Inferior tuning?

Greetings,
John writes:
<<I recently did an interval analysis on Bach's "Well-Tempered Clavier",

> from the standpoint of calculating what fixed tuning (with no more than

> 12 pitch classes per octave) would result in the most consonance. The

> results are depressingly close to 12-tET.<<

This is interesting from a static standpoint, but as far as drawing a
value judgement inre the best tuning for this music, a basic assumption seems
to have been made, and it is one that I cannot accept. That is, that
consonance is desirable to the point of exclusion of dissonance. I think
there is a place for beats (tempering), and their absence deprives music of
an essential resource.
12 ET may give the lowest average amount of dissonance, but it doesn't
necessarily make the best music. The analysis that says ET was the most
consonant tuning for the WTC doesn't account for the value of musical effects
created by contrasting values of the tempering. Are those important? I say,
'Yes".

> But when it comes to arguing which well-temperament is "objectively

> best" for the WTC, I'm sorry to report that they're all worse than

> 12-tET by any rational measure I have seen to date.<

"Any rational measure"? How about the consonance created by the prelude
in Cmaj ( in any plausible tuning of 1722). You can't achieve that sound in
ET, since the partials of the harmony are far away from the melodic line.
And what about the stimulative quality of the prelude in C#? In the
Werckmeister, Kirnberger, or Young, you will have a harmonic value of the 20-
21 cent third. This creates a sound that is unavailable in ET, and in direct
comparisons, every audience I have presented the choice to has favored the
more highly tempered rendition.
There is nothing magic about 13.8 cent thirds, they are simply the
result of averaging the comma. However, there is something lacking about the
homoginized harmonic texture of ET that virtually any of the
well-temperaments seem to musically provide.
There is also the consideration of the instrument, in that the modern
piano makes a 21 cent third a very busy interval, more so than a harpsichord
of clavichord. It is for this reason that I don't think there is a "proper"
temperament for Bach unless the instrument is specified, and even then, the
subjective values take over.
Our "Six Degrees" CD included a 1/4 comma version of a Mozart piece( along
with a well-tempered and ET version). The wolf howls in this piece, makes
the hair stand up on my neck, but there have been several correspondants that
have written me to tell me that they really prefer the meantone sound.
There is a lot of room for taste when it comes to temperament, but
setting the value by the simple barometer of consonance misses out on the
emotive-effective power of contrast. Let's not dis dissonance!
regards,
Ed Foote
Nashville, Tn.

> From: <a440a@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, July 01, 2001 7:28 PM
> Subject: [tuning] Inferior tuning?
>
>
> There is nothing magic about 13.8 cent thirds, they are simply
> the result of averaging the comma. However, there is something
> lacking about the homoginized harmonic texture of ET that virtually
> any of the well-temperaments seem to musically provide.

Ed, did you see this post I sent the other day?
/tuning/topicId_25865.html#25865
Sat Jun 30, 2001 2:42 pm

(Only repeating it because I know you love WTs so much.)

-monz
http://www.monz.org
"All roads lead to n^0"

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[I wrote:]
>>I recently did an interval analysis on Bach's "Well-Tempered Clavier",
>>from the standpoint of calculating what fixed tuning (with no more
>>than 12 pitch classes per octave) would result in the most consonance.
>>The results are depressingly close to 12-tET.

[Ed Foote:]
>This is interesting from a static standpoint, but as far as drawing a
>value judgement inre the best tuning for this music, a basic assumption
>seems to have been made, and it is one that I cannot accept. That is,
>that consonance is desirable to the point of exclusion of dissonance.
>I think there is a place for beats (tempering), and their absence
>deprives music of an essential resource.

>12 ET may give the lowest average amount of dissonance, but it doesn't
>necessarily make the best music. The analysis that says ET was the
>most consonant tuning for the WTC doesn't account for the value of
>musical effects created by contrasting values of the tempering. Are
>those important? I say, 'Yes".

Right, and we've been through this before. My analyses can only address
the question of consonance, and not these other important contributions.
I try to make this clear, but from your reaction, it would seem that I
did not succeed in doing so.

>>But when it comes to arguing which well-temperament is "objectively
>>best" for the WTC, I'm sorry to report that they're all worse than
>>12-tET by any rational measure I have seen to date.<

>"Any rational measure"? How about the consonance created by the
>prelude in Cmaj ( in any plausible tuning of 1722). You can't achieve
>that sound in ET, since the partials of the harmony are far away from
>the melodic line. And what about the stimulative quality of the
>prelude in C#? In the Werckmeister, Kirnberger, or Young, you will
>have a harmonic value of the 20- 21 cent third. This creates a sound
>that is unavailable in ET, and in direct comparisons, every audience I
>have presented the choice to has favored the more highly tempered
>rendition.

Right, I'm aware of the numbers and of the key coloration achieved by
them.

>There is nothing magic about 13.8 cent thirds, they are simply the
>result of averaging the comma. However, there is something lacking
>about the homoginized harmonic texture of ET that virtually any of the
>well-temperaments seem to musically provide.

Quite true.

>There is also the consideration of the instrument, in that the modern
>piano makes a 21 cent third a very busy interval, more so than a
>harpsichord of clavichord. It is for this reason that I don't think
>there is a "proper" temperament for Bach unless the instrument is
>specified, and even then, the subjective values take over.

I agree.

>Our "Six Degrees" CD included a 1/4 comma version of a Mozart piece
>(along with a well-tempered and ET version). The wolf howls in this
>piece, makes the hair stand up on my neck, but there have been several
>correspondants that have written me to tell me that they really prefer
>the meantone sound.

I wouldn't try to claim that they're wrong. I have that CD (and wrote
a brief and favorable review on this list a while back). I notice the
interestingly uneven melodic steps of the meantone as much as the wolf
fifths.

>There is a lot of room for taste when it comes to temperament, but
>setting the value by the simple barometer of consonance misses out on
>the emotive-effective power of contrast. Let's not dis dissonance!

Yes. But you are taking my post out of context, I believe. I was
responding to Herbert Anton Kellner's posts, which compare two
well-temperaments, and which make the statement that one is measurably
better than another. My point is simply that we must use other
criteria (historical clues and our own ears' tastes) to make the
decision of what tuning(s) to use.

JdL