# 103169edo

 ← 103168edo 103169edo 103170edo →
Prime factorization 11 × 83 × 113
Step size 0.0116314¢
Fifth 60350\103169 (701.955¢)
Semitones (A1:m2) 9774:7757 (113.7¢ : 90.22¢)
Consistency limit 15
Distinct consistency limit 15

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

Approximation of prime harmonics in 103169edo
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.