1272edo
| ← 1271edo | 1272edo | 1273edo → |
1272 equal divisions of the octave (abbreviated 1272edo or 1272ed2), also called 1272-tone equal temperament (1272tet) or 1272 equal temperament (1272et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1272 equal parts of about 0.943 ¢ each. Each step represents a frequency ratio of 21/1272, or the 1272nd root of 2.
1272edo is consistent in the 5-odd-limit, though the error on the harmonic 5 is quite large. It is better read as a strong 2.3.7.13.21.23 subgroup tuning.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.068 | -0.465 | +0.042 | -0.136 | -0.375 | +0.038 | +0.411 | -0.238 | -0.343 | -0.026 | +0.028 |
| Relative (%) | -7.2 | -49.3 | +4.5 | -14.5 | -39.7 | +4.1 | +43.5 | -25.3 | -36.4 | -2.8 | +2.9 | |
| Steps (reduced) |
2016 (744) |
2953 (409) |
3571 (1027) |
4032 (216) |
4400 (584) |
4707 (891) |
4970 (1154) |
5199 (111) |
5403 (315) |
5587 (499) |
5754 (666) | |
Subsets and supersets
Since 1272 factors as 23 × 3 × 53, 1272edo has subset edos 1, 2, 3, 4, 6, 8, 12, 24, 53, 106, 159, 212, 318, 424, 636. This list has many notable systems such as 12edo, 24edo, 53edo, 159edo, and 212edo.
2544edo, twice as large, provides consistent corrections for the 15-odd-limit.