103169edo

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← 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

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.