1590edo: Difference between revisions
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1590}} | {{Harmonics in equal|1590}} | ||
=== Subsets and supersets === | |||
Since 1590edo factors as {{Factorization|1590}}, it has subset edos {{EDOs|1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795}}. | |||
Revision as of 20:57, 14 December 2023
| ← 1589edo | 1590edo | 1591edo → |
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 (%) | +0.0 | -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.