# 1520edo

 ← 1519edo 1520edo 1521edo →
Prime factorization 24 × 5 × 19
Step size 0.789474¢
Fifth 889\1520 (701.842¢)
Semitones (A1:m2) 143:115 (112.9¢ : 90.79¢)
Consistency limit 11
Distinct consistency limit 11

1520 equal divisions of the octave (abbreviated 1520edo or 1520ed2), also called 1520-tone equal temperament (1520tet) or 1520 equal temperament (1520et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1520 equal parts of about 0.789 ¢ each. Each step represents a frequency ratio of 21/1520, or the 1520th root of 2.

1520edo is consistent in the 11-odd-limit and it is a distinctly flat system, with optional additions of either 17, 19, or 29.

In the 5-limit, it tempers out the enneadeca as well as provides the optimal patent val for 5-limit soviet ferris wheel temperament. In the 7-limit, it tempers out 4375/4374. In the 11-limit, it is a tuning for hemienneadecal and provides an alternate 2.3.5.7.11.17 subgroup extension for it, reaching 17th harmonic in 3 steps and tempering 119/64 to 17\19. The equal temperament also tunes thor and skadi.

In the 2.3.5.7.11.17.19.29, 1520edo tempers out 2205/2204, 2500/2499, 5985/5984, 11400/14399.

### Prime harmonics

Approximation of prime harmonics in 1520edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.113 -0.261 -0.142 -0.265 +0.262 +0.045 +0.119 +0.147 -0.104 -0.299
Relative (%) +0.0 -14.3 -33.1 -17.9 -33.6 +33.2 +5.6 +15.0 +18.6 -13.1 -37.8
Steps
(reduced)
1520
(0)
2409
(889)
3529
(489)
4267
(1227)
5258
(698)
5625
(1065)
6213
(133)
6457
(377)
6876
(796)
7384
(1304)
7530
(1450)

### Subsets and supersets

Since 1520 factors as 24 × 5 × 19, 1520edo has subset edos 1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760.