1553edo
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| ← 1552edo | 1553edo | 1554edo → |
Theory
1553edo is only consistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 subgroup, where it notably tempers out 4096/4095 and 140625/140608.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.345 | +0.035 | +0.137 | +0.082 | -0.384 | +0.168 | -0.310 | +0.132 | -0.024 | -0.208 | -0.071 |
| Relative (%) | -44.7 | +4.6 | +17.8 | +10.6 | -49.7 | +21.7 | -40.1 | +17.0 | -3.1 | -26.9 | -9.2 | |
| Steps (reduced) |
2461 (908) |
3606 (500) |
4360 (1254) |
4923 (264) |
5372 (713) |
5747 (1088) |
6067 (1408) |
6348 (136) |
6597 (385) |
6821 (609) |
7025 (813) | |
Subsets and supersets
1553edo is the 245th prime edo. 3106edo, which doubles it, provides a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [4923 -1553⟩ | ⟨1553 4923] | -0.0130 | 0.0130 | 1.68 |
| 2.9.5 | [93 -33 5⟩, [-36 -26 51⟩ | ⟨1553 4923 3606] | -0.0137 | 0.0106 | 1.38 |
| 2.9.5.7 | [-5 5 5 -8⟩, [2 -10 14 -1⟩, [37 1 -4 -11⟩ | ⟨1553 4923 3606 4360] | -0.0225 | 0.0178 | 2.31 |
| 2.9.5.7.13 | 4096/4095, 140625/140608, 28829034/28824005, [4 10 -9 0 -4⟩ | ⟨1553 4923 3606 4360 5372] | -0.0271 | 0.0184 | 2.38 |
Music
- Stumbling Over Mystery by Francium