8736edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|8736}} 8736edo is an excellent 2.7.13.17 subgroup tuning. It also excellently represents such intervals as 53/49, 47/38. {{harmonics in eq..." |
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8736edo is an excellent 2.7.13.17 subgroup tuning. It also excellently represents such intervals as [[53/49]], [[47/38]]. | 8736edo is an excellent 2.7.13.17 subgroup tuning. It also excellently represents such intervals as [[53/49]], [[47/38]]. | ||
=== Odd harmonics === | |||
{{harmonics in equal|8736}} | {{harmonics in equal|8736}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Revision as of 16:07, 25 February 2024
| ← 8735edo | 8736edo | 8737edo → |
8736edo is an excellent 2.7.13.17 subgroup tuning. It also excellently represents such intervals as 53/49, 47/38.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0319 | -0.0500 | -0.0072 | -0.0638 | +0.0557 | -0.0057 | +0.0555 | -0.0104 | +0.0145 | -0.0391 | +0.0224 |
| Relative (%) | -23.2 | -36.4 | -5.3 | -46.5 | +40.5 | -4.1 | +40.4 | -7.5 | +10.5 | -28.5 | +16.3 | |
| Steps (reduced) |
13846 (5110) |
20284 (2812) |
24525 (7053) |
27692 (1484) |
30222 (4014) |
32327 (6119) |
34131 (7923) |
35708 (764) |
37110 (2166) |
38371 (3427) |
39518 (4574) | |
Subsets and supersets
Since 8736 factors as 25 × 3 × 7 × 13, 8736edo has subset edos 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 39, 42, 48, 52, 56, 78, 84, 91, 96, 104, 112, 156, 168, 182, 208, 224, 273, 312, 336, 364, 416, 546, 624, 672, 728, 1092, 1248, 1456, 2184, 2912, 4368.
Its abundancy index is 29/16 = 2.23, which means 8736edo has strong potential with regards to polymicrotonality. Some notable divisors are 12, 84, 91, 224, 364, 624.