Re: Limit Terminology

[Paul E:]
>So perhaps you do "get it" after all?

No, I'm more confused than ever, because you began this discussion by
suggesting that I *not* use the term "7-limit" to describe a tuning
that can include 4:5:6:7:9, but now you seem to be saying I *should*:

[I wrote:]
>>Perhaps it would be simpler just to qualify using the term "prime
>>limit" as opposed to "odd limit". Though I am aware of, and largely
>>agree with, the argument that "odd limit" more accurately reflects the
>>difficulty of tuning a complex dyad to JI by ear, when it comes to the
>>actual process of assigning tunings to notes, designating a prime
>>limit makes more sense to me.

[Paul:]
>Well, if you look at my definition of "limit" in the Monzo Dictionary,
>I specifically state that the prime definition of limit is the one to
>use when describing JI tuning systems, and the odd definition is the
>one to use when describing consonance of isolated sonorities. Since
>the context of adaptively tuning pieces of music is perhaps somewhere
>between these two contexts, it's no wonder the terminology gets
>confusing . . .

Hmmm, you seem to be saying that neither term satisfies you.

[Paul:]
>As for "11/13-limit", I still think
>(a) you should just call it 13-limit.
>(b) the 4:5:6:7:9:11:13 chord might be better approximated by
>C-E-G-Bb-D-F#-A than by C-E-G-Bb-D-F#-A, since 11:13 is very close to
>3 semitones, and 7:13 is a lot closer to 11 semitones than to 10
>semitones.

You mean rather than with Ab/G# at the top. Yes, that could be done,
but the problem is that then there's no way to produce a normal A,C,E,G
chord. The answer to THAT problem is to combine additional tuning files
into the mix, which my program does already support.

And yes, I agree that just plain "13-limit" probably better describes
the output of this file, but it means that I need to split out a
separate 11-limit file, so that there isn't a gap. I'll do that if I
can find the time.

[JdL:]
>>As for my "tuning file methodology", I'm still not sure if the basic
>>process I use is clear. Can you enlighten me?

[Paul:]
>I think I understand the rough idea of the process you use, though it
>seems highly "nonlinear", if you know what I mean.

Well, tuning itself is highly "nonlinear", but I think I get what you
mean. I suppose that a more "linear" approach would, without the aid
of tuning files, look at every possible permutation of tuning from the
set of notes on. Then, of course, there'd have to be a separate
mechanism for otonal/utonal differentiation, one of the nice immediate
side benefits of the tuning file methodology. When/if chordal harmonic
entropy becomes possible in a reasonably finite amount of computing
time, there will be more options available.

[Paul:]
>. . . Do you mean enlighten you as to my ignorance?

If you want to put it that way. I don't want to cover ground again if
it's already clear, but will be glad to if it's not. I'm actually very
satisfied with the tuning file aspect of the program, since it allows
for a conscious manipulation of target tuning in a way that I think
would be difficult for a program that didn't use them. It is weak, as
we've discussed, in finding the best compromise for chain-of-fifth
chords, which I've recently patched around with a late wiring in of
non-self-consistent vertical springs.

JdL

John wrote,

>No, I'm more confused than ever, because you began this discussion by
>suggesting that I *not* use the term "7-limit" to describe a tuning
>that can include 4:5:6:7:9,

I think you misunderstood me there! I said that it's not clear given your
methodology . . .

>but now you seem to be saying I *should*:

What I was saying is that if you were _specifically_ targeting 7:9 for a
single interval, that would be 9-limit. But in your tuning file methodology,
there is no way to determine whether, in tuning C-E-G-Bb-D to 4:5:6:7:9, you
are really "targeting" 7:9, or whether 7:9 is a _resultant_ from combining
the targeting of a 6:7 with the targeting of a 2:3 (acting as 6:9). If one
were to use a different methodology, one could allow deviations in G-Bb from
6:7 to contribute to the "pain" calculation, and one could allow deviations
in G-D from 2:3 (acting as 6:9) to contribute to the "pain" calculation,
_without_ allowing deviations in Bb-D from 7:9 to contribute to the "pain"
calculation. This would be a 7-limit approach. It can actually have
different consequences than a 9-limit approach even in this case, because
the 7-limit approach wouldn't care if the errors in G-Bb and G-D were of the
same or different sign, whether they cancelled each other out or reinforced
one another in the deviation of Bb-D from 7:9; while a 9-limit approach
would of course favor the scenario in which these errors cancelled out and
the 7:9 was better tuned.

>Hmmm, you seem to be saying that neither term satisfies you.

For your "tuning file" methodology, that may be the case, but perhaps
another methodology would be applicable where the distinction would become
meaningful.

>You mean rather than with Ab/G# at the top. Yes, that could be done,
>but the problem is that then there's no way to produce a normal A,C,E,G
>chord. The answer to THAT problem is to combine additional tuning files
>into the mix, which my program does already support.

You're already using a number of tuning files in the mix, correct?

>And yes, I agree that just plain "13-limit" probably better describes
>the output of this file, but it means that I need to split out a
>separate 11-limit file, so that there isn't a gap.

I don't get it -- you're saying that people would be upset if there were a
13-limit version but not an 11-limit version? Surely you don't mean that!
If, hypothetically, you were to make a 29-limit version right now, you
wouldn't have to call it 17/19/23/29-limit just to fill in the gaps, would
you? What am I missing?

>which I've recently patched around with a late wiring in of
>non-self-consistent vertical springs.

Perhaps this idea would be the key to truly differentiating 7- and 9-limit
formulations? Does that make any sense in light of my explanation above (if
the explanation is finally making sense to you)?

[I wrote:]
>>No, I'm more confused than ever, because you began this discussion by
>>suggesting that I *not* use the term "7-limit" to describe a tuning
>>that can include 4:5:6:7:9,

[Paul E:]
>I think you misunderstood me there! I said that it's not clear given
>your methodology . . .

[JdL:]
>>but now you seem to be saying I *should*:

[Paul:]
>What I was saying is that if you were _specifically_ targeting 7:9 for
>a single interval, that would be 9-limit. But in your tuning file
>methodology, there is no way to determine whether, in tuning
>C-E-G-Bb-D to 4:5:6:7:9, you are really "targeting" 7:9, or whether
>7:9 is a _resultant_ from combining the targeting of a 6:7 with the
>targeting of a 2:3 (acting as 6:9). If one were to use a different
>methodology, one could allow deviations in G-Bb from 6:7 to contribute
>to the "pain" calculation, and one could allow deviations in G-D from
>2:3 (acting as 6:9) to contribute to the "pain" calculation, _without_
>allowing deviations in Bb-D from 7:9 to contribute to the "pain"
>calculation. This would be a 7-limit approach. It can actually have
>different consequences than a 9-limit approach even in this case,
>because the 7-limit approach wouldn't care if the errors in G-Bb and
>G-D were of the same or different sign, whether they cancelled each
>other out or reinforced one another in the deviation of Bb-D from 7:9;
>while a 9-limit approach would of course favor the scenario in which
>these errors cancelled out and the 7:9 was better tuned.

Well, in point of fact, I DON'T target the interval 7:9 specifically;
the "goodness" of the tuning depends upon the sum of all the intervals
sounding, and 7:9 on its own is not favored. Of course, in a C,E,G,
Bb,D chord, there are 10 intervals altogether.

[JdL:]
>>Hmmm, you seem to be saying that neither term satisfies you.

[Paul:]
>For your "tuning file" methodology, that may be the case, but perhaps
>another methodology would be applicable where the distinction would
>become meaningful.

[JdL:]
>>You mean rather than with Ab/G# at the top. Yes, that could be done,
>>but the problem is that then there's no way to produce a normal
>>A,C,E,G chord. The answer to THAT problem is to combine additional
>>tuning files into the mix, which my program does already support.

[Paul:]
>You're already using a number of tuning files in the mix, correct?

Yes.

[JdL:]
>>And yes, I agree that just plain "13-limit" probably better describes
>>the output of this file, but it means that I need to split out a
>>separate 11-limit file, so that there isn't a gap.

[Paul:]
>I don't get it -- you're saying that people would be upset if there
>were a 13-limit version but not an 11-limit version? Surely you don't
>mean that!

We're having some kind of major miscommunication here, and I'm not sure
what you're reading into my words. I'm really just saying that, by
agreeing with your suggestion (which I do), I have some work ahead of
me!

[Paul:]
>If, hypothetically, you were to make a 29-limit version right now, you
>wouldn't have to call it 17/19/23/29-limit just to fill in the gaps,
>would you? What am I missing?

Your statement is correct, and I'm not sure what you took from my words.

[JdL:]
>>which I've recently patched around with a late wiring in of
>>non-self-consistent vertical springs.

[Paul:]
>Perhaps this idea would be the key to truly differentiating 7- and
>9-limit formulations? Does that make any sense in light of my
>explanation above (if the explanation is finally making sense to you)?

"Finally" ;-> . Again, I'm not quite sure what point you're making
here, but to take a stab at responding, in general I'm very content with
self-consistent tunings whenever possible, as I said. There are just a
few classes of chords for which they don't work well, chains of fifths
being perhaps the most common.

I really like the fact that, when a 7:9 IS specified because it's part
of some larger chord, then ALL the intervals in that chord get vertical
springs as rigid as any other chord, because, as I think we may agree,
there is a synergistic effect to the many intervals of a large chord
when they are consistently tuned. Am I making sense?

JdL

I wrote,

>>What I was saying is that if you were _specifically_ targeting 7:9 for
>>a single interval, that would be 9-limit. But in your tuning file
>>methodology, there is no way to determine whether, in tuning
>>C-E-G-Bb-D to 4:5:6:7:9, you are really "targeting" 7:9, or whether
>>7:9 is a _resultant_ from combining the targeting of a 6:7 with the
>>targeting of a 2:3 (acting as 6:9). If one were to use a different
>>methodology, one could allow deviations in G-Bb from 6:7 to contribute
>>to the "pain" calculation, and one could allow deviations in G-D from
>>2:3 (acting as 6:9) to contribute to the "pain" calculation, _without_
>>allowing deviations in Bb-D from 7:9 to contribute to the "pain"
>>calculation. This would be a 7-limit approach. It can actually have
>>different consequences than a 9-limit approach even in this case,
>>because the 7-limit approach wouldn't care if the errors in G-Bb and
>>G-D were of the same or different sign, whether they cancelled each
>>other out or reinforced one another in the deviation of Bb-D from 7:9;
>>while a 9-limit approach would of course favor the scenario in which
>>these errors cancelled out and the 7:9 was better tuned.

John wrote,

>Well, in point of fact, I DON'T target the interval 7:9 specifically;
>the "goodness" of the tuning depends upon the sum of all the intervals
>sounding, and 7:9 on its own is not favored. Of course, in a C,E,G,
>Bb,D chord, there are 10 intervals altogether.

Hmm . . . but you are saying the goodness of the tuning depends on the
goodnesses of all 10 intervals, _including_ 7:9, right? So that would be
9-limit, in my book. If you ignored the goodness of 7:9, 5:9, and 4:9, you'd
be engaging in a 7-limit evaluation of the chord, as I (and I believe
Partch, the coiner of the term) would consider it. Is that something you
could do with your current methodology?

>>>You mean rather than with Ab/G# at the top. Yes, that could be done,
>>>but the problem is that then there's no way to produce a normal
>>>A,C,E,G chord. The answer to THAT problem is to combine additional
>>>tuning files into the mix, which my program does already support.

[Paul:]
>>You're already using a number of tuning files in the mix, correct?

>Yes.

Well then, it's not really a problem of any new sort, is it . . .

[JdL:]
>>>And yes, I agree that just plain "13-limit" probably better describes
>>>the output of this file, but it means that I need to split out a
>>>separate 11-limit file, so that there isn't a gap.

[Paul:]
>>I don't get it -- you're saying that people would be upset if there
>>were a 13-limit version but not an 11-limit version? Surely you don't
>>mean that!

>We're having some kind of major miscommunication here, and I'm not sure
>what you're reading into my words. I'm really just saying that, by
>agreeing with your suggestion (which I do), I have some work ahead of
>me!

There still must be some misunderstanding, since I was just suggesting that
you use the term "13-limit" instead of "11/13-limit", and just changing the
terminology doesn't require a substantial amount of work, right?

>I really like the fact that, when a 7:9 IS specified because it's part
>of some larger chord, then ALL the intervals in that chord get vertical
>springs as rigid as any other chord, because, as I think we may agree,
>there is a synergistic effect to the many intervals of a large chord
>when they are consistently tuned. Am I making sense?

In general, yes (though the interesting synergies happen in otonal chords
and not in utonal chords with the same intervals) Not really sure how this
applies here, though.

Do you understand why I'm suggesting that it might be useful to allow for a
case where you _don't_ directly consider deviations in the 7:9, 5:9, and
4:9?

[I wrote:]
>>Well, in point of fact, I DON'T target the interval 7:9 specifically;
>>the "goodness" of the tuning depends upon the sum of all the intervals
>>sounding, and 7:9 on its own is not favored. Of course, in a C,E,G,
>>Bb,D chord, there are 10 intervals altogether.

[Paul:]
>Hmm . . . but you are saying the goodness of the tuning depends on the
>goodnesses of all 10 intervals, _including_ 7:9, right? So that would
>be 9-limit, in my book. If you ignored the goodness of 7:9, 5:9, and
>4:9, you'd be engaging in a 7-limit evaluation of the chord, as I (and
>I believe Partch, the coiner of the term) would consider it. Is that
>something you could do with your current methodology?

Not without some modifications, which I'm not convinced would improve
the tuning at all. Quite the contrary, in fact.

[Paul:]
>>>You're already using a number of tuning files in the mix, correct?

[JdL:]
>>Yes.

[Paul:]
>Well then, it's not really a problem of any new sort, is it . . .

Nope. EXCEPT that it means that two files need to be balanced against
each other, which in practice is a pain.

[JdL:]
>>We're having some kind of major miscommunication here, and I'm not
>>sure what you're reading into my words. I'm really just saying that,
>>by agreeing with your suggestion (which I do), I have some work ahead
>>of me!

[Paul:]
>There still must be some misunderstanding, since I was just suggesting
>that you use the term "13-limit" instead of "11/13-limit", and just
>changing the terminology doesn't require a substantial amount of work,
>right?

Well, it seems silly to me to offer 7 and 13, but not 11.

[JdL:]
>>I really like the fact that, when a 7:9 IS specified because it's part
>>of some larger chord, then ALL the intervals in that chord get
>>vertical springs as rigid as any other chord, because, as I think we
>>may agree, there is a synergistic effect to the many intervals of a
>>large chord when they are consistently tuned. Am I making sense?

[Paul:]
>In general, yes (though the interesting synergies happen in otonal
>chords and not in utonal chords with the same intervals).

Right, and the tuning files I use are overwhelmingly otonal.

[Paul:]
>Not really sure how this applies here, though.

I think it does. We've discussed virtual fundamentals and methods by
which to ensure that they're consistent. One quick way to do this is
to wire a full set of self-consistent otonal vertical springs. Leaving
any of them out is a direct invitation to a poorly tuned chord, I
believe.

[Paul:]
>Do you understand why I'm suggesting that it might be useful to allow
>for a case where you _don't_ directly consider deviations in the 7:9,
>5:9, and 4:9?

Actually, no. If the main point is whether such a practice would be
more consistent with a particular definition of the term "7-limit",
then I'd rather concede the terminological point than modify my tuning
practice. But I have a feeling that your main point is not strictly
a matter of terminology?

Oh, and on the subject of octave invariance: it is true, as you say,
that I collapse everything into a set of 12 pitch classes, thus
discarding information about the power of 2 in the original note. But,
if I'm not mistaken, you've recommended that I NOT do this collapse.
Which would be consistent with even OR odd limit reckoning, yes?

JdL

John deLaubenfels wrote,

>Not without some modifications, which I'm not convinced would improve
>the tuning at all. Quite the contrary, in fact.

Well, might I venture than your perception here is similar to that which
always prefers 7-limit retunings over 5-limit retunings? Essentially, you're
saying that you're likely to prefer 9-limit retunings over 7-limit
retunings. Perhaps someone else wouldn't, for a particular piece of music.
But certainly I appreciate that the modifications involved may be difficult
and only have a relatively minor effect, as far as I can see right now.

>Nope. EXCEPT that it means that two files need to be balanced against
>each other, which in practice is a pain.

Doesn't this happen all the time anyway in your runs?

>>There still must be some misunderstanding, since I was just suggesting
>>that you use the term "13-limit" instead of "11/13-limit", and just
>>changing the terminology doesn't require a substantial amount of work,
>>right?

>Well, it seems silly to me to offer 7 and 13, but not 11.

Oh, so that's what you meant! Well then, let me just add to the silliness by
saying you should call 7 "9" and offer a real 7 as well. :)

>I think it does. We've discussed virtual fundamentals and methods by
>which to ensure that they're consistent. One quick way to do this is
>to wire a full set of self-consistent otonal vertical springs. Leaving
>any of them out is a direct invitation to a poorly tuned chord, I
>believe.

I don't think so. In this case the 7:9 will be brought into tune by a
combination of the 2:3 (as 6:9) spring and the 6:7 spring. In effect, 7:9
will have a spring of half (or is it 1/sqrt(2)) the strength of the spring
constant you're using.

A similar situation arises in the 5-limit, as we discussed, with major
seventh chords. I don't think the 8:15 should get a spring of its own, while
the other five intervals are within the 5-odd-limit and should get their own
springs. In fact, I really like major seventh chords in 26-tET, where the
five intervals within the 5-odd-limit are reasonably well in tune, while the
major seventh is actually very close to 7:13 rather than 8:15! This doesn't
affect the consonance of the chord, to my ears, since 8:15 was never a
consonance anyway. In other words, the "odd-limit of my hearing" is at least
5 but is definitely less than 15.

>>Do you understand why I'm suggesting that it might be useful to allow
>>for a case where you _don't_ directly consider deviations in the 7:9,
>>5:9, and 4:9?

>Actually, no. If the main point is whether such a practice would be
>more consistent with a particular definition of the term "7-limit",
>then I'd rather concede the terminological point than modify my tuning
>practice. But I have a feeling that your main point is not strictly
>a matter of terminology?

Right -- see my 5/15-limit example above.

>Oh, and on the subject of octave invariance: it is true, as you say,
>that I collapse everything into a set of 12 pitch classes, thus
>discarding information about the power of 2 in the original note. But,
>if I'm not mistaken, you've recommended that I NOT do this collapse.

Well, I never would have seriously suggested that, given the work involved
-- imagine the tuning files!

>Which would be consistent with even OR odd limit reckoning, yes?

You would use _integer_ limit, or better yet, _product_ limit (product of
numerator times denominator).

[I wrote:]
>>Not without some modifications, which I'm not convinced would improve
>>the tuning at all. Quite the contrary, in fact.

[Paul:]
>Well, might I venture than your perception here is similar to that
>which always prefers 7-limit retunings over 5-limit retunings?
>Essentially, you're saying that you're likely to prefer 9-limit
>retunings over 7-limit retunings. Perhaps someone else wouldn't, for a
>particular piece of music.

That's plausible.

>But certainly I appreciate that the modifications involved may be
>difficult and only have a relatively minor effect, as far as I can see
>right now.

Hey! You're trying reverse psychology, aren't you? ;->

>>Nope. EXCEPT that it means that two files need to be balanced against
>>each other, which in practice is a pain.

>Doesn't this happen all the time anyway in your runs?

Well, I use certain combinations of files together: typically 12-tET
and one other (in 5-limit, I also have a "u" version specifically for
half-diminished chords; in 7, I do them 5:6:7:9 so don't need a "u").
The file I've been calling just11.tun is quite old now, and probably
would not be well balanced in use with, say, just7.tun.

>>it seems silly to me to offer 7 and 13, but not 11.

>Oh, so that's what you meant! Well then, let me just add to the
>silliness by saying you should call 7 "9" and offer a real 7 as well.
>:)

I'll take it under consideration!

>>I think it does. We've discussed virtual fundamentals and methods by
>>which to ensure that they're consistent. One quick way to do this is
>>to wire a full set of self-consistent otonal vertical springs.
>>Leaving any of them out is a direct invitation to a poorly tuned
>>chord, I believe.

>I don't think so. In this case the 7:9 will be brought into tune by a
>combination of the 2:3 (as 6:9) spring and the 6:7 spring. In effect,
>7:9 will have a spring of half (or is it 1/sqrt(2)) the strength of
>the spring constant you're using.

It's half. But, using that measure, if the direct spring IS in place,
the interval actually has stiffness 1.5, so it's more realistic to say
that it's cut to 1/3 of its original stiffness. Well, that'd be for
a triad; larger chords would have a smaller effective change per spring
removed. Of course, you were going to remove three springs from the
4:5:6:7:9, so that'd be significant: a 30% reduction in total stiffness.

>A similar situation arises in the 5-limit, as we discussed, with major
>seventh chords. I don't think the 8:15 should get a spring of its own,
>while the other five intervals are within the 5-odd-limit and should
>get their own springs. In fact, I really like major seventh chords in
>26-tET, where the five intervals within the 5-odd-limit are reasonably
>well in tune, while the major seventh is actually very close to 7:13
>rather than 8:15! This doesn't affect the consonance of the chord, to
>my ears, since 8:15 was never a consonance anyway. In other words, the
>"odd-limit of my hearing" is at least 5 but is definitely less than 15.

I hear you. I'll add it to my list of things to do when possible.

>>Oh, and on the subject of octave invariance: it is true, as you say,
>>that I collapse everything into a set of 12 pitch classes, thus
>>discarding information about the power of 2 in the original note.
>>But, if I'm not mistaken, you've recommended that I NOT do this
>>collapse.

>Well, I never would have seriously suggested that, given the work
>involved -- imagine the tuning files!

Yes. Natch, I knew you meant the suggestion to be used in a program
with a different methodology, but the point I took was that you were
saying that octaves DO matter.

>>Which would be consistent with even OR odd limit reckoning, yes?

>You would use _integer_ limit,

That's the term I was groping for.

>or better yet, _product_ limit (product of numerator times
denominator).

Yow - what would THAT imply as far as intervals to be considered or
ignored? We'd best leave that for another time, or else we'll be forced
to spin off a separate "Limit Terminology" list! :-)

JdL

John deLaubenfels wrote,

>(in 5-limit, I also have a "u" version specifically for
>half-diminished chords; in 7, I do them 5:6:7:9 so don't need a "u").

Can you explain this further? What is your target for half-diminished chords
in the 5-limit?

>>I don't think so. In this case the 7:9 will be brought into tune by a
>>combination of the 2:3 (as 6:9) spring and the 6:7 spring. In effect,
>>7:9 will have a spring of half (or is it 1/sqrt(2)) the strength of
>>the spring constant you're using.

>It's half. But, using that measure, if the direct spring IS in place,
>the interval actually has stiffness 1.5, so it's more realistic to say
>that it's cut to 1/3 of its original stiffness. Well, that'd be for
>a triad; larger chords would have a smaller effective change per spring
>removed. Of course, you were going to remove three springs from the
>4:5:6:7:9, so that'd be significant: a 30% reduction in total stiffness.

OK, good thinking.

>>A similar situation arises in the 5-limit, as we discussed, with major
>>seventh chords. I don't think the 8:15 should get a spring of its own,
>>while the other five intervals are within the 5-odd-limit and should
>>get their own springs. In fact, I really like major seventh chords in
>>26-tET, where the five intervals within the 5-odd-limit are reasonably
>>well in tune, while the major seventh is actually very close to 7:13
>>rather than 8:15! This doesn't affect the consonance of the chord, to
>>my ears, since 8:15 was never a consonance anyway. In other words, the
>>"odd-limit of my hearing" is at least 5 but is definitely less than 15.

>I hear you. I'll add it to my list of things to do when possible.

Cool. So I'm _finally_ making sense to you, yes?

[I wrote:]
>>(in 5-limit, I also have a "u" version specifically for
>>half-diminished chords; in 7, I do them 5:6:7:9 so don't need a "u").

[Paul E:]
>Can you explain this further? What is your target for half-diminished
>chords in the 5-limit?

This is based on critiques from both you and Mark Nowitzky. The notes
E,G,Bb,D, which I map to 5:6:7:9 in 7-limit (thus, otonal) become an
upside-down dom 7th in the utonal 5-limit, the main idea being to tune
G,Bb,D as a normal minor chord, and let the E at the bottom be 9/16
of D. This is consistent with the way I tune otonal dom 7ths in
5-limit, with the 7th degree 16/9 of the root (to my ear, the higher 7th
option at 9/5 of root sounds awful).

[JdL:]
>>I hear you. I'll add it to my list of things to do when possible.

[Paul:]
>Cool. So I'm _finally_ making sense to you, yes?

I see that the word "finally" is not enough this time; it's even got
emphasis! I suppose I should be glad you didn't scream it ("FINALLY")
;-> . But yes, I think you are making some sense to me now, Paul.

BTW, as I've briefly mentioned in the past, I do have a routine,
calcKReduction() which is called in the creation of every vertical
spring, which makes intervals such as seconds of less tuning importance
than more concordant intervals. It does not reduce their vertical
strength to zero, as you advocate doing past a certain limit, but the
reduction can be extreme for some intervals.

JdL

John deLaubenfels wrote,

>This is based on critiques from both you and Mark Nowitzky. The notes
>E,G,Bb,D, which I map to 5:6:7:9 in 7-limit (thus, otonal) become an
>upside-down dom 7th in the utonal 5-limit, the main idea being to tune
>G,Bb,D as a normal minor chord, and let the E at the bottom be 9/16
>of D. This is consistent with the way I tune otonal dom 7ths in
>5-limit, with the 7th degree 16/9 of the root (to my ear, the higher 7th
>option at 9/5 of root sounds awful).

Oh.

Hey, you know what? Since 12-tET has unique representations of the
5-(odd)-limit, it would be possible to dispense with tuning files altogether
in the 5-limit case and simply use vertical springs for each consonant
interval! The springs will naturally tug all major and minor triads toward
JI, while the "necessarily tempered" chords will find a natural equilibrium
due to the various springs. Does that make sense? Is it something you could
try?

[I wrote:]
>>This is based on critiques from both you and Mark Nowitzky. The notes
>>E,G,Bb,D, which I map to 5:6:7:9 in 7-limit (thus, otonal) become an
>>upside-down dom 7th in the utonal 5-limit, the main idea being to tune
>>G,Bb,D as a normal minor chord, and let the E at the bottom be 9/16
>>of D. This is consistent with the way I tune otonal dom 7ths in
>>5-limit, with the 7th degree 16/9 of the root (to my ear, the higher
>>7th option at 9/5 of root sounds awful).

[Paul E:]
>Oh.

>Hey, you know what? Since 12-tET has unique representations of the
>5-(odd)-limit, it would be possible to dispense with tuning files
>altogether in the 5-limit case and simply use vertical springs for each
>consonant interval! The springs will naturally tug all major and minor
>triads toward JI, while the "necessarily tempered" chords will find a
>natural equilibrium due to the various springs. Does that make sense?
>Is it something you could try?

Funny you should mention that right after the paragraph above! When
I made the change, recently discussed, that re-springs vertical
intervals when they've been targeted as 12-tET, I realized that if I
processed a sequence with no tuning file available except equal.tun
(12-tET), it'd do just that. Guess what happened? Dom 7th chords,
which contain two consecutive "minor thirds", wired them both to 6:5,
which forces the 7th to be 9/5 of root, VERY high to my ear. I hated
it!!

But I realize that my ear, unusually accustomed to a very flat 7th
degree, might be particularly sensitive. I'll be glad to post an
example or two if you're interested - you pick the sequence.

JdL

John deLaubenfels wrote,

>Dom 7th chords,
>which contain two consecutive "minor thirds", wired them both to 6:5,
>which forces the 7th to be 9/5 of root, VERY high to my ear. I hated
>it!!

Well, John, I can relate to that, because when I retuned my piano to
meantone, the one thing that took the longest to get used to were the
dominant seventh chords. And, if I've been listening to/playing 12-tET music
for a while, they sound odd to me again.

But, for most music written 1500-1800, this may actually be a more
"authentic" way of doing things -- the two consecutive minor thirds would
indeed, in general, be close approximations of 6:5. And Joseph Pehrson, for
one, said he liked the meantone dominant seventh very much in the I-IV-V7-I
listening tests we did a while back. So, yeah, how 'bout some Bach and
Mozart "sans tuning files" renditions?

[I wrote:]
>>Dom 7th chords, which contain two consecutive "minor thirds", wired
>>them both to 6:5, which forces the 7th to be 9/5 of root, VERY high to
>>my ear. I hated it!!

[Paul E:]
>Well, John, I can relate to that, because when I retuned my piano to
>meantone, the one thing that took the longest to get used to were the
>dominant seventh chords. And, if I've been listening to/playing 12-tET
>music for a while, they sound odd to me again.

And, if your meantone was 1/4 tone, the minor thirds were a few cents
narrow, as was the fifth, so the 7th degree would be not nearly as sharp
as you'd hear here! In fact, no matter what flavor of meantone you
used, that statement about the 7th degree would apply.

[Paul:]
>But, for most music written 1500-1800, this may actually be a more
>"authentic" way of doing things -- the two consecutive minor thirds
>would indeed, in general, be close approximations of 6:5. And Joseph
>Pehrson, for one, said he liked the meantone dominant seventh very much
>in the I-IV-V7-I listening tests we did a while back. So, yeah, how
>'bout some Bach and Mozart "sans tuning files" renditions?

'Course you know how I feel about "authentic", but I'd be glad to
do up some sequences. Let's start with a li'l Mozart, wamk280: Sonata
No.2 in F, K.280, sequenced by F.Raborn. The cs5 version is as before,
targeting the 7th degree at 16/9 of root; the es version uses what
you're calling "no tuning file" - every interval (well, 3, 4, 5, 7, 8,
9 semitone intervals) sprung to 5-limit JI, with the 7th degree tending
toward 9/5 of root. See what you think!

http://www.egroups.com/files/tuning/
change into the JMids directory, and download wamk280.zip.

Here's a few stats on the two tunings:

wamk280cs5.dbg (2001 Jan 31 16:52:50):
1 Didn't have to drop any notes; used 8 channels.
2 12-tET Total spring pain: 1227955.897
3 Werckmeister III spring pain: 1165442.008
4 Kirnberger III Total spring pain: 1150937.833
5 Thomas Young Total spring pain: 1053757.421
6 COFT Total spring pain: 692889.657
7 After relaxing, Total spring pain: 332110.111
8 Final vertical spring pain: 191436.200
9 Final horizontal spring pain: 20027.657
10 Final grounding spring pain: 120646.255
[end]

wamk280es.dbg (2001 Jan 31 16:30:00):
1 Didn't have to drop any notes; used 8 channels.
2 12-tET Total spring pain: 1329377.851
3 Werckmeister III spring pain: 1288811.376
4 Kirnberger III Total spring pain: 1278440.349
5 Thomas Young Total spring pain: 1166996.659
6 COFT Total spring pain: 775545.284
7 After relaxing, Total spring pain: 457587.573
8 Final vertical spring pain: 331451.024
9 Final horizontal spring pain: 19554.168
10 Final grounding spring pain: 106582.382
[end]

JdL

John deLaubenfels wrote,

>And, if your meantone was 1/4 tone, the minor thirds were a few cents
>narrow, as was the fifth, so the 7th degree would be not nearly as sharp
>as you'd hear here! In fact, no matter what flavor of meantone you
>used, that statement about the 7th degree would apply.

Well, the comparison may depend in some circumstances on how strong your
springs are, correct?

>the es version uses what
>you're calling "no tuning file"

Wouldn't you call it that too?

I'll listen later . . . got a meeting now . . .

[I wrote:]
>>And, if your meantone was 1/4 tone, the minor thirds were a few cents
>>narrow, as was the fifth, so the 7th degree would be not nearly as
>>sharp as you'd hear here! In fact, no matter what flavor of meantone
>>you used, that statement about the 7th degree would apply.

[Paul E:]
>Well, the comparison may depend in some circumstances on how strong
>your springs are, correct?

Yes, though horizontal and grounding springs could pull the 7th either
sharper or flatter. A bare C7 dom 7th chord, with only vertical springs
active, gives the following tuning:

Ptch Tuning Ptch Tuning Strength Ideal Actual Force Pain
---- ------ ---- ------ -------- -------- -------- ---------- ----------
0 1.12 4 -12.41 20.480 386.314 386.474 3.274 0.262
0 1.12 7 0.49 20.480 701.955 699.373 -52.885 68.282
0 1.12 10 10.81 5.120 1000.000 1009.690 49.611 240.355
4 -12.41 0 1.12 20.480 813.686 813.526 -3.274 0.262
4 -12.41 7 0.49 20.480 315.641 312.899 -56.159 76.998
4 -12.41 10 10.81 2.560 600.000 623.216 59.433 689.900
7 0.49 0 1.12 20.480 498.045 500.627 52.885 68.282
7 0.49 4 -12.41 20.480 884.359 887.101 56.159 76.998
7 0.49 10 10.81 20.480 315.641 310.317 -109.044 290.297
10 10.81 0 1.12 5.120 200.000 190.310 -49.611 240.355
10 10.81 4 -12.41 2.560 600.000 576.784 -59.433 689.900
10 10.81 7 0.49 20.480 884.359 889.683 109.044 290.297
---- ------ ---- ------ -------- -------- -------- ---------- ----------
painSum 1366.092

Note the flattening of the fifth down to 699.4 cents, due to pressure
from note 10 (Bb), itself pushed downward by C above. And the
attenuation of the Strength of certain intervals: major seconds are cut
to 1/4 of their nominal value; tritones are cut to 1/8 of nominal.
Notice also the targeting of some intervals to 12-tET values. Perhaps
these should be even smaller in strength, near zero. Though, that would
make the 7th degree even sharper!

[JdL:]
>>the es version uses what you're calling "no tuning file"

[Paul:]
>Wouldn't you call it that too?

Yes and no: it does have the equal.tun file, whose target specifications
are retained for intervals not marked as JI (i.e. 1, 2, and 6 semitones,
plus inversions).

[Paul:]
>I'll listen later . . . got a meeting now . . .

I created and uploaded that piece last thing last night, and didn't get
a chance to listen to it till just now. The es doesn't sound so bad to
me this time around. I'll be interested to hear what you think!

JdL

In my previous post, /tuning/topicId_18070.html#18203,
I tabulated some tuning numbers for a dom 7 chord with "no tuning file".
It really doesn't present intervals consistent with not caring about
seconds and tritones, so I've done up another version, with the
following tuning for bare C7 (vertical springs only):

Ptch Tuning Ptch Tuning Strength Ideal Actual Force Pain
---- ------ ---- ------ -------- -------- -------- ---------- ----------
0 -1.25 4 -14.89 20.480 386.314 386.359 0.931 0.021
0 -1.25 7 0.49 20.480 701.955 701.740 -4.394 0.471
0 -1.25 10 15.66 0.205 1000.000 1016.907 3.463 29.271
4 -14.89 0 -1.25 20.480 813.686 813.641 -0.931 0.021
4 -14.89 7 0.49 20.480 315.641 315.381 -5.325 0.692
4 -14.89 10 15.66 0.205 600.000 630.548 6.256 95.558
7 0.49 0 -1.25 20.480 498.045 498.260 4.394 0.471
7 0.49 4 -14.89 20.480 884.359 884.619 5.325 0.692
7 0.49 10 15.66 20.480 315.641 315.167 -9.719 2.306
10 15.66 0 -1.25 0.205 200.000 183.093 -3.463 29.271
10 15.66 4 -14.89 0.205 600.000 569.452 -6.256 95.558
10 15.66 7 0.49 20.480 884.359 884.833 9.719 2.306
---- ------ ---- ------ -------- -------- -------- ---------- ----------
painSum 128.320

Now the spring strength of the intervals that "don't matter" have been
cut by a factor of 1/100, so that they barely distore the intervals
that "do matter". The fifth is flat by only .2 cents, rather than 2.5
cents, as before. And so on for the other intervals.

Paul, if you'd prefer to wait, I'll post the Mozart with this tuning in
place of the other one.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_18070.html#18177

Let's start with a li'l Mozart, wamk280:
Sonata No.2 in F, K.280, sequenced by F.Raborn. The cs5 version is
as before,targeting the 7th degree at 16/9 of root; the es version
uses what you're calling "no tuning file" - every interval (well, 3,
4, 5, 7, 8,9 semitone intervals) sprung to 5-limit JI, with the 7th
degree tending toward 9/5 of root. See what you think!
>

Thank you, John, for the opportunity to listen again to your
fascinating tuning experiments with some great music of the past.
Well, after listening to the files for a while, the 12-tET really
sounds horrible, I have to admit.

I'm hearing the "es" version as somewhere between the 5-limit version
and the 7-limit version. Does that make any sense??

However, for me the 7-limit version is really the one that makes an
"impact." Everything seems really balanced and smooth, the
sonorities and transitions are incredibly beautiful. It seems to
make a BIG difference over all the other files.

Could that make any sense, or am I just "hearing things..?"

__________ _______ ______ _
Joseph Pehrson

On Fri, 02 Feb 2001 01:55:50 -0000, jpehrson@rcn.com wrote:

>--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
>/tuning/topicId_18070.html#18177
>
> Let's start with a li'l Mozart, wamk280:
>Sonata No.2 in F, K.280, sequenced by F.Raborn. The cs5 version is
>as before,targeting the 7th degree at 16/9 of root; the es version
>uses what you're calling "no tuning file" - every interval (well, 3,
>4, 5, 7, 8,9 semitone intervals) sprung to 5-limit JI, with the 7th
>degree tending toward 9/5 of root. See what you think!
>>
>
>Thank you, John, for the opportunity to listen again to your
>fascinating tuning experiments with some great music of the past.
>Well, after listening to the files for a while, the 12-tET really
>sounds horrible, I have to admit.
>
>I'm hearing the "es" version as somewhere between the 5-limit version
>and the 7-limit version. Does that make any sense??

I'm really liking this new version. It's definitely a bit "spicier" than
the 5-limit version, while still sounding appropriate for this music. The
7-limit version is nice, but stylistically seems just a bit odd in places
(like a barbershop version of Mozart).

[I wrote:]
>Let's start with a li'l Mozart, wamk280...

[Joseph Pehrson:]
>Thank you, John, for the opportunity to listen again to your
>fascinating tuning experiments with some great music of the past.
>Well, after listening to the files for a while, the 12-tET really
>sounds horrible, I have to admit.

Doesn't it, though?

>I'm hearing the "es" version as somewhere between the 5-limit version
>and the 7-limit version. Does that make any sense??

Well... the 7th degree tends to make it the other way around; that is,
7-limit has the lowest, my usual 5-limit has an intermediate, and the
es has the highest 7th degrees. But the ear has its own perceptions,
to be sure!

>However, for me the 7-limit version is really the one that makes an
>"impact." Everything seems really balanced and smooth, the
>sonorities and transitions are incredibly beautiful. It seems to
>make a BIG difference over all the other files.

Uh oh! Don't let Paul see that! ;-> But I'm with you. Even Paul
can't deny (I think) that 7-limit gives more concordant chords than
5-limit. He'll say it's "inauthentic" and "inappropriate", however...
(right, Paul?)

>Could that make any sense, or am I just "hearing things..?"

I would say you're hearing the beauty of 7-limit, something Mozart,
alas, couldn't (couldn't produce, I mean, and also certainly might not
like!).

[Herman Miller:]
>I'm really liking this new version. It's definitely a bit "spicier"
>than the 5-limit version, while still sounding appropriate for this
>music. The 7-limit version is nice, but stylistically seems just a bit
>odd in places (like a barbershop version of Mozart).

Hi, Herman! Yes, it's harmonically akin to barbershop, and is quite
"odd", unless and until the ear comes around to embracing it. All a
matter of taste. Glad you like the es!

JdL

John deLaubenfels wrote,

>Yes and no: it does have the equal.tun file, whose target specifications
>are retained for intervals not marked as JI (i.e. 1, 2, and 6 semitones,
>plus inversions).

What if you got rid of that, too?

[I wrote:]
>>Yes and no: it does have the equal.tun file, whose target
>>specifications are retained for intervals not marked as JI (i.e. 1, 2,
>>and 6 semitones, plus inversions).

[Paul E:]
>What if you got rid of that, too?

Did you see my post,

/tuning/topicId_18070.html#18212

There, for all intents and purposes there is no tuning file. Close
enough?

JdL

[I wrote:]
>Paul, if you'd prefer to wait, I'll post the Mozart with this tuning in
>place of the other one.

and figured I'd post the new version only if there was specific
interest. But I realized the words are ambiguous, and could be taken
as meaning I'd do it without being asked, which might mean YOU are
waiting for me to get off my duff...

Anyway, all the versions are up now:

wamk280.zip
wamk280.mid - 12-tET, as originally sequenced.
wamk280cs5.mid - 5-limit as before, w/ 7th targeting 16/9 of root.
wamk280es.mid - new 5-limit, w/ 7th targeting 9/5 of root.
wamk280cs7.mid - 7-limit, w/ 7th targeting 7/4 of root.
wamk280es2.zip
wamk280es2.mid - even newer 5-limit, w/ 7th targeting 9/5 of root,
and other springs reduced to near zero.

This last, the "es2" version, will have a 7th even sharper than the
original "es", though I'm not sure how audible the difference will be.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> Did you see my post,
>
> /tuning/topicId_18070.html#18212
>
> There, for all intents and purposes there is no tuning file. Close
> enough?
>
> JdL

I suppose it would be close enough, and I'd love to listen to it, but I'm just wondering if, in
principle, it would be possible to do without a tuning file, and hence engage in what I would call a
true 5-odd-limit adaptive retuning.

[I wrote:]
>>Did you see my post,
>>
>> /tuning/topicId_18070.html#18212
>>
>>There, for all intents and purposes there is no tuning file. Close
>>enough?
>>
>>JdL

[Paul E:]
>I suppose it would be close enough, and I'd love to listen to it, but
>I'm just wondering if, in principle, it would be possible to do without
>a tuning file, and hence engage in what I would call a true 5-odd-limit
>adaptive retuning.

In principle, sure, but my program's flow is deeply dependent upon
having one or more tuning files, and to change that would be a major
project. The es2 version I've posted is extremely close, however, so
it seems silly to quibble about the difference. Let's just say that
es2 is "no tuning file."

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> In principle, sure, but my program's flow is deeply dependent upon
> having one or more tuning files, and to change that would be a major
> project. The es2 version I've posted is extremely close, however, so
> it seems silly to quibble about the difference. Let's just say that
> es2 is "no tuning file."
>
OK, I will listen when I get a chance. BTW, I can see potential problems with having a tuning file
which targets the 12-tET tuning of 2-semitone intervals with significant force. If you have the
chord C-D-E-G, a 5-limit "no tuning file" approach would immediately target 8:9:10:12, which is
(I believe) what you want; while targeting 12-tET for 2-semitone intervals would force D-E away
from 9:10, and hence hurt the consonance of D-G, C-E, or both.

[Paul E:]
>OK, I will listen when I get a chance. BTW, I can see potential
>problems with having a tuning file which targets the 12-tET tuning of
>2-semitone intervals with significant force. If you have the chord
>C-D-E-G, a 5-limit "no tuning file" approach would immediately target
>8:9:10:12, which is (I believe) what you want; while targeting 12-tET
>for 2-semitone intervals would force D-E away from 9:10, and hence hurt
>the consonance of D-G, C-E, or both.

Please read

/tuning/topicId_18070.html#18212

again. The strength of intervals of 1, 2, or 6 semitones is made
negligible here, don't you agree? Do you want to see the tuning that
results for a C-D-E-G chord, or is it clear it'll be fine?

JdL

John deLaubenfels wrote,

>Please read

> /tuning/topicId_18070.html#18212

>again. The strength of intervals of 1, 2, or 6 semitones is made
>negligible here, don't you agree? Do you want to see the tuning that
>results for a C-D-E-G chord, or is it clear it'll be fine?

It's clear. The reason I brought this up is to show you a possible case
where even _you_, let alone many others, might like this way better than
your original "5-limit" methodology.

[Paul E wrote:]
>>>I can see potential problems with having a tuning file which targets
>>>the 12-tET tuning of 2-semitone intervals with significant force. If
>>>you have the chord C-D-E-G, a 5-limit "no tuning file" approach would
>>>immediately target 8:9:10:12, which is (I believe) what you want;
>>>while targeting 12-tET for 2-semitone intervals would force D-E away
>>>from 9:10, and hence hurt the consonance of D-G, C-E, or both.

[JdL:]
>>Please read
>>
>> /tuning/topicId_18070.html#18212
>>
>>again. The strength of intervals of 1, 2, or 6 semitones is made
>>negligible here, don't you agree? Do you want to see the tuning that
>>results for a C-D-E-G chord, or is it clear it'll be fine?

[Paul:]
>It's clear. The reason I brought this up is to show you a possible case
>where even _you_, let alone many others, might like this way better
>than your original "5-limit" methodology.

Ahhhh, I see what you're saying. But my original 5-limit methodology
works just fine on that chord, since the template file targets D at
9:8 of C. There might possibly be other chords which have trouble, but
I'm not aware of what they might be. The half-diminished chord does
need the utonal tuning file, as we've recently discussed. There is, of
course, an appealing purity to having "no tuning file", but those high
7th degrees, well, tell me what you think of them!

JdL

John, the first 4 minutes of wamk280es2.zip sound absolutely glorious (still
listening)! I wonder what Daniel Wolf and Johnny Reinhard would think?

[Paul E:]
>John, the first 4 minutes of wamk280es2.zip sound absolutely glorious
>(still listening)! I wonder what Daniel Wolf and Johnny Reinhard would
>think?

So glad you like it! My ear is coming around to accepting that high
7th degree as well, though, as I have no doubt repeated ad nauseum, I'm
most partial to the unauthentic and inappropriate 7-limit version. The
3rd movement is the real capper to the piece... I wish there were
composers like Mozart alive today.

JdL

John wrote,

>So glad you like it! My ear is coming around to accepting that high
>7th degree as well, though, as I have no doubt repeated ad nauseum, I'm
>most partial to the unauthentic and inappropriate 7-limit version.

I think if you accustom yourself to this version, your ear will miss the
consistent tuning of diatonic minor thirds to 6:5 when you go back to the
7-limit version. This "true 5-odd-limit" version also gives the illusion
that it _could_ have been performed on a real, fixed-pitch keyboard --
though of course that would be impossible in reality.

>The
>3rd movement is the real capper to the piece... I wish there were
>composers like Mozart alive today.

Oh yeah . . . Watch out, my sister is going to be a premier Mozart
interpreter someday (she's a world-class 16-year old now), perhaps we can
develop some kind of real-time adaptive tuning mechanism for an acoustic
piano in the next 15 years . . .? :)

[I wrote:]
>>So glad you like it! My ear is coming around to accepting that high
>>7th degree as well, though, as I have no doubt repeated ad nauseum,
>>I'm most partial to the unauthentic and inappropriate 7-limit version.

[Paul E:]
>I think if you accustom yourself to this version, your ear will miss
>the consistent tuning of diatonic minor thirds to 6:5 when you go back
>to the 7-limit version.

Uh-huh: you can start holding your breath now! ;->

>This "true 5-odd-limit" version also gives the illusion that it _could_
>have been performed on a real, fixed-pitch keyboard -- though of
>course that would be impossible in reality.

Though my own tastes are probably irrevocably off in that other place,
I'm very glad you experience this tuning so positively.

>>The 3rd movement is the real capper to the piece... I wish there were
>>composers like Mozart alive today.

>Oh yeah . . . Watch out, my sister is going to be a premier Mozart
>interpreter someday (she's a world-class 16-year old now), perhaps we
>can develop some kind of real-time adaptive tuning mechanism for an
>acoustic piano in the next 15 years . . .? :)

Hey, very cool, Paul! She's a real caboose, no? Though I realize
you're not so old, I seem to have the idea you're pushing 30. But
the hard part is getting an acoustic piano to be real-time tunable, as
discussed in the last few weeks. Are you saying you want the tuning
to be chosen by a computer rather than by pedals available to the
performer? I'd pick the latter as the ideal. Or, I "have a dream" that
a piece could be pre-tuned by the artist (following a leisure retuning
chosen by a program if desired) and that in real-time a computer follows
that tuning as the piece is played.

JdL

John A. deLaubenfels wrote,

<<I wish there were composers like Mozart alive today.>>

Hmm, how so -- i.e., "like Mozart" in what way exactly?

--Dan Stearns

John wrote,

>Or, I "have a dream" that
>a piece could be pre-tuned by the artist (following a leisure retuning
>chosen by a program if desired) and that in real-time a computer follows
>that tuning as the piece is played.

Yeah, that's what I was thinking.

[I wrote:]
>>I wish there were composers like Mozart alive today.

[Dan Stearns:]
>Hmm, how so -- i.e., "like Mozart" in what way exactly?

I really wish I could answer that question precisely, because then I'd
stand a better chance of composing music that I like as well as I do
this piece!

I very much do NOT believe that the best music has already been written
- I see an almost endless potential for new wonderful works in the
future - but most modern music leaves me cold. Well, that's not right:
there's plenty of artists I love who are still alive, including Paul
Simon, Rutter, "Phantom of the Opera" (can't think of his name!),
Peter Schickele, Randy Newman, etc., etc. But there was a flowering of
a certain scale of piece in the 18th and 19th centuries that has largely
been lost in the last hundred years, IMHO.

Sorry that I don't have a better answer...

JdL

Have you looked at Justonic's software? They claim to be able to do
exactly that. I believe they have demo software. They're at:

http://www.justonic.com/default3.htm

"Paul H. Erlich" wrote:

> John wrote,
>
> >Or, I "have a dream" that
> >a piece could be pre-tuned by the artist (following a leisure retuning
> >chosen by a program if desired) and that in real-time a computer follows
> >that tuning as the piece is played.
>
> Yeah, that's what I was thinking.
>
>
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[I wrote:]
>>>Or, I "have a dream" that
>>>a piece could be pre-tuned by the artist (following a leisure
>>>retuning chosen by a program if desired) and that in real-time a
>>>computer follows that tuning as the piece is played.

[Paul E:]
>>Yeah, that's what I was thinking.

[Steve Sycamore:]
>Have you looked at Justonic's software? They claim to be able to do
>exactly that. I believe they have demo software. They're at:

>http://www.justonic.com/default3.htm

I haven't run their software, but it's my understanding from e-mail
exchanges with them and from others on this list that, while it can
be preset to tune certain chords in certain ways, it would not handle
a fast complex piece with transitions and inversions very well. Perhaps
it can do more than I think?

JdL

Steve Sycamore wrote,

>>Have you looked at Justonic's software? They claim to be able to do
>>exactly that. I believe they have demo software. They're at:

>>http://www.justonic.com/default3.htm

John deLaubenfels wrote,

>I haven't run their software, but it's my understanding from e-mail
>exchanges with them and from others on this list that, while it can
>be preset to tune certain chords in certain ways, it would not handle
>a fast complex piece with transitions and inversions very well. Perhaps
>it can do more than I think?

Yes, my understanding is that it is quite primitive compared with the kind
of approaches you've developed. Probably lots of comma problems, etc.