1236edo: Difference between revisions

Approximation of prime harmonics in 1236edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.013	+0.094	+0.106	+0.138	+0.249	-0.101	-0.426	-0.119	-0.451	-0.375
Error	Relative (%)	+0.0	-1.4	+9.7	+10.9	+14.3	+25.7	-10.4	-43.8	-12.3	-46.5	-38.7
Steps (reduced)		1236 (0)	1959 (723)	2870 (398)	3470 (998)	4276 (568)	4574 (866)	5052 (108)	5250 (306)	5591 (647)	6004 (1060)	6123 (1179)

Since 1236 factors into 2² × 3 × 103, 1236edo has subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an atomic system.

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 {{EDO intro|1236}}
-edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.
+edo is a [[zeta peak edo]], though not [[zeta integral edo|zeta integral]] nor [[zeta gap edo|zeta gap]]. It is a strong 17-limit system and [[consistency|distinctly consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.
 === Prime harmonics ===
 {{Harmonics in equal|1236|columns=11}}
-=== Divisors ===
+=== Subsets and supersets ===
-= 2<sup>2</sup> × 3 × 103, with subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.
+Since 1236 factors into {{factorization|1236}}, 1236edo has subset edos {{EDOs| 2, 3, 6, 12, 103, 206, 309, and 618 }}. It is divisible by 12, and is an [[atomic]] system.

Revision as of 09:54, 31 October 2023