9ed10
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| ← 8ed10 | 9ed10 | 10ed10 → |
(semiconvergent)
9ED10 is the equal division of the 10th harmonic into nine parts of 442.9237 cents each. It is related to the sensi temperament, which tempers out 91/90, 126/125, and 169/168 in the 2.3.5.7.13 subgroup, which is supported by 19edo, 27edo, 46edo, and 73edo.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 442.9237 | 9/7, 84/65, 13/10 | |
| 2 | 885.8475 | 5/3 | |
| 3 | 1328.7712 | 15/7, 28/13, 54/25, 13/6 | |
| 4 | 1771.6950 | (11/4), 36/13, 25/9, 39/14 | |
| 5 | 2214.6187 | 140/39, 18/5, 65/18, (40/11) | |
| 6 | 2657.5425 | 60/13, 65/14, 14/3 | |
| 7 | 3100.4662 | 6/1 | |
| 8 | 3543.3900 | 100/13, 54/7, 70/9 | |
| 9 | 3986.3137 | exact 10/1 | just major third plus three octaves |