Yahoo Tuning Groups Ultimate Backup tuning Latest refinements: is it smooth...

I've just posted a couple of examples at

http://www.idcomm.com/personal/jadl/

With some refinements new to the program:

. The highest pitch sounding is given extra volume weight, to reflect
the evident fact that the ear "watches" it more closely.

. Volumes of different notes are somewhat flattened, so that if a
note sounds only half as loud as another, it is given more than
half as much consideration.

. Reduced "credit" when a change in tuning is partially masked by
new notes beginning at the same moment.

. A couple of adjustments to the tuning files to reduce the
likelihood of a "backside" augmented triad major third of 25:32
(427+ cents!).

Included are first results of "floating Bach", using Paul E's suggestion
to hold only D grounded. Altogether, b-b-brs.zip contains ten tunings:

b-b-b.mid: as originally recorded by Bunji Hisamori, 12-tET.
b-b-bf5.mid: floating pitches except D.

b-b-br5.mid: 5-limit. Some relaxation of exact vertical JI, but not
much.
b-b-bs5.mid: Softer springs in vertical tuning by a factor of
1/4 of the original.
b-b-bss5.mid: Even softer springs in vertical tuning by a factor
of 1/16 of the original.
b-b-bsss5.mid: Even softer springs in vertical tuning by a factor
of 1/64 of the original.

b-b-br7.mid: 7-limit. Some relaxation of exact vertical JI, but not
much.
b-b-bs7.mid: Softer springs in vertical tuning by a factor of
1/4 of the original.
b-b-bss7.mid: Even softer springs in vertical tuning by a factor
of 1/16 of the original.
b-b-bsss7.mid: Even softer springs in vertical tuning by a factor
of 1/64 of the original.

And, who can resist Gershwin's "Rhapsody in Blue"? Even if you don't
like seven for the old boys, you might like it here! Original 2-hand
piano version, sequenced by Gary D. Lloyd. Tunings as above, except
no floating tuning. rh-n-blurs.zip.

JdL

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗John A. deLaubenfels <jadl@idcomm.com>

[Paul Erlich, TD 509.24:]
>JdL,
>
>Now that you've implemented "floating tuning", do you finally get the
>"classic comma pump" progression to come out with one 1/7-comma and
>three 2/7-comma shifts (or at least something with the same symmetry
>but some of the shifting absorbed into deviations from vertical JI)?

No. That's due to something else, the "credit" given when new note(s)
begin, that partially masks (in my model) the pain of retuning for notes
that are moving. When one note is retuned and two notes sound new, the
credit is higher than when two notes are retuned and one note sounds
new. Thus, in the transition C major to A minor, the only one in which
two notes continuously sound, I'm moving less than the expected 1/7
comma. I now can turn that credit completely off, which I will boldly
predict will achieve close to theoretical values; I'll do the actual
experiment soon, both floating and grounded; the floating should be a
bit closer but both should be quite close.

A quick peek at the tuning resulting from "floating Bach" shows that the
floating notes wander both above and below 12-tET. A disappointment,
perhaps, for the idea that the piece would fall naturally into a
meantone spacing. But further refinements might change the picture, and
I've barely looked at the results.

[JdL:]
>>A couple of adjustments to the tuning files to reduce the
>>likelihood of a "backside" augmented triad major third of 25:32
>>(427+ cents!).

[Paul, TD 510.1:]
>Why did this happen in the first place? Didn't you say your program
>sought to tune augmented triads in 12-tET?

Yes, when the notes are of equal volume, within some range. Imagine an
augmented triad with one note very loud, the other two very soft.
There, forming two 4:5 intervals would be worth enduring the nearly
inaudible 25:32 on the backside. It's all a matter of balance, and
clearly I'm still playing with that. By flattening the volumes of the
individual notes (tending to move them toward the same values), I'm
discouraging adventures like the JI augmented triad. But I'm reluctant
to forbid it completely.

[Paul, TD 510.2:]
>In "floating Bach", the chord at 5:11 with two high notes sounds rough,
>even more so than the usual dissonant meantone dominant seventh chord.
>What's happening there?

I'll check it out.

>For the most part, however you implemented the floating, it seems to be
>working well.

good...

>How does it compare with the other approaches as far as relaxation (or
>lack thereof) of vertical JI?

I'm using the same springs as the r5 version: pretty tight.

>Why is it hard not to allow any relaxation from vertical JI (I didn't
>understand your previous explanation)?

It's only that I haven't written fancy matrix relaxation methods yet.
If you imagine two or more nodes wired together with very strong
springs, they can move as a unit but not individually. So, if you try
to relax them one node at a time, you get lousy convergence, tending
toward no convergence whatever. I've planned, but not yet written,
methods that recognize and deal with such situations.

>That might be valuable so as to answer those who say "You can't play
>Bach in JI" -- well, not strict JI, but adaptive JI, yes.

Not following you there.

Thanks for listening, Paul! Have you sampled that Gershwin? It's
awful sweet...

JdL

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

JdL wrote,

>That's due to something else, the "credit" given when new note(s)
>begin, that partially masks (in my model) the pain of retuning for notes
>that are moving. When one note is retuned and two notes sound new, the
>credit is higher than when two notes are retuned and one note sounds
>new. Thus, in the transition C major to A minor, the only one in which
>two notes continuously sound, I'm moving less than the expected 1/7
>comma.

Sounds backwards to me. If anything, I'd want the transition from C major to
A minor to move more than 1/7 comma, so that the other transitions can move
less than 2/7 comma.

>Yes, when the notes are of equal volume, within some range. Imagine an
>augmented triad with one note very loud, the other two very soft.
>There, forming two 4:5 intervals would be worth enduring the nearly
>inaudible 25:32 on the backside. It's all a matter of balance, and
>clearly I'm still playing with that. By flattening the volumes of the
>individual notes (tending to move them toward the same values), I'm
>discouraging adventures like the JI augmented triad. But I'm reluctant
>to forbid it completely.

Did Busoni's arrangement specify certain voices louder than others? Seems
odd.

>>That might be valuable so as to answer those who say "You can't play
>>Bach in JI" -- well, not strict JI, but adaptive JI, yes.

>Not following you there.

They're right that you can't play Bach in strict JI, but it seems you _can_
play Bach in adaptive JI where the vertical intervals are pure and the
horizontal shifts are well-hidden.

🔗John A. deLaubenfels <jadl@idcomm.com>

[Paul Erlich, TD 509.24:]
>>>Now that you've implemented "floating tuning", do you finally get the
>>>"classic comma pump" progression to come out with one 1/7-comma and
>>>three 2/7-comma shifts (or at least something with the same symmetry
>>>but some of the shifting absorbed into deviations from vertical JI)?

[JdL:]
>>That's due to something else, the "credit" given when new note(s)
>>begin, that partially masks (in my model) the pain of retuning for
>>notes that are moving. When one note is retuned and two notes sound
>>new, the credit is higher than when two notes are retuned and one note
>>sounds new. Thus, in the transition C major to A minor, the only one
>>in which two notes continuously sound, I'm moving less than the
>>expected 1/7 comma.

[Paul, TD 511.10:]
>Sounds backwards to me. If anything, I'd want the transition from C
>major to A minor to move more than 1/7 comma, so that the other
>transitions can move less than 2/7 comma.

That would be supported by wildly non-linear springs, but, as you know,
a linear model leads to optimization at exactly 1/7 comma in that
transition.

Here's the "comma pump" as before, with the disputed credit turned off,
high note credit turned off, and the vertical springs made 100x what I'd
normally use:

C major:
C +5.36
E -8.45
G +7.19 (change: +5.83 cents)

A minor:
C +8.40 (change: +3.04 cents)
E -5.41 (change: +3.04 cents)
A -7.22

D minor:
D -3.16
F +12.53
A -1.38 (change: +5.84 cents)

G major:
B -12.56
D +3.14 (change: +6.30 cents)
G +1.36

Very close to theoretical, yes? Does this satisfy you that the model is
working as planned? BTW, this is with all 12 notes grounded to 12-tET,
so that doesn't seem to have cramped its style much. There's a problem
floating all but one note: first, five of 12 notes (the black keys, in
this case) aren't in the sequence at all, so if one of them were chosen,
the sequence would float away. Second, if we hold C, D, E, G, or A,
we're holding a note that needs to move to absorb the changing tuning,
so we're distorting the shape of the response to the pump. If we hold
F or B, which appear only once each, that problem goes away, but we have
a highly artificial response.

[Paul, TD 510.1:]
>>>Why did this happen in the first place? Didn't you say your program
>>>sought to tune augmented triads in 12-tET?

[JdL:]
>>Yes, when the notes are of equal volume, within some range. Imagine
>>an augmented triad with one note very loud, the other two very soft.
>>There, forming two 4:5 intervals would be worth enduring the nearly
>>inaudible 25:32 on the backside. It's all a matter of balance, and
>>clearly I'm still playing with that. By flattening the volumes of the
>>individual notes (tending to move them toward the same values), I'm
>>discouraging adventures like the JI augmented triad. But I'm
>>reluctant to forbid it completely.

[Paul:]
>Did Busoni's arrangement specify certain voices louder than others?
>Seems odd.

Yes, just by doubling a particular pitch12, it came out louder enough
than the rest to tip the tuning in that undesirable way. With the
revised tuning files and volume flattening, that's much less likely to
happen.

[Paul:]
>>>That might be valuable so as to answer those who say "You can't play
>>>Bach in JI" -- well, not strict JI, but adaptive JI, yes.

[JdL:]
>>Not following you there.

[Paul:]
>They're right that you can't play Bach in strict JI, but it seems you
>_can_ play Bach in adaptive JI where the vertical intervals are pure
>and the horizontal shifts are well-hidden.

But you agree with me that deviating a few cents from exact vertical JI
in order to smooth transitions is worthwhile, yes? So, you're speaking
of others who haven't gone along with vertical relaxation?

JdL

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

>That would be supported by wildly non-linear springs, but, as you know,
>a linear model leads to optimization at exactly 1/7 comma in that
>transition.

Not necessarily. There's no reason to say two notes shifting is twice as
painful as one note shifting. Maybe it should be the square root of two
times as painful?

>Second, if we hold C, D, E, G, or A,
>we're holding a note that needs to move to absorb the changing tuning,
>so we're distorting the shape of the response to the pump.

True. You got me there. But I still think 12 notes grounded to 12-tET
distorts things too. But I guess I no longer have a better solution that
will apply generally to all MIDI files. So I'm ready to concede this issue
(I'd still use a meantone grounding for Baroque and Renaissance music, if I
could have a choice).

>But you agree with me that deviating a few cents from exact vertical JI
>in order to smooth transitions is worthwhile, yes? So, you're speaking
>of others who haven't gone along with vertical relaxation?

Yes, and there are many of those around. Carl Lumma, for instance. And there
are many other people on this list I'd bet would feel the same way, based on
their previous comments.

🔗John A. deLaubenfels <jadl@idcomm.com>

[I wrote:]
>>That would be supported by wildly non-linear springs, but, as you
>>know, a linear model leads to optimization at exactly 1/7 comma in
>>that transition.

[Paul Erlich, TD 512.17:]
>Not necessarily. There's no reason to say two notes shifting is twice
>as painful as one note shifting. Maybe it should be the square root of
>two times as painful?

One of many non-linearities that might make sense. Consider this,
however: you have expressed skepticism (I think) that my model normally
reduces the pain of a re-tuning when new notes sound. Would it not be
an even greater stretch to say that one note's retuning partially masks
another's?

[JdL:]
>>Second, if we hold C, D, E, G, or A, we're holding a note that needs
>>to move to absorb the changing tuning, so we're distorting the shape
>>of the response to the pump.

[Paul:]
>True. You got me there. But I still think 12 notes grounded to 12-tET
>distorts things too. But I guess I no longer have a better solution
>that will apply generally to all MIDI files. So I'm ready to concede
>this issue (I'd still use a meantone grounding for Baroque and
>Renaissance music, if I could have a choice).

I'm not closed to other options (I hope I'm NEVER closed to new
options!), but what I've seen so far suggests that grounding all notes
to 12-tET works well, both at controlling drift and at allowing other
factors sufficient consideration.

I very much DO intend to play with different grounding options as time
goes on. At this point, it's still very unclear what the implications
will be.

I would think that, for retunings with weaker vertical springs (my s7,
ss7, and sss7 files in the latest zips), grounding to 12-tET becomes
more important. The idea is to begin with what is familiar,
un-disturbing, and deviate only slightly from it, hopefully to achieve
noticeable gain with negligible pain.

[JdL:]
>>But you agree with me that deviating a few cents from exact vertical
>>JI in order to smooth transitions is worthwhile, yes? So, you're
>>speaking of others who haven't gone along with vertical relaxation?

[Paul:]
>Yes, and there are many of those around. Carl Lumma, for instance. And
>there are many other people on this list I'd bet would feel the same
>way, based on their previous comments.

Carl, is that true? I know you said that for your proposed method you'd
hold exact vertical JI, but do you feel that the latest sequences I've
posted with some relaxation suffer because of it?

I do realize that some on this list believe that intervals need to be
exact even to within a fraction of a cent to achieve complete audible
desirability. Perhaps it would be fun to make some MIDI files that
would put the ear to the test!

Speaking of MIDI files, Paul E, you've often asked others (even
"begged") to make files that would fulfil a recommendation you have.
Why are you not able to make MIDI files yourself? You seem like a
natural for it! If what you are lacking is a translator between a text
representation and an actual MIDI file (with is a bit tricky in its
precise details), I can bridge that gap. You'd still have to calculate
your bends by hand, but I know you're able to do the math!!

JdL

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

JdL wrote,

>Consider this,
>however: you have expressed skepticism (I think) that my model normally
>reduces the pain of a re-tuning when new notes sound.

I'm not following.

>Would it not be
>an even greater stretch to say that one note's retuning partially masks
>another's?

I don't think any masking is going on -- I just think that if small retuning
motions occur, they may be just as painful regardless of how many notes are
involved in the motion (if they all move simultaneously and by the same
amount).

>If what you are lacking is a translator between a text
>representation and an actual MIDI file (with is a bit tricky in its
>precise details), I can bridge that gap.

OK, please do! (I remember trying to download something and it not working;
and then not having a chance to download some other thing . . .)

🔗Carl Lumma <clumma@nni.com>

>Carl, is that true? I know you said that for your proposed method you'd
>hold exact vertical JI, but do you feel that the latest sequences I've
>posted with some relaxation suffer because of it?

They sound great. I can hear suffering in the sss versions, but not in the
z, or r (or whatever) versions. But I'm experiencing funky-default-win2K
driver problems with my SB Live... can't turn off the chorus. Bleck.
Looks like I'll have to boot 98 to listen to ... Nah. :)

Have you thought about testing these things with shorter works, and/or ones
better suited for testing? Howabout a Bach chorale or two? The current
paradigm requires hours of listening, or bothersome fast-forwarding.

Incidentally, to actually answer your question: yes, it is true. I am
thoroughly opposed to vertical relaxation because I think it's unnecessary.
If you disagree, perhaps you could explain what exactly is so
un-satisfactory about the original Erlich/Vincentio root-in-meantone method?

-Carl

P.S. By all means keep your original (un-smooth) treatments on the menu.
They're already classics!

🔗John A. deLaubenfels <jadl@idcomm.com>

[Carl Lumma, TD 515.9:]
>Have you thought of using some sort of long file names to better
>identify your files? It's to the point where I need to have a copy of
>your web page open side-by-side with my collection of your midi files
>in order to figure out what I'm listening to.

Sorry, as my methods have evolved I've changed the naming conventions
all around, and I don't wonder you're confused. To make matters worse,
I messed up my postings of 01-30-00, and zipped up some old files with
older names (z7 and z5) rather than newer files with newer names (r7 and
r5, standing for "relaxed"). Arggh, I'm even confusing myself!

Tell you what I'll do: I'll include a file in each zip file with
explanatory text; in rh-n-blurs.zip, there'll be rh-n-blurs.txt, with
a brief description of what each .mid file is.

Better?

JdL

🔗John A. deLaubenfels <jadl@idcomm.com>

[I wrote:]
>>Carl, is that true? I know you said that for your proposed method
>>you'd hold exact vertical JI, but do you feel that the latest
>>sequences I've posted with some relaxation suffer because of it?

[Carl Lumma, TD 516.13
>They sound great. I can hear suffering in the sss versions, but not in
>the z, or r (or whatever) versions. But I'm experiencing
>funky-default-win2K driver problems with my SB Live... can't turn off
>the chorus. Bleck. Looks like I'll have to boot 98 to listen to ...
>Nah. :)

Oh, you've got a beta of Win2K? Kyool! Yeah, the sss versions are
pretty close to 12-tET; I don't wonder if they sound out of tune!

[Carl:]
>Have you thought about testing these things with shorter works, and/or
>ones better suited for testing? Howabout a Bach chorale or two? The
>current paradigm requires hours of listening, or bothersome
>fast-forwarding.

Understood; I guess I've imagined that people might not listen to the
whole sequence, but it's become a big download as well, what with so
many tunings in each zip file lately.

Do you have one or more sequences you'd like to suggest?

[Carl:]
>Incidentally, to actually answer your question: yes, it is true. I am
>thoroughly opposed to vertical relaxation because I think it's
>unnecessary. If you disagree, perhaps you could explain what exactly
>is so un-satisfactory about the original Erlich/Vincentio
>root-in-meantone method?

"Unnecessary" is a relative term. For me, a constant flattening of
fifths by 5+ cents starts to become uncomfortable over time. On the
other hand, to flatten a fifth, or other note, by that or even more in
the heat of a difficult transition can be well worthwhile.

I do agree that if you're tuning chords with high harmonics, 11 thru
19, for example, then vertical tuning won't tolerate much deviation.

JdL

🔗Carl Lumma <clumma@nni.com>

>Oh, you've got a beta of Win2K? Kyool!

Yeah, a beta... (cough!)

>>Understood; I guess I've imagined that people might not listen to the
>>whole sequence, but it's become a big download as well, what with so
>>many tunings in each zip file lately.
>
>Do you have one or more sequences you'd like to suggest?

Please see http://lumma.org/ForJdL.zip.

>>Incidentally, to actually answer your question: yes, it is true. I am
>>thoroughly opposed to vertical relaxation because I think it's
>>unnecessary. If you disagree, perhaps you could explain what exactly
>>is so un-satisfactory about the original Erlich/Vincentio
>>root-in-meantone method?
>
>"Unnecessary" is a relative term. For me, a constant flattening of
>fifths by 5+ cents starts to become uncomfortable over time. On the
>other hand, to flatten a fifth, or other note, by that or even more in
>the heat of a difficult transition can be well worthwhile.

Possibly, but I'd be a lot more inclined to believe it if the
Vincentio/Erlich method was first demonstrated to be wanting in some way.

-Carl

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗John A. deLaubenfels <jadl@idcomm.com>

[I wrote:]
>>Oh, you've got a beta of Win2K? Kyool!

[Carl Lumma, TD 521.5:]
>Yeah, a beta... (cough!)

Bugs and all...

[JdL:]
>>Do you have one or more sequences you'd like to suggest?

[Carl:]
>Please see http://lumma.org/ForJdL.zip.

Consider it seen! Thanks!!

[Carl:]
>>Incidentally, to actually answer your question: yes, it is true. I am
>>thoroughly opposed to vertical relaxation because I think it's
>>unnecessary. If you disagree, perhaps you could explain what exactly
>>is so un-satisfactory about the original Erlich/Vincentio
>>root-in-meantone method?

[JdL:]
>>"Unnecessary" is a relative term. For me, a constant flattening of
>>fifths by 5+ cents starts to become uncomfortable over time.

[Paul Erlich, TD 521.17:]
>John, in the Erlich/Vicentino root-in-meantone method, all vertical
>fifths are just.

Yes, I do know that. From the context of Carl's post, I took it, I
guess erroneously, that he was referring to the "pre-Erlich" version,
though as I understand, even Vicentino himself wanted a few just fifths
added to the mix.

The Erlich/Vicentino method may prove formidable, if one of them
(presumably, the one who is alive) decides to move it from idea to
reality. It is weak at handling 19th century pumps, and IMHO could use
a touch of springs, but I for one am not writing it off, at least for
18th century and earlier music.

JdL

🔗Carl Lumma <clumma@nni.com>

>>Yeah, a beta... (cough!)
>
>Bugs and all...

Yeah -- even in the final version I'm using. :)

>Yes, I do know that. From the context of Carl's post, I took it, I
>guess erroneously, that he was referring to the "pre-Erlich" version,
>though as I understand, even Vicentino himself wanted a few just fifths
>added to the mix.

I should say that I don't really know what the Vincentio method is. I was
just following the example of some posts here that it was equivalent to
Erlich's method. Perhaps I misunderstood those posts. I was referring to
a method where a meantone score would be tuned in 1/4 comma (say), and then
as a second step, all 5-limit consonances are made just.

>The Erlich/Vicentino method may prove formidable, if one of them
>(presumably, the one who is alive) decides to move it from idea to
>reality. It is weak at handling 19th century pumps, and IMHO could use
>a touch of springs, but I for one am not writing it off, at least for
>18th century and earlier music.

It is true that pumps based on 3- and 4-tet will not be preserved in
Erlich's method. And I must say that your latest r versions are amazingly
smooth-sounding. Methinks my fickle ear prefers the "pre-spring" 1999
versions, though.

-Carl

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

I wrote,

>>John, in the Erlich/Vicentino root-in-meantone method, all vertical
>>fifths are just.

John deLaubenfels wrote,

Vicentino suggested two different tunings for his 36-tone instrument. The
first was essentially 31-tET with 5 just fifths. The second was 19 notes of
meantone with 17 just fifths. The latter is the one that "Erlich/Vicentino"
refers to.

That's what it's for. Maybe I'll get around to programming it someday. But
as we've seen, your program, with the right parameters, can get pretty close
-- certainly it would get close enough if you were to use a meantone
grounding.