Tetracot: Difference between revisions

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| Subgroups = 2.3.5, 2.3.5.11, 2.3.5.11.13

| Comma basis = [[20000/19683]] (2.3.5); [[100/99]], [[243/242]] (2.3.5.11) [[100/99]], [[144/143]], [[243/242]] (2.3.5.11.13)

| Edo join 1 = 7 | Edo join 2 = ~~27e~~

| Edo join 1 = 7 | Edo join 2 = 34

| Mapping = 1; 4 9 10 -2

| Generators = 10/9

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[[Equal temperament]]s that [[support]] tetracot include {{EDOs| 27, 34, and 41 }}.

Tetracot has four strong [[extension]]s for the 7-, 11-, and 13-limit, which ~~differ in their methods of obtaining the [[7/1|7th harmonic]], but~~ use the same methods of obtaining the [[11/1|11th]] and [[13/1|13th]] harmonics.

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]])3;

* [[Bunya]] (34d & 41) obtains the 7th harmonic at 26 generators up, tempering out [[225/224]] and thereby equating [[7/2]] with ([[15/8]])2;

@@ Line 9: / Line 9: @@
 | 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)
-| Edo join 1 = 7 | Edo join 2 = 27e
+| Edo join 1 = 7 | Edo join 2 = 34
 | Mapping = 1; 4 9 10 -2
 | Generators = 10/9
@@ Line 26: / Line 26: @@
 [[Equal temperament]]s that [[support]] tetracot include {{EDOs| 27, 34, and 41 }}.
-Tetracot has four strong [[extension]]s for the 7-, 11-, and 13-limit, which differ in their methods of obtaining the [[7/1|7th harmonic]], but use the same methods of obtaining the [[11/1|11th]] and [[13/1|13th]] harmonics.
+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>;