1236edo: Difference between revisions
Clarify, simplify comma basis, note it being an atomic system, and replace irrelevant number theory with factorization and subset edos |
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{{Infobox ET}} | |||
{{ED intro}} | |||
1236edo 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}. | |||
{{Harmonics in equal|1236}} | === Prime harmonics === | ||
{{Harmonics in equal|1236|columns=11}} | |||
[[ | === Subsets and supersets === | ||
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. | |||
Latest revision as of 16:58, 18 February 2025
| ← 1235edo | 1236edo | 1237edo → |
1236 equal divisions of the octave (abbreviated 1236edo or 1236ed2), also called 1236-tone equal temperament (1236tet) or 1236 equal temperament (1236et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1236 equal parts of about 0.971 ¢ each. Each step represents a frequency ratio of 21/1236, or the 1236th root of 2.
1236edo is a zeta peak edo, though not zeta integral nor zeta gap. It is a strong 17-limit system and 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
| 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 |
| 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) | |
Subsets and supersets
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.