1012edo: Difference between revisions
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== Theory == | == Theory == | ||
It is a strong 13-limit system, distinctly consistent through the 15 limit. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is 2401/2400, 4096/4095, 6656/6655, 9801/9800 and | 2 6 -1 2 0 4 | It is a strong 13-limit system, distinctly consistent through the 15 limit. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is 2401/2400, 4096/4095, 6656/6655, 9801/9800 and {{monzo|2 6 -1 2 0 4}}. | ||
1012 has divisors {{EDOs|1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506}}. | |||
In addition to containing 22edo and 23edo, it contains a [[22L 1s|quartismoid]] scale produced by generator of 45\1012 associated with [[33/32]], and is associated with a 45 & 1012 temperament, making it [[concoctic]]. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, {{monzo|18 15 -12 -1 0 -3}}. | |||
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Revision as of 17:35, 21 October 2022
| ← 1011edo | 1012edo | 1013edo → |
Theory
It is a strong 13-limit system, distinctly consistent through the 15 limit. It is a zeta peak edo, though not zeta integral nor zeta gap. A basis for the 13-limit commas is 2401/2400, 4096/4095, 6656/6655, 9801/9800 and [2 6 -1 2 0 4⟩.
1012 has divisors 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506.
In addition to containing 22edo and 23edo, it contains a quartismoid scale produced by generator of 45\1012 associated with 33/32, and is associated with a 45 & 1012 temperament, making it concoctic. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, [18 15 -12 -1 0 -3⟩.