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]]. | 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}} | |||
Revision as of 07:37, 23 April 2021
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 relative error than any division until 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 limit and with a lower 23-limit relative error than any division until 16808. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are 12, 16, 24, 27, 72, 81 and 243.
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