1590edo: Difference between revisions
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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. | 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. | ||
1590edo is also the last tuning system to have the same mapping for 11 as 159edo, and hence it is the largest multiple of 159 tempering out the [[frameshift comma]] and [[nexus comma]] together. | |||
=== Prime harmonics === | === Prime harmonics === | ||
Revision as of 20:14, 29 July 2024
| ← 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.
1590edo is also the last tuning system to have the same mapping for 11 as 159edo, and hence it is the largest multiple of 159 tempering out the frameshift comma and nexus comma together.
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.