952edo
| ← 951edo | 952edo | 953edo → |
952 equal divisions of the octave (abbreviated 952edo or 952ed2), also called 952-tone equal temperament (952tet) or 952 equal temperament (952et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 952 equal parts of about 1.26 ¢ each. Each step represents a frequency ratio of 21/952, or the 952nd root of 2.
Theory
952edo is inconsistent in the 5-odd-limit despite having a decent approximation to harmonic 3. To start with, as an 11-limit temperament we may consider the 952ce val ⟨952 1509 2211 2673 3294] and the 952d val ⟨952 1509 2210 2672 3293].
Despite having bad approximations, in light of having 28 as a divisor 952edo provides the optimal patent val for the oquatonic temperament in the 7-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.146 | -0.599 | +0.502 | +0.292 | -0.478 | +0.229 | -0.454 | -0.334 | -0.034 | -0.613 | -0.543 |
| Relative (%) | +11.6 | -47.6 | +39.8 | +23.1 | -37.9 | +18.1 | -36.0 | -26.5 | -2.7 | -48.6 | -43.1 | |
| Steps (reduced) |
1509 (557) |
2210 (306) |
2673 (769) |
3018 (162) |
3293 (437) |
3523 (667) |
3719 (863) |
3891 (83) |
4044 (236) |
4181 (373) |
4306 (498) | |
Subsets and supersets
Since 952's factorization is 23 × 7 × 17, 952edo has subset EDOs 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476.
Miscellaneous properties
952edo is notable for having a concoctic scale which represents a natural phenomenon—169\952 is useful both as a cycle length for a leap week calendar and its generator, thus being associated with a 169 & 952 mos sequence. The resulting calendar has a year length of 365 days 5h 49m 24.7s. 169/952 of a week, 1d 5h 49m 24.7s is roughly the fraction by which Earth's year length exceeds 52 weeks. The leap day cycle of 33\136 shares the exact same property of concoction, thus 952edo can be viewed as a compound of 7 such MOSes.
Scales
- SouthSolstitial[169]