RE: Digest 600, XH16 article, Brian

I have seen neither TD 600 nor XH16, but I thought I'd throw in my 21.5
cents:

Paul Rapoport wrote:

>10. <22-tET has nothing in common with traditional tunings.> Does anyone
>agree with this?

Well, in Paul Rapoport's point of view, 22 would fall into the same category
as 27, 41, 46, and 53, where syntotic comma (81:80) displacements are
necessary to get good thirds, and if 27, 41, 46, or 53 is traditional, then
so is 22. Paul Rapoport's notation probably deals with 15 and 34 in the same
way. Is this correct?

However, I'm not aware of much of a "tradition" of notating comma
displacements in actual musical practice, so I'd have to say the only
traditional tunings are 12, 19, 31, 43, 50, 55, etc.

I have a feeling I would have a bigger problem with Paul Rapoport's system,
since it seems the minor third and its purity are being ignored. It's that
consistency issue again. If the best approximation of the perfect fifth
minus the best approximation of the major third is not the best
approximation of the minor third, a notation based on just 5-limit intervals
is not appropriate for the tuning. In 20tet, for example, the perfect fifth
is 12 steps, and the closest approximation to the major third is 6 steps, so
should the minor third be 6 steps too? No, 5 steps is a far better minor
third. This seems to be a fatal blow to notating 20tet with Pythagorean
scales and syntotic commas. However, I should shut up now because I haven't
read Rapoport's article.

Getting back to 22tet, I've written a paper on it, which includes a very
convenient method of notating 22tet based on 7-limit harmony. While
traditional notation and musical practice benefit from the vanishing of the
syntotic comma in traditional tunings, 7-limit notation and practice will
benefit from the vanishing of the septimal comma (64:63) in 22tet. This
paper is in the process of being rethunk for the purposes of publication,
but I've been e-mailing around a summary of my current ideas to a few tuning
list members in exchange for additions to my music collection. Any more
takers?


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