Tour of regular temperaments: Difference between revisions

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; [[Vishnuzmic family|Vishnuzmic or Sasepbigu family]] (P8/2, P4/7)

: This tempers out the vishnuzma, {{Monzo|23 6 -14}}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)^7. The period is ~{{Monzo|-11 -3 7}} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators.

; [[Unicorn family|Unicorn or Laquadbigu family]] (P8, P4/8)

: This tempers out the unicorn comma, 1594323/1562500 = {{Monzo|-2 13 -8}}. The generator is ~250/243 = ~62¢ and eight of them equal ~4/3.

; [[Würschmidt family|Würschmidt or Saquadbigu family]] (P8, ccP5/8)

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; [[Escapade family|Escapade or Sasa-tritrigu family]] (P8, P4/9)

: This tempers out the [[escapade comma]], {{Monzo|32 -7 -9}}, which is the difference between nine just major thirds and seven just fourths. The generator is ~{{Monzo|-14 3 4}} = ~55¢, and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritrilu temperament.

: This tempers out the [[escapade comma]], {{Monzo|32 -7 -9}}, which is the difference between nine just major thirds and seven just fourths. The generator is ~{{Monzo|-14 3 4}} = ~55¢ and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritrilu temperament.

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

@@ Line 126: / Line 126: @@
 ; [[Vishnuzmic family|Vishnuzmic or Sasepbigu family]] (P8/2, P4/7)
 : This tempers out the vishnuzma, {{Monzo|23 6 -14}}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)^7. The period is ~{{Monzo|-11 -3 7}} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators.
+; [[Unicorn family|Unicorn or Laquadbigu family]] (P8, P4/8)
+: This tempers out the unicorn comma, 1594323/1562500 = {{Monzo|-2 13 -8}}. The generator is ~250/243 = ~62¢ and eight of them equal ~4/3.
 ; [[Würschmidt family|Würschmidt or Saquadbigu family]] (P8, ccP5/8)
@@ Line 131: / Line 134: @@
 ; [[Escapade family|Escapade or Sasa-tritrigu family]] (P8, P4/9)
-: This tempers out the [[escapade comma]], {{Monzo|32 -7 -9}}, which is the difference between nine just major thirds and seven just fourths. The generator is ~{{Monzo|-14 3 4}} = ~55¢, and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritrilu temperament.
+: This tempers out the [[escapade comma]], {{Monzo|32 -7 -9}}, which is the difference between nine just major thirds and seven just fourths. The generator is ~{{Monzo|-14 3 4}} = ~55¢ and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritrilu temperament.
 ; [[Shibboleth family|Shibboleth or Tritriyo family]] (P8, ccP4/9)