126edo
| ← 125edo | 126edo | 127edo → |
The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit srutal temperament. It also creates an excellent Porcupine[8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.81 | +4.16 | +2.60 | -3.91 | +1.06 | -2.43 | -2.55 | -0.19 | -2.27 | -4.11 | +0.30 |
| Relative (%) | +29.5 | +43.7 | +27.3 | -41.1 | +11.2 | -25.5 | -26.8 | -2.0 | -23.9 | -43.2 | +3.1 | |
| Steps (reduced) |
200 (74) |
293 (41) |
354 (102) |
399 (21) |
436 (58) |
466 (88) |
492 (114) |
515 (11) |
535 (31) |
553 (49) |
570 (66) | |