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.

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~~|~~######]] ~~

=== Prime harmonics ===

=== 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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-'''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&gt;, |-92 -17 21 25&gt;, and |110 -71 -11 10&gt;. 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&gt;, |-29 16 5 -9 5&gt;, |3 -26 13 -7 8&gt;, and |-6 2 -24 11 8&gt; in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and |-17 -5 -13 0 17 -1&gt; in the 13-limit.
+{{Mathematical interest}}
+{{Infobox ET}}
+{{ED intro}}
-{{Primes in edo|103169|prec=7}}
+edo 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.