11664edo: Difference between revisions

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The '''11664 division''' divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[18355edo|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo|12]], [[16edo|16]], [[24edo|24]], [[27edo|27]], [[72edo|72]], [[81edo|81]] and [[243edo|243]].

~~{{Primes~~ in ~~edo|11664~~|~~prec=5}}~~

11664edo is a very strong [[7-limit]] system, with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until [[18355edo|18355]]. It is a [[zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly [[consistent]] through the [[27-odd-limit]] and with a lower [[23-limit]] relative error than any division until [[16808edo|16808]]. Aside from this peculiar double threat property, it is also very composite, giving itself another edge over similar systems.

[[~~Category:Equal divisions of the octave~~|~~#####~~]]

Some of the simpler commas [[tempering out|tempered out]] include [[123201/123200]] and [[1990656/1990625]] in the [[13-limit]]; [[194481/194480]] and [[336141/336140]] in the [[17-limit]]; 23409/23408 and 89376/89375 in the [[19-limit]]; 43264/43263, 71875/71874, and 76545/76544 in the [[23-limit]].

=== Prime harmonics ===

{{Harmonics in equal|11664|intervals=prime|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 11664edo (continued)}}

=== Subsets and supersets ===

11664 factors into primes as {{nowrap| 2<sup>3</sup> × 3<sup>6</sup> }}. Among its divisiors are [[12edo|12]], [[16edo|16]], [[24edo|24]], [[27edo|27]], [[72edo|72]], [[81edo|81]] and [[243edo|243]].

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-The '''11664 division''' divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit  [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]  than any division until [[18355edo|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo|12]], [[16edo|16]], [[24edo|24]], [[27edo|27]], [[72edo|72]], [[81edo|81]] and [[243edo|243]].
+{{Infobox ET}}
+{{ED intro}}
-{{Primes in edo|11664|prec=5}}
+edo is a very strong [[7-limit]] system, with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until [[18355edo|18355]]. It is a [[zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly [[consistent]] through the [[27-odd-limit]] and with a lower [[23-limit]] relative error than any division until [[16808edo|16808]]. Aside from this peculiar double threat property, it is also very composite, giving itself another edge over similar systems.
-[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
+Some of the simpler commas [[tempering out|tempered out]] include [[123201/123200]] and [[1990656/1990625]] in the [[13-limit]]; [[194481/194480]] and [[336141/336140]] in the [[17-limit]]; 23409/23408 and 89376/89375 in the [[19-limit]]; 43264/43263, 71875/71874, and 76545/76544 in the [[23-limit]].
+=== Prime harmonics ===
+{{Harmonics in equal|11664|intervals=prime|columns=9}}
+{{Harmonics in equal|11664|intervals=prime|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 11664edo (continued)}}
+=== Subsets and supersets ===
+factors into primes as {{nowrap| 2<sup>3</sup> × 3<sup>6</sup> }}. Among its divisiors are [[12edo|12]], [[16edo|16]], [[24edo|24]], [[27edo|27]], [[72edo|72]], [[81edo|81]] and [[243edo|243]].