8736edo

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← 8735edo 8736edo 8737edo →
Prime factorization 25 × 3 × 7 × 13
Step size 0.137363 ¢ 
Fifth 5110\8736 (701.923 ¢) (→ 365\624)
Semitones (A1:m2) 826:658 (113.5 ¢ : 90.38 ¢)
Consistency limit 9
Distinct consistency limit 9

8736edo is an excellent 2.7.13.17 subgroup tuning. It also excellently represents such intervals as 53/49, 47/38.


Approximation of odd harmonics in 8736edo
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.