Octave Invariance by Partch?

I found this reference to Partch in:

/tuning/topicId_23937.html#23980

Paul Erlich (in response to Ed Borasky):

>EB: 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.

PE: 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).

J Gill

--- In tuning@y..., J Gill <JGill99@i...> wrote:
> I found this reference to Partch in:
>
> /tuning/topicId_23937.html#23980
>
>
> Paul Erlich (in response to Ed Borasky):
>
> >EB: 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.
>
> PE: 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).
>
>
> J Gill

Is there a particular reason you bring this up now?

--- In tuning@y..., J Gill <JGill99@i...> wrote:

/tuning/topicId_31808.html#31808

> I found this reference to Partch in:
>
> /tuning/topicId_23937.html#23980
>
>
> Paul Erlich (in response to Ed Borasky):
>
> >EB: 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.
>
> PE: 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).
>
>
> J Gill

Hello J. Gill!

Wouldn't the crucial factor be Harry Partch's use of octave
equivalence in his *music??* We'll have to ask Jon Szanto. Jon?

I don't believe he uses much of such. For one thing, 43 tones make
pretty big octaves and large spans on any instrument. That right
there would tend to discourage the use of octave equivalence.

Am I right on that with Partch, Jon Szanto, or am I off my rocker
again... (My rocker rocks...)

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., J Gill <JGill99@i...> wrote:
>
> /tuning/topicId_31808.html#31808
>
> > I found this reference to Partch in:
> >
> > /tuning/topicId_23937.html#23980
> >
> >
> > Paul Erlich (in response to Ed Borasky):
> >
> > >EB: 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.
> >
> > PE: 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).
> >
> >
> > J Gill
>
>
> Hello J. Gill!
>
> Wouldn't the crucial factor be Harry Partch's use of octave
> equivalence in his *music??* We'll have to ask Jon Szanto. Jon?
>
> I don't believe he uses much of such. For one thing, 43 tones make
> pretty big octaves and large spans on any instrument. That right
> there would tend to discourage the use of octave equivalence.
>
> Am I right on that with Partch, Jon Szanto, or am I off my rocker
> again... (My rocker rocks...)
>
> JP

JG: What stuck me about this statement was the fact that -
IF Partch did not consider the various octaves to be equally
consonant, then this seems to call into question whether the
"One Footed Bride" diagram (and, perhaps other such attempts
to catalogue consonance on the basis of an assumed "octave
equivalence") is a valid representation of what is going on,
or (perhaps, by practical necessity) is only a simplification.

Best Regards, J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> JG: What stuck me about this statement was the fact that -
> IF Partch did not consider the various octaves to be equally
> consonant,

You mean he did not consider the various octave-inversions and octave-
extensions of a particular interval to be equally consonant.

> then this seems to call into question whether the
> "One Footed Bride" diagram (and, perhaps other such attempts
> to catalogue consonance on the basis of an assumed "octave
> equivalence") is a valid representation of what is going on,
> or (perhaps, by practical necessity) is only a simplification.

Yes -- he says himself that it is a practical simplification. Since
the vast majority of musicians, including Partch, think of pitch-
names in octave-invariant terms, then the concept of "interval
classes" (widespread in mainstream 20th century music theory, by the
way) becomes a very important one. Hence a rating of interval classes
by consonance becomes an interesting exercise -- for example if you
wish to design a scale which repeats itself exactly every octave,
then you can just use this kind of consonance measure for the pairs
of notes within one octave, rather than the much more complex
enterprise of using a "true" consonance measure for every pair of
notes within the audible range.

>
>
> Best Regards, J Gill