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A ten-tone, 2401/2400 scale

🔗Gene W Smith <genewardsmith@juno.com>

5/31/2002 8:25:28 AM

It occurred to me that one way to get a smooth scale might be to enforce
the epimorphic property for a suitable mapping, meaning one consistent
with 2401/2400 and as close to being a good et mapping as possible. The
h11 mapping is too irregular for this to work well, but h10 is excellent.
We get from it the following scale in 612-et:

[0, 43, 104, 179, 222, 297, 358, 401, 476, 537]

Step sizes are 75, 61, and 43, and it has 19 intervals and 6 triads in
the 7-limit, 23 intervals and 14 triads in the 9-limit. This is a fair
amount of harmony for something which is effectively JI.