# 1590edo

← 1589edo | 1590edo | 1591edo → |

**1590 equal divisions of the octave** (abbreviated **1590edo** or **1590ed2**), also called **1590-tone equal temperament** (**1590tet**) or **1590 equal temperament** (**1590et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1590 equal parts of about 0.755 ¢ each. Each step represents a frequency ratio of 2^{1/1590}, or the 1590th root of 2.

1590edo is consistent in the 9-odd-limit.

Aside from this, it is a strong 2.3.5.17.29.31 subgroup tuning. A comma basis for this subgroup is {128061/128000, 1966113/1965200, 11337408/11328125, 12115968/12109375, 81310473/81264640}. It can also be used with the 2.3.5.13/7.17.29.31 fractional subgroup, having a strong approximation of 13/7. There it tempers out 4901/4900.

1590edo is also the last tuning system to have the same mapping for 11 as 159edo, and hence it is the largest multiple of 159 tempering out the frameshift comma and nexus comma together.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | -0.068 | +0.101 | +0.231 | -0.375 | +0.227 | -0.050 | -0.155 | -0.350 | -0.143 | -0.130 |

Relative (%) | +0.0 | -9.0 | +13.4 | +30.6 | -49.6 | +30.1 | -6.6 | -20.5 | -46.4 | -19.0 | -17.2 | |

Steps (reduced) |
1590 (0) |
2520 (930) |
3692 (512) |
4464 (1284) |
5500 (730) |
5884 (1114) |
6499 (139) |
6754 (394) |
7192 (832) |
7724 (1364) |
7877 (1517) |

### Subsets and supersets

Since 1590edo factors as 2 × 3 × 5 × 53, it has subset edos 1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795.