Tetracot: Difference between revisions
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34 is more of a central tuning |
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| Subgroups = 2.3.5, 2.3.5.11, 2.3.5.11.13 | | Subgroups = 2.3.5, 2.3.5.11, 2.3.5.11.13 | ||
| Comma basis = [[20000/19683]] (2.3.5);<br>[[100/99]], [[243/242]] (2.3.5.11)<br>[[100/99]], [[144/143]], [[243/242]] (2.3.5.11.13) | | Comma basis = [[20000/19683]] (2.3.5);<br>[[100/99]], [[243/242]] (2.3.5.11)<br>[[100/99]], [[144/143]], [[243/242]] (2.3.5.11.13) | ||
| Edo join 1 = 7 | Edo join 2 = | | Edo join 1 = 7 | Edo join 2 = 34 | ||
| Mapping = 1; 4 9 10 -2 | | Mapping = 1; 4 9 10 -2 | ||
| Generators = 10/9 | | Generators = 10/9 | ||
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[[Equal temperament]]s that [[support]] tetracot include {{EDOs| 27, 34, and 41 }}. | [[Equal temperament]]s that [[support]] tetracot include {{EDOs| 27, 34, and 41 }}. | ||
Tetracot has | Tetracot has four strong [[extension]]s for the 7-, 11-, and 13-limit, which use the same methods of obtaining the [[11/1|11th]] and [[13/1|13th]] harmonics (10 generators up and 2 generators down, respectively) but differ in their methods of obtaining the [[7/1|7th harmonic]]: | ||
* [[Monkey]] (34 & 41) obtains the 7th harmonic at 15 generators down, tempering out [[875/864]] and thereby equating [[7/4]] with ([[6/5]])<sup>3</sup>; | |||
* [[Bunya]] (34d & 41) obtains the 7th harmonic at 26 generators up, tempering out [[225/224]] and thereby equating [[7/2]] with ([[15/8]])<sup>2</sup>; | |||
* [[Modus]] (27e & 34d) obtains the 7th harmonic at 8 generators down, tempering out [[64/63]] and thereby equating 7/4 with [[16/9]]; | |||
* [[Wollemia]] (27e & 34) obtains the 7th harmonic at 19 generators up, tempering out [[126/125]] and thereby equating [[7/1]] with ([[5/3]])<sup>3</sup>([[3/2]]). | |||
See [[Tetracot family]] for technical data. | See [[Tetracot family]] for technical data. | ||