260edo: Difference between revisions
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Review (-properties not related to the edo) |
→Theory: a harmonic doesnt yield tempering, subgroups do. |
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== Theory == | == Theory == | ||
260edo is [[enfactoring|enfactored]] in the [[7-limit]], with the same tuning as [[65edo]] in the 5-limit, and the same as [[130edo]] in the 7-limit. The mappings for [[harmonic]]s [[11/1|11]] and [[17/1|17]] differ, but 260edo's are hardly an improvement over 130edo's. [[29/1|29]] is the first harmonic that is offered as a sizeable improvement over 130edo, | 260edo is [[enfactoring|enfactored]] in the [[7-limit]], with the same tuning as [[65edo]] in the 5-limit, and the same as [[130edo]] in the 7-limit. The mappings for [[harmonic]]s [[11/1|11]] and [[17/1|17]] differ, but 260edo's are hardly an improvement over 130edo's. [[29/1|29]] is the first harmonic that is offered as a sizeable improvement over 130edo. In the 2.3.5.7.29 subgroup, 260edo tempers out 841/840, 16820/16807, and 47096/46875. | ||
=== Prime harmonics === | === Prime harmonics === | ||
Revision as of 19:11, 11 November 2024
| ← 259edo | 260edo | 261edo → |
Theory
260edo is enfactored in the 7-limit, with the same tuning as 65edo in the 5-limit, and the same as 130edo in the 7-limit. The mappings for harmonics 11 and 17 differ, but 260edo's are hardly an improvement over 130edo's. 29 is the first harmonic that is offered as a sizeable improvement over 130edo. In the 2.3.5.7.29 subgroup, 260edo tempers out 841/840, 16820/16807, and 47096/46875.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.42 | +1.38 | +0.40 | -2.09 | -0.53 | +1.20 | -2.13 | -0.58 | -0.35 | -0.42 |
| Relative (%) | +0.0 | -9.0 | +29.9 | +8.8 | -45.2 | -11.4 | +26.0 | -46.1 | -12.6 | -7.5 | -9.1 | |
| Steps (reduced) |
260 (0) |
412 (152) |
604 (84) |
730 (210) |
899 (119) |
962 (182) |
1063 (23) |
1104 (64) |
1176 (136) |
1263 (223) |
1288 (248) | |
Scales
- Kartvelian Tetradecatonic: 18 18 18 18 18 18 19 19 19 19 19 19 19 19