777edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|777}} | |||
777edo is a [[dual-fifth system]] with a [[consistency|consistency limit]] of only 3, but otherwise it is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], and [[13/1|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation with the comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200, 105644/105625}. In addition, it tempers out the [[landscape comma]] in the 2.9.5.7 subgroup. | |||
777edo is a dual | |||
=== Odd harmonics === | |||
{{Harmonics in equal|777}} | {{Harmonics in equal|777}} | ||
=== Subsets and supersets === | |||
Since 777 factors into 3 × 7 × 37, 777edo has subset edos {{EDOs| 3, 7, 21, 37, 111, and 333 }}. | |||
Revision as of 11:52, 20 October 2023
| ← 776edo | 777edo | 778edo → |
777edo is a dual-fifth system with a consistency limit of only 3, but otherwise it is excellent in approximating harmonics 5, 7, 9, 11, and 13, making it suitable for a 2.9.5.7.11.13 subgroup interpretation with the comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200, 105644/105625}. In addition, it tempers out the landscape comma in the 2.9.5.7 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.748 | -0.213 | -0.486 | -0.049 | +0.033 | -0.373 | +0.534 | +0.064 | +0.556 | +0.262 | +0.297 |
| Relative (%) | +48.4 | -13.8 | -31.5 | -3.2 | +2.2 | -24.2 | +34.6 | +4.1 | +36.0 | +16.9 | +19.2 | |
| Steps (reduced) |
1232 (455) |
1804 (250) |
2181 (627) |
2463 (132) |
2688 (357) |
2875 (544) |
3036 (705) |
3176 (68) |
3301 (193) |
3413 (305) |
3515 (407) | |
Subsets and supersets
Since 777 factors into 3 × 7 × 37, 777edo has subset edos 3, 7, 21, 37, 111, and 333.