Tour of regular temperaments: Difference between revisions

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; [[Augmented family|Augmented or Trigu family]] (P8/3, P5)

: The augmented family tempers out the diesis of {{Monzo|7 0 -3}} = [[128/125]], the difference between three 5/4 major thirds and a 2/1 octave, and so identifies the major third with the third-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo|12EDO]], which is an excellent tuning for augmented. It is the temperament that results in what is commonly called the "augmented scale" ([[3L 3s]]) in common 12-based music theory, as well as what is commonly called "[http://www.tcherepnin.com/alex/basic_elem1.htm#9step Tcherepnin's scale]" ([[3L 6s]]).

; [[Misty family|Misty or Sasa-trigu family]] (P8/3, P5)

: The misty family tempers out the [[misty comma]] of {{monzo| 26 -12 -3 }}, the difference between the Pythagorean comma and a stack of three schismas.

; [[Porcupine family|Porcupine or Triyo family]] (P8, P4/3)

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; [[Dimipent family|Dimipent or Quadgu family]] (P8/4, P5)

: The dimipent (or diminished) family tempers out the major diesis or diminished comma, {{Monzo|3 4 -4}} or [[648/625]], the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo|12EDO]]. 5/4 is equated to 1 fifth minus 1 period.

; [[Undim family|Undim or Trisa-quadgu family]] (P8/4, P5)

: The undim family tempers out the [[undim comma]] of {{monzo| 41 -20 -4 }}, the difference between the Pythagorean comma and a stack of four schismas.

; [[Negri|Negri or Laquadyo family]] (P8, P4/4)

@@ Line 51: / Line 51: @@
 ; [[Augmented family|Augmented or Trigu  family]] (P8/3, P5)
 : The augmented family tempers out the diesis of {{Monzo|7 0 -3}} = [[128/125]], the difference between three 5/4 major thirds and a 2/1 octave, and so identifies the major third with the third-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo|12EDO]], which is an excellent tuning for augmented. It is the temperament that results in what is commonly called the "augmented scale" ([[3L 3s]]) in common 12-based music theory, as well as what is commonly called "[http://www.tcherepnin.com/alex/basic_elem1.htm#9step Tcherepnin's scale]" ([[3L 6s]]).
+; [[Misty family|Misty or Sasa-trigu family]] (P8/3, P5)
+: The misty family tempers out the [[misty comma]] of {{monzo| 26 -12 -3 }}, the difference between the Pythagorean comma and a stack of three schismas.
 ; [[Porcupine family|Porcupine or Triyo family]] (P8, P4/3)
@@ Line 60: / Line 63: @@
 ; [[Dimipent family|Dimipent or Quadgu family]] (P8/4, P5)
 : The dimipent (or diminished) family tempers out the major diesis or diminished comma, {{Monzo|3 4 -4}} or [[648/625]], the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo|12EDO]]. 5/4 is equated to 1 fifth minus 1 period.
+; [[Undim family|Undim or Trisa-quadgu family]] (P8/4, P5)
+: The undim family tempers out the [[undim comma]] of {{monzo| 41 -20 -4 }}, the difference between the Pythagorean comma and a stack of four schismas.
 ; [[Negri|Negri or Laquadyo family]] (P8, P4/4)