177edo
| ← 176edo | 177edo | 178edo → |
177 equal divisions of the octave (abbreviated 177edo or 177ed2), also called 177-tone equal temperament (177tet) or 177 equal temperament (177et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 177 equal parts of about 6.78 ¢ each. Each step represents a frequency ratio of 21/177, or the 177th root of 2.
177edo is consistent to the 7-odd-limit, but harmonic 3 is about halfway between its steps. It has good approximations to 5, 7, 9, 13, and 19, making it suitable for a 2.9.5.7.13.19 subgroup interpretation, which is equivalent to every other step of 354edo.
Consider the full 7-limit patent val nonetheless, the equal temperament tempers out 245/243 and 2401/2400, supporting and providing a good tuning for the octacot temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +3.13 | +0.13 | +0.67 | -0.52 | -2.17 | +0.15 | +3.26 | -3.26 | +0.79 | -2.98 | +2.23 |
| relative (%) | +46 | +2 | +10 | -8 | -32 | +2 | +48 | -48 | +12 | -44 | +33 | |
| Steps (reduced) |
281 (104) |
411 (57) |
497 (143) |
561 (30) |
612 (81) |
655 (124) |
692 (161) |
723 (15) |
752 (44) |
777 (69) |
801 (93) | |
Subsets and supersets
Since 177 factors into 3 × 59, 177edo contains 3edo and 59edo as its subsets. 354edo, which doubles it, provides good correction for the approximation of harmonic 3.