103169edo
| ← 103168edo | 103169edo | 103170edo → |
103169 equal divisions of the octave (abbreviated 103169edo or 103169ed2), also called 103169-tone equal temperament (103169tet) or 103169 equal temperament (103169et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 103169 equal parts of about 0.0116 ¢ each. Each step represents a frequency ratio of 21/103169, or the 103169th root of 2.
103169edo provides an extraordinarily strong 7-limit system, tempering out [9 -28 37 -18⟩, [-92 -17 21 25⟩, and [110 -71 -11 10⟩. It maps the starling comma (126/125) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma (225/224) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma (2401/2400) to 62 steps, and the ragisma (4375/4374) to 34 steps. The patent val tempers out [20 3 -9 -10 7⟩, [-29 16 5 -9 5⟩, [3 -26 13 -7 8⟩, and [-6 2 -24 11 8⟩ in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and [-17 -5 -13 0 17 -1⟩ in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000000 | +0.0000438 | +0.0000044 | +0.0000005 | -0.0011709 | +0.0038933 | -0.0052791 | -0.0050438 | -0.0042274 | -0.0004802 | -0.0055731 |
| Relative (%) | +0.0 | +0.4 | +0.0 | +0.0 | -10.1 | +33.5 | -45.4 | -43.4 | -36.3 | -4.1 | -47.9 | |
| Steps (reduced) |
103169 (0) |
163519 (60350) |
239551 (33213) |
289632 (83294) |
356906 (47399) |
381771 (72264) |
421699 (9023) |
438254 (25578) |
466691 (54015) |
501193 (88517) |
511119 (98443) | |
Subsets and supersets
Since 103169 factors into 11 × 83 × 113, 103169edo has subset edos 11, 83, 113, 913, 1243, and 9379.