# 952edo

952edo divides the octave into steps of 1.26 cents each.

952edo's factorization is 2^{3} x 7 x 17, and its divisors are 1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476.

## Theory

Prime number | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +0.000 | +0.146 | -0.599 | +0.502 | -0.478 | +0.229 | -0.334 | -0.034 | -0.543 | +0.255 | -0.498 | -0.504 | -0.491 | +0.247 | +0.040 |

relative (%) | +0 | +12 | -48 | +40 | -38 | +18 | -26 | -3 | -43 | +20 | -39 | -40 | -39 | +20 | +3 | |

Steps (reduced) | 952 (0) | 1509 (557) | 2210 (306) | 2673 (769) | 3293 (437) | 3523 (667) | 3891 (83) | 4044 (236) | 4306 (498) | 4625 (817) | 4716 (908) | 4959 (199) | 5100 (340) | 5166 (406) | 5288 (528) |

In the 2.3.13.17.19 subgroup, 952edo tempers out 793152/793117.

In the 19-limit as a whole, 952edo tempers out 1445/1444, 1540/1539.

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. 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]