11664edo: Difference between revisions

11664edo 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-odd-limit and with a lower 23-limit relative error than any division until 16808. Aside from this peculiar double threat property, it is also very composite, since 11664 = 2³ × 3⁶. Among its divisiors are 12, 16, 24, 27, 72, 81 and 243.

Prime harmonics

Approximation of prime harmonics in 11664edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00000	-0.00027	+0.00316	+0.00125	+0.01951	+0.00732	-0.01714	+0.01785	+0.01783	-0.05045	+0.02616
Error	Relative (%)	+0.0	-0.3	+3.1	+1.2	+19.0	+7.1	-16.7	+17.3	+17.3	-49.0	+25.4
Steps (reduced)		11664 (0)	18487 (6823)	27083 (3755)	32745 (9417)	40351 (5359)	43162 (8170)	47676 (1020)	49548 (2892)	52763 (6107)	56663 (10007)	57786 (11130)

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 {{Infobox ET}}
-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]].
+{{EDO intro|11664}}
-{{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 [[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]].
-[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
+=== Prime harmonics ===
+{{Harmonics in equal|11664|prec=5}}

11664edo: Difference between revisions

Revision as of 11:18, 7 January 2023

Prime harmonics

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