1106edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1106}} | {{EDO intro|1106}} | ||
== Theory == | |||
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]]. | ||
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=== Divisors === | === Divisors === | ||
Since 1106 factors into 2 × 7 × 79, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}. | Since 1106 factors into 2 × 7 × 79, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}. | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
! Periods<br>per 8ve | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 213\1106 | |||
| 231.103 | |||
| 8/7 | |||
| [[Orga]] | |||
|- | |||
| 1 | |||
| 401\1106 | |||
| 435.081 | |||
| 9/7 | |||
| [[Supermajor]] | |||
|- | |||
| 2 | |||
| 401\1106 | |||
| 435.081 | |||
| 9/7 | |||
| [[Semisupermajor]] | |||
|- | |||
| 7 | |||
| 479\1106<br>(5\1106) | |||
| 519.711<br>(5.424) | |||
| 27/20<br>(325/324) | |||
| [[Brahmagupta]] | |||
|- | |||
| 79 | |||
| 459\1106<br>(11\1106) | |||
| 498.011<br>(11.935) | |||
| 4/3<br>(?) | |||
| [[Gold]] | |||
|} | |||
Revision as of 00:34, 6 July 2023
| ← 1105edo | 1106edo | 1107edo → |
Theory
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.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 213\1106 | 231.103 | 8/7 | Orga |
| 1 | 401\1106 | 435.081 | 9/7 | Supermajor |
| 2 | 401\1106 | 435.081 | 9/7 | Semisupermajor |
| 7 | 479\1106 (5\1106) |
519.711 (5.424) |
27/20 (325/324) |
Brahmagupta |
| 79 | 459\1106 (11\1106) |
498.011 (11.935) |
4/3 (?) |
Gold |