759edo: Difference between revisions
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759 = 3 × 253, and 759edo shares its excellent perfect fifth with [[253edo]]. However, the primes [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] are mapped differently. With [[stretched and compressed tuning|octave stretching]], one may use 2.7.11.13 subgroup, all sharp, or 2.5.17.19.23.29.31 subgroup, all tuned flat. The 759def val [[support]]s [[noletaland]], the 282 & 759def temperament, in the 23-limit. 759edo is an amazingly accurate 2.3.37.103.229 system. <!-- explain the significance of this subgroup --> | 759 = 3 × 253, and 759edo shares its excellent perfect fifth with [[253edo]]. However, the primes [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] are mapped differently. With [[stretched and compressed tuning|octave stretching]], one may use 2.7.11.13 subgroup, all sharp, or 2.5.17.19.23.29.31 subgroup, all tuned flat. The 759def val [[support]]s [[noletaland]], the 282 & 759def temperament, in the 23-limit. 759edo is an amazingly accurate 2.3.37.103.229 system. <!-- explain the significance of this subgroup --> | ||
Revision as of 17:20, 20 February 2025
| ← 758edo | 759edo | 760edo → |
759 equal divisions of the octave (abbreviated 759edo or 759ed2), also called 759-tone equal temperament (759tet) or 759 equal temperament (759et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 759 equal parts of about 1.58 ¢ each. Each step represents a frequency ratio of 21/759, or the 759th root of 2.
759 = 3 × 253, and 759edo shares its excellent perfect fifth with 253edo. However, the primes 5, 7, 11, and 13 are mapped differently. With octave stretching, one may use 2.7.11.13 subgroup, all sharp, or 2.5.17.19.23.29.31 subgroup, all tuned flat. The 759def val supports noletaland, the 282 & 759def temperament, in the 23-limit. 759edo is an amazingly accurate 2.3.37.103.229 system.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.021 | -0.543 | +0.344 | +0.461 | +0.579 | -0.608 | -0.280 | -0.606 | -0.328 | -0.372 |
| Relative (%) | +0.0 | +1.3 | -34.3 | +21.8 | +29.1 | +36.6 | -38.4 | -17.7 | -38.4 | -20.8 | -23.5 | |
| Steps (reduced) |
759 (0) |
1203 (444) |
1762 (244) |
2131 (613) |
2626 (349) |
2809 (532) |
3102 (66) |
3224 (188) |
3433 (397) |
3687 (651) |
3760 (724) | |
Subsets and supersets
759edo notably contains 253edo.