Re : F in G7 as 21/16 rather than 4/3...

>
> If you actually SANG an F in G7 as 16/9 relative to C then I suspect that
> you wouldn't make the cut at an audition for Gerald Eskelin's L.A. Jazz
> Choir, or any good barbershop quartet.
>

How about the Mormon Tabernacil Choir? I'm sure you are correct with
the settings you site, and I am not against septimal intervals, but
are (and others in this thread) you saying that 7/4 (21/16) is ALWAYS
the right choice for the dominant seventh?

Bob Valentine

>From: DWolf77309@cs.com
>
>In einer Nachricht vom 11/11/99 8:50:23 AM (MEZ) Mitteleurop�ische
>Zeitschreibt bval@iil.intel.com:
>
><<
> How about the Mormon Tabernacil Choir? I'm sure you are correct with
> the settings you site, and I am not against septimal intervals, but
> are (and others in this thread) you saying that 7/4 (21/16) is ALWAYS
> the right choice for the dominant seventh?
>
> Bob Valentine >>
>
>While this thread is fairly septimal, this list has been of two minds about
>the dominant seventh. In blues, where seventh chords can be built over every
>degree, the seventh in the chord is functionally consonant, suggesting a 7/4.
> But in classical, functional tonality, the dominant seventh chord is a
>dissonance to be resolved, and using 16/9 as the seventh fits the bill for
>both smooth voice leading (which is something different to jazz "voicing")
>and the required dissonance. The augmented sixth chord, on the other hand,
>can be very close to a 7/4 in meantone, the tuning environment in which the
>classical tonal grew up.

My view is that the 7/4 seventh is exactly the one used by good string
quartets in the dominant 7th chord leading to the tonic in e.g., Mozart's
music.

Let's remember that meantone tuning is a possible tuning for keyboards, but
that singers and unfretted strings have never been constrained by such
tuning, except when accompanied by meantone instruments. Meantone tuning,
like any system of fixed tuning, can never be the standard of intonation.

John Link
ALMOST ACAPPELLA

[John Link:]
> Let's remember that meantone tuning is a possible tuning for
keyboards, but that singers and unfretted strings have never been
constrained by such tuning, except when accompanied by meantone
instruments. Meantone tuning, like any system of fixed tuning, can
never be the standard of intonation.

While I can't vouch for the authenticity of the claim, I do know that
Joseph Yasser (_A THEORY OF EVOLVING TONALITY_ p. 193) used the
example of Russian a cappella church music (which he said did not use
the V. 4:5:6:7) to contest the claim that anything other than the 7/4
in the dominant seventh is due to the influence of equal temperament
(I don't have the book anymore, and I can't quite seem to remember to
what degree he meant this to also broadly imply all fixed
intonations).

Dan

>From: "D.Stearns" <stearns@capecod.net>
>
>While I can't vouch for the authenticity of the claim, I do know that
>Joseph Yasser (_A THEORY OF EVOLVING TONALITY_ p. 193) used the
>example of Russian a cappella church music (which he said did not use
>the V. 4:5:6:7) to contest the claim that anything other than the 7/4
>in the dominant seventh is due to the influence of equal temperament
>(I don't have the book anymore, and I can't quite seem to remember to
>what degree he meant this to also broadly imply all fixed
>intonations).

I once had that book but think that I sold it. I'll look for it.

John Link
ALMOST ACAPPELLA

Daniel Wolf wrote,

>While this thread is fairly septimal, this list has been of two minds about

>the dominant seventh. In blues, where seventh chords can be built over
every
>degree, the seventh in the chord is functionally consonant, suggesting a
7/4.
>But in classical, functional tonality, the dominant seventh chord is a
>dissonance to be resolved, and using 16/9 as the seventh fits the bill for
>both smooth voice leading (which is something different to jazz "voicing")
>and the required dissonance.

I agree wholeheartedly and emphatically -- John Link take note!

>The augmented sixth chord, on the other hand,
>can be very close to a 7/4 in meantone, the tuning environment in which the

>classical tonal grew up.

Yes yes!

Dan Stearns wrote,

>While I can't vouch for the authenticity of the claim, I do know that
>Joseph Yasser (_A THEORY OF EVOLVING TONALITY_ p. 193) used the
>example of Russian a cappella church music (which he said did not use
>the V. 4:5:6:7) to contest the claim that anything other than the 7/4
>in the dominant seventh is due to the influence of equal temperament

That reminds me, the Bulgarian Women's Choir are decidedly un-barbershop in
that they seem to avoid 7:4s.

Daniel Wolf wrote,

>baroque and classical tonal music
>_largely_ follows the resources and restrictions of the meantone gamut.

This is an important point when interpreting music from this period (and I
would definitely add the Renaissance to this). It is very unfaithful to the
composers' wishes to try to render this music in the kind of strict JI being
discussed lately, with drifts and/or shifts of a full comma being introduced
somewhat arbitrarily. I strongly believe that music is shaped by the tuning
in which it is written -- for example, the amount of time and repetition a
composer in the meantone period might give to a note forming a second with
the root of a major triad could depend greatly on the dissonance it would
form in his/her tuning, while in JI it might be too consonant at 9:8 to make
sense in the musical context. I'm all for writing music that exploits the
possibilities of JI or any other tuning system, but am very wary of
transcribing music -- especially great music -- from one tuning system into
another.

[Paul Erlich, TD 392.1:]
> It is very unfaithful to the composers' wishes to try to render this
> music in the kind of strict JI being discussed lately, with drifts
> and/or shifts of a full comma being introduced somewhat arbitrarily.

Full comma? Surely you have not forgotten our exchanges on this list
in which I demonstrated that, even without sophisticated look-forward
algorithms, maximum shifts can be held to far below a comma?

> I'm all for writing music that exploits the possibilities of JI or any
> other tuning system, but am very wary of transcribing music --
> especially great music -- from one tuning system into another.

Are you wary, or are you closed to the idea?

[Paul Erlich, TD 392.13:]
> That's an excellent strategy for trying to play JI. But I would argue
> that if you are trying to play Bach or Mozart and interpret every
> major second as one of the above, you are doing a disservice to these
> composers.

If I have children, and my children have children, my genes are cut into
tiny pieces, contributing to beings who look very different from me,
yet who retain something from me. Is this a "disservice" to me? If I
am "great", is this an even greater "disservice"?

Paul, I have numerous examples of 19th century piano music rendered in
both 5-limit and 7-limit adaptive tuning on my web site:

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

Last time I asked, you had found listening to them too difficult to fit
your schedule. You recently chided John Link for (in your speculation)
making guesses about the appropriateness of tunings without having heard
them. Does the same apply to you, or not?

If you have listened to the 7-limit tunings and find them not to your
ear's taste, that's fine. Some of us happen to think the 7-limit tuning
is divine. Tell me: in your opinion, does this represent some kind of
slap in the face ("disservice", "unfaithful") to the composer of the
original 12-tET piece? I find the suggestion absurd.

It is impossible to know what Beethoven, Schubert, Brahms, Ravel, etc.,
would think of 7-limit dynamic tuning. I won't presume to say that I'm
certain they'd like it. Are you willing to say that you're not certain
they wouldn't be delighted?

JdL

I wrote,

>> It is very unfaithful to the composers' wishes to try to render this
>> music in the kind of strict JI being discussed lately, with drifts
>> and/or shifts of a full comma being introduced somewhat arbitrarily.

John deLaubenfels wrote,

>Full comma? Surely you have not forgotten our exchanges on this list
>in which I demonstrated that, even without sophisticated look-forward
>algorithms, maximum shifts can be held to far below a comma?

Of course I haven't forgotten -- have you forgotten that I improved your
maximum shift for the I-vi-ii-V-I progression from 11 cents to 3+ cents?
Anyway, John, I wasn't referring to you above -- there have been plenty of
posts very recently that do suggest full-comma shifts.

>> I'm all for writing music that exploits the possibilities of JI or any
>> other tuning system, but am very wary of transcribing music --
>> especially great music -- from one tuning system into another.

>Are you wary, or are you closed to the idea?

Very open to the idea, but wary.

>Paul, I have numerous examples of 19th century piano music rendered in
>both 5-limit and 7-limit adaptive tuning on my web site:

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

>Last time I asked, you had found listening to them too difficult to fit
>your schedule.

I've listened to a few of them and mostly enjoyed the 5-limit ones except
for a few rough spots. But you're not using too many full-comma shifts, are
you? The 7-limit ones don't seem to work, musically speaking.

I wrote,

>> That's an excellent strategy for trying to play JI. But I would argue
>> that if you are trying to play Bach or Mozart and interpret every
>> major second as one of the above, you are doing a disservice to these
>> composers.

John wrote,

>It is impossible to know what Beethoven, Schubert, Brahms, Ravel, etc.,
>would think of 7-limit dynamic tuning. I won't presume to say that I'm
>certain they'd like it. Are you willing to say that you're not certain
>they wouldn't be delighted?

I'm all for experimentation, but there are some JI advocates around who seem
to think even Bach and Mozart should be in JI, and with full-comma shifts no
less. I guess I just disagree.

John deLabenfels wrote,

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

There's a disturbing upward shift in the Bach 5-limit example,
02:00:22-00:23, and an even worse one at 02:44-02:45. Also, what's that
crazy chord at 01:44?

Did you say you were tuning diminished seventh chords in 12-tET?

[Paul Erlich, TD 395.21:]
>John deLaubenfels wrote,

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

> There's a disturbing upward shift in the Bach 5-limit example,
> 02:00:22-00:23, and an even worse one at 02:44-02:45. Also, what's
> that crazy chord at 01:44?

I listened to the 5-limit Bach and couldn't find the effects you
describe. Please check the date of your file (should be 10-19-99)
and the size (88540 bytes). I suspect you have an older version.

As to the chords around 1:44: I don't know about you, but I love'm!
There are a couple of minor second suspensions in the sequence, as I'm
sure you noticed.

[Paul:]
> Did you say you were tuning diminished seventh chords in 12-tET?

Yes. That's all controllable from the tuning file(s) in use on a given
run. I tune full diminished sevenths, augmented triads, and long
chains of fifths, all in 12-tET.

JdL

>>John deLaubenfels wrote,

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

>> There's a disturbing upward shift in the Bach 5-limit example,
>> 02:00:22-00:23, and an even worse one at 02:44-02:45. Also, what's
>> that crazy chord at 01:44?

>I listened to the 5-limit Bach and couldn't find the effects you
>describe. Please check the date of your file (should be 10-19-99)
>and the size (88540 bytes). I suspect you have an older version.

It's the right version. The above should read "00:22=00:23". I don't know
how the 02: got in front.

>> Did you say you were tuning diminished seventh chords in 12-tET?

>Yes. That's all controllable from the tuning file(s) in use on a given
>run. I tune full diminished sevenths, augmented triads, and long
>chains of fifths, all in 12-tET.

Then there must be melodic reasons why many of the diminished 7th chords in
your sequences sound odd to me.

[Paul Erlich, TD 396.9:]
>>>> http://www.idcomm.com/personal/jadl/
>>> There's a disturbing upward shift in the Bach 5-limit example,
>>> 02:00:22-00:23, and an even worse one at 02:44-02:45. Also, what's
>>> that crazy chord at 01:44?
>>I listened to the 5-limit Bach and couldn't find the effects you
>>describe. Please check the date of your file (should be 10-19-99)
>>and the size (88540 bytes). I suspect you have an older version.
>It's the right version. The above should read "00:22=00:23". I don't
>know how the 02: got in front.

OK, I'll listen again. Am I right in thinking that you're referring not
to something sounding out of tune, but something sliding in tuning?
This set of sequences, dated 10-19-99, and the later set I posted just
last night, all try very hard not to change the tuning of a note that is
continuously sounding, even at the expense of the best possible tuning
at a given moment.

>>> Did you say you were tuning diminished seventh chords in 12-tET?
>>Yes. That's all controllable from the tuning file(s) in use on a given
>>run. I tune full diminished sevenths, augmented triads, and long
>>chains of fifths, all in 12-tET.
>Then there must be melodic reasons why many of the diminished 7th
>chords in your sequences sound odd to me.

Well, I'm not sure I'd call the reasons "melodic", but a sequence can
be put in a bind by circumstance, and something's gotta give! Also, of
course, I'm not claiming that I have achieved the height of perfection
in this game! I do think these tunings may represent the current edge
of the envelope, and to my ear the 7-limit sequences sound wonderful,
if not honed to absolute perfection.

JdL

John deLaubenfels wrote,

>OK, I'll listen again. Am I right in thinking that you're referring not
>to something sounding out of tune, but something sliding in tuning?

Yes. It's very disturbing to me, maybe since I grew up hearing mostly Bach
and Chopin until I was 12.

[Paul Erlich, TD 397.11:]
> Yes. It's very disturbing to me, maybe since I grew up hearing mostly
> Bach and Chopin until I was 12.

Try as I might, I can't come up with any glitchy sound in the 5-limit
Bach file (b-b-bz5.mid, 10-19-99, 88540 bytes) at 00:22-00:23 or
2:44-2:45. Would one of the other list members who has this file (Carl?
Jay?) listen and see if you can help me understand what Paul is talking
about?

JdL

John deLaubenfels wrote,

>Try as I might, I can't come up with any glitchy sound in the 5-limit
>Bach file (b-b-bz5.mid, 10-19-99, 88540 bytes) at 00:22-00:23 or
>2:44-2:45.

It's not a glitchy sound but a slight but noticeable difference in tuning in
two successive instances of a note.

[Paul Erlich, TD 399.10:]
> It's not a glitchy sound but a slight but noticeable difference in
> tuning in two successive instances of a note.

Ahh, ok; for some reason I though you had said it was a continuously
sounding note that you objected to. It is true that successive notes
of the same nominal pitch need to shift to accommodate the changing
harmonies.

I do have the program try to minimize such shifts, and it can be made to
call them more "painful", but of course doing so tends to result in more
places where the tuning can't change and therefore won't be ideal over
part of a passage. In adaptive tuning of rapidly modulating or
chromatic music, such tradeoffs occur up to several times per second.

One nice thing about fixed tunings is that shifts are eliminated
altogether, and one can always return to them for that rock-solid
feeling. Still, I have found that the objectionability of adaptive
movement diminishes greatly once one's ears are "stretched" to the
possibility.

If the five-limit sounds irritating, then the seven-limit is probably
going to be completely inaccessible to you for awhile, since, of
necessity, motion there is greater.

Thanks, Carl (TD 400.12) and Jay (TD 400.2) for your research and
comments!

JdL

John deLaubenfels wrote,

>I do have the program try to minimize such shifts, and it can be made to
>call them more "painful", but of course doing so tends to result in more
>places where the tuning can't change and therefore won't be ideal over
>part of a passage. In adaptive tuning of rapidly modulating or
>chromatic music, such tradeoffs occur up to several times per second.

I would recommend that you do call them more "painful", since in chords
going by several times per second, small deviations from JI should not be
noticeable. Even if you call shifts infinitely painful (which I wouldn't),
you can do Bach in meantone and never deviate more than 5-6 cents from
5-odd-limit JI.

[Paul Erlich, TD 401.10:]
> John deLaubenfels wrote,
>> I do have the program try to minimize such shifts, and it can be made
>> to call them more "painful", but of course doing so tends to result
>> in more places where the tuning can't change and therefore won't be
>> ideal over part of a passage. In adaptive tuning of rapidly
>> modulating or chromatic music, such tradeoffs occur up to several
>> times per second.

> I would recommend that you do call them more "painful", since in
> chords going by several times per second, small deviations from JI
> should not be noticeable.

Your ear is very different from mine in this regard; I think the tuning
is held just a little TOO fixed. I find that even very brief moments
of mistuning are quite audible (though sometimes unavoidable); I would
probably tend toward more movement and better tuning rather than the
reverse.

> Even if you call shifts infinitely painful (which I wouldn't), you can
> do Bach in meantone and never deviate more than 5-6 cents from
> 5-odd-limit JI.

I'm interested in an approach which can also be applied to pieces that
modulate freely. Meantone has serious problems when the harmony jumps
about in a 19th century way. A flatness of 5-6 cents in the 3:2
interval, required by meantone, seems excessive, and unnecessary, to me.
Five-limit is something my ear has long eschewed now that it can get
seven.

Of course, what your ear likes is absolutely valid for YOU. I'll make
a tighter version of the Bach if you're interested. Too bad we don't
have a meantone sequence of it for comparison!

JdL

>> Even if you call shifts infinitely painful (which I wouldn't), you can
>> do Bach in meantone and never deviate more than 5-6 cents from
>> 5-odd-limit JI.

>I'm interested in an approach which can also be applied to pieces that
>modulate freely. Meantone has serious problems when the harmony jumps
>about in a 19th century way. A flatness of 5-6 cents in the 3:2
>interval, required by meantone, seems excessive, and unnecessary, to me.

But Bach's music doesn't modulate in a 19th century way, and as I've shown,
adaptively altering meantone triads to JI shouldn't result in any shifts as
large as the ones I heard in your sequence (which were in the top voice, not
the bass).

>Of course, what your ear likes is absolutely valid for YOU. I'll make
>a tighter version of the Bach if you're interested. Too bad we don't
>have a meantone sequence of it for comparison!

There really needs to be one. BTW, Wendy Carlos did "Switched-On Bach" in
1/5-comma meantone, and there was an article called "the 48 in 31" by one of
the Scalatron people claiming that the entire WTC worked better in meantone
(specifically, 31-tET).

On Fri, 19 Nov 1999 13:35:28 -0500, "Paul H. Erlich"
<PErlich@Acadian-Asset.com> wrote:

>There really needs to be one. BTW, Wendy Carlos did "Switched-On Bach" in
>1/5-comma meantone, and there was an article called "the 48 in 31" by one of
>the Scalatron people claiming that the entire WTC worked better in meantone
>(specifically, 31-tET).

Actually, some parts (of the 25th anniversary version) were in 1/5-comma
meantone, and others were in a kind of well-tempered scale ("circular"
tuning in her terminology). But either tuning sounds good for Bach to me; I
usually use a well-tempered scale of one kind or another. I haven't tried
the WTC in 31-TET, but it sounds like an interesting idea, since it's so
close to 1/4-comma meantone.

--
see my music page ---> +--<http://www.io.com/~hmiller/music/music.html>--
Thryomanes /"If all Printers were determin'd not to print any
(Herman Miller) / thing till they were sure it would offend no body,
moc.oi @ rellimh <-/ there would be very little printed." -Ben Franklin

[Paul Erlich, TD 402.5:]
>>I'm interested in an approach which can also be applied to pieces that
>>modulate freely. Meantone has serious problems when the harmony jumps
>>about in a 19th century way. A flatness of 5-6 cents in the 3:2
>>interval, required by meantone, seems excessive, and unnecessary, to me.

> But Bach's music doesn't modulate in a 19th century way, and as I've
>shown, adaptively altering meantone triads to JI shouldn't result in
>any shifts as large as the ones I heard in your sequence (which were in
>the top voice, not the bass).

>>Of course, what your ear likes is absolutely valid for YOU. I'll make
>>a tighter version of the Bach if you're interested. Too bad we don't
>>have a meantone sequence of it for comparison!

>There really needs to be one. BTW, Wendy Carlos did "Switched-On Bach"
>in 1/5-comma meantone, and there was an article called "the 48 in 31"
>by one of the Scalatron people claiming that the entire WTC worked
>better in meantone (specifically, 31-tET).

OK, first, I just posted a tighter version of the Bach on my web:

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

Near the top, b-b-btight.zip. This makes motion of tuning between
successive notes of the same nominal pitch four times as painful as
the one you listened to before. I listened to it, and it sounds good
from a tuning standpoint, meaning that MAYBE it could be tightened
even more. But, if you would, listen to this and see what you think.

Second, regarding your idea of doing adaptive tuning from meantone, let
me ask: Paul, do you program? You seem like an ideal candidate: your
mind is sharp enough and picky enough (I mean this as a compliment;
remember, I am a programmer). I'm not sure that your claims about
meantone would be born out in practice, but I would very much urge you
to try. The field of adaptive tuning is wide open, but is also
hands-on. My guess is that those who speculate and do not program will
find their ideas left behind, which might be a shame for music.

JdL

John deLaubenfels wrote,

>OK, first, I just posted a tighter version of the Bach on my web:

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

>Near the top, b-b-btight.zip. This makes motion of tuning between
>successive notes of the same nominal pitch four times as painful as
>the one you listened to before. I listened to it, and it sounds good
>from a tuning standpoint, meaning that MAYBE it could be tightened
>even more. But, if you would, listen to this and see what you think.

Even in this version, the chord at 00:06 has a chord with the "melody"
(scale degree 2) noticeably shifted upwards from its previous pitch. Can you
give us an analysis of how the first 6 seconds of the piece are tuned in
your various schemes?

>Second, regarding your idea of doing adaptive tuning from meantone, let
>me ask: Paul, do you program?

Yes (every day), but I've never done MIDI (except on a Commodore 64 back
when I was in high school. Perhaps (off the list) you could teach me to
construct these files. For one thing, I'd like to put some of my own 22-tET
music in MIDI form.

[Paul Erlich, TD 404.7:]
> Even in this version, the chord at 00:06 has a chord with the "melody"
> (scale degree 2) noticeably shifted upwards from its previous pitch.
> Can you give us an analysis of how the first 6 seconds of the piece
> are tuned in your various schemes?

The following analysis applies to the b-b-btight.zip file b-b-bp5.mid,
dated 11-20-99 (88614 bytes). The piece is in D minor, though it ends
in typical fashion with a Picardy (sp?) third, in D major.

The first chord is at 0:02.319; it's D,F,A, the tonic minor, and it's
tuned in F major (i.e., D minor). The same chord repeats at 0:04.341,
and the tuning stays the same.

At 0:05.515, we have D,G,Bb,E, which the program tunes as C major.
At 0:06.368, we have C#,G,A,E, which the program tunes as A major.

In the transition between C major and A major, the E sharpens, as you've
noted; the raw bend message goes from E4 58 3A to E4 73 3F, or -680
bend units to -13 bend units, or (using 40.96 bu/cent) -16.60 cents to
-0.32 cents, or a change of +16.28 cents, well over half a comma.

The program recognizes this movement as painful (all the more so with
the increased coefficients!), but is strongly influenced by the tuning
file to use the keys indicated.

The chord which forces C major is a strange one: a dominant 9th with the
root missing. How else, I wonder, might that chord plausibly be tuned?

JdL

[JdL:]
>> ... regarding your idea of doing adaptive tuning from meantone,
>> let me ask: Paul, do you program?

[Paul Erlich, TD 404.7:]
> Yes (every day), but I've never done MIDI (except on a Commodore 64
> back when I was in high school. Perhaps (off the list) you could teach
> me to construct these files. For one thing, I'd like to put some of my
> own 22-tET music in MIDI form.

It's funny how long we can post without talking about what else we do in
life... I have a feeling that describing how to construct MIDI files is
something worthy of sharing on the list. Am I right in thinking that
the page I have on my web:

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

is more basic than you need? It describes how to calculate the number
of midi bend units for a particular number of cents shift, but does not
go into how a midi file is constructed.

Actually, I'm thinking of sharing a subset of my C++ source, not (at the
moment at least) including the inner guts of how a final tuning decision
is made, but including the picky file I/O and midi-event classes I've
put together. One or two list members already have an older version of
JI Relay source, but it does not include MIDI file I/O.

JdL

I wrote,

>> Even in this version, the chord at 00:06 has a chord with the "melody"
>> (scale degree 2) noticeably shifted upwards from its previous pitch.
>> Can you give us an analysis of how the first 6 seconds of the piece
>> are tuned in your various schemes?

John deLaubenfels wrote,

>The following analysis applies to the b-b-btight.zip file b-b-bp5.mid,
>dated 11-20-99 (88614 bytes). The piece is in D minor, though it ends
>in typical fashion with a Picardy (sp?) third, in D major.

BTW, if the piece ended on a minor triad, I might recommend tuning that
triad 16:19:24.

>The first chord is at 0:02.319; it's D,F,A, the tonic minor, and it's
>tuned in F major (i.e., D minor). The same chord repeats at 0:04.341,
>and the tuning stays the same.

>At 0:05.515, we have D,G,Bb,E, which the program tunes as C major.
>At 0:06.368, we have C#,G,A,E, which the program tunes as A major.

Not sure how you translate these into specific tuning numbers.

>In the transition between C major and A major, the E sharpens, as you've
>noted; the raw bend message goes from E4 58 3A to E4 73 3F, or -680
>bend units to -13 bend units, or (using 40.96 bu/cent) -16.60 cents to
>-0.32 cents, or a change of +16.28 cents, well over half a comma.

Then I wasn't hallucinating! In my opinion, this shift disturbs the flow of
the music, the new pitch introducing new "information" on the pitch set to
the listener, where the motivic structure of the composition rests on an
exact repetition being perceived here.

>The chord which forces C major is a strange one: a dominant 9th with the
>root missing. How else, I wonder, might that chord plausibly be tuned?

A C would sound totally inappropriate under the chord in question,
suggesting a modulation to the relative major rather than a dominant
preparation in the original key. The chord in question is simply a
supertonic half-diminished seventh, or subdominant minor with added major
sixth. If you allow 7-limit interpretations, I might tune the chord
1/7:1/6:1/5:1/4. In the 5-limit case (more appropriate, I feel), the chord
is a dissonant one, so we must analyze E as an added note. In this case it's
an anticipation, and should simply take its tuning from the next chord. If
you do it my way, and base everything on meantone, you'd start out with the
chord in meantone and, in the 5-limit case, just adjust the tuning so that
the _triad_ is in tune.

Dissonant additions to chords in common-practice harmony are best analyzed
in terms of their _linear_ function; that is, they acquire their musical
meaning through their _melodic_ or _contrapuntal_ role as anticipations,
suspensions, or (often the case with sevenths, flat ninths, or secondary
leading tones) by supplying the classic tritone resolution. You may be
surprised to learn how strictly their usage in the common-practice musical
literature has been confined to these roles. See, for example, Allen Forte,
_Tonal Harmony in Concept and Practice_. I would say that you must first
learn to analyze a piece of music in these terms before you can effectively
offer improvements in its tuning.

John deLaubenfels wrote,

>It describes how to calculate the number
>of midi bend units for a particular number of cents shift, but does not
>go into how a midi file is constructed.

I need the latter. I've tried to get CSound and Rocky but experienced
problems in downloading.

Here is a midi retuning program with source.

http://www.kees.cc/tuning/midimap.html

Let me know if it works and is complete. I put it together in great haste.

Kees

John deLaubenfels wrote:
> Too bad we don't have a meantone sequence of it for comparison!

I have made one with Scala. I'll mail it to you.

Manuel Op de Coul coul@ezh.nl

[Paul Erlich, TD 405.5:]
>>>Even in this version, the chord at 00:06 has a chord with the
>>>"melody" (scale degree 2) noticeably shifted upwards from its
>>>previous pitch. Can you give us an analysis of how the first 6
>>>seconds of the piece are tuned in your various schemes?

[JdL:]
>>The following analysis applies to the b-b-btight.zip file b-b-bp5.mid,
>>dated 11-20-99 (88614 bytes). The piece is in D minor, though it ends
>>in typical fashion with a Picardy (sp?) third, in D major.

[Paul:]
>BTW, if the piece ended on a minor triad, I might recommend tuning that
>triad 16:19:24.

Well, that's one of many things that my program doesn't have knowledge
about; another is whether a particular scale degree is the "melody"
or not.

[JdL:]
>>The first chord is at 0:02.319; it's D,F,A, the tonic minor, and it's
>>tuned in F major (i.e., D minor). The same chord repeats at 0:04.341,
>>and the tuning stays the same.

>>At 0:05.515, we have D,G,Bb,E, which the program tunes as C major.
>>At 0:06.368, we have C#,G,A,E, which the program tunes as A major.

[Paul:]
>Not sure how you translate these into specific tuning numbers.

See TD 330.7 for an in-depth description and example 7-limit tuning
file; see TD 333.9 for a 5-limit tuning file which follows the same
rules.

[JdL:]
>>In the transition between C major and A major, the E sharpens, as
>>you've noted; the raw bend message goes from E4 58 3A to E4 73 3F, or
>>-680 bend units to -13 bend units, or (using 40.96 bu/cent) -16.60
>>cents to -0.32 cents, or a change of +16.28 cents, well over half a
>>comma.

[Paul:]
>Then I wasn't hallucinating!

Not about that, anyway (sorry, couldn't resist...)

[Paul:]
>In my opinion, this shift disturbs the flow of the music, the new
>pitch introducing new "information" on the pitch set to the listener,
>where the motivic structure of the composition rests on an exact
>repetition being perceived here.

Well, to me that's a fancy way of saying your ear doesn't like it, which
I can accept. To my ear it slides right by without difficulty or flow
disruption.

[JdL:]
>>The program recognizes this movement as painful (all the more so with
>>the increased coefficients!), but is strongly influenced by the tuning
>>file to use the keys indicated.

>>The chord which forces C major is a strange one: a dominant 9th with
>>the root missing. How else, I wonder, might that chord plausibly be
>>tuned?

[Paul:]
>A C would sound totally inappropriate under the chord in question,
>suggesting a modulation to the relative major rather than a dominant
>preparation in the original key. The chord in question is simply a
>supertonic half-diminished seventh, or subdominant minor with added
>major sixth. If you allow 7-limit interpretations, I might tune the
>chord 1/7:1/6:1/5:1/4. In the 5-limit case (more appropriate, I feel),
>the chord is a dissonant one, so we must analyze E as an added note. In
>this case it's an anticipation, and should simply take its tuning from
>the next chord. If you do it my way, and base everything on meantone,
>you'd start out with the chord in meantone and, in the 5-limit case,
>just adjust the tuning so that the _triad_ is in tune.

>Dissonant additions to chords in common-practice harmony are best
>analyzed in terms of their _linear_ function; that is, they acquire
>their musical meaning through their _melodic_ or _contrapuntal_ role as
>anticipations, suspensions, or (often the case with sevenths, flat
>ninths, or secondary leading tones) by supplying the classic tritone
>resolution. You may be surprised to learn how strictly their usage in
>the common-practice musical literature has been confined to these
>roles. See, for example, Allen Forte, _Tonal Harmony in Concept and
>Practice_. I would say that you must first learn to analyze a piece of
>music in these terms before you can effectively offer improvements in
>its tuning.

I hear you saying two contradictory things: you champion the idea of
tuning through an intermediate meantone representation, saying that
this, in and of itself, effectively deals with fractional comma motion
(at least in well-behaved sequences such as Bach might have written),
but you also say that it's a waste of time to pursue "effective" tuning
without considering a number of other factors in a given sequence.

To the second point, I would say this: eventually I want to consider as
many relevant contributions as possible, but I think we're a long way
from the edge of what can be accomplished with a simpler view such as my
program takes.

To the first point, let's look at a 31-tET ("meantone") representation
of the Bach fragment. The basic 31-tET intervals are:

2:1 31
3:2 18 (12 of 'em make 7*31 - 1)
4:3 13
5:4 10 (3 of 'em make 31 - 1)
6:5 8 (4 of 'em make 31 + 1)
7:6 7
8:7 6
9:8 5
10:9 5 (it's a meantone scale)
16:15 3
25:24 2

Each 31-tET microtone is about 38.71 cents.

A dom9 chord stacked from C would be:

00, 10, 18, 25, (31), 36 (7-limit)
00, 10, 18, 26, (31), 36 (5-limit)

So, D minor would become 5, 13, 23
D, G, Bb, E would become 5, 18, 26, 41
C#,G, A, E would become 2, 18, 23, 41

As you stated, this chord sequence does not skew the tuning in 31-tET.
And, there's no motion whatever between chords; it's "perfect", yes?

But there's a problem: you've said that after going through the meantone
intermediate tuning, you would then fix the tuning of the chords to be
true JI.

Here's the catch: once you fix the tuning, you'll be looking at exactly
the same tradeoffs that my program is looking at! So I don't think that
an intermediate meantone representation adds anything useful to the
tuning process. But it does offer a hindrance whenever a sequence
modulates more freely and there are meantone "comma pumps" (in this case
a lot closer to TWO commas per microtone).

JdL

>Here's the catch: once you fix the tuning, you'll be looking at exactly
>the same tradeoffs that my program is looking at!

I don't think so! In particular, what tradeoff could possibly lead to a
16-cent shift?

>So I don't think that
>an intermediate meantone representation adds anything useful to the
>tuning process.

Think again.

>But it does offer a hindrance whenever a sequence
>modulates more freely and there are meantone "comma pumps" (in this case
>a lot closer to TWO commas per microtone).

Not sure what you have in mind, but you won't find it in Bach.

I wrote,

>>BTW, if the piece ended on a minor triad, I might recommend tuning that
>>triad 16:19:24.

John deLaubenfels wrote,

>Well, that's one of many things that my program doesn't have knowledge
>about; another is whether a particular scale degree is the "melody"
>or not.

I don't see what melody has to do with this.

>>In my opinion, this shift disturbs the flow of the music, the new
>>pitch introducing new "information" on the pitch set to the listener,
>>where the motivic structure of the composition rests on an exact
>>repetition being perceived here.

>Well, to me that's a fancy way of saying your ear doesn't like it, which
>I can accept. To my ear it slides right by without difficulty or flow
>disruption.

Then we must agree to disagree.

>I hear you saying two contradictory things: you champion the idea of
>tuning through an intermediate meantone representation, saying that
>this, in and of itself, effectively deals with fractional comma motion
>(at least in well-behaved sequences such as Bach might have written),
>but you also say that it's a waste of time to pursue "effective" tuning
>without considering a number of other factors in a given sequence.

>To the second point, I would say this: eventually I want to consider as
>many relevant contributions as possible, but I think we're a long way
>from the edge of what can be accomplished with a simpler view such as my
>program takes.

Precisely. I'd say the meantone idea takes you a long way forward toward
what you'd ultimately want for Bach.

>So, D minor would become 5, 13, 23
>D, G, Bb, E would become 5, 18, 26, 41
>C#,G, A, E would become 2, 18, 23, 41

>As you stated, this chord sequence does not skew the tuning in 31-tET.
>And, there's no motion whatever between chords; it's "perfect", yes?

>But there's a problem: you've said that after going through the meantone
>intermediate tuning, you would then fix the tuning of the chords to be
>true JI.

Right -- I'd render the consonant _triads_ in JI. The chord sequence in
31-tET, in cents, is

193.5 503.2 890.3
193.5 387.1 696.8 1006.5
77.4 387.1 696.8 890.3

The consonant triads are D minor, G minor, and A major. Let's use the
procedure I described (from Brett Barbaro's e-mail, many months ago; there I
used QCmeantone instead of 31-tET) and keep the roots of these triads in
31-tET, adjusting the other notes to form triads in JI, and leaving the
sevenths alone. Then we get

193.5 509.1 895.5
198.8 (387.1) 696.8 1012.4
76.6 392.3 (503.2) 890.3

So, even though in this case the tradeoff was weighted 100% for harmony and
0% for avoiding shifts, you still get a much lower shift (5.2� vs. 16.3�)
compared with your program where you put four times as much importance on
avoiding shifts than you had earlier!

So it seems you should reconsider this statement:

>Here's the catch: once you fix the tuning, you'll be looking at exactly
>the same tradeoffs that my program is looking at! So I don't think that
>an intermediate meantone representation adds anything useful to the
>tuning process.

I wrote,

>193.5 509.1 895.5
>198.8 (387.1) 696.8 1012.4
> 76.6 392.3 (503.2) 890.3

That should have read

>193.5 509.1 895.5
>198.8 (387.1) 696.8 1012.4
> 76.6 392.3 (696.8) 890.3

Sorry!

Paul, unless I lost count, you posted at least three responses in
TD 406 on this subject. Unfortunately, I've got a work crisis going
on today, followed by the long Thanksgiving weekend with family, etc.
But I promise I'll show you what I'm talking about once I can spare a
moment!

JdL

First, let me re-state where I'm coming from. My ear demands
everything, Bach included, in 7-limit tuning. There, a tritone is
something to be tuned, either as 7/5 or as 10/7, according to context.
In 5-limit, as I am slowly learning, a tritone is something to be
subject to creative fudging, along with creative rationalizations about
why it should be dissonant, yet we should still call this "Just
Intonation".

To reach an understanding of the beauty of 7-limit dynamic tuning, it is
necessary to get past an intolerance for shifts of sub-comma and perhaps
even an occasional super-comma step. I am here to say that it IS
possible to stretch one's ear's tolerance, and that the tradeoffs are
well worth it, with a beauty that 5-limit falls far short of.

I would gladly leave 5-limit adaptive tuning to someone else, since I
never listen to 5-limit unless there's some non-musical reason to do so.
In fact, I have often considered withdrawing the 5-limit versions of
the pieces I tune, if for no other reason than because I generate them
and post them without hearing them.

However, some people still like 5-limit tuning, for whatever reason,
and it is fun to dabble in pleasing other people's taste. And, as for
leaving 5-limit tuning to others, so far no one has stepped up to the
plate with more than the barest vaporware.

For all the lack of programs to choose from, we seem to have no shortage
of those who consider themselves "experts" in the field, whether or not
they've written a line of code or actually tuned a single sequence.

[JdL, TD 406.8:]
>>So I don't think that an intermediate meantone representation adds
>>anything useful to the tuning process.

[Paul Erlich, TD 406.9:]
>Think again.

Would you believe that, with no modification whatever to my executable,
but with a new set of tuning files, I can achieve essentially the same
close motion? No, I didn't think you would! It's up on my website,
however: http://www.idcomm.com/personal/jadl/ as file b-b-bextrm.zip.
I've zipped up the tuning files in use, which you can compare with
ones I've previously posted. For the initial fragment in question,

>193.5 509.1 895.5
D F A
>194.14 509.77 896.09

>198.8 (387.1) 696.8 1012.4
D E G Bb
>194.75 383.11 692.80 1008.42

> 76.6 392.3 (696.8) 890.3
C# E G A
> 74.41 390.04 693.75 888.09

Where the upper numbers are yours and the lower ones are from my
latest sequence. Close enough for your ear, Paul?

[Paul Erlich, TD 406.11:]
>>>BTW, if the piece ended on a minor triad, I might recommend tuning
>>>that triad 16:19:24.

[JdL:]
>>Well, that's one of many things that my program doesn't have knowledge
>>about; another is whether a particular scale degree is the "melody"
>>or not.

[Paul:]
>I don't see what melody has to do with this.

It has to do with your complaint, a few digests ago, that a melody pitch
moved, as if that were especially painful to you.

[Paul:]
>So, even though in this case the tradeoff was weighted 100% for harmony
>and 0% for avoiding shifts, you still get a much lower shift (5.2� vs.
>16.3�) compared with your program where you put four times as much
>importance on avoiding shifts than you had earlier!

>So it seems you should reconsider this statement:

[JdL:]
>>Here's the catch: once you fix the tuning, you'll be looking at
>>exactly the same tradeoffs that my program is looking at! So I don't
>>think that an intermediate meantone representation adds anything
>>useful to the tuning process.

Paul, you are completely missing the point! The 16.36 cents had nothing
to do with a four times pain increase, in that I was still overriding
that "pain" with a more urgent imperative from the tuning file, which
was based upon a 7-limit file where tuning really means something.

My statement is confirmed by my latest sequence. Meantone adds nothing.

[JdL:]
>>So I don't think that an intermediate meantone representation adds
>>anything useful to the tuning process. But it does offer a hindrance
>>whenever a sequence modulates more freely and there are meantone
>>"comma pumps" (in this case a lot closer to TWO commas per microtone).

[Paul:]
>Not sure what you have in mind, but you won't find it in Bach.

If you'd get off your virtual behind and write some code, I think you'd
come across exactly what I'm talking about! Or, you might find that
you're able to show that I'm talking about nothing of substance - you'd
like that. But you won't find this understanding in the realm of
vaporware.

Vaporware is a wonderful thing. It never crashes. It never gives an
erroneous answer. It is, in fact, perfect in every way. Its only small
flaw is that it doesn't actually exist. Oh, and one other thing: it
never can exist quite as imagined. In real life, every idea goes
through tremendous testing and at least some transformation as it moves
from fantasy to reality. Many many things that once seemed useful
inevitably fall by the wayside. Your idea of using meantone would, I
believe, be one.

Please do come out and prove me wrong on this, Paul! But do so in the
real world, with a real sequence!

JdL

John deLaubenfels wrote,

>Would you believe that, with no modification whatever to my executable,
>but with a new set of tuning files, I can achieve essentially the same
>close motion?

Sure, why not?

>No, I didn't think you would!

Sheesh.

>>193.5 509.1 895.5
> D F A
>194.14 509.77 896.09

>>198.8 (387.1) 696.8 1012.4
> D E G Bb
>194.75 383.11 692.80 1008.42

>> 76.6 392.3 (696.8) 890.3
> C# E G A
> 74.41 390.04 693.75 888.09

>Where the upper numbers are yours and the lower ones are from my
>latest sequence. Close enough for your ear, Paul?

Ah -- now you're getting somewhere! You've satisfied my ears in this
progression, though a more sensitive ear might object to the 12-cent move in
the pitch A. But even to my ears, this file (b-b-be5.mid) sounds funny at
around 01:13 and 01:16.

>It has to do with your complaint, a few digests ago, that a melody pitch
>moved, as if that were especially painful to you.

OK -- Bach is polyphonic, so you might as well consider all lines melodies,
in which case every pitch is a melody pitch (except sometimes in the final
chord where Bach thickens the texture).

>Paul, you are completely missing the point! The 16.36 cents had nothing
>to do with a four times pain increase, in that I was still overriding
>that "pain" with a more urgent imperative from the tuning file, which
>was based upon a 7-limit file where tuning really means something.

Well, if the tuning file was overriding the "pain", what difference did it
make that you increased the "pain" by a factor of four?

>Many many things that once seemed useful
>inevitably fall by the wayside. Your idea of using meantone would, I
>believe, be one.

>Please do come out and prove me wrong on this, Paul! But do so in the
>real world, with a real sequence!

I'd like to. I need to spend some time figuring out how to do this (perhaps
you can help me). But I don't see what could possibly "fall by the wayside".
Ken Wauchope's sequences sound wonderful, to my ears. And the 6-cent
non-cumulative adjustments required to adjust meantone triads into JI triads
would certainly not change this.

Hi!
In relation to Bach and the WTC. I once noticed that bach in the fugues
would use the most dissonant inversion of triads (according to Helmholtz
approach) more than the more consonant. I had taken a rather sample of some of
this work and by no means extensive statistical analysis. Possibly because of
the accent on the linear he might have heard that these inversions are better
for keeping an independence of voices. Something to keep in mind. Also in
looking at some late 16th century polyphony (Burgundian mainly) I noticed that
these type of inversion many times would precede the "bars" leading to a
cadence. Looking at the inversions in general from these last mentioned works,
it was noticed an almost lack of repetitions in specific inversions until many
others where used that it struck me that although not serial it appeared to
strive toward something similar in a more organic way.

>

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

Thanks to everyone who responded to my post in TD 411.

I usually try to be very clear regarding what is my taste vs. what I
think ought to be some kind of universal musicality; any venturing at
all into the latter is fraught with perils of every sort. I think that
in my post I was a bit forceful, as if to imply that my perspective
ought to be everyone's. Any such implication is wrong, of course!

Paul, you asked if I'd work with you on further refinements to the Bach.
I would be happy to; I'm very certain it could be refined to even less
motion, using tritone fudging within a larger range. But, I am
reluctant to say yes. While sometimes you seem to put music ahead of
all else, and therefore would be an ally in exploration, at other times
I feel very strongly that you've got a huge chip on your shoulder, that
you're looking for any excuse to trumpet your own pet theories while
dissing everyone else on the face of the planet. Is there a Jeckle/Hyde
thing going on here?

It seems very strange for you to claim you're not surprised that I could
pull out new tuning files and achieve close motion in the Bach; I invite
you to re-read your posts of late in which, to my eyes at least, you
had concluded without doubt that my method ensures three times the
motion of yours. The term "gleeful chortling" comes to mind.

I have a nightmare fantasy of sharing some low-level source code with
you, to help you put your ideas into practice, only to find that, in
return, you want to dissect every last aspect of my design decisions and
brag about how much better you would have done it.

[Joe Monzo, TD 412.2:]
>But I think you're off the mark when you say 'the tradeoffs
>are well worth it, with a beauty that 5-limit falls far short
>of'. Indeed, you don't even listen to the retuned 5-limit
>stuff you post, so what kind of authority do you have to
>make statements like that?

I have no authority whatever, except regarding my own ears! But I do,
I very much do, listen to 5-limit music, for one reason or another, and
every time I do I long for seven again. To add even further irony, this
latest 5-limit Bach tuning, which Paul E. thinks his ear might finally
begin to accept (in brief passages, at least), sounds really stale and
dull to me, much worse than the more bouncy 5-limit version I posted
before (and which is still on my web, under b-b-b.zip), and of course
much MUCH worse than the 7-limit versions (IMHO).

Margo, thanks for your post, thoughtful and courteous as always.

JdL

John deLaubenfles wrote,

>While sometimes you seem to put music ahead of
>all else, and therefore would be an ally in exploration, at other times
>I feel very strongly that you've got a huge chip on your shoulder, that
>you're looking for any excuse to trumpet your own pet theories while
>dissing everyone else on the face of the planet.

I'm very sorry if I give the latter impression. I really don't mean to.
Perhaps hearing Bach with large melodic shifts makes me irritable. :) I
sincerely apologize. I think it also inflamed me a bit that you just wrote
"meantone adds nothing" when I've spent quite a bit of time (remember the
exchange with "Brett Barbaro"?) showing what it "adds". My "pet theory" on
this issue can almost certainly be given some sort of mathematical proof
(given certain assumptions I thought we shared but it's turned out we
probably don't), and perhaps my "trumpetings" have been poorly-worded
attempts to outline this proof. Basically, I'm claiming that in order to
decide the best way to tune the triads of a piece relative to one another,
given that you're going to tune them in JI within themselves, the first step
should be to decide on the optimal fixed-pitch (though not necessarily only
12-pitch) rendition of the piece, in terms of approximation to JI. The
reason that is true is that then the adjustments leading to the tuning of
the triads in JI will result in the smallest possible melodic shifts and
will also never cause any drift. Now deciding the optimal fixed-pitch
rendition of a piece involves optimizing the tuning of each note with
respect to all the consonant harmonic relations it encounters over the
course of the piece. In the case of most music from the Renaissance,
Baroque, and Classical eras, those consonant relations involve, in nearly
equal measure, all occurences of one, three, or four steps along the chain
of fifths as conventionally notated. Optimizing the tuning of each note in
this context leads to meantone temperament, as some of us were discussing
when I was using Brett Barbaro's e-mail. For example, minimizing the maximum
error relative to JI leads to 1/4-comma meantone temperament. Since the
triads are then within 6 cents of JI, the final retuning will not involve
any shifts of more than 6 cents.

>It seems very strange for you to claim you're not surprised that I could
>pull out new tuning files and achieve close motion in the Bach; I invite
>you to re-read your posts of late in which, to my eyes at least, you
>had concluded without doubt that my method ensures three times the
>motion of yours.

I was thinking back to the exchanges we had when I was posting from Brett
Barbaro's e-mail and you were using centered shifts from 12-tET as the basis
of your algorithm. You then explained that your program was now doing
something totally different, after which I don't think I made any such
claims. Your new method still seems to involve slightly larger shifts than
necessary for the Bach. I'm very happy with how the opening progression of
the Chaconne sounds in your latest version, but . . .

>this
>latest 5-limit Bach tuning, which Paul E. thinks his ear might finally
>begin to accept (in brief passages, at least), sounds really stale and
>dull to me, much worse than the more bouncy 5-limit version I posted
>before

. . . indicates that perhaps your ears are craving something else, something
quite different than minimizing melodic shifts.

>But I do,
>I very much do, listen to 5-limit music, for one reason or another, and
>every time I do I long for seven again.

By "5-limit music" are you speaking of these MIDI files -- the same ones
that you prefer in 7-limit tuning? Do you believe that the connection
between composition and tuning only flows in one direction? Is it not
possible (as Margo has been suggesting) that there are different
compositional practices that have been developed that are appropriate to
different tunings, and that bringing out the structural logic, and hence the
beauty, of a given composition could depend in some way on performing it in
a tuning that befits these aspects? Or does any given composition tuned one
way qualify as "5-limit music" and tuned another way qualify as "7-limit
music"?

You may know that my main interest in microtonal music was to find a way to
really create _essentially_ "7-limit music", with logical cohesiveness equal
to that of common-practice "5-limit music". In my opinion, taking
common-practice works and tuning certain chords with ratios of 7 falls very
short of that goal. What I found was that 10-tone scales in something very
close to 22-tone equal temperament are to 7-limit what a diatonic scale in
meantone temperament is to 5-limit. Hence one of the main reasons I'm
interested in adaptive JI is ultimately as a way to allow music written in
22-tET to be performed with greater consonance in the 7-limit harmonies,
without sacrificing the melodic integrity of the 10-tone scales.

>I have a nightmare fantasy of sharing some low-level source code with
>you, to help you put your ideas into practice, only to find that, in
>return, you want to dissect every last aspect of my design decisions and
>brag about how much better you would have done it.

John, at this point it is quite clear that we have very different aesthetic
goals, and we hear Bach very differently. At least one person, Ken Wauchope,
has made aesthetic remarks that lead me to believe that maybe he hears Bach
much the way I do. So perhaps there are others who do as well. If my ideas
lead to renditions of Bach that sound really nice to me and at least a few
other people, I will have accomplished my goal. It would be very generous of
you to offer to help in this regard. What practical relevance low-level
design decisions have to do with the sound of the music, I can't imagine.

John, again I'm sorry and I'll try to keep Mr. Hyde under control!

Paul, thanks for your response! No doubt I'm partly to blame for any
electronic "guns drawn" standoff we may have been having. I want to
address some of the issues still outstanding, but (once again!) am
having a terrible day at work, so it may not happen today.

JdL

On this list (and indeed in life), my fondest hope is to feel that I
can be forthright, to show off my accomplishments (such as they may be)
and at the same time be open about where my techniques yield results
short of perfection. Paul, when you asked for a detailed breakdown of
the opening bars of the Bach piece, and I looked and found 16 cents
movement between successive notes, I knew that this motion could be
seized upon for criticism. I briefly considered blowing you off, to
avoid trouble, but decided to post the results and let the chips fall
where they may. I did feel that you were a bit gleeful in response, and
that you made unfair comparisons between my approach and yours. BUT,
let me acknowledge that any "guilt" is far from one-sided! For example,

[Paul Erlich, TD 413.7:]
> I think it also inflamed me a bit that you just wrote "meantone adds
> nothing" .

Mea culpa! Actually, your meantone approach clearly WILL result in
nice tight tuning motion, and it certainly quashes drift, as long as the
sequence doesn't introduce microtone shifts (still an open question in
my mind).

You note that my tuning emphasis
> . . . indicates that perhaps your ears are craving something else,
> something quite different than minimizing melodic shifts.

Yes! In fact, I am coming to realize that I actually WANT some shifting
going on, to chase away a staleness (to my ears) in the sound. Mainly,
though, I want to hear chords well tuned, even brief ones, even if it
means doing some sub-commatic shifts. Setting these criteria makes
shifts inevitable to one degree or another.

As far as the question of melodic influence to tuning, which several
list members have touched upon, I DO recognize that, for the best in
dynamic tuning, this should be considered, and it's NOT in my present
method. Still, I think it is incorrect to say, as you did in TD 405.5:

>I would say that you must first learn to analyze a piece of music in
>these terms before you can effectively offer improvements in its
>tuning.

Now that really torqued me off, I have to admit. If, as we all seem
to agree, 12-tET is not at any kind of tuning optimum, then could it not
be shown that ANY slight shift away from 12-tET would be an improvement
in one direction and a worsening in the other? Even if that assertion
is off the wall, I think it's unjust to make a blanket statement along
the lines of "it is necessary to consider everything to get anything
effective."

BTW, I think that your ear's taste, favoring small motion over
well-tuned tritones, would be shared by many on this list and elsewhere,
probably with far greater representation than my own taste; so far, only
about 2.5 other people on the list have shown wild enthusiasm for the
tunings I like best (the 1/2 is for someone who sometimes likes 7,
sometimes 5, sometimes something else). I say this to second your
thought that your work might be appreciated!

(Of course I'd be thrilled if the world beat a path to my 7-limit
tuning examples, but I'll settle for pleasing myself).

I will prepare some C++ source code that you might find helpful to
handle low-level chores: with it, you can read a midi file, hold and
manipulate the sequence in a linked list, and then write it back out
as a new midi file. The only things I'm going to strip out from my
current working program are a few of the routines unique to my method,
which are still in great flux, and about which I still feel proprietary
ownership.

I will ask that you use this for non-commercial work, and that you refer
others who might want it to me rather than passing it along yourself.
This specific message is directed to Paul E., but other programmers are
welcome to the same source - just ask! Give me about a week to get it
ready.

Do you have a PGP key? I prefer to send source encrypted, on general
principle, and to piss off the gov't as an added bonus! (they think they
should be able to read all our e-mail at will, the #$%&*@! Oops, there
I go again!!).

Enough for now! I think I've left some aspects unaddressed, but it can
wait...

JdL

I wrote,

>> . . . indicates that perhaps your ears are craving something else,
>> something quite different than minimizing melodic shifts.

John deLaubenfels wrote,

>Yes! In fact, I am coming to realize that I actually WANT some shifting
>going on, to chase away a staleness (to my ears) in the sound.

OK! My ears, on the other hand, feel that small microtonal shifts are best
explored in the context of composing new, experimental music, not in
retuning old classics.

>Mainly,
>though, I want to hear chords well tuned, even brief ones, even if it
>means doing some sub-commatic shifts. Setting these criteria makes
>shifts inevitable to one degree or another.

Again, as far as acheiving JI in 5-limit triads, in music such as Bach's or
Mozart's, there should never be a need for melodic shifts of more than 6
cents, as my meantone argument indicates. The just-noticeable-difference for
melodic pitches is at least 8 cents, so there should be no need for audible
shifts (other than your desire for a lack of staleness).

>>I would say that you must first learn to analyze a piece of music in
>>these terms before you can effectively offer improvements in its
>>tuning.

>Now that really torqued me off, I have to admit. If, as we all seem
>to agree, 12-tET is not at any kind of tuning optimum, then could it not
>be shown that ANY slight shift away from 12-tET would be an improvement
>in one direction and a worsening in the other? Even if that assertion
>is off the wall, I think it's unjust to make a blanket statement along
>the lines of "it is necessary to consider everything to get anything
>effective."

First of all, I'd use meantone, not 12-tET, as the neutral point for the
music of Bach. Bach carefully _notated_ all his music as if it were in
meantone but used 12-tone well-temperament in practice because he did not
have (or want) more than 12 keys on his instruments. Handel, by the way,
used an organ that was equipped to play extended meantone with 16 pitches,
so that he could choose G# or Ab, D# or Eb, C# or Db, depending on the key
of the music. Bach was, in a sense, the last composer in the great Western
polyphonic tradition; by the end of his life his style was considered quite
antiquated. Although the transcendence of his music relative to that of his
time (with Handel perhaps coming in a distant second) was ultimately
appreciated, it is still the case that his _language_ (including notation)
was derived from a meantone-oriented practice that began about 200 years
before his birth. In that sense, he was as steeped in meantone as we today
are in 12-tET.

Secondly, as Ivor Darreg pointed out, melodic and harmonic judgements are
often in direct conflict as to their influence on tuning. So any slight
shift from the norm in a particular direction might be an improvement
melodically but not harmonically, or vice versa. I'm not sure whether that
agrees or disagrees with you were trying to say above, or what any of this
has to do with the main point.

The main point: it is useful to discover how the musical establishment
understands the music of one of its great heroes before one proceeds to try
to "improve" it. Although one should never simply accept the standard
academic ideology, in this case it's been shaped by hundreds of years of
artistic/pedagogical work on a single body of evidence (the notated music
itself), and represents a point of view that should at least be understood
before it is modified or dismissed entirely. Looking over a book such as
Forte's _Tonal Harmony in Concept and Practice_ should give you a fair idea
of the major elements of this point of view in a reasonable period of time,
and represents the distillation of centuries of artists trying to "consider
everything". All I ask is that you try to get a grasp of what this mode of
analysis is all about, and what it says about how music works.

>I will prepare some C++ source code that you might find helpful to
>handle low-level chores: with it, you can read a midi file, hold and
>manipulate the sequence in a linked list, and then write it back out
>as a new midi file. The only things I'm going to strip out from my
>current working program are a few of the routines unique to my method,
>which are still in great flux, and about which I still feel proprietary
>ownership.

Hmm... I might need a compiled executable, as I'm currently only working
with high-level programming languages such as Matlab. Thanks, John!

Paul, I might agree that meantone is a better place to start for Bach than
12TET, but don't you mean 1/6th comma meantone? Bach is reputed to have
insisted that all major thirds be tuned sharp.

Johnny Reinhard
AFMM

[I wrote:]
>>Mainly, though, I want to hear chords well tuned, even brief ones,
>>even if it means doing some sub-commatic shifts. Setting these
>>criteria makes shifts inevitable to one degree or another.

[Paul Erlich, TD 418.2:]
>Again, as far as acheiving JI in 5-limit triads...

Right. But it's clear now, even when I don't say so explicitly in a
given paragraph, that I'm talking about 7-limit tuning in order to
please my ears, yes?

Something I've been meaning to ask you, Paul: do you not care for 19th
century music at all? It seems you never talk about its challenges when
you speak of tuning. Do you take it as given that it shouldn't be
touched? As one can tell from the music selections on my web page, I'm
much more 19th than 18th century in my tastes: that Bach piece is the
ONLY one before Beethoven (I'm afraid I find most of Mozart's work too
nicey-dicey for my taste).

[Paul:]
>The main point: it is useful to discover how the musical establishment
>understands the music of one of its great heroes before one proceeds to
>try to "improve" it. Although one should never simply accept the
>standard academic ideology, in this case it's been shaped by hundreds
>of years of artistic/pedagogical work on a single body of evidence (the
>notated music itself), and represents a point of view that should at
>least be understood before it is modified or dismissed entirely.
>Looking over a book such as Forte's _Tonal Harmony in Concept and
>Practice_ should give you a fair idea of the major elements of this
>point of view in a reasonable period of time, and represents the
>distillation of centuries of artists trying to "consider everything".
>All I ask is that you try to get a grasp of what this mode of analysis
>is all about, and what it says about how music works.

Yeah, well... I don't want to be maneuvered into the position of
championing ignorance! The more we know about what went into music, the
more it'll help us do whatever we're going to do with it, UNLESS that
body of knowledge is so vast and top-heavy that studying it completely
is a full-time life in itself, which may or may not be the case here.
Like you, my time is limited, and my own approach to this whole game is
to boldly charge ahead (cue StarTrek music), as if mysterious musical
manuscripts had landed on my doorstep, source unknown, with the command
"tune me!"

I actually took a couple of courses in Harmony in college. Didn't do a
darn thing for me: I was looking for clues as to how to pursue nice
sounds, and all the classes did was hand out prohibitions. The one that
sticks in my head, 30 years later, is parallel fifths: forbidden.
Trouble is, I LIKE parallel fifths! I'm afraid I found that experience
frustrating and ultimately worthless. Not to say that all musical study
is worthless, but you can see that I have a different perspective from
you as a result.

I want to avoid falling into the trap of gloating, "I've already GOT
software and you DON'T, so I'm the expert, not you!" yet I will say that
I think it does count for something to have actually gone through the
pain of writing a retuning program, facing unforseen challenges, making
difficult design decisions, fixing bugs, listening, refining, and all
that. Of course, you are absolutely free to think the results are
uninteresting! Or unoptimized, or incomplete, or whatever word suits
your ear's and/or mind's reaction. I think it's important to be careful
about how you tout the features of something you haven't yet written,
however.

>>I will prepare some C++ source code that you might find helpful ...

>Hmm... I might need a compiled executable, as I'm currently only
>working with high-level programming languages such as Matlab.

Dang! Don't know if I can help you, then! Do you see any way to
connect the pieces?

JdL

John deLaubenfels wrote,

>Right. But it's clear now, even when I don't say so explicitly in a
>given paragraph, that I'm talking about 7-limit tuning in order to
>please my ears, yes?

OK, and given that you'd like to tune half-diminished seventh chords
5:6:7:9, to avoid large shifts you might have to allow some minor triads to
be tuned 6:7:9, and then maybe even some major triads 14:18:21. Since you
wouldn't do that, you are forced to end up with large shifts, which you seem
to enjoy anyway. Is that a fair assessment?

>Something I've been meaning to ask you, Paul: do you not care for 19th
>century music at all? It seems you never talk about its challenges when
>you speak of tuning. Do you take it as given that it shouldn't be
>touched? As one can tell from the music selections on my web page, I'm
>much more 19th than 18th century in my tastes: that Bach piece is the
>ONLY one before Beethoven (I'm afraid I find most of Mozart's work too
>nicey-dicey for my taste).

As I just finished discussing, 19th century music tends to depend on a
closed 12-pitch system. That doesn't make its tuning untouchable; it simply
makes the challenges greater if trying to acheive JI harmony. I've been
focusing on Bach because it's a simpler case (and because I do feel closer
to his music than to most anything before Stravinsky). BTW, Lindley and
Vogel have suggested (in their respective books) 7-limit harmony in
connection with late 19th-century music, but I'm pretty sure they both view
the half-diminished seventh as 1/7:1/6:1/5:1/4 rather than 5:6:7:9.

>I actually took a couple of courses in Harmony in college. Didn't do a
>darn thing for me: I was looking for clues as to how to pursue nice
>sounds, and all the classes did was hand out prohibitions. The one that
>sticks in my head, 30 years later, is parallel fifths: forbidden.
>Trouble is, I LIKE parallel fifths!

Me too! But understanding Bach's aesthetic involves understanding this
prohibition. Parallel fifths would stick out like a sore thumb in Bach-style
composition. It's a stylistic thing. It's trying to get in touch with what
makes Bach sound like Bach. That's useful if Bach's music gives you a very
special feeling and you're a musician who is looking for his own way of
getting feelings across. The discipline of being forced to write in one
style is useful training for ultimately producing original, stylistically
coherent compositions.

>Dang! Don't know if I can help you, then! Do you see any way to
>connect the pieces?

Daniel Wolf recently posted about shareware utilities for converting MIDI to
text and vice versa. I'll try to check them out. Meanwhile, I'll try to get
a score of the Chaconne so we won't be limited to the 12 notes in the MIDI
file.