Tour of regular temperaments: Difference between revisions

Line 135:

; [[Shibboleth family|Shibboleth or Tritriyo family]] (P8, ccP4/9)

: This tempers out the shibboleth comma, {{Monzo|-5 -10 9}} = 1953125/1889568. Nine generators of ~6/5 equal a double compound 4th of ~16/3. 5/4 is equated to 3 octaves minus 10 generators.

; [[Mabila family|Mabila or Sasa-quinbigu family]] (P8, c<sup>4</sup>P4/10)

: The sycamore family tempers out the mabila comma, {{Monzo|28 -3 -10}} = 268435456/263671875. The generator is ~512/375 = ~530¢, three generators equals ~5/2 and ten of them equals a quadruple-compound 4th of ~64/3. An obvious 11-limit interpretation of the generator is ~15/11.

; [[Sycamore family|Sycamore or Laleyo family]] (P8, P5/11)

: The sycamore family tempers out the sycamore comma, {{Monzo|-16 -6 11}} = 48828125/47775744, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. Eleven of these generators equals ~3/2.

; [[Ditonmic family|Ditonmic or Lala-theyo family]] (P8, c<sup>4</sup>P4/13)

Line 143:

Line 146:

; [[Luna family|Luna or Sasa-quintrigu family]] (P8, ccP4/15)

: This tempers out the luna comma, {{Monzo|38 -2 -15}} (274877906944/274658203125). The generator is ~{{Monzo|18 -1 -7}} = ~193¢. Two generators equals ~5/4, and fifteen generators equals a double-compound 4th of ~16/3.

: This tempers out the luna comma, {{Monzo|38 -2 -15}} = 274877906944/274658203125. The generator is ~{{Monzo|18 -1 -7}} = ~193¢. Two generators equals ~5/4, and fifteen generators equals a double-compound 4th of ~16/3.

; [[Minortonic family|Minortonic or Trila-segu family]] (P8, ccP5/17)

Line 155:

Line 158:

; [[Gammic family|Gammic or Laquinquadyo family]] (P8, P5/20)

: The gammic family tempers out the gammic comma, {{Monzo|-29 -11 20}}. Nine generators of about 35¢ equals ~6/5, eleven ~~equal~~ ~5/4 and twenty ~~equal~~ ~3/2. 34EDO is an obvious tuning. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is Neptune temperament.

: The gammic family tempers out the gammic comma, {{Monzo|-29 -11 20}}. Nine generators of about 35¢ equals ~6/5, eleven equals ~5/4 and twenty equals ~3/2. 34EDO is an obvious tuning. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is Neptune temperament.

=== Clans defined by a 2.3.7 (za) comma ===

@@ Line 135: / Line 135: @@
 ; [[Shibboleth family|Shibboleth or Tritriyo family]] (P8, ccP4/9)
 : This tempers out the shibboleth comma, {{Monzo|-5 -10 9}} = 1953125/1889568. Nine generators of ~6/5 equal a double compound 4th of ~16/3.  5/4 is equated to 3 octaves minus 10 generators.
+; [[Mabila family|Mabila or Sasa-quinbigu family]] (P8, c<sup>4</sup>P4/10)
+: The sycamore family tempers out the mabila comma, {{Monzo|28 -3 -10}} = 268435456/263671875. The generator is ~512/375 = ~530¢, three generators equals ~5/2 and ten of them equals a quadruple-compound 4th of ~64/3. An obvious 11-limit interpretation of the generator is ~15/11.
 ; [[Sycamore family|Sycamore or Laleyo family]] (P8, P5/11)
 : The sycamore family tempers out the sycamore comma, {{Monzo|-16 -6 11}} = 48828125/47775744, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. Eleven of these generators equals ~3/2.
 ; [[Ditonmic family|Ditonmic or Lala-theyo family]] (P8, c<sup>4</sup>P4/13)
@@ Line 143: / Line 146: @@
 ; [[Luna family|Luna or Sasa-quintrigu family]] (P8, ccP4/15)
-: This tempers out the luna comma, {{Monzo|38 -2 -15}} (274877906944/274658203125). The generator is ~{{Monzo|18 -1 -7}} = ~193¢. Two generators equals ~5/4, and fifteen generators equals a double-compound 4th of ~16/3.
+: This tempers out the luna comma, {{Monzo|38 -2 -15}} = 274877906944/274658203125. The generator is ~{{Monzo|18 -1 -7}} = ~193¢. Two generators equals ~5/4, and fifteen generators equals a double-compound 4th of ~16/3.
 ; [[Minortonic family|Minortonic or Trila-segu family]] (P8, ccP5/17)
@@ Line 155: / Line 158: @@
 ; [[Gammic family|Gammic or Laquinquadyo family]] (P8, P5/20)
-: The gammic family tempers out the gammic comma, {{Monzo|-29 -11 20}}. Nine generators of about 35¢ equals ~6/5, eleven equal ~5/4 and twenty equal ~3/2. 34EDO is an obvious tuning. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is Neptune temperament.
+: The gammic family tempers out the gammic comma, {{Monzo|-29 -11 20}}. Nine generators of about 35¢ equals ~6/5, eleven equals ~5/4 and twenty equals ~3/2. 34EDO is an obvious tuning. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is Neptune temperament.
 === Clans defined by a 2.3.7 (za) comma ===