three-tetrachord technique (was Re: reply to Paul Hahn)

On Mon, 1 Mar 1999, Paul H. Erlich wrote:
> Remind me -- what is the technique you described, and what are the
> scales in question?

Basically, the idea is that instead of starting from the
1:1-4:3-3:2-2:1 (or 1:1-9:8-3:2-2:1) framework and filling in the 4:3s,
I start with 1:1-5:4-8:5-2:1 instead, and fill in the middle section as
well. So far the most interesting scales seem to be (in 31TET):

3-5-2|5-3-3|4-3-3 (3 tetrads, 22 7-limit consonances)

3-4-3|3-5-3|4-3-3 (3 tetrads, 22 7-limit consonances)

3-3-4|3-5-3|4-3-3 (4 tetrads, 21 7-limit consonances)

Note that the latter two can also be analyzed using 4:3 pentachords; in
the one they are identical, and in the other they are inversions of each
other.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "

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