8736edo: Difference between revisions
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{{EDO intro|8736}} | {{EDO intro|8736}} | ||
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 === | === Odd harmonics === | ||
{{ | {{Harmonics in equal|8736}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 8736 factors as {{ | Since 8736 factors as {{factorization|8736}}, 8736edo has subset edos {{EDOs| 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 | Its abundancy index is 2.23, which means 8736edo has strong potential with regards to [[polymicrotonality]]. Some notable divisors are {{EDOs| 12, 84, 91, 224, 364, 624 }}. | ||
Revision as of 08:10, 27 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 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 2.23, which means 8736edo has strong potential with regards to polymicrotonality. Some notable divisors are 12, 84, 91, 224, 364, 624.