# 496edo

← 495edo | 496edo | 497edo → |

^{4}× 31**496 equal divisions of the octave** (abbreviated **496edo**), or **496-tone equal temperament** (**496tet**), **496 equal temperament** (**496et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 496 equal parts of about 2.42 ¢ each. Each step of 496edo represents a frequency ratio of 2^{1/496}, or the 496th root of 2.

496edo is enfactored in the 11-limit, with the same tuning as 248edo, but the patent vals differ on the mapping for 13. As such, in the 11-limit it supports a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, it tempers out 4225/4224.

496edo is good with the 2.3.11.19 subgroup. For higher limits, it has good approximations of 31, 37, and 47. In the 2.3.11.19 subgroup, it tempers out 131072/131043.

### Odd harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | -0.34 | +0.78 | -1.08 | -0.68 | +0.29 | -1.01 | +0.44 | -0.92 | +0.07 | +0.99 | +0.76 |

relative (%) | -14 | +32 | -45 | -28 | +12 | -42 | +18 | -38 | +3 | +41 | +31 | |

Steps (reduced) |
786 (290) |
1152 (160) |
1392 (400) |
1572 (84) |
1716 (228) |
1835 (347) |
1938 (450) |
2027 (43) |
2107 (123) |
2179 (195) |
2244 (260) |

### Subsets and supersets

496 is the 3rd perfect number, factoring into 2^{4} × 31. Its nontrivial divisors are 2, 4, 8, 16, 31, 62, 124, 248, the most notable being 31.