1520edo
| ← 1519edo | 1520edo | 1521edo → |
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
| 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 | -14 | -33 | -18 | -34 | +33 | +6 | +15 | +19 | -13 | -38 | |
| 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.