1106edo: Difference between revisions
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1106edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13 and 17 limits, but even so is distinctly [[consistent]] through the [[17-odd-limit]]. | 1106edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13 and 17 limits, but even so is distinctly [[consistent]] through the [[17-odd-limit]]. | ||
It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and notably [[semisupermajor]] in the 11-limit. | It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and notably [[semisupermajor]] in the 11-limit. In higher limits, it supports the 79th-octave temperament [[gold]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
Revision as of 20:01, 3 July 2023
| ← 1105edo | 1106edo | 1107edo → |
1106edo is a zeta peak edo. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit relative error being 171, 270, 342, 441 and 612. It is even stronger in the 11-limit; the only ones beating it out now being 270, 342 and 612. It is less strong in the 13 and 17 limits, but even so is distinctly consistent through the 17-odd-limit.
It notably supports supermajor, brahmagupta, and orga in the 7-limit, and notably semisupermajor in the 11-limit. In higher limits, it supports the 79th-octave temperament gold.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.034 | -0.057 | +0.071 | -0.143 | +0.340 | +0.289 | -0.225 | -0.065 | +0.079 | -0.370 |
| Relative (%) | +0.0 | +3.1 | -5.2 | +6.5 | -13.1 | +31.4 | +26.6 | -20.8 | -6.0 | +7.3 | -34.1 | |
| Steps (reduced) |
1106 (0) |
1753 (647) |
2568 (356) |
3105 (893) |
3826 (508) |
4093 (775) |
4521 (97) |
4698 (274) |
5003 (579) |
5373 (949) |
5479 (1055) | |
Divisors
Since 1106 factors into 2 × 7 × 79, it has subset edos 2, 7, 14, 79, 158, and 553.