11664edo: Difference between revisions

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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 [[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 {{nowrap|11664 {{=}} 23 × 36}}. Among its divisiors are [[12edo|12]], [[16edo|16]], [[24edo|24]], [[27edo|27]], [[72edo|72]], [[81edo|81]] and [[243edo|243]].

=== Prime harmonics ===

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 {{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 [[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 {{nowrap|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]].
 === Prime harmonics ===
 {{Harmonics in equal|11664|prec=5}}