Bach's Chaconne and Busoni

> [Paul Erlich, TD 499.16]
>
> [Paul]
>>> Aha! By the way, Busoni would probably have no qualms about
>>> writing an Ab for a G# or vice-versa.
>
> [me, monz]
>> I wouldn't be too hasty to assert that.
>
>> Even tho (AFAIK) Busoni left no microtonal compositions,
>> theoretically, he was an advocate of 36-tET/-EDO.
>> (see Busoni 1962, p 93-95)
>
> [Paul]
> That doesn't matter. 36-tET has the basic structural intervals
> of tonal music (fifths and thirds) in exactly the same tuning
> as 12-tET. Therefore, Ab and G# are unequivocally the same
> in 36-tET. Busoni wasn't after restoring the subtle pitch
> distinction of the meantone era. He was satisfied with his
> Bach in 12-tET. 36-tET was meant to be an expansion for
> future music, not past music.

OK, those are both good points.

But still, 36-tET *does* provide 2^(23/36) = ~767 cents,
which is a pretty good approximation of 16:25 = ~773 cents,
and which I would be tempted to use in some of Busoni/Bach's
'augmented chords'.

The other possibility, 2^25/36 = ~833 cents, doesn't have
as obvious a cognate in 5-limit JI, the only ones close
enough being 16384/10125 = (3^-4)*(5^-3) = ~833 cents and
its schismatic relative 81/25 = (3^4)*(5^-2) = ~835 cents.
I say that these are not as obvious because they're quite
far from 1/1, and thus would most likely only be implied
in a fairly large set of pitches; unless 'extended-reference'
comes into play (heh heh...).

Do you have a reference that confirms that Busoni 'was
satisfied with his Bach in 12-tET'?

Altho not tuning-related, I would like to point out that
Busoni made a 'concert arrangement' of the 2nd of Schoenberg's
_3 Piano Pieces, op 11_ (changing 'octave'-registration, etc.,
to make it 'more pianistic', and for which he was severely
criticized by Schoenberg), indicating that he had no problem
with producing his own version of 'past music', even when
the composer was still alive.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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Joe Monzo wrote,

>But still, 36-tET *does* provide 2^(23/36) = ~767 cents,
>which is a pretty good approximation of 16:25 = ~773 cents,
>and which I would be tempted to use in some of Busoni/Bach's
>'augmented chords'.

I wouldn't. Since the 16:25 would be constructed out of two 4:5s, and since
each 4:5 would best be tuned @ 400�, the 16:25 (not being a consonant
interval or one recongnizable on its own) automatically gets assigned the
800� tuning.

>I say that these are not as obvious because they're quite
>far from 1/1, and thus would most likely only be implied
>in a fairly large set of pitches; unless 'extended-reference'
>comes into play (heh heh...).

Extended reference requires JI and strictly speaking, could not operate in
36-tET. Speaking more loosely, in 36-tET, each link in the chain of
reference would be forced to its nearest approximation, which (for the
5-limit case we're discussing) would end up limiting you to 12-tET.

>Do you have a reference that confirms that Busoni 'was
>satisfied with his Bach in 12-tET'?

I think the burden of proof is on the other side, given what Busoni did with
Bach and the time in which he lived.