142edo
| ← 141edo | 142edo | 143edo → |
142 equal divisions of the octave (abbreviated 142edo or 142ed2), also called 142-tone equal temperament (142tet) or 142 equal temperament (142et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 142 equal parts of about 8.45 ¢ each. Each step represents a frequency ratio of 21/142, or the 142nd root of 2.
The equal temperament tempers out 32805/32768 (schisma) in the 5-limit; 1728/1715, 3136/3125, and 16875/16807 in the 7-limit; 176/175, 540/539 and 1375/1372 in the 11-limit. It is an excellent tuning for orwellismic, the rank-3 temperament tempering out 1728/1715, and a good one for guanyin, the 11-limit extension also tempering out 176/175. It is also excellent for semisept, the 31 & 111 temperament tempering out 1728/1715 and 3136/3125 and the 53 & 89 temperament tempering out both 1728/1715 and 32805/32768.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.55 | +2.42 | +3.01 | -2.02 | -3.91 | -3.55 | -1.74 | -2.92 | +1.41 | -4.19 |
| Relative (%) | +0.0 | -6.5 | +28.6 | +35.6 | -23.9 | -46.2 | -42.0 | -20.6 | -34.6 | +16.7 | -49.6 | |
| Steps (reduced) |
142 (0) |
225 (83) |
330 (46) |
399 (115) |
491 (65) |
525 (99) |
580 (12) |
603 (35) |
642 (74) |
690 (122) |
703 (135) | |