# 506edo

← 505edo | 506edo | 507edo → |

**506 equal divisions of the octave** (abbreviated **506edo**), or **506-tone equal temperament** (**506tet**), **506 equal temperament** (**506et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 506 equal parts of about 2.37 ¢ each. Each step of 506edo represents a frequency ratio of 2^{1/506}, or the 506th root of 2.

506edo is a strong 5-limit system, correcting 253edo's mapping for 5. It tunes a number of strong 5-limit temperaments like vishnu, monzismic, and lafa. It also tunes stockhausenic and geb temperaments, providing the optimal patent val for 11- and 17-limit stockhausenic. The 506e val tempers out the swetisma and tunes hades.

506edo tempers out the major arcana comma, tempering out which divides the octave in 22 parts. It also tunes the palladium temperament in the 5-limit.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +0.00 | +0.02 | +0.25 | +1.13 | -1.12 | -1.00 | -0.61 | -1.07 | +0.18 | -0.33 | +0.42 |

relative (%) | +0 | +1 | +10 | +48 | -47 | -42 | -26 | -45 | +8 | -14 | +18 | |

Steps (reduced) |
506 (0) |
802 (296) |
1175 (163) |
1421 (409) |
1750 (232) |
1872 (354) |
2068 (44) |
2149 (125) |
2289 (265) |
2458 (434) |
2507 (483) |

### Subsets and supersets

Since 506 factors into 2 × 11 × 23, 506edo has subset edos 2, 11, 22, 23, 46, and 253. 1012edo, which is a zeta edo, provides correction for the 13-limit.