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 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
| 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.