Yahoo Tuning Groups Ultimate Backup tuning Michael Harrison tuning

Well, Michael Harrison's piece _Revelation_ as played on last night's
AFMM concert by Josh Pierce was a great success. Although, I'm on
the board of the AFMM, I really don't get paid to always say
this... :) Really it was spellbinding. Although the piece was 70
minutes long, it didn't seem long at all, and when I saw that the big
score on the piano was nearing the end, I felt disappointed, rather
than elated, as I usually do with long scores.

However, whether the piece can tolerate the "full" version rather
than this "abbreviated" one is anybody's guess. My feeling is that
it was *exactly* the right length last night, and left people wanting
more which, personally I believe should be one of the main objectives
of any composition...

Anyway, I had a question about Michael Harrison's tuning, and Michael
couldn't really seem to entirely answer it himself, so I turn again
to the Tuning List.

Harrison likes pure Pythagorean fifths, and his tuning is built up
from these, starting with a 1:1 on F, ergo:

F- 3:2 - C - 3:2 - G - 3:2 - D - 3:2 - A - 3:2 - E - 3:2 - B

Now he creates *another* string of just 702 cent fifths starting on
Eb. The relationship of this Eb to the 1:1 F is a just 7:4...

Then he goes on from that in just fifths on the "black keys":

Eb - Bb - F# (actually, in this system Bb to F# is a pure 3:2) - C#
and G#.

C to Bb is also 7:4, G to F# is 7:4, D to C# is 7:4 and A to G# is 7:4

Now my question is this:

Isn't this related in some way to the "schismatic" tunings we have
discussed from time to time on this list? Don't those tunings
consist of strings of pure fifths superimposed on one another?

As I recall, the schismatic tuning had two such perfect, just fifth
strings, and I believe they were transposed by a just 5:4, although
my memory may be failing me... (and I know that Paul's won't... :)

ALSO,

Harrison only uses a 12-note tuning, with every octave the same.
This makes notation a breeze, and the pianist just, well, plays... :)

But, this does limit a just intonation system rather severely, yes,
with every octave having the same pitches??

Could somebody fill me in a bit. That *has* to make a significant
drawback as far as a "pure" just intonation system is concerned.

Or am I offbase on that? Regardless, it really is a practical way to
go. I can't imagine a system with more than 12 notes on a
conventional piano like this. It seems one would need a specially
designed instrument... (and a specially-designed *pianist* :)

Thanks!

Joseph P.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> Harrison likes pure Pythagorean fifths, and his tuning is built up
> from these, starting with a 1:1 on F, ergo:
>
> F- 3:2 - C - 3:2 - G - 3:2 - D - 3:2 - A - 3:2 - E - 3:2 - B
>
> Now he creates *another* string of just 702 cent fifths starting on
> Eb. The relationship of this Eb to the 1:1 F is a just 7:4...
>
> Then he goes on from that in just fifths on the "black keys":
>
> Eb - Bb - F# (actually, in this system Bb to F# is a pure 3:2) - C#
> and G#.
>
> C to Bb is also 7:4, G to F# is 7:4, D to C# is 7:4 and A to G# is
7:4
>
> Now my question is this:
>
> Isn't this related in some way to the "schismatic" tunings we have
> discussed from time to time on this list? Don't those tunings
> consist of strings of pure fifths superimposed on one another?
>
> As I recall, the schismatic tuning had two such perfect, just fifth
> strings, and I believe they were transposed by a just 5:4, although
> my memory may be failing me... (and I know that Paul's won't... :)

schismatic or schismic tunings (really the same things, despite
different dictionary entries) consist of a *single* chain of fifths,
and the consonant "major thirds" are actually diminished fourths,
constructed from eight fifths down instead of four fifths up. in just
intonation (that is to say, pythagorean tuning, since it's only a
chain of fifths), these "major thirds" are only 2 cents, or a schisma
(thus the name) different from a just 5:4. if you flatten the fifths
by a quarter of a cent each, this 5:4 becomes just. there is no
superposition of more than one string of fifths in such tunings.

> But, this does limit a just intonation system rather severely, yes,
> with every octave having the same pitches??
>
> Could somebody fill me in a bit. That *has* to make a significant
> drawback as far as a "pure" just intonation system is concerned.

well, of course . . . but every time you choose different pitches for
different octaves, you're sacrificing some consonant octave
relationships, and probably others, to obtain the differences you
want.

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43510.html#43512

> schismatic or schismic tunings (really the same things, despite
> different dictionary entries) consist of a *single* chain of
fifths,

***Thanks, Paul. I remember this now... So really there isn't much
similarity except for the fact that superimposed chains of fifths are
being considered. (One chain in the case of schmatic and,
apparently, *two* for Harrison...)

> well, of course . . . but every time you choose different pitches
for different octaves, you're sacrificing some consonant octave
> relationships, and probably others, to obtain the differences you
> want.

***Got it. And it also makes the execution of this much more
difficult, I believe...

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_43510.html#43512
>
> > schismatic or schismic tunings (really the same things, despite
> > different dictionary entries) consist of a *single* chain of
> fifths,
>
> ***Thanks, Paul. I remember this now... So really there isn't much
> similarity except for the fact that superimposed chains of fifths
are
> being considered. (One chain in the case of schmatic and,
> apparently, *two* for Harrison...)

"superimposed" implies that one thing is laid over another . . . but
really, there is only one of these "things" in schismic or
pythagorean, right?

>
> > well, of course . . . but every time you choose different pitches
> for different octaves, you're sacrificing some consonant octave
> > relationships, and probably others, to obtain the differences you
> > want.
>
> ***Got it. And it also makes the execution of this much more
> difficult, I believe...
>
> JP

i don't think performing ben johnston's sonata for microtonal piano
would be any easier if all the octaves were in tune -- in the
prescribed tuning, the 88 keys form 81 different pitch-classes -- but
since you're just reading a score, what diffference does it make?

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

>Isn't this related in some way to the "schismatic" tunings we have
>discussed from time to time on this list?

It depends on what approximations, if any, Harrison uses in the
piece. If he doesn't use any, it's just JI, related to any tuning
with good 3:2s and 7:4s.

>Don't those tunings consist of strings of pure fifths superimposed
>on one another?

If you're asking about the schismic linear temperament, then no,
since linear temperaments consist of only a single chain of
something. In the case of schismic, that something is a near-3:2.

>But, this does limit a just intonation system rather severely, yes,
>with every octave having the same pitches??

You heard the music. Did it sound limited to you?

>Could somebody fill me in a bit. That *has* to make a significant
>drawback as far as a "pure" just intonation system is concerned.

I don't believe in a tuning in which beautiful music can't be made.

The question of how much can one pack into 12-tones has been deeply
investigated on this and the tuning-math list.

>Or am I offbase on that? Regardless, it really is a practical way to
>go. I can't imagine a system with more than 12 notes on a
>conventional piano like this. It seems one would need a specially
>designed instrument... (and a specially-designed *pianist* :)

The pianist could still just play from notation. The distance of the
octave has nothing to do with that, as long as you don't score
something that's impossible to reach. You're right though that more
than 12 notes/oct can't be done on a conventional acoustic piano.

-Carl

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Did you listen to my octave-flattening example? I found it astonishing
> how much less harsh it sounded than 12-et, and I wonder why it's gotten
> no attention over the centuries. It combines good features from both
> meantone and 12-equal, plus it uses the dominant seventh approximation
> for the seventh partial. As a system of well-tempering for dummies, it
> seems to be remarkably successful.

I was surprised at how much octave flattening one can get away with.
The above example flattens by 9 cents; in comparison, the Riemann Zeta
tuning I proposed some time ago flattens by a mere 2.314 cents. Anyway
it seems clear that all of the people who want to sharpen octaves to
brighten things up are indeed headed in the wrong direction if we are
talking about common practice music.

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43510.html#43515

<>
> "superimposed" implies that one thing is laid over another . . .
but really, there is only one of these "things" in schismic or
> pythagorean, right?
>

***Hi Paul,

Yes, I suppose that's true. It's really only "transposition"
not "super-imposition." The latter would really only apply to the
Harrison example and similar...

> i don't think performing ben johnston's sonata for microtonal piano
> would be any easier if all the octaves were in tune -- in the
> prescribed tuning, the 88 keys form 81 different pitch-classes --
but since you're just reading a score, what diffference does it make?

***Well, I suppose such a "template" score would work, and I'm sure
the results would be a "purer" form of Just Intonation. However,
pianists are *still* accustomed to octave equivalence, so I'm
assuming having such would make the performance/learning curve easier
still...

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Why say you this? Exist there no temperaments found in 12-et
that
> >> might benefit by a sharpened 2?
> >
> >For 7-limit, at least, it appears 12-et wants to have flattened
> >octaves.

> Awesome! Flat it is!
>
> -Carl

carl, is this reaction of yours based on how the compressed tuning
actually sounded? i have yet to hear it, but i'd have reservations
about making such a rapid conclusion. while fifths and then thirds
have been significantly tempered in western musical history, octaves
have not. when a harmonic timbre evokes a clear pitch, the phenomenon
of octave equivalence dictates that a pitch 1191 cents away would
sound very subtly, yet noticeably, different. this means that the
system loses its capacity for literal octave transposition. and that
means quite different musical logic than what you find in western
musical compositions (just theorizing).

🔗Carl Lumma <ekin@lumma.org>

>>>For 7-limit, at least, it appears 12-et wants to have flattened
>>>octaves.
>
>> Awesome! Flat it is!
>>
>> -Carl
>
>carl, is this reaction of yours based on how the compressed tuning
>actually sounded? i have yet to hear it, but i'd have reservations
>about making such a rapid conclusion. while fifths and then thirds
>have been significantly tempered in western musical history, octaves
>have not. when a harmonic timbre evokes a clear pitch, the phenomenon
>of octave equivalence dictates that a pitch 1191 cents away would
>sound very subtly, yet noticeably, different. this means that the
>system loses its capacity for literal octave transposition. and that
>means quite different musical logic than what you find in western
>musical compositions (just theorizing).

The octave is stretched in Western music. Gene just said that this
is not the way to better approximations in common-practice harmony.

Truth be told, tempered octaves hurts my brain. I have a hard time
even imagining the pitch set... Aiyeyeye.

The demo sounded smoother, though melodically warped, as I reported
on tuning-math. What happened to your sound? You used to listen
to demos all the time. And it's the weekend.

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> The octave is stretched in Western music.
> >
> >sort of. it's stretched most on pianos,
>
> That's also the same place the thirds and fifths
> are tempered.

the same place? you mean the piano? i don't see many instruments
designed to play G# differently from Ab these days . . .

> >you would expect that overtones can have only so much
> >power to rein it back down to 1200.
>
> ?

harmonic complex tones will still show a slight residual bias toward
stretching.

i listened to gene's examples and they don't make much of a case. the
music is far more 5-limit than 7-limit. gene, what is the optimal
stretching for 5-limit? also, i don't see why linear temperaments
come into this at all, you're just compressing or stretching an equal
temperament by a constant factor, right gene? in the examples, which
both sound very un-bachlike, the roughness seems about the same, the
minor thirds, minor sixths, fourths, fifths, and octaves being
rougher in the compressed-octaves example (while only major sixths
and maybe major thirds are noticeably smoother). the bass sounds
sharp in the latter example, but not beyond what you'd hear on a
beatles (love me do) or jimi hendrix (machine gun) recording . . .

🔗Carl Lumma <ekin@lumma.org>

>> That's also the same place the thirds and fifths
>> are tempered.
>
>the same place? you mean the piano? i don't see many
>instruments designed to play G# differently from Ab
>these days . . .

Wha? You said Western music tempers 3rds and 5ths but
not 8ths. I said that isn't true.

>>>you would expect that overtones can have only so much
>>>power to rein it back down to 1200.
>>
>> ?
>
>harmonic complex tones will still show a slight residual
>bias toward stretching.

I would guess that the stretching result is completely
overwhelmed once the virtual pitch thing gets into the
game. Do you have any references?

>also, i don't see why linear temperaments come into this
>at all, you're just compressing or stretching an equal
>temperament by a constant factor, right gene?

I assumed Gene was finding the optimal generators for
linear temperaments compatible with common-practice
music. That is, 'including the 2s', as we discussed
a while back.

>in the examples, which both sound very un-bachlike,

The 12-tET version sounds un-bachlike?

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> That's also the same place the thirds and fifths
> >> are tempered.
> >
> >the same place? you mean the piano? i don't see many
> >instruments designed to play G# differently from Ab
> >these days . . .
>
> Wha? You said Western music tempers 3rds and 5ths but
> not 8ths. I said that isn't true.

by "the same place", did you mean the piano or not?

> >>>you would expect that overtones can have only so much
> >>>power to rein it back down to 1200.
> >>
> >> ?
> >
> >harmonic complex tones will still show a slight residual
> >bias toward stretching.
>
> I would guess that the stretching result is completely
> overwhelmed once the virtual pitch thing gets into the
> game.

when is it not in the game?

> Do you have any references?

i no longer have that hall acoustics book, but there were good
references in there.

> >also, i don't see why linear temperaments come into this
> >at all, you're just compressing or stretching an equal
> >temperament by a constant factor, right gene?
>
> I assumed Gene was finding the optimal generators for
> linear temperaments compatible with common-practice
> music. That is, 'including the 2s', as we discussed
> a while back.

right, but in this sound example it's a simple stretching or
compression of equal temperament.

> >in the examples, which both sound very un-bachlike,
>
> The 12-tET version sounds un-bachlike?

yes.

🔗Carl Lumma <ekin@lumma.org>

>>>the same place? you mean the piano? i don't see many
>>>instruments designed to play G# differently from Ab
>>>these days . . .
>>
>> Wha? You said Western music tempers 3rds and 5ths but
>> not 8ths. I said that isn't true.
>
>by "the same place", did you mean the piano or not?

I did.

>>>harmonic complex tones will still show a slight residual
>>>bias toward stretching.
>>
>> I would guess that the stretching result is completely
>> overwhelmed once the virtual pitch thing gets into the
>> game.
>
>when is it not in the game?

Good question. It depends on what's causing the stretch in
the first place. I've never read a convincing explanation
of the stretch result. Martin's gloss is actually the best
thing I've heard to date. :(

One answer is to see the vf process as iterative, taking a
list of (stretched) sine tones from some earlier process and
grouping them into a *nest* of 'pitches'. Stretch could be
factored out between branches of the nest but not within a
branch. That would allow stretch between two sine tones but
not between two complex tones.

>> Do you have any references?
>
>i no longer have that hall acoustics book, but there were
>good references in there.

I'll bump it up a position on my 'to get' list.

>> I assumed Gene was finding the optimal generators for
>> linear temperaments compatible with common-practice
>> music. That is, 'including the 2s', as we discussed
>> a while back.
>
>right, but in this sound example it's a simple stretching or
>compression of equal temperament.

Isn't this, in this example, also equivalent to the optimal
generators for 'dominant 7ths'?

>>>in the examples, which both sound very un-bachlike,
>>
>>The 12-tET version sounds un-bachlike?
>
>yes.

You mean you don't believe the music is typical of Bach?
It's very typical of his cantatas ("surely, an opera-comedy!"),
which make up a sizeable portion of his output. There's
certainly nothing un-common-practicelike about them.

>the roughness seems about the same, the minor thirds, minor
>sixths, fourths, fifths, and octaves being rougher in the
>compressed-octaves example (while only major sixths and maybe
>major thirds are noticeably smoother)

Gene, what's the RMS on these?

For those of you following along at home, we're talking about
the magni*.mid files at...

/tuning-math/files/Gene/

-Carl

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> i listened to gene's examples and they don't make much of a case. the
> music is far more 5-limit than 7-limit. gene, what is the optimal
> stretching for 5-limit?

I wasn't trying to compute optimal flattenings, though I think now I
will, since it seems clear to me, at least, that this is a good idea.
In the 5-limit, the canonical map is just 1/4-comma meantone;
therefore, with pure octaves.

also, i don't see why linear temperaments
> come into this at all, you're just compressing or stretching an equal
> temperament by a constant factor, right gene?

The octave flattening was suggested by the dominant seventh
temperament, and Carl asked about other temperaments. It doesn't seem
there is any percentage in sharpening the octave in 12-et; this is
connected to the "tendency" business I talked about long ago, actually.

in the examples, which
> both sound very un-bachlike, the roughness seems about the same, the
> minor thirds, minor sixths, fourths, fifths, and octaves being
> rougher in the compressed-octaves example (while only major sixths
> and maybe major thirds are noticeably smoother). the bass sounds
> sharp in the latter example, but not beyond what you'd hear on a
> beatles (love me do) or jimi hendrix (machine gun) recording . . .

I think your midi file player is not rendering the example much like
Timidity would. To my ears, the flat example was *much* less rough. I
was surprised by how well 9 cents flat seems to work, but of course a
lot less flat (such as the zeta funcion 2.3 cent flat octave) would
also make sense. Really wild and crazy people could flatten an octave
on a circulating temperament other than equal, come to that; the
octave flattening business would seem to be complimentary to this.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > I assumed Gene was finding the optimal generators for
> > linear temperaments compatible with common-practice
> > music. That is, 'including the 2s', as we discussed
> > a while back.
>
> I wasn't, actually. However, I think I will now do this.

For the dominant seventh temperament, the results are disconcertingly
varied:

even 7-limit minimax [1190.496, 493.917]
(This is the canonical map.)

even 7-limit rms [1192.064, 494.731]

even 8-limit rms [1194.349, 496.068]

even 8-limit minimax [1200, 497.085]

Here's the same calculation for septimal miracle:

even 7-limit minimax [1200, 116.588]

even 8-limit minimax [1200, 116.588]

even 7-limit rms [1200.859, 116.701]

even 8-limit rms [1200.526, 116.650]

canonical map [1201.263, 116.782]

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >by "the same place", did you mean the piano or not?
>
> I did.

i was just pointing out that the piano is not the only place that
temperament happens. even adaptive ji, rarely acheived, is a form of
temperament.

> >when is it not in the game?
>
> Good question. It depends on what's causing the stretch in
> the first place. I've never read a convincing explanation
> of the stretch result. Martin's gloss is actually the best
> thing I've heard to date. :(

you're telling me that's more convincing to you than terhardt's
explanation? :( indeed.

> One answer is to see the vf process as iterative, taking a
> list of (stretched) sine tones from some earlier process and
> grouping them into a *nest* of 'pitches'. Stretch could be
> factored out between branches of the nest but not within a
> branch. That would allow stretch between two sine tones but
> not between two complex tones.

what overall audition model are you invoking?

> >> I assumed Gene was finding the optimal generators for
> >> linear temperaments compatible with common-practice
> >> music. That is, 'including the 2s', as we discussed
> >> a while back.
> >
> >right, but in this sound example it's a simple stretching or
> >compression of equal temperament.
>
> Isn't this, in this example, also equivalent to the optimal
> generators for 'dominant 7ths'?

no, the likelihood that those would form a closed system is probably
nil.

> >>>in the examples, which both sound very un-bachlike,
> >>
> >>The 12-tET version sounds un-bachlike?
> >
> >yes.
>
> You mean you don't believe the music is typical of Bach?

somehow the arrangement and/or scoring kills the music for me.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
> > > I assumed Gene was finding the optimal generators for
> > > linear temperaments compatible with common-practice
> > > music. That is, 'including the 2s', as we discussed
> > > a while back.
> >
> > I wasn't, actually. However, I think I will now do this.
>
> For the dominant seventh temperament, the results are
disconcertingly
> varied:
>
> even 7-limit minimax [1190.496, 493.917]
> (This is the canonical map.)
>
> even 7-limit rms [1192.064, 494.731]
>
> even 8-limit rms [1194.349, 496.068]
>
> even 8-limit minimax [1200, 497.085]
>
>
> Here's the same calculation for septimal miracle:
>
> even 7-limit minimax [1200, 116.588]
>
> even 8-limit minimax [1200, 116.588]
>
> even 7-limit rms [1200.859, 116.701]
>
> even 8-limit rms [1200.526, 116.650]
>
> canonical map [1201.263, 116.782]

gene, i was going to say this before, and now would be a perfect
opportunity: clearly you mean *integer* limit, rather than either or
the usual senses (odd- or prime-limit), but referred to here:

http://sonic-arts.org/dict/consiste.htm

would you please be clear and say 7-integer-limit or 8-integer-limit
in the future?

and why wouldn't you accept a viewpoint (such as my own) that bach is
essentially 5-odd-limit (including minor sixths as consonant but no
consonant tritones), not 7-odd-limit of 7-integer-limit or 8-integer-
limit?

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> gene, i was going to say this before, and now would be a perfect
> opportunity: clearly you mean *integer* limit, rather than either or
> the usual senses (odd- or prime-limit), but referred to here:

That's why I said "even 7-limit", not "7-limit". I didn't know there
was a term already available.

> and why wouldn't you accept a viewpoint (such as my own) that bach is
> essentially 5-odd-limit (including minor sixths as consonant but no
> consonant tritones), not 7-odd-limit of 7-integer-limit or 8-integer-
> limit?

I can't recall making such a comment about Bach. If you recall, I
tried to do Brahms but it didn't work. What would you regard as a good
7-limit test piece?

🔗Carl Lumma <ekin@lumma.org>

>>>by "the same place", did you mean the piano or not?
>>
>>I did.
>
>i was just pointing out that the piano is not the only place
>that temperament happens.

Where else does it happen? If we take standard notation to be
specifying pitches, then we could say the notation is an act
of temperament. But I'm not sure such a take is warranted.
Nobody really knows what instruments play. Keyboard and fretted
string instruments are really the only place in music we can
point and say with absolute certainty, "here is temperament",
and of what kind is it.

>even adaptive ji, rarely acheived, is a form of temperament.

How so? JdL's brand is, but that's "adaptive tuning" not
"adaptive JI".

>> Good question. It depends on what's causing the stretch in
>> the first place. I've never read a convincing explanation
>> of the stretch result. Martin's gloss is actually the best
>> thing I've heard to date. :(
>
>you're telling me that's more convincing to you than terhardt's
>explanation? :( indeed.

Maybe I haven't understood Terhardt's explanation. Can you sum
it up in two sentences? What about Martin's objection to it?

>> One answer is to see the vf process as iterative, taking a
>> list of (stretched) sine tones from some earlier process and
>> grouping them into a *nest* of 'pitches'. Stretch could be
>> factored out between branches of the nest but not within a
>> branch. That would allow stretch between two sine tones but
>> not between two complex tones.
>
>what overall audition model are you invoking?

? You mean psychoacoustic model? Care to coin a name? Both
neuroscience and musical experience appear to be far ahead of
existing psychoacoustic models.

Any such model must allow listeners to have subjective access
to both raw spectral stuff and to rootedness/vf sensations, as
they appear to have. I'm suggesting that stretch applies only
when comparing pitches from the former, not the latter.

>> Isn't this, in this example, also equivalent to the optimal
>> generators for 'dominant 7ths'?
>
>no, the likelihood that those would form a closed system is
>probably nil.

>>>>>in the examples, which both sound very un-bachlike,
>>>>
>>>>The 12-tET version sounds un-bachlike?
>>>
>>>yes.
>>
>> You mean you don't believe the music is typical of Bach?
>
>somehow the arrangement and/or scoring kills the music for me.

This sort of circus music is very typical, and for me enjoyable,
Bach. Typically three-voice, foot-stopping bass, woodwinds.

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

well, as long as your bach sequences use a simple
stretching/compression of 12-equal, and not a linear (meaning 2D)
temperament, let's look at the 12-equal results (which i'm sure i've
posted before, perhaps more correctly). least squares is meant:

optimal octave for 12-equal based on 3-integer-limit: 1201.10 cents
optimal octave for 12-equal based on 4-integer-limit: 1200.38 cents
optimal octave for 12-equal based on 5-integer-limit: 1196.27 cents
optimal octave for 12-equal based on 6-integer-limit: 1198.18 cents
optimal octave for 12-equal based on 7-integer-limit: 1193.25 cents
optimal octave for 12-equal based on 8-integer-limit: 1195.37 cents
optimal octave for 12-equal based on 9-integer-limit: 1197.27 cents
optimal octave for 12-equal based on 10-integer-limit: 1196.58 cents
optimal octave for ~12-equal based on 11-integer-limit: 1191.11 cents
(nothing in the vicinity is consistent for 12-integer-limit or higher)

a problem for 7-integer-limit and higher is that some intervals need
to represent two different ratios (such as the minor third with 6:5
and 7:6). optimizing for both may be a good idea for music with a
thicker texture, but for those bach examples the stark minor thirds
suffer from such a compromise.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>>by "the same place", did you mean the piano or not?
> >>
> >>I did.
> >
> >i was just pointing out that the piano is not the only place
> >that temperament happens.
>
> Where else does it happen?

try the guitar, for one example.

> Nobody really knows what instruments play.

the guitar plays. i can do it myself :)

> >even adaptive ji, rarely acheived, is a form of temperament.
>
> How so?

because the melodic intervals must be tempered relative to any ideal
just values.

> >you're telling me that's more convincing to you than terhardt's
> >explanation? :( indeed.
>
> Maybe I haven't understood Terhardt's explanation. Can you sum
> it up in two sentences?

simultaneous pitches push each other apart (that is, they appear
further apart than when presented successively); we're conditioned to
hearing sounds with rich harmonic series, in which the partials push
one another apart; thus we expect the pushed-apart octave, fifth,
twelfth . . . intervals even when we hear successive tones.

> What about Martin's objection to it?

let's just say that i have more respect for the authority of every
single member of *this* list.

> >> One answer is to see the vf process as iterative, taking a
> >> list of (stretched) sine tones from some earlier process and
> >> grouping them into a *nest* of 'pitches'. Stretch could be
> >> factored out between branches of the nest but not within a
> >> branch. That would allow stretch between two sine tones but
> >> not between two complex tones.
> >
> >what overall audition model are you invoking?
>
> ? You mean psychoacoustic model? Care to coin a name? Both
> neuroscience and musical experience appear to be far ahead of
> existing psychoacoustic models.

this sounds like apples and oranges to me, but when you're talking
about branches of a nest, it sure sounds more like ornithology than
musical experience. my question stands -- don't change the subject!

> Any such model must allow listeners to have subjective access
> to both raw spectral stuff and to rootedness/vf sensations, as
> they appear to have. I'm suggesting that stretch applies only
> when comparing pitches from the former, not the latter.

there is no sharp boundary between the two. at what level of
distortion do synthesized sine waves jump from one domain to the
other?

> >> Isn't this, in this example, also equivalent to the optimal
> >> generators for 'dominant 7ths'?
> >
> >no, the likelihood that those would form a closed system is
> >probably nil.
>
> ?

they form an infinite system.

> >>>>>in the examples, which both sound very un-bachlike,
> >>>>
> >>>>The 12-tET version sounds un-bachlike?
> >>>
> >>>yes.
> >>
> >> You mean you don't believe the music is typical of Bach?
> >
> >somehow the arrangement and/or scoring kills the music for me.
>
> This sort of circus music is very typical, and for me enjoyable,
> Bach. Typically three-voice, foot-stopping bass, woodwinds.

maybe i'll try listening again here at work. last night was on ara's
computer, which *should* have an excellent sound card . . .

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Carl Lumma <ekin@lumma.org>

>> Where else does it happen?
>
>try the guitar, for one example.

I said "fretted string[s]"...

>> Nobody really knows what instruments play.
>
>the guitar plays. i can do it myself :)

I was referring to instruments other than the
ones I mentioned as exceptions.

>>>even adaptive ji, rarely acheived, is a form of temperament.
>>
>> How so?
>
>because the melodic intervals must be tempered relative to any
>ideal just values.

I suppose JI does have a melodic aspect.

>>>you're telling me that's more convincing to you than terhardt's
>>>explanation? :( indeed.
>>
>>Maybe I haven't understood Terhardt's explanation. Can you sum
>>it up in two sentences?
>
>simultaneous pitches push each other apart (that is, they appear
>further apart than when presented successively); we're conditioned to
>hearing sounds with rich harmonic series, in which the partials push
>one another apart;

How do partials in a harmonic series 'push eachother apart'?

>> >what overall audition model are you invoking?
>>
>> ? You mean psychoacoustic model? Care to coin a name? Both
>> neuroscience and musical experience appear to be far ahead of
>> existing psychoacoustic models.
>
>this sounds like apples and oranges to me, but when you're talking
>about branches of a nest, it sure sounds more like ornithology than
>musical experience. my question stands -- don't change the subject!

How was I changing the subject? I was asking what an "audition
model is", and providing an answer in advance in case it meant
"psychoacoustic model".

>> Any such model must allow listeners to have subjective access
>> to both raw spectral stuff and to rootedness/vf sensations, as
>> they appear to have. I'm suggesting that stretch applies only
>> when comparing pitches from the former, not the latter.
>
>there is no sharp boundary between the two. at what level of
>distortion do synthesized sine waves jump from one domain to the
>other?

Both domains are always active. Regardless of how the wave is
represented in your synth, the ear will perform spectral analysis.
The difference is ontological. In the pure-tone experiment, the
experimenter measures an interval between pure tones. In the
complex tone variation, he measures an interval between the roots
of tones. As we know, it's very hard to deliver pure sines to the
cochlea, anyway. If distortion is slowly added, we should find
the stretch slowly goes to zero.

>>>>Isn't this, in this example, also equivalent to the optimal
>>>>generators for 'dominant 7ths'?
>>>
>>>no, the likelihood that those would form a closed system is
>>>probably nil.
>>
>> ?
>
>they form an infinite system.

What else would you expect from a linear temperament?

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >simultaneous pitches push each other apart (that is, they appear
> >further apart than when presented successively); we're conditioned
to
> >hearing sounds with rich harmonic series, in which the partials
push
> >one another apart;
>
> How do partials in a harmonic series 'push eachother apart'?

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

> >> >what overall audition model are you invoking?
> >>
> >> ? You mean psychoacoustic model? Care to coin a name? Both
> >> neuroscience and musical experience appear to be far ahead of
> >> existing psychoacoustic models.
> >
> >this sounds like apples and oranges to me, but when you're talking
> >about branches of a nest, it sure sounds more like ornithology
than
> >musical experience. my question stands -- don't change the subject!
>
> How was I changing the subject? I was asking what an "audition
> model is", and providing an answer in advance in case it meant
> "psychoacoustic model".

on what basis do you say that neuroscience and musical experience
appear to be far ahead of existing psychoacoustic models? and what
does "musical experience" have to say as an audition model?

> >> Any such model must allow listeners to have subjective access
> >> to both raw spectral stuff and to rootedness/vf sensations, as
> >> they appear to have. I'm suggesting that stretch applies only
> >> when comparing pitches from the former, not the latter.
> >
> >there is no sharp boundary between the two. at what level of
> >distortion do synthesized sine waves jump from one domain to the
> >other?
>
> Both domains are always active. Regardless of how the wave is
> represented in your synth, the ear will perform spectral analysis.
> The difference is ontological. In the pure-tone experiment, the
> experimenter measures an interval between pure tones. In the
> complex tone variation, he measures an interval between the roots
> of tones.

i'm still failing to see the "ontological" difference. there will
always be some level of distortion present, creating overtones. so
where does one domain give way to the other?

> As we know, it's very hard to deliver pure sines to the
> cochlea, anyway. If distortion is slowly added, we should find
> the stretch slowly goes to zero.

so the same should be true if you replace "distortion" with "harmonic
partials" above, right?

> >>>>Isn't this, in this example, also equivalent to the optimal
> >>>>generators for 'dominant 7ths'?
> >>>
> >>>no, the likelihood that those would form a closed system is
> >>>probably nil.
> >>
> >> ?
> >
> >they form an infinite system.
>
> What else would you expect from a linear temperament?

i thought you were implying, in the most-indented quote above, that a
simple compression of the 12-equal system was equivalent to the
system defined by the optimal generators for 'dominant 7ths'.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

>> How do partials in a harmonic series 'push eachother apart'?
>
>http://www.mmk.ei.tum.de/persons/ter/top/octstretch.html

Oh, you're referring to an experiment showing melodic pitch
stretch!? Hasn't a harmonic stretch for pure tones also
been observed?

Anyway,

"Due to that kind of pitch multiplicity, harmonic complex tones
whose oscillation frequencies are in a 1:2 ratio (or close to that)
inevitably will have a number of pitches in common - which yields
a kind of similarity. This is my explanation of octave equivalence."

Of course we now now that there are cells which specially detect
2:1 ratios, while a system that counts the number of partials two
tones have in common remains undiscovered.

"The explanation of octave stretch immediately follows from that,
i.e., by taking into account that the intervals between the pitches
of a harmonic complex tone must be expected to be stretched by pitch
shifts."

I'm lost.

"Due to this stretch of the pitch pattern, the best match of the two
pitch patterns is obtained for an oscillation-frequency ratio that,
on the average, somewhat exceeds the value 2:1 [86], [88], [93],
[104] p. 197."

??? The references given at the end link to short blurbs that don't
help.

>> How was I changing the subject? I was asking what an "audition
>> model is", and providing an answer in advance in case it meant
>> "psychoacoustic model".
>
>on what basis do you say that neuroscience and musical experience
>appear to be far ahead of existing psychoacoustic models?

Neuroscience has explained the auditory pathway to the point
where it can be modeled with a computer. Psychoacoustics failed
to do that. Typical psychoacoustic experiments do not involve
stimuli and judgements as rich as typical musical experience.

>and what does "musical experience" have to say as an audition
>model?

That depends on what an "audition model" is!

>>>>Any such model must allow listeners to have subjective access
>>>>to both raw spectral stuff and to rootedness/vf sensations, as
>>>>they appear to have. I'm suggesting that stretch applies only
>>>>when comparing pitches from the former, not the latter.
>>>
>>>there is no sharp boundary between the two. at what level of
>>>distortion do synthesized sine waves jump from one domain to the
>>>other?
>>
>>Both domains are always active. Regardless of how the wave is
>>represented in your synth, the ear will perform spectral analysis.
>>The difference is ontological. In the pure-tone experiment, the
>>experimenter measures an interval between pure tones. In the
>>complex tone variation, he measures an interval between the roots
>>of tones.
>
>i'm still failing to see the "ontological" difference. there will
>always be some level of distortion present, creating overtones. so
>where does one domain give way to the other?

I don't understand what you're asking / don't know how to make my
statement clearer.

>> As we know, it's very hard to deliver pure sines to the
>> cochlea, anyway. If distortion is slowly added, we should find
>> the stretch slowly goes to zero.
>
>so the same should be true if you replace "distortion" with
>"harmonic partials" above, right?

Yes, obviously; I was assuming you meant harmonic distortion.

>>>>>>Isn't this, in this example, also equivalent to the optimal
>>>>>>generators for 'dominant 7ths'?
>>>>>
>>>>>no, the likelihood that those would form a closed system is
>>>>>probably nil.
>>>>
>>>> ?
>>>
>>>they form an infinite system.
>>
>>What else would you expect from a linear temperament?
>
>i thought you were implying, in the most-indented quote above,
>that a simple compression of the 12-equal system was equivalent
>to the system defined by the optimal generators for
>'dominant 7ths'.

I was indeed (though we then saw from Gene's results that the
latter involves flatter 4ths when the octaves match the former).
Dominant 7ths is a linear temperament, and 12-et supports it.
You seem to be reverting to the view of ets as atomic tunings?

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> How do partials in a harmonic series 'push eachother apart'?
> >
> >http://www.mmk.ei.tum.de/persons/ter/top/octstretch.html
>
> Oh, you're referring to an experiment showing melodic pitch
> stretch!? Hasn't a harmonic stretch for pure tones also
> been observed?

observed deep within certain nutty ramblings, yes. it's just *so*
damn hard to ignore those ear-level and brain-level intermodulatory
beats which disappear always *exactly* at the 2:1.

>
> Anyway,
>
> "Due to that kind of pitch multiplicity, harmonic complex tones
> whose oscillation frequencies are in a 1:2 ratio (or close to that)
> inevitably will have a number of pitches in common - which yields
> a kind of similarity. This is my explanation of octave
equivalence."
>
> Of course we now now that there are cells which specially detect
> 2:1 ratios, while a system that counts the number of partials two
> tones have in common remains undiscovered.
>
> "The explanation of octave stretch immediately follows from that,
> i.e., by taking into account that the intervals between the pitches
> of a harmonic complex tone must be expected to be stretched by
pitch
> shifts."
>
> I'm lost.

where did you lose it? i'll help you pick up the pieces.

> "Due to this stretch of the pitch pattern, the best match of the
two
> pitch patterns is obtained for an oscillation-frequency ratio that,
> on the average, somewhat exceeds the value 2:1 [86], [88], [93],
> [104] p. 197."
>
> ??? The references given at the end link to short blurbs that
don't
> help.
>
> >> How was I changing the subject? I was asking what an "audition
> >> model is", and providing an answer in advance in case it meant
> >> "psychoacoustic model".
> >
> >on what basis do you say that neuroscience and musical experience
> >appear to be far ahead of existing psychoacoustic models?
>
> Neuroscience has explained the auditory pathway to the point
> where it can be modeled with a computer.

according to whom? where's this model and how much does it cost?

> >> As we know, it's very hard to deliver pure sines to the
> >> cochlea, anyway. If distortion is slowly added, we should find
> >> the stretch slowly goes to zero.
> >
> >so the same should be true if you replace "distortion" with
> >"harmonic partials" above, right?
>
> Yes, obviously; I was assuming you meant harmonic distortion.

so you agree with me. all i was arguing was that there is no sharp
boundary between the two types of pitch perception -- they form a
continuous whole.

> >i thought you were implying, in the most-indented quote above,
> >that a simple compression of the 12-equal system was equivalent
> >to the system defined by the optimal generators for
> >'dominant 7ths'.
>
> I was indeed (though we then saw from Gene's results that the
> latter involves flatter 4ths when the octaves match the former).

ok, another one done.

> Dominant 7ths is a linear temperament, and 12-et supports it.
> You seem to be reverting to the view of ets as atomic tunings?

what view? how reverting?

🔗Carl Lumma <ekin@lumma.org>

>> Oh, you're referring to an experiment showing melodic pitch
>> stretch!? Hasn't a harmonic stretch for pure tones also
>> been observed?
>
>observed deep within certain nutty ramblings, yes. it's just *so*
>damn hard to ignore those ear-level and brain-level intermodulatory
>beats which disappear always *exactly* at the 2:1.

I seem to remember reading a paper. Maybe I'll come across it
again...

>> intervals between the pitches of a harmonic complex tone must
>> be expected to be stretched by pitch shifts."
>>
>> I'm lost.
>
>where did you lose it? i'll help you pick up the pieces.

That quoted bit there. He's just re-stating his thesis, not
explaining anything.

>> Neuroscience has explained the auditory pathway to the point
>> where it can be modeled with a computer.
>
>according to whom? where's this model and how much does it cost?

According to me. The model is still under development, funded by
Paul Allen, among others. Lloyd Watts' thesis and work at Interval
are available, but the last few years of work are not yet public.
They do have something for sale, for very big customers. Consumer
applications are probably only several years away.

>> >> As we know, it's very hard to deliver pure sines to the
>> >> cochlea, anyway. If distortion is slowly added, we should find
>> >> the stretch slowly goes to zero.
>> >
>> >so the same should be true if you replace "distortion" with
>> >"harmonic partials" above, right?
>>
>> Yes, obviously; I was assuming you meant harmonic distortion.
>
>so you agree with me. all i was arguing was that there is no sharp
>boundary between the two types of pitch perception -- they form a
>continuous whole.

Sure. Since you were talking about melodic stretch and I was
talking about harmonic, there wasn't any disagreement.

>> Dominant 7ths is a linear temperament, and 12-et supports it.
>> You seem to be reverting to the view of ets as atomic tunings?
>
>what view? how reverting?

You said something about 2s-included dominant 7ths being not
closed, as if this were a bad thing.

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Oh, you're referring to an experiment showing melodic pitch
> >> stretch!? Hasn't a harmonic stretch for pure tones also
> >> been observed?
> >
> >observed deep within certain nutty ramblings, yes. it's just *so*
> >damn hard to ignore those ear-level and brain-level
intermodulatory
> >beats which disappear always *exactly* at the 2:1.
>
> I seem to remember reading a paper. Maybe I'll come across it
> again...
>
> >> intervals between the pitches of a harmonic complex tone must
> >> be expected to be stretched by pitch shifts."
> >>
> >> I'm lost.
> >
> >where did you lose it? i'll help you pick up the pieces.
>
> That quoted bit there. He's just re-stating his thesis, not
> explaining anything.

why don't you quote the quoted bit for reference and we'll work
through the logic. it's easier after you've read *all* his webpages.

> >> Neuroscience has explained the auditory pathway to the point
> >> where it can be modeled with a computer.
> >
> >according to whom? where's this model and how much does it cost?
>
> According to me. The model is still under development,

i guess i'll wait to see the result before putting down any money!

> >> Dominant 7ths is a linear temperament, and 12-et supports it.
> >> You seem to be reverting to the view of ets as atomic tunings?
> >
> >what view? how reverting?
>
> You said something about 2s-included dominant 7ths being not
> closed, as if this were a bad thing.

no, not a bad thing at all. but of course you're already aware of
what i *actually* meant, so no need to rehash.

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Eric W DuBarry <genital3@hotmail.com>

example of dorkyness.......

>From: Carl Lumma >Reply-To: tuning@yahoogroups.com>To: tuning@yahoogroups.com
>Subject: Re: [tuning] Re: Octave flattening>Date: Mon, 28 Apr 2003 22:52:18
-0700>> >if so, would it be your view that psychoacoustics (assuming i can get>
>you to understand the terhardt stuff) has the upper hand over> >neuroscience in
the ability to explain the octave stretch phenomenon?>>No, not necessarily. I
cited the Audience stuff as an example of a>successful application of
neuroscience, not as a complete representation>of neuroscience. But it's quite
possible there are phenomena which>psychoacoustics has the upper hand in
explaining. For now.>>-Carl>

--------------------------------------------------------------------------------

STOP MORE SPAM with the new MSN 8 [http://g.msn.com/8HMZENUS/2728] and get 2
months FREE*

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>>>the intervals between the pitches of a harmonic complex tone
must
> >>>>be expected to be stretched by pitch shifts.
> >>//
> >>>
> >>>and it's a perfectly sound conclusion from the clauses before it.
> >>
> >>I read octave stretch page again, and the page on pitch shifts,
> >>and I beg to differ.
> >
> >where's your beef?
>
> Why must they be expected to suffer pitch shifts? Why would they
> be stretched rather than contracted?
>
> -Carl

because they're merely sine waves and sine waves have been *observed*
to "push one another apart" when occuring simultaneously. see
Terhardt, E. (1974). Pitch, consonance, and harmony. J. Acoust. Soc.
Am. 55, 1061-1069 . . .

anyhow, anyone interested in the topic of musical octaves and when to
stretch (but not necessarily why) should read
http://www.mmk.ei.tum.de/persons/ter/top/scalestretch.html . . .

🔗Carl Lumma <ekin@lumma.org>

>>>>"the intervals between the pitches of a harmonic complex tone must
>>>>be expected to be stretched by pitch shifts."
>>>
>>>it's a perfectly sound conclusion from the clauses before it.
>>
>>Why must they be expected to suffer pitch shifts? Why would they be
>>stretched rather than contracted?
>
>because they're merely sine waves and sine waves have been *observed*
>to "push one another apart" when occuring simultaneously. see
>Terhardt, E. (1974). Pitch, consonance, and harmony.
>J. Acoust. Soc. Am. 55, 1061-1069 . . .

Ok, so it's not a perfectly sound conclusion of the clauses before it.
It requires an outside reference. Which I will try to get. In fact
I think you once sent me this paper, but it's in Montana.

>anyhow, anyone interested in the topic of musical octaves and when
>to stretch (but not necessarily why) should read
>http://www.mmk.ei.tum.de/persons/ter/top/scalestretch.html . . .

"The only keyboard type of instrument (i.e. with a fixed tuning) that
produces steady periodic tones is the organ (pipe or electronic)."

What about the harpsichord?

Terhardt does put his money where his mouth is, though, according to
these abstracts...

Terhardt, E. (1979).
Calculating virtual pitch.
Hear. Res. 1, 155-182.

Terhardt, E., Stoll, G., Seewann, M. (1982).
Algorithm for extraction of pitch and pitch salience...
J. Acoust. Soc. Am. 71, 679-688.

Terhardt, E., Stoll, G., Seewann, M. (1982).
Pitch of complex signals according to virtual-pitch theory...
J. Acoust. Soc. Am. 71, 671-678.

...so it only remains to get these papers and determine if the
model works as advertised.

By the way, the acid test for a complete model of hearing is unmixing.
If it can take a Phish tune in stereo and put Page, Trey, Mike and
Fish on separate tracks with some degree of accuracy and recombine
them with little or no loss, we're happy.

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >anyhow, anyone interested in the topic of musical octaves and when
> >to stretch (but not necessarily why) should read
> >http://www.mmk.ei.tum.de/persons/ter/top/scalestretch.html . . .
>
> "The only keyboard type of instrument (i.e. with a fixed tuning)
that
> produces steady periodic tones is the organ (pipe or electronic)."
>
> What about the harpsichord?

like the piano, the harpsichord's tones decay exponentially (i.e.,
are not steady), and have slightly inharmonic partials.

> By the way, the acid test for a complete model of hearing is
unmixing.
> If it can take a Phish tune in stereo and put Page, Trey, Mike and
> Fish on separate tracks with some degree of accuracy and recombine
> them with little or no loss, we're happy.

i don't think our hearing apparatus really performs this feat, but
rather gives some of us (musicians) the *illusion* of having done so.
a lot of stretch (my band, not octave stretch) fans, meanwhile have
no idea what sound is coming from what instrument, but simply love
the overall effect. speaking of which, check out this lineup:

http://www.guyholmes.com/artist.ivnu

🔗Carl Lumma <ekin@lumma.org>

>> By the way, the acid test for a complete model of hearing is
>> unmixing. If it can take a Phish tune in stereo and put Page,
>> Trey, Mike and Fish on separate tracks with some degree of
>> accuracy and recombine them with little or no loss, we're happy.
>
>i don't think our hearing apparatus really performs this feat, but
>rather gives some of us (musicians) the *illusion* of having done so.

How do you explain...

() Our ability to selectively listen to any one voice in a crowd.

() Musicians' ability to transcribe music by voice.

...?

>speaking of which, check out this lineup:
>
>http://www.guyholmes.com/artist.ivnu

You're playing in Washington?!

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> By the way, the acid test for a complete model of hearing is
> >> unmixing. If it can take a Phish tune in stereo and put Page,
> >> Trey, Mike and Fish on separate tracks with some degree of
> >> accuracy and recombine them with little or no loss, we're happy.
> >
> >i don't think our hearing apparatus really performs this feat, but
> >rather gives some of us (musicians) the *illusion* of having done
so.
>
> How do you explain...
>
> () Our ability to selectively listen to any one voice in a crowd.
>
> () Musicians' ability to transcribe music by voice.
>
> ...?

the illusion works pretty well especially if we decide in advance
what to focus on. the abilities you bring up above are ones i'm
constantly referencing in these debates on music theory and
acoustics -- they are very important clues as to what goes on in the
hearing mechanism. but, as in visual perception, the idea of a
coherent, separable presentation of the elements of our sensations in
our brains is a wonderful illusion.

> >speaking of which, check out this lineup:
> >
> >http://www.guyholmes.com/artist.ivnu
>
> You're playing in Washington?!

yup!