# 8736edo

← 8735edo | 8736edo | 8737edo → |

^{5}× 3 × 7 × 13**8736 equal divisions of the octave** (abbreviated **8736edo** or **8736ed2**), also called **8736-tone equal temperament** (**8736tet**) or **8736 equal temperament** (**8736et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8736 equal parts of about 0.137 ¢ each. Each step represents a frequency ratio of 2^{1/8736}, or the 8736th root of 2.

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 | -36 | -5 | -46 | +41 | -4 | +40 | -8 | +11 | -29 | +16 | |

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 2^{5} × 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.