# 1506edo

← 1505edo | 1506edo | 1507edo → |

**1506 equal divisions of the octave** (abbreviated **1506edo** or **1506ed2**), also called **1506-tone equal temperament** (**1506tet**) or **1506 equal temperament** (**1506et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1506 equal parts of about 0.797 ¢ each. Each step represents a frequency ratio of 2^{1/1506}, or the 1506th root of 2.

1506edo is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit relative error, and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13-limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | +0.037 | +0.140 | +0.098 | +0.076 | +0.110 | +0.224 | -0.302 | -0.386 | -0.095 | -0.016 |

Relative (%) | +0.0 | +4.6 | +17.6 | +12.3 | +9.6 | +13.8 | +28.1 | -37.9 | -48.4 | -11.9 | -2.0 | |

Steps (reduced) |
1506 (0) |
2387 (881) |
3497 (485) |
4228 (1216) |
5210 (692) |
5573 (1055) |
6156 (132) |
6397 (373) |
6812 (788) |
7316 (1292) |
7461 (1437) |

### Subsets and supersets

Since 1506 factors into 2 × 3 × 251, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.