1106edo: Difference between revisions
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completed the regular temperament table |
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| Line 25: | Line 25: | ||
|- | |- | ||
|2.3 | |2.3 | ||
| | |{{monzo|1753 -1106}} | ||
|1106 1753 | |{{val|1106 1753}} | ||
| -0.010 | | -0.010 | ||
|0.010 | |0.010 | ||
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|- | |- | ||
|2.3.5 | |2.3.5 | ||
| | |{{monzo|-53 10 16}}, {{monzo|40 -56 21}} | ||
|1106 1753 2568 | |{{val|1106 1753 2568}} | ||
| +0.001 | | +0.001 | ||
|0.019 | |0.019 | ||
| Line 39: | Line 39: | ||
|- | |- | ||
|2.3.5.7 | |2.3.5.7 | ||
|4375/4374, 52734375/52706752, 46 -14 -3 -6 | |4375/4374, 52734375/52706752, {{monzo|46 -14 -3 -6}} | ||
|1106 1753 2568 3105 | |{{val|1106 1753 2568 3105}} | ||
|<nowiki>-0.006</nowiki> | |<nowiki>-0.006</nowiki> | ||
|0.020 | |0.020 | ||
| Line 46: | Line 46: | ||
|- | |- | ||
|2.3.5.7.11 | |2.3.5.7.11 | ||
|3025/3024, 4375/4374, 5767168 | |3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041 | ||
|1106 1753 2568 3105 3826 | |{{val|1106 1753 2568 3105 3826}} | ||
| +0.004 | | +0.004 | ||
|0.026 | |0.026 | ||
| Line 54: | Line 54: | ||
|2.3.5.7.11.13 | |2.3.5.7.11.13 | ||
|3025/3024, 4096/4095, 4375/4374, 456533/456300, 928125/927472 | |3025/3024, 4096/4095, 4375/4374, 456533/456300, 928125/927472 | ||
|1106 1753 2568 3105 3826 4093 | |{{val|1106 1753 2568 3105 3826 4093}} | ||
|<nowiki>-0.012</nowiki> | |<nowiki>-0.012</nowiki> | ||
|0.043 | |0.043 | ||
| Line 61: | Line 61: | ||
|2.3.5.7.11.13.17 | |2.3.5.7.11.13.17 | ||
|2500/2499, 3025/3024, 4096/4095, 8624/8619, 9801/9800, 14875/14572 | |2500/2499, 3025/3024, 4096/4095, 8624/8619, 9801/9800, 14875/14572 | ||
|1106 1753 2568 3105 3826 4093 4521 | |{{val|1106 1753 2568 3105 3826 4093 4521}} | ||
|<nowiki>-0.021</nowiki> | |<nowiki>-0.021</nowiki> | ||
|0.045 | |0.045 | ||
Revision as of 00:50, 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
| 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, 456533/456300, 928125/927472 | ⟨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, 8624/8619, 9801/9800, 14875/14572 | ⟨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 |
| 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 |