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Optimized 15-note, 7-limit JI scales

🔗Gene W Smith <genewardsmith@juno.com>

8/3/2002 2:25:14 PM

I did a search on these, using (16/15)^4 (21/20)^3 (25/24)^5 (36/35)^3 as
step sizes, and constraining the search by requiring there to be two
complete tetrads a iifth apart. I found two optimal solutions:

opti15a 42 intervals 37 triads 6 tetrads
[1, 21/20, 28/25, 7/6, 6/5, 5/4, 4/3, 7/5, 35/24, 3/2, 8/5, 5/3, 7/4,
28/15, 35/18]

opti15b 42 intervals 37 triads 6 tetrads
[1, 21/20, 35/32, 7/6, 6/5, 5/4, 4/3, 7/5, 35/24, 3/2, 8/5, 5/3, 7/4,
28/15, 35/18]

These are both good candidates for miracle, where they have in the
11-limit
69 intervals and 128 triads. Both tempered and untempered they are
graph-isomorphic without being isomorphic.