1590edo

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← 1589edo1590edo1591edo →
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 1590-tone equal temperament (1590tet), 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 of 1590edo 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 -9 +13 +31 -50 +30 -7 -20 -46 -19 -17
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.