777edo: Difference between revisions
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777edo is in[[consistent]] to [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], and [[17/1|17]], making it suitable for a 2.9.5.7.11.13.17 [[subgroup]] interpretation. A [[comma basis]] for the 2.9.5.7.11.13 subgroup is {4459/4455, [[41503/41472]], 496125/495616, 105644/105625, [[123201/123200]]}. In addition, it [[tempering out|tempers out]] the [[landscape comma]] in the 2.9.5.7 subgroup. | |||
777edo is | |||
=== Odd harmonics === | |||
{{Harmonics in equal|777}} | {{Harmonics in equal|777}} | ||
=== Subsets and supersets === | |||
Since 777 factors into {{factorization|777}}, 777edo has subset edos {{EDOs| 3, 7, 21, 37, 111, and 333 }}. | |||
Latest revision as of 23:13, 20 February 2025
| ← 776edo | 777edo | 778edo → |
777 equal divisions of the octave (abbreviated 777edo or 777ed2), also called 777-tone equal temperament (777tet) or 777 equal temperament (777et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 777 equal parts of about 1.54 ¢ each. Each step represents a frequency ratio of 21/777, or the 777th root of 2.
777edo is inconsistent to 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise it is excellent in approximating harmonics 5, 7, 9, 11, 13, and 17, making it suitable for a 2.9.5.7.11.13.17 subgroup interpretation. A comma basis for the 2.9.5.7.11.13 subgroup is {4459/4455, 41503/41472, 496125/495616, 105644/105625, 123201/123200}. 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.