1092edo: Difference between revisions
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{{ED intro}} | {{ED intro}} | ||
1092edo is related to [[364edo]], but it differs in mapping for [[5/1|5]] and [[11/1|11]]. Despite having large errors on | 1092edo is related to [[364edo]], but it differs in mapping for [[5/1|5]] and [[11/1|11]]. Despite having large errors on the [[harmonic]]s, it is [[consistent]] in the [[13-odd-limit]], and except for [[15/8]], [[21/16]] and their [[octave complement]]s, the [[23-odd-limit]]. | ||
It provides the [[optimal patent val]] for [[sextile]], the 270 & 822 temperament, the rank-3 [[loki]] temperament, and the rank-4 [[vishdelismic]] temperament, which tempers out [[5632/5625]], as well as its no-7 [[retraction]] thereof. | |||
In higher limits, 1092edo is accurate in the 2.13.29.31.53.59 subgroup. | In higher limits, 1092edo is accurate in the 2.13.29.31.53.59 subgroup. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1092 factors into {{ | Since 1092 factors into primes as {{nowrap| 2<sup>2</sup> × 3 × 7 × 13 }}, 1092edo has subset edos {{EDOs| 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, and 546 }}. | ||
[[Category:Sextile]] | [[Category:Sextile]] | ||
[[Category:Loki]] | [[Category:Loki]] | ||
[[Category:Vishdelismic]] | |||
Latest revision as of 13:05, 5 September 2026
| ← 1091edo | 1092edo | 1093edo → |
1092 equal divisions of the octave (abbreviated 1092edo or 1092ed2), also called 1092-tone equal temperament (1092tet) or 1092 equal temperament (1092et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1092 equal parts of about 1.1 ¢ each. Each step represents a frequency ratio of 21/1092, or the 1092nd root of 2.
1092edo is related to 364edo, but it differs in mapping for 5 and 11. Despite having large errors on the harmonics, it is consistent in the 13-odd-limit, and except for 15/8, 21/16 and their octave complements, the 23-odd-limit.
It provides the optimal patent val for sextile, the 270 & 822 temperament, the rank-3 loki temperament, and the rank-4 vishdelismic temperament, which tempers out 5632/5625, as well as its no-7 retraction thereof.
In higher limits, 1092edo is accurate in the 2.13.29.31.53.59 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.243 | +0.499 | +0.405 | +0.486 | +0.330 | +0.132 | -0.357 | +0.539 | +0.289 | -0.451 | +0.297 |
| Relative (%) | +22.1 | +45.5 | +36.8 | +44.2 | +30.1 | +12.0 | -32.5 | +49.1 | +26.3 | -41.1 | +27.0 | |
| Steps (reduced) |
1731 (639) |
2536 (352) |
3066 (882) |
3462 (186) |
3778 (502) |
4041 (765) |
4266 (990) |
4464 (96) |
4639 (271) |
4796 (428) |
4940 (572) | |
Subsets and supersets
Since 1092 factors into primes as 22 × 3 × 7 × 13, 1092edo has subset edos 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, and 546.