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 →
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

Template:EDO intro

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

Odd harmonics

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.