question on Sethares

OK... I have a question on Sethares _Tuning, Timbre, Spectrum, Scale_
which I am enjoying...

The question lies in the overall philosophy of the construction of
his scales.

Clearly he takes inharmonic timbres and creates scales based upon the
maxima of the various inharmonic partials.

Then, seemingly, he arranges them all in a row to create his scale...

Does that make any sense at all??

If so, wouldn't the analogy for *harmonic* scales, be a scale that
would progress by the *harmonic* series, say C, C, G, C, E, G, etc.,
etc...

But, we don't make scales that way... so why does this inharmonic
method make any more sense...??

Any assistance would be appreciated...

Thanks!

________ ________ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> OK... I have a question on Sethares _Tuning, Timbre, Spectrum,
Scale_
> which I am enjoying...
>
> The question lies in the overall philosophy of the construction of
> his scales.
>
> Clearly he takes inharmonic timbres and creates scales based upon
the
> maxima of the various inharmonic partials.
>
> Then, seemingly, he arranges them all in a row to create his
scale...
>
> Does that make any sense at all??
>
> If so, wouldn't the analogy for *harmonic* scales, be a scale that
> would progress by the *harmonic* series, say C, C, G, C, E, G,
etc.,
> etc...
>
> But, we don't make scales that way... so why does this inharmonic
> method make any more sense...??

You're absolutely right, Joseph! This is one of the many problems I
have with Sethares. But I don't make a big deal out of this, because
Sethares does end up using his methods to prescribe, for example,
certain unusual ETs for certain inharmonic timbres, and vice versa.
One could go further and similarly define periodicity blocks using
inharmonic series and some associated unison vectors, and find
Setharean analogues to the diatonic scale -- I think this would make
more sense as a scale-construction approach, _if_ one accepts the
Sethares view of harmony . . . But as you know, I don't accept the
Sethares view of harmony in the first place! I think Terhardt, though
still too Setharean for my taste, has got the picture much more
clearly . . . I'd go over to his website

http://www.mmk.ei.tum.de/persons/ter.html

and carefully study the topics under

Perception of Auditory Pitch
and
Perception of Musical Sound

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28015.html#28020

>
> You're absolutely right, Joseph! This is one of the many problems I
> have with Sethares. But I don't make a big deal out of this,
because
> Sethares does end up using his methods to prescribe, for example,
> certain unusual ETs for certain inharmonic timbres, and vice versa.
> One could go further and similarly define periodicity blocks using
> inharmonic series and some associated unison vectors, and find
> Setharean analogues to the diatonic scale -- I think this would
make
> more sense as a scale-construction approach, _if_ one accepts the
> Sethares view of harmony . . . But as you know, I don't accept the
> Sethares view of harmony in the first place! I think Terhardt,
though
> still too Setharean for my taste, has got the picture much more
> clearly . . . I'd go over to his website
>
> http://www.mmk.ei.tum.de/persons/ter.html
>
> and carefully study the topics under
>
> Perception of Auditory Pitch
> and
> Perception of Musical Sound

Thank you, Paul, for this interesting link. Somehow, I don't think I
ever saw that page before...!

My question is this:

Sethares analyzes inharmonic timbres and plots them, and then
calculates the "dissonance curves..."

Well and good. But then, he transposes this all down many octaves to
create scales out of it!

Is there really *any* concrete relationship between the scales he
creates and the partials of his inharmonic sounds??

That is, aside from the fact, that you mention, that he comes up with
a lot of interesting stuff... ET's etc. that correspond to inharmonic
frequencies transposed, etc., etc. So, the resulting scales can be
new and fascinating.

HOWEVER, is there *really* any kind of correlation? Is there any
reason that a scale constructed of the ratios of a timbre that was
stratospherically higher in the first place sounds "better" in that
timbre.

Is there really anything to that??

I'm a little skeptical... It seems to me a bit like these guys we
get on the list every now and then who say that if you keep
multiplying the frequencies of sound waves you will eventually get
LIGHT waves, and then *somehow* the resulting light waves will
correspond to the original sound!

Isn't it exactly the same kind of fallacy???????

________ ________ ________
Joseph Pehrson

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > But, we don't make scales that way... so why does this inharmonic
> > method make any more sense...??

> You're absolutely right, Joseph! This is one of the many problems I
> have with Sethares.

I had the following idea, which I never tried to put into practice.
Suppose we pick a scale in advance, and then come up with timbres
suitable to it. For instance, we could have an approximate overtone
series of 2^0, 2^1, 2^(11/7), 2^2, 2^(16/7) ..., and have timbres
which never had strong clashes of critical bands.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_28015.html#28020
>
> >
> > You're absolutely right, Joseph! This is one of the many problems
I
> > have with Sethares. But I don't make a big deal out of this,
> because
> > Sethares does end up using his methods to prescribe, for example,
> > certain unusual ETs for certain inharmonic timbres, and vice
versa.
> > One could go further and similarly define periodicity blocks
using
> > inharmonic series and some associated unison vectors, and find
> > Setharean analogues to the diatonic scale -- I think this would
> make
> > more sense as a scale-construction approach, _if_ one accepts the
> > Sethares view of harmony . . . But as you know, I don't accept
the
> > Sethares view of harmony in the first place! I think Terhardt,
> though
> > still too Setharean for my taste, has got the picture much more
> > clearly . . . I'd go over to his website
> >
> > http://www.mmk.ei.tum.de/persons/ter.html
> >
> > and carefully study the topics under
> >
> > Perception of Auditory Pitch
> > and
> > Perception of Musical Sound
>
>
> Thank you, Paul, for this interesting link. Somehow, I don't think
I
> ever saw that page before...!
>
> My question is this:
>
> Sethares analyzes inharmonic timbres and plots them, and then
> calculates the "dissonance curves..."
>
> Well and good. But then, he transposes this all down many octaves
to
> create scales out of it!
>
> Is there really *any* concrete relationship between the scales he
> creates and the partials of his inharmonic sounds??

Hmm . . . I guess as much so as harmonic series scales have to do
with harmonic sounds. The scale is just one big otonal
chord/arpeggio. A pretty limited way to use harmonic sounds, I would
say!
>
> That is, aside from the fact, that you mention, that he comes up
with
> a lot of interesting stuff... ET's etc. that correspond to
inharmonic
> frequencies transposed, etc., etc. So, the resulting scales can be
> new and fascinating.
>
> HOWEVER, is there *really* any kind of correlation?

In the ET case, there is. Because whatever intervals you try to
approximate, not only do _pitches_ above the tonic appear at those
relationships, as Sethares may seemingly emphasize, but also, these
intervals are available _endlessly_, in _all directions_ spanned by
the intervals of interest. Then one can create periodicity blocks and
find interesting scales.

> Is there any
> reason that a scale constructed of the ratios of a timbre that was
> stratospherically higher in the first place sounds "better" in that
> timbre.

What do you mean, stratospherically higher? I may be missing
something -- can you quote me the appropriate Sethares?

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > > But, we don't make scales that way... so why does this
inharmonic
> > > method make any more sense...??
>
> > You're absolutely right, Joseph! This is one of the many problems
I
> > have with Sethares.
>
> I had the following idea, which I never tried to put into practice.
> Suppose we pick a scale in advance, and then come up with timbres
> suitable to it. For instance, we could have an approximate overtone
> series of 2^0, 2^1, 2^(11/7), 2^2, 2^(16/7) ..., and have timbres
> which never had strong clashes of critical bands.

The solution is covered in Sethares' book.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> The solution is covered in Sethares' book.

I'm not sure what you mean by a solution. An algorithm? Some
examples? An entire GM sound font adapted to 12-et? (Now there's an
idea for someone to peddle!)

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > The solution is covered in Sethares' book.
>
> I'm not sure what you mean by a solution. An algorithm?

Yes.

> Some
> examples?

Yes, on the accompanying CD.

My modest suggestion...
We must try to hear melodicaly also when we play one
triad :) Keep the tonic function-it's one musical
aproach, I think

--- jpehrson@rcn.com a �crit�: > OK... I have a
question on Sethares _Tuning, Timbre,
> Spectrum, Scale_
> which I am enjoying...
>
> The question lies in the overall philosophy of the
> construction of
> his scales.
>
> Clearly he takes inharmonic timbres and creates
> scales based upon the
> maxima of the various inharmonic partials.
>
> Then, seemingly, he arranges them all in a row to
> create his scale...
>
> Does that make any sense at all??
>
> If so, wouldn't the analogy for *harmonic* scales,
> be a scale that
> would progress by the *harmonic* series, say C, C,
> G, C, E, G, etc.,
> etc...
>
> But, we don't make scales that way... so why does
> this inharmonic
> method make any more sense...??
>
> Any assistance would be appreciated...
>
> Thanks!
>
> ________ ________ ______
> Joseph Pehrson
>
>
>

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
Yahoo! Courrier : http://fr.mail.yahoo.com

Hi Gene,

> I had the following idea, which I never tried to put into practice.
> Suppose we pick a scale in advance, and then come up with timbres
> suitable to it. For instance, we could have an approximate overtone
> series of 2^0, 2^1, 2^(11/7), 2^2, 2^(16/7) ..., and have timbres
> which never had strong clashes of critical bands.

I tried this out of matching a timbre to a scale in 7-tet with a
timbre that had 7-tet fifths in it.

It worked rather well.

You can experiment with this in FTS, using midi instruments to play
the partials of the timbre. (Voices | Custom Voices | Edit Custom Melod. voices
| Edit as Timbre

For my 7-et experiment:

http://members.tripod.com/~robertinventor/tunes/improvisations.htm
and scroll down to the 7_equal_seth_timbre.mid

Robert

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:

> http://members.tripod.com/~robertinventor/tunes/improvisations.htm
> and scroll down to the 7_equal_seth_timbre.mid

Sounds interesting, but I couldn't find it. I've been listening to
some of the exotic music I've so recently collected, it makes me feel
better for some reason.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28015.html#28034

> > That is, aside from the fact, that you mention, that he comes up
> with a lot of interesting stuff... ET's etc. that correspond to
> inharmonic frequencies transposed, etc., etc. So, the resulting
scales can be new and fascinating.
> >
> > HOWEVER, is there *really* any kind of correlation?
>
> In the ET case, there is. Because whatever intervals you try to
> approximate, not only do _pitches_ above the tonic appear at those
> relationships, as Sethares may seemingly emphasize, but also, these
> intervals are available _endlessly_, in _all directions_ spanned by
> the intervals of interest. Then one can create periodicity blocks
and find interesting scales.
>
> > Is there any
> > reason that a scale constructed of the ratios of a timbre that
was stratospherically higher in the first place sounds "better" in
that timbre.
>
> What do you mean, stratospherically higher? I may be missing
> something -- can you quote me the appropriate Sethares?

Hello Paul, and others...

I'm going to *try* to continue this discussion we were having
September 11...

There is no quote, per se, from Sethares regarding
anything "stratospheric..."

I guess my confusion was the fact that, somehow, I wasn't thinking
of "overtones" as within a range one would use to create a scale...
but thinking about this some more, I realize they frequently are...

Still, I can't quite understand the reasoning that a scale built of
the intervals of a timbre, ET or otherwise, would necessarily sound
best in the timbre from which it is constructed...

Isn't that somewhat a subjective judgement?? It seems a somewhat
central notion to Sethares idea...

___________ _________ __________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Still, I can't quite understand the reasoning that a scale built of
> the intervals of a timbre, ET or otherwise, would necessarily sound
> best in the timbre from which it is constructed...

I don't know what Sethares had in mind, but my reasoning in thinking
that timbres built up from scales might be interesting had to do with
critical bands; if we adjust overtones to follow the 12-et, for
instance, the overtones can never be closer than a semitone. Since
the critical band harshness peaks somewhere around a quarter-tone,
that should have a definite effect when such tones are played
together. The point is not that the scale sounds better, but that the
harmonies should sound smoother.

I'm glad to see you back in action; I hope when you are up to it
you'll take a look at the miracle stuff I recently posted.

--- In tuning@y..., jpehrson@r... wrote:

> Hello Paul, and others...
>
> I'm going to *try* to continue this discussion we were having
> September 11...
>
> There is no quote, per se, from Sethares regarding
> anything "stratospheric..."
>
> I guess my confusion was the fact that, somehow, I wasn't thinking
> of "overtones" as within a range one would use to create a scale...
> but thinking about this some more, I realize they frequently are...

It's not the overtones themselves, but the relationships between
them. I think you may need to go back to Helmholtz . . .
>
> Still, I can't quite understand the reasoning that a scale built of
> the intervals of a timbre, ET or otherwise, would necessarily sound
> best in the timbre from which it is constructed...

It sounds "special" (but not necessarily _most_ "special") in such a
timbre because you very frequently get _coinciding pairs of
partials_. But the partials coincide even more strikingly if you use
a scale which is an "upside-down" or "utonal" version of the timbre.
Because then there will be a _common frequency_ such that _every
note_ in the scale will have a partial at this frequency. I'm not
sure if Sethares emphasizes such an "upside-down" construction, but
it would seem to be quite consistent with his philosophy.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., jpehrson@r... wrote:
>
> > Still, I can't quite understand the reasoning that a scale built
of
> > the intervals of a timbre, ET or otherwise, would necessarily
sound
> > best in the timbre from which it is constructed...
>
> I don't know what Sethares had in mind, but my reasoning in
thinking
> that timbres built up from scales might be interesting had to do
with
> critical bands; if we adjust overtones to follow the 12-et, for
> instance, the overtones can never be closer than a semitone.

This is in fact what's done in the Hammond organ . . . the "partial"
stops produce 12-tET frequencies, rather than true harmonic overtones.

> Since
> the critical band harshness peaks somewhere around a quarter-tone,
> that should have a definite effect when such tones are played
> together. The point is not that the scale sounds better, but that
the
> harmonies should sound smoother.

Love those Hammond organ harmonies!

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_28015.html#28326

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Still, I can't quite understand the reasoning that a scale built
of
> > the intervals of a timbre, ET or otherwise, would necessarily
sound
> > best in the timbre from which it is constructed...
>
> I don't know what Sethares had in mind, but my reasoning in
thinking
> that timbres built up from scales might be interesting had to do
with
> critical bands; if we adjust overtones to follow the 12-et, for
> instance, the overtones can never be closer than a semitone. Since
> the critical band harshness peaks somewhere around a quarter-tone,
> that should have a definite effect when such tones are played
> together. The point is not that the scale sounds better, but that
the
> harmonies should sound smoother.
>
> I'm glad to see you back in action; I hope when you are up to it
> you'll take a look at the miracle stuff I recently posted.

Thanks, Gene for your nice message. Yes, this is a gradual
process... I can still see the smoldering from my window...

_______ _______ __________
Joseph Pehrson

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28015.html#28331

>
> It sounds "special" (but not necessarily _most_ "special") in such
a timbre because you very frequently get _coinciding pairs of
> partials_. But the partials coincide even more strikingly if you
use a scale which is an "upside-down" or "utonal" version of the
timbre. Because then there will be a _common frequency_ such that
_every note_ in the scale will have a partial at this frequency. I'm
not sure if Sethares emphasizes such an "upside-down" construction,
but it would seem to be quite consistent with his philosophy.

Hi Paul...

I'm not "getting" this... Is there any way you could illustrate it,
say, with a simple harmonic timbre??

_______ _______ _______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_28015.html#28331
>
> >
> > It sounds "special" (but not necessarily _most_ "special") in
such
> a timbre because you very frequently get _coinciding pairs of
> > partials_. But the partials coincide even more strikingly if you
> use a scale which is an "upside-down" or "utonal" version of the
> timbre. Because then there will be a _common frequency_ such that
> _every note_ in the scale will have a partial at this frequency.
I'm
> not sure if Sethares emphasizes such an "upside-down" construction,
> but it would seem to be quite consistent with his philosophy.
>
> Hi Paul...
>
> I'm not "getting" this... Is there any way you could illustrate
it,
> say, with a simple harmonic timbre??

Sure . . .

Let's say your common overtone was a high C. Let that be the highest
note in your scale. We'll construct the scale downwards from there.

The next note will be C an octave below that. Its second partial is
the high C.

The next note will be F a fifth below that C. Its third partial is
the high C.

The next note will be a C a fourth below the F. Its fourth partial is
the high C.

The next note will be an Ab a major third below that C. Its fifth
partial is the high C.

The next note will be an F a minor third below the Ab. Its sixth
partial is the high C.

And so on.

Now anytime you play two notes together, they will have a common
partial. But this is true of a "right-side up", otonal scale as well.

However, this utonal scale has the additional property that anytime
you play three, or four, or five . . . notes together, they will
_all_ have a common partial (the high C). So in a sense, the utonal
scale reflects the Helmholtz/Plomp/Sethares philosophy (that of
matching partials) even more strongly.

Did I address your confusion, or not really?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28015.html#28536

> Now anytime you play two notes together, they will have a common
> partial. But this is true of a "right-side up", otonal scale as
well.
>
> However, this utonal scale has the additional property that anytime
> you play three, or four, or five . . . notes together, they will
> _all_ have a common partial (the high C). So in a sense, the utonal
> scale reflects the Helmholtz/Plomp/Sethares philosophy (that of
> matching partials) even more strongly.
>
> Did I address your confusion, or not really?

Oh... sure... thanks. The so-called "guide tone" becomes a
prominent "shared" partial...

However, didn't you say at one time that the ear would try to
controvert this, and try to make regular "right-side up" harmonic
series using each of the scale notes as a fundamental??

??

_________ _________ ________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
>
> Oh... sure... thanks. The so-called "guide tone" becomes a
> prominent "shared" partial...
>
> However, didn't you say at one time that the ear would try to
> controvert this, and try to make regular "right-side up" harmonic
> series using each of the scale notes as a fundamental??

Well, sometimes, perhaps . . . that just goes to show how limited the
Sethares view of harmony is.