777edo
| ← 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 | -14 | -31 | -3 | +2 | -24 | +35 | +4 | +36 | +17 | +19 | |
| 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.