# 1590edo

 ← 1589edo 1590edo 1591edo →
Prime factorization 2 × 3 × 5 × 53
Step size 0.754717¢
Fifth 930\1590 (701.887¢) (→31\53)
Semitones (A1:m2) 150:120 (113.2¢ : 90.57¢)
Consistency limit 9
Distinct consistency limit 9

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 21/1590, 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.

### Prime harmonics

Approximation of prime harmonics in 1590edo
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.