126edo
| ← 125edo | 126edo | 127edo → |
126 equal divisions of the octave (abbreviated 126edo or 126ed2), also called 126-tone equal temperament (126tet) or 126 equal temperament (126et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 126 equal parts of about 9.52 ¢ each. Each step represents a frequency ratio of 21/126, or the 126th root of 2.
126edo 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 | +44 | +27 | -41 | +11 | -26 | -27 | -2 | -24 | -43 | +3 | |
| Steps (reduced) |
200 (74) |
293 (41) |
354 (102) |
399 (21) |
436 (58) |
466 (88) |
492 (114) |
515 (11) |
535 (31) |
553 (49) |
570 (66) | |