1106edo: Difference between revisions
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| 2.38 | | 2.38 | ||
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|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 3025/3024, 4096/4095, 4375/4374, | | 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625 | ||
| {{val| 1106 1753 2568 3105 3826 4093 }} | | {{val| 1106 1753 2568 3105 3826 4093 }} | ||
| -0.012 | | -0.012 | ||
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| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 2500/2499, 3025/3024, 4096/4095, | | 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619 | ||
| {{val| 1106 1753 2568 3105 3826 4093 4521 }} | | {{val| 1106 1753 2568 3105 3826 4093 4521 }} | ||
| -0.021 | | -0.021 | ||
| Line 79: | Line 79: | ||
| 231.103 | | 231.103 | ||
| 8/7 | | 8/7 | ||
| [[Orga]] | | [[Orga]] (11-limit) | ||
|- | |- | ||
| 1 | | 1 | ||
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|- | |- | ||
| 2 | | 2 | ||
| 401\1106 | | 401\1106<br>(152\1106) | ||
| 435.081 | | 435.081<br>(164.919) | ||
| 9/7 | | 9/7<br>(11/10) | ||
| [[Semisupermajor]] | | [[Semisupermajor]] | ||
|- | |- | ||
| Line 96: | Line 96: | ||
| 479\1106<br>(5\1106) | | 479\1106<br>(5\1106) | ||
| 519.711<br>(5.424) | | 519.711<br>(5.424) | ||
| 27/20<br>( | | 27/20<br>(5120/5103) | ||
| [[Brahmagupta]] | | [[Brahmagupta]] (7-limit) | ||
|- | |- | ||
| 79 | | 79 | ||
Revision as of 01:38, 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-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 |