Bach Chaconne in MT

I've posted 1/4-comma and 1/5-comma meantone versions of JdL's Bach
Chaconne in D- at

http://www.aic.nrl.navy.mil/~wauchope/audio/tuning/b-b-b-MT.zip

I settled on meantone in C (F and G were close seconds) based mostly
on the chord progression from 2:09-2:20. Since meantone does contain
several good 7-limit intervals, I hear quite a bit of lovely "septimal
buzz" in these versions, which perhaps supports JdL's preference for a
7-limit approach.

Like Wendy Carlos (and according to her, Bach also), I prefer the
1/5-comma tuning where the thirds have a bit more forward momentum --
in 1/4-comma they "sit back on their haunches", which is great for
Renaissance polyphony but not dynamic enough for the Baroque.

P.S. I zipped the file above because I've found that Netscape
Navigator 4.0 for Windows won't transfer .MID files in binary mode
from our Unix file server, but treats them as text files and adds
extra bytes making them unplayable. Internet Explorer and (binary)
FTP don't have this problem. Anybody know how to make Navigator for
Windows use binary mode for .MID file transfers?

--Ken Wauchope

Actually, Wendy Carlos is not claiming that J.S. Bach used 1/5th comma
meantone. She recorded in that tuning because it worked for her. As time
went on, Wendy began to appreciate the irregular circular tunings. She has
indicated this to me many times.

Similarly, J.S. Bach will "work" in just about any tuning. It's the power of
his composition. Years ago I did an arangement of Bach by Ezra Sims in JI
and I thought it was terrible. Bach without temperament is not Bach. It
goes against the composers wishes. However, in non-chromatic pieces that
modulate little, it's likely that Bach wanted other tuning sensibilities,
perhaps simpler sensibilities, would be covered well enough by a meantone
tuning that emutlates intonationally a particular key form "well-temperament."

Johnny Reinhard
AFMM

Ken Wauchope wrote,

>I've posted 1/4-comma and 1/5-comma meantone versions of JdL's Bach
>Chaconne in D- at

> http://www.aic.nrl.navy.mil/~wauchope/audio/tuning/b-b-b-MT.zip

>I settled on meantone in C (F and G were close seconds) based mostly
>on the chord progression from 2:09-2:20

Thanks, Ken! I'll listen to these when I can.

>Since meantone does contain
>several good 7-limit intervals, I hear quite a bit of lovely "septimal
>buzz" in these versions, which perhaps supports JdL's preference for a
>7-limit approach.

These 7-limit intervals appear in meantone as augmented sixths and other
chromatically altered intervals. For diatonic dominant sevenths and
half-diminshed sevenths, a 7-limit tuning certainly has no _historical_
substantiation.

Johnny Reinhard wrote,

>However, in non-chromatic pieces that
>modulate little, it's likely that Bach wanted other tuning sensibilities,
>perhaps simpler sensibilities, would be covered well enough by a meantone
>tuning that emutlates intonationally a particular key form
"well-temperament."

Although the WTC seems to demand well-temperament, the author of the
Scalatron article claims that many of the pieces were simply earlier works
transposed from simpler keys to harder ones. I think he also claims that
each individual piece in WTC can be performed with only a 12-tone meantone
tuning.

<<
These 7-limit intervals appear in meantone as augmented sixths and other
chromatically altered intervals. For diatonic dominant sevenths and
half-diminshed sevenths, a 7-limit tuning certainly has no _historical_
substantiation. >>

>Not quite. Although I agree heartily that the harmonic language of the
>Baroque and Classical eras was profoundly determined by the resources of
>meantone, there are important exception. Tartini, who emphasized purity of
>intervals, tuned to difference tones, and recognized the 7th partial, is
one.

Tartini suggested using it in the repertoire of his day for dominant seventh
chords? I thought he simply felt it to be a _new_ interval with as-yet
unexplored possibilities for consonance harmony.

On Wed, 24 Nov 1999 16:04:52 -0500, "Paul H. Erlich"
<PErlich@Acadian-Asset.com> wrote:

>Although the WTC seems to demand well-temperament, the author of the
>Scalatron article claims that many of the pieces were simply earlier works
>transposed from simpler keys to harder ones. I think he also claims that
>each individual piece in WTC can be performed with only a 12-tone meantone
>tuning.

Most of them probably can. I found right away when I tried this that the C#
major prelude from Book I has 14 different written pitches, and the fugue
even has 3 different A's (natural, sharp, and double sharp!) But a few
"misspelled" notes might be tolerable, especially in 1/5-comma meantone
where the difference between B and Ax (what an unusual note!) is "only" 28
cents, not 39 cents as in 31-TET or 41 cents as in 1/4-comma meantone. And
I still have a long way to go before I find out whether this range of notes
is typical of the WTC or not.
--
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

>I've posted 1/4-comma and 1/5-comma meantone versions of JdL's Bach Chaconne
>in D- at http://www.aic.nrl.navy.mil/~wauchope/audio/tuning/b-b-b-MT.zip

Thanks, Ken! What do you think of them compared to JdL's 5-limit version?
I find the JI version noticably smoother (and more fun!) than either of the
meantone versions.

-C.

> Johnny Reinhard:
> Actually, Wendy Carlos is not claiming that J.S. Bach used 1/5th comma
> meantone. She recorded in that tuning because it worked for her. As time
> went on, Wendy began to appreciate the irregular circular tunings. She
> has indicated this to me many times.

Okay, I was going by the "Bach 2000" liner notes where she references
your thesis and says he preferred a Meantone "close to 1/5 comma" with
slightly sharper thirds than 1/4-comma Meantone. I had always thought
he used the irregular circular tunings myself.

> Carl Lumma:
> What do you think of them compared to JdL's 5-limit version?
> I find the JI version noticably smoother (and more fun!) than either of
> the meantone versions.

The JI versions are certainly both of those, and are an avenue well
worth exploring. They also exhibit a great variety of "mood", as Ivor
Darreg would say -- when the pitch drifts flat the piece can get very
spooky and melancholy, but then it will move off in a completely
different direction. The problem is how to control these shifts so
that the piece retains an overall sense of horizontal logic and
consistency.

The challenge as I see it in tuning this kind of music has always been
to reconcile melody and harmony, the horizontal and vertical. Static
JI has the purest harmonies, but even a simple melodic motive like
1/1-9/8-5/4 can be unsatisfying because you start off on a bold
204-cent step and then "back off" suddenly with a hesitant 182-cent step.
1/4-C MT evens this out melodically by splitting the 5/4 in half --
allowing consistent melodies in a consonant 5-limit harmonic context
-- but melodies that have a "laid-back" quality since the emphasis is
still on vertical sonority.

Since much of Bach does indeed "work" in MT in the sense that it is
possible to pick a key of MT that will get through the entire piece
without ever sounding perfectly awful (tuned in C MT the Chaconne has
only one very brief wolf fifth at beat 69:1:254), 1/5-C MT is a
nice compromise because the overall horizonal structure remains
logically consistent while trading off vertical consonance just a bit
for slightly more melodically aggressive seconds and thirds. At the
same time, there are noticeable changes in consonance as the piece
modulates, just as in irregular circular temperaments -- including the
occasional 5:6:7 or 4:5:6:7 harmony, such as the diminished chords
from 2:09-2:39 and the Bb7 and Eb7 around 5:01-5:17, a happy side
effect of the tuning that adds moments of spice and variety.

As I say, some of the pitch shifts in the tighter 5-limit adaptive JI
versions are evocative, but others strike me as weird or disturbing, a
disruption of the horizontal flow of the piece. Maybe there's some
relatively simple set of horizontal constraints that could control
that and result in a choir-like naturalness in both dimensions.

--Ken

I wrote,

>>Although the WTC seems to demand well-temperament, the author of the
>>Scalatron article claims that many of the pieces were simply earlier works
>>transposed from simpler keys to harder ones. I think he also claims that
>>each individual piece in WTC can be performed with only a 12-tone meantone
>>tuning.

>Most of them probably can. I found right away when I tried this that the C#
>major prelude from Book I has 14 different written pitches, and the fugue
>even has 3 different A's (natural, sharp, and double sharp!) But a few
>"misspelled" notes might be tolerable, especially in 1/5-comma meantone
>where the difference between B and Ax (what an unusual note!) is "only" 28
>cents, not 39 cents as in 31-TET or 41 cents as in 1/4-comma meantone. And
>I still have a long way to go before I find out whether this range of notes
>is typical of the WTC or not.

I don't consider 28 cents a tolerable mistuning so, based on what you wrote,
I'd have to disagree with the Scalatron article (though the basic point,
that the WTC could be performed on a 31-equal instrument and sound "better",
stands).

Ken Wauchope wrote,

>The challenge as I see it in tuning this kind of music has always been
>to reconcile melody and harmony, the horizontal and vertical. Static
>JI has the purest harmonies, but even a simple melodic motive like
>1/1-9/8-5/4 can be unsatisfying because you start off on a bold
>204-cent step and then "back off" suddenly with a hesitant 182-cent step.

Agreed!

>1/4-C MT evens this out melodically by splitting the 5/4 in half --
>allowing consistent melodies in a consonant 5-limit harmonic context
>-- but melodies that have a "laid-back" quality since the emphasis is
>still on vertical sonority.

I just listened to your 1/4-comma version and the "laid-back" quality seems
to lend the music a reverential flavor. Beautiful. Far preferred to JdL's
version. But there is still room to combine the best of both worlds (as I
was explaining to John a couple of days ago)!

>(tuned in C MT the Chaconne has
>only one very brief wolf fifth at beat 69:1:254),

By C MT I assume you mean G#-Eb? I don't know if C MT is standard
terminolgy. Anyway, I see no need to restrict yourself to 12 pitches in this
exercise -- except maybe the following:

>1/5-C MT is a
>nice compromise because the overall horizonal structure remains
>logically consistent while trading off vertical consonance just a bit
>for slightly more melodically aggressive seconds and thirds. At the
>same time, there are noticeable changes in consonance as the piece
>modulates, just as in irregular circular temperaments -- including the
>occasional 5:6:7 or 4:5:6:7 harmony, such as the diminished chords
>from 2:09-2:39 and the Bb7 and Eb7 around 5:01-5:17, a happy side
>effect of the tuning that adds moments of spice and variety.

Yes! That's a wonderful new harmonic twist that sounds very "right" in the
context and is missed out on in well- or equal-tempered renditions of Bach,
and possibly versions which use more than 12 pitches of meantone (can you
tell us whether Bach really spelled these chords as dominant sevenths or
augmented sixths?). Thanks for bringing this to light! But doesn't 1/4-comma
meantone do an even better job for these harmonies? I find the 1/4-comma
version more distinctive due to the just major thirds, but overall both
meantones work great. Thanks for the enjoyable listening!

-Paul

On Fri, 26 Nov 1999 16:12:16 -0500, "Paul H. Erlich"
<PErlich@Acadian-Asset.com> wrote:

>I don't consider 28 cents a tolerable mistuning so, based on what you wrote,
>I'd have to disagree with the Scalatron article (though the basic point,
>that the WTC could be performed on a 31-equal instrument and sound "better",
>stands).

It most cases it wouldn't be, but it depends on how those notes are used.
Even in 31-equal, with its larger errors for mistuned notes, the particular
"mistuned" notes don't sound too bad: the Ax in the melody is a dissonant
note, an augmented fourth above the E# root (might just as well be a B if
the note following it weren't B#), and the E-naturals later on belong to a
diminished 7th chord, and sound just fine as Dx. The single A-natural
actually sounds better as Gx, since it occurs in combination with B#. In
any case, only the most remote pitches would need to be mistuned.

But the WTC certainly does sound nice in 31-equal.