1957edo
| ← 1956edo | 1957edo | 1958edo → |
1957 equal divisions of the octave (abbreviated 1957edo or 1957ed2), also called 1957-tone equal temperament (1957tet) or 1957 equal temperament (1957et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1957 equal parts of about 0.613 ¢ each. Each step represents a frequency ratio of 21/1957, or the 1957th root of 2.
1957edo is notable for an extremely good approximation of the 2.5.7 subgroup.
In terms of regular temperaments, as a multiple of 19, it tempers out the enneadeca, equating 6/5 to 5 steps of 19edo, while in the 2.5.7 subgroup it tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also inherits its mapping of 10/7 from 103edo (which is a convergent), and equates six of this interval to 17/2, thereby tempering out S49/S50 = 2000033/2000000.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.140 | -0.008 | +0.004 | -0.066 | +0.147 | -0.101 | -0.119 | +0.239 | -0.042 | -0.222 |
| Relative (%) | +0.0 | +22.8 | -1.3 | +0.6 | -10.8 | +23.9 | -16.5 | -19.4 | +38.9 | -6.9 | -36.2 | |
| Steps (reduced) |
1957 (0) |
3102 (1145) |
4544 (630) |
5494 (1580) |
6770 (899) |
7242 (1371) |
7999 (171) |
8313 (485) |
8853 (1025) |
9507 (1679) |
9695 (1867) | |