11664edo: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 1:

~~{{novelty}}{{stub}}~~{{Infobox ET}}

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 [[~~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-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, ~~since 11664 = 23 × 36~~. ~~Among its divisiors are~~ [[~~12edo~~|12]], [[~~16edo|16~~]], [[~~24edo|24~~]], [[~~27edo|27~~]], [[~~72edo|72~~]], [[~~81edo|81~~]] and [[~~243edo|243~~]].

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.

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| 23 × 36 }}. Among its divisiors are [[12edo|12]], [[16edo|16]], [[24edo|24]], [[27edo|27]], [[72edo|72]], [[81edo|81]] and [[243edo|243]].

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|11664}}
+{{ED intro}}
-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 [[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-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, since 11664 = 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]].
+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.
+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|prec=5}}
+{{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]].