1106edo
|
This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 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-limit, 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 the 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) | |
Subsets and supersets
Since 1106 factors into 2 × 7 × 79, it has subset edos 2, 7, 14, 79, 158, and 553.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1753 -1106⟩ | ⟨1106 1753] | -0.010 | 0.010 | 0.99 |
| 2.3.5 | [-53 10 16⟩, [40 -56 21⟩ | ⟨1106 1753 2568] | +0.001 | 0.019 | 1.73 |
| 2.3.5.7 | 4375/4374, 52734375/52706752, [46 -14 -3 -6⟩ | ⟨1106 1753 2568 3105] | -0.006 | 0.020 | 1.83 |
| 2.3.5.7.11 | 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041 | ⟨1106 1753 2568 3105 3826] | +0.004 | 0.026 | 2.38 |
| 2.3.5.7.11.13 | 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625 | ⟨1106 1753 2568 3105 3826 4093] | -0.012 | 0.043 | 3.94 |
| 2.3.5.7.11.13.17 | 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619 | ⟨1106 1753 2568 3105 3826 4093 4521] | -0.021 | 0.045 | 4.11 |
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 213\1106 | 231.103 | 8/7 | Orga (11-limit) |
| 1 | 401\1106 | 435.081 | 9/7 | Supermajor |
| 2 | 401\1106 (152\1106) |
435.081 (164.919) |
9/7 (11/10) |
Semisupermajor |
| 7 | 479\1106 (5\1106) |
519.711 (5.424) |
27/20 (5120/5103) |
Brahmagupta (7-limit) |
| 79 | 459\1106 (11\1106) |
498.011 (11.935) |
4/3 (?) |
Gold |