1861edo: Difference between revisions
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== Theory == | == Theory == | ||
1861edo is only [[consistent]] to the [[5-odd-limit]], and the | 1861edo is only [[consistent]] to the [[5-odd-limit]], and the [[harmonic]] [[3/1|3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.21.11 [[subgroup]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1861edo is the 284th [[prime edo]]. 3722edo, which doubles it, provides a good correction to | 1861edo is the 284th [[prime edo]]. 3722edo, which doubles it, provides a good correction to harmonics 3, 7, and 13. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
Revision as of 12:30, 30 October 2023
| ← 1860edo | 1861edo | 1862edo → |
Theory
1861edo is only consistent to the 5-odd-limit, and the harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.21.11 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.248 | -0.070 | -0.314 | -0.149 | -0.001 | +0.311 | +0.178 | +0.149 | -0.253 | -0.066 | -0.225 |
| Relative (%) | +38.5 | -10.8 | -48.8 | -23.0 | -0.2 | +48.2 | +27.7 | +23.2 | -39.3 | -10.3 | -34.9 | |
| Steps (reduced) |
2950 (1089) |
4321 (599) |
5224 (1502) |
5899 (316) |
6438 (855) |
6887 (1304) |
7271 (1688) |
7607 (163) |
7905 (461) |
8174 (730) |
8418 (974) | |
Subsets and supersets
1861edo is the 284th prime edo. 3722edo, which doubles it, provides a good correction to harmonics 3, 7, and 13.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-5899 1861⟩ | [⟨1861 5899]] | +0.0234 | 0.0234 | 3.63 |