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Johnny Reinhard's Harmonic-17 tuning: suggested changes

🔗"Paul H. Erlich" <PErlich@...>

8/11/1998 12:54:45 PM
Sorry for unintentionally repeating Paul Hahn's point about 34/20
reducing to 17/10. As for notes that scream to be included, Manuel's
diagram contains holes at 17/12, 17/9, and 30/17, so these would make
nice additions. The diagram also suggests the omission of 19/17, 34/31,
and 31/17, which are outside the 17-limit. The resulting scale would
still have 17 (!) notes:

ratio cents
1/1 0
18/17 99
17/16 105
17/15 217
20/17 281
17/14 336
22/17 446
17/13 464
24/17 597
17/12 603
26/17 736
17/11 754
28/17 864
17/10 919
30/17 983
32/17 1095
17/9 1101

As a result of these changes, the 3:2s (& 4:3s) would increase in number
from three to six: 17/12:17/16, 17/9:17/12, 17/15:17/10, 24/17:32/17,
18/17:24/17, and 30/17:20/17.