Tetracot: Difference between revisions

Line 8:

| Title = Tetracot

| 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)

| 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

| Mapping = 1; 4 9 10 -2

Line 107:

[[File: Tetracot 7et Detempering.png|thumb|Tetracot as a 34-tone 7et detempering]]

Tetracot is considered as a [[cluster temperament]] with 7 clusters of notes in an octave, so it is naturally a [[detemperament]] of the [[7edo|7 equal temperament]]. The diagram on the right shows a 34-tone detempered scale, with a generator range of ~~-16~~ to +17, which covers all the intervals in the no-7 13-odd-limit. Each category is divided into four or five qualities separated by 7 generator steps, which represent [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once.

Tetracot is considered as a [[cluster temperament]] with 7 clusters of notes in an octave, so it is naturally a [[detemperament]] of the [[7edo|7 equal temperament]]. The diagram on the right shows a 34-tone detempered scale, with a generator range of −16 to +17, which covers all the intervals in the no-7 13-odd-limit. Each category is divided into four or five qualities separated by 7 generator steps, which represent [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once.

== Scales ==

Line 136:

|

| 171.429

| Lower bound of 2.3.5.11 subgroup 11-odd-limit, 2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone

| Lower bound of 2.3.5.11 subgroup 11-odd-limit, 2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone

|-

|

@@ Line 8: / Line 8: @@
 | Title = Tetracot
 | 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 = 27e
 | Mapping = 1; 4 9 10 -2
@@ Line 107: / Line 107: @@
 [[File: Tetracot 7et Detempering.png|thumb|Tetracot as a 34-tone 7et detempering]]
-Tetracot is considered as a [[cluster temperament]] with 7 clusters of notes in an octave, so it is naturally a [[detemperament]] of the [[7edo|7 equal temperament]]. The diagram on the right shows a 34-tone detempered scale, with a generator range of -16 to +17, which covers all the intervals in the no-7 13-odd-limit. Each category is divided into four or five qualities separated by 7 generator steps, which represent [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once.
+Tetracot is considered as a [[cluster temperament]] with 7 clusters of notes in an octave, so it is naturally a [[detemperament]] of the [[7edo|7 equal temperament]]. The diagram on the right shows a 34-tone detempered scale, with a generator range of −16 to +17, which covers all the intervals in the no-7 13-odd-limit. Each category is divided into four or five qualities separated by 7 generator steps, which represent [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once.
 == Scales ==
@@ Line 136: / Line 136: @@
 |
 | 171.429
-| Lower bound of 2.3.5.11 subgroup 11-odd-limit, <br />2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone
+| Lower bound of 2.3.5.11 subgroup 11-odd-limit,<br />2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone
 |-
 |