source file: m1589.txt
Date: Sat, 21 Nov 1998 14:25:11 -0800

Subject: 22tET vs. 12tET

From: Carl Lumma <clumma@nni.com>

>Please elaborate. If you mean the properties I describe in my paper,
>note that virtually all these properties presuppose representations of
>ratios of small whole numbers. If you don't mean those, then which ones
>do you mean? 

I think he means that 22tET commits some serious errors against the
consonance of 7-limit intervals.  7 to 5's are off 17 cents.  That's quite
a bit.

>12tET evolved in, and largely superceded the authentic tunings of, a
>musical style where 5-limit ratios were of primary importance (it could
>do so because the quality of its approximations was sufficient).

This is sort of false.  12tET really only happens on pianos and guitars.
And it's only been happening there for 100 years.  And during this time,
solo music for these instruments has become increasing less using of the
5-limit consonances.

>I do examine non-ET 7-limit tunings which contain the scales in my paper,
>but find that they are optimally tuned very close to 22tET. The impetus for
>choosing an ET rather than an open, meantone-type system is certainly a
>"group" property, that of infinite transposability with a finite number
>of notes. I would be more than happy to advocate a non-ET, open 7-limit
>tuning if it had any significant acoustical advantages over 22tET. It
>doesn't.

22tET seems to be just about the best "meantone" for the decatonic scale,
yes.  But would you accept JI?  Or 41tET?

Carl