
pitch of the fundamental.

Of course, theres the matter that Partch was plotting consonance,
whereas sensory dissonance (as with Plomp and Levelt and Helmholtz) is the inverse,
but basically if you look at Partch's curve, he has peaks of consonance
where partials coincide. This is qualitatively
what you expect from sensory dissonance, except that you must invert
the "peaks of consonance" into "valleys of dissonance".

Which brings up an interesting question: what timbres was Partch listening
to when he was drawing these curves? From the look of the curve, clearly
something with many strong harmonics... maybe his reed organ?
It is also very possible that Partch drew these curves not from a single
listening to a single instrument, but as an integration of his experiences
with a variety of sounds over a length of time. If it is this latter,
then its less likely that a single dissonance curve will capture all the
detail. Does anyone know?

Bill Sethares

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--- In tuning@y..., SETHARES@E... wrote:
>
> Which brings up an interesting question: what timbres was Partch
listening
> to when he was drawing these curves? From the look of the curve,
clearly
> something with many strong harmonics... maybe his reed organ?
> It is also very possible that Partch drew these curves not from a
single
> listening to a single instrument, but as an integration of his
experiences
> with a variety of sounds over a length of time.

This is true, and also, Partch was taking octave-equivalence into
account -- for example, his rating for 6:5 also applies to 5:3, 10:3,
12:5 . . . thus the symmetry of the one-footed bride.

> If it is this latter,
> then its less likely that a single dissonance curve will capture
all the
> detail. Does anyone know?

Octave-equivalent harmonic entropy does a surprisingly good job, and
also reflects features (namely, local minima at the primary ratios)
that should be inferred from Partch's text but are not present in his
coarse graph.

Partch was very clear that he could accurately tune all his "primary
ratios" on his Chromelodeon (a reed organ) by ear, by eliminating
beats. In fact, I believe he tuned the Chromelodeon first, and then
tuned his other instruments to that.

Paul,

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Partch was very clear that he could accurately tune all
his "primary
> ratios" on his Chromelodeon (a reed organ) by ear, by eliminating
> beats. In fact, I believe he tuned the Chromelodeon first, and then
> tuned his other instruments to that.

This is true. Of course, before the Chromelodeon he had the Adapted
Viola and the Adapted Guitars (which evolved), so he was doing tuning
before he had an instrument as a reference source. After the Ch., he
did use it to tune the other instruments to, as we did for all the
subsequent years. There were times when the Ch. had started to stray,
but since it (and the mallet instruments) *couldn't* be adjusted on
stage, the others were tuned to them.

Cheers,
Jon

--- In tuning@y..., SETHARES@E... wrote:
> Michael Saunders asked about the relationship between
> Partch's one footed bride and dissonance curves:
>
> I havent actually done it, but I'll bet you could get very close
> to the one footed bride using the sensory dissonance methods.
> While some people don't like the fact that the method
> is dependent on the details of the spectrum of the sound, one
> advantage is that by using different spectra you can shape
> the curve in many ways. In this case, you pretty clearly want to
> use a harmonic spectrum, but you are left with a number of degrees
> of freedom as regards the amplitudes of the partials, and the
> pitch of the fundamental.
I am actually looking into another approach -- digitizing the curve
out of the book, then fitting a formula and spectrum to match the
curve. If someone has digitized the curve, I'd appreciate a pointer
to it.

> Of course, there's the matter that Partch was plotting consonance,
> whereas sensory dissonance (as with Plomp and Levelt and Helmholtz)
is the inverse,
> but basically if you look at Partch's curve, he has peaks of
consonance
> where partials coincide. This is qualitatively
> what you expect from sensory dissonance, except that you must invert
> the "peaks of consonance" into "valleys of dissonance".
Still, the dissonance curves in your book have some *very* sharp
valleys of dissonance -- much sharper than Partch's peaks of
consonance. It's almost as if Partch is operating with the logarithm
rather than the actual function. IIRC taking the log of a Gaussian
gives a parabola. In any event, there are lots of ways to approximate
a curve like the one-footed bride. What I was hoping to do was
generate some sounds in Partch's scale in a timbre fitted to that
scale -- generating a curve resembling the one-footed bride -- and
then listen to various combinations of notes.

> Which brings up an interesting question: what timbres was Partch
listening
> to when he was drawing these curves? From the look of the curve,
clearly
> something with many strong harmonics... maybe his reed organ?
My guess is the Chromelodeon -- the reed organ. Most of his other
instruments were percussion instruments with typical percussion
envelopes, hardly the sort of thing that would facilitate curve
fitting by ear.

> It is also very possible that Partch drew these curves not from a
single
> listening to a single instrument, but as an integration of his
experiences
> with a variety of sounds over a length of time. If it is this
latter,
> then its less likely that a single dissonance curve will capture
all the
> detail. Does anyone know?
I've been reading over the chapter on the One-Footed Bride and it
isn't clear ... I think the curve he presents is *his* perception of
the relative consonance of the listed intervals. For one thing, the
curve is symmetrical about the tritone -- e.g., the fourth and fifth
have equal consonance, as do the major third and minor sixth, etc.
Partch had, of course, seen Helmholtz's curves, which again are
smoother in the valleys than yours are.
--
M. Edward (Ed) Borasky, Chief Scientist, Borasky Research
http://www.borasky-research.net http://www.aracnet.com/~znmeb
mailto:znmeb@borasky-research.com mailto:znmeb@aracnet.com

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

--- In tuning@y..., "Ed Borasky" <znmeb@a...> wrote:

> I am actually looking into another approach -- digitizing the curve
> out of the book, then fitting a formula and spectrum to match the
> curve. If someone has digitized the curve, I'd appreciate a pointer
> to it.

I'm highly opposed to this approach in principle (unless this is all
artistic in conception), because the only points on the curve where
Partch attempted to accurately portray its values are at the "primary
ratios" and at the "secondary ratios". Partch simply connected the
curve between each of these points with a smooth, monotonic curve, as
you can verify. But if you read Partch's text, it's clear that he
thought of each of the "primary ratios" (but not the "secondary
ratios") as local minima of consonance.

> Still, the dissonance curves in your book have some *very* sharp
> valleys of dissonance -- much sharper than Partch's peaks of
> consonance. It's almost as if Partch is operating with the
logarithm
> rather than the actual function.

A spiky peak remains a spiky peak even if you take the logarithm.

> IIRC taking the log of a Gaussian
> gives a parabola.

Yup. Guys -- wanna move this over to the tuning-math list?

> In any event, there are lots of ways to approximate
> a curve like the one-footed bride.

I try to do it from basic principles and as few assumptions as
possible.

> What I was hoping to do was
> generate some sounds in Partch's scale in a timbre fitted to that
> scale -- generating a curve resembling the one-footed bride -- and
> then listen to various combinations of notes.

That's going to be nice.

> I've been reading over the chapter on the One-Footed Bride and it
> isn't clear ... I think the curve he presents is *his* perception
of
> the relative consonance of the listed intervals. For one thing, the
> curve is symmetrical about the tritone -- e.g., the fourth and
fifth
> have equal consonance, as do the major third and minor sixth, etc.

As he makes clear in the text, he doesn't consider an interval, and
intervals obtained by multiplying or dividing by powers of 2, to be
identical in consonance. He _does_, however, portray them as
identical in consonance, because his considerations as a theorist
often oblige him to refer to pitches in octave-invariant form
(omitting considerations of octave register). Again, this kind
of "language" is troublesome for a lot of people . . . maybe tuning-
math would be a better place.

You know, Partch may have liked the "pointy" graphs if he had ever
gotten to see them.