103169edo: Difference between revisions

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'''103169edo''' is the [[EDO|equal division of the octave]] into 103169 parts of 0.011631401 [[cent]]s each. It 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.
{{EDO intro|103169}}


{{Primes in edo|103169|prec=7}}
103169edo provides an extraordinarily strong 7-limit system, tempering out {{monzo| 9 -28 37 -18 }}, {{monzo| -92 -17 21 25 }}, and {{monzo| 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 {{monzo| 20 3 -9 -10 7 }}, {{monzo| -29 16 5 -9 5 }}, {{monzo| 3 -26 13 -7 8 }}, and {{monzo| -6 2 -24 11 8 }} in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and {{monzo| -17 -5 -13 0 17 -1 }} in the 13-limit.


[[Category:Equal divisions of the octave|######]] <!-- 6-digit number -->
=== Prime harmonics ===
{{Harmonics in equal|103169|prec=7}}
 
=== Subsets and supersets ===
Since 103169 factors into 11 × 83 × 113, 103169edo has subset edos 11, 83, 113, 913, 1243, and 9379.

Revision as of 08:52, 20 February 2023

← 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

Template:EDO intro

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.

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