Tour of regular temperaments: Difference between revisions

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; [[Ripple family|Ripple or Quingu family]] (P8, P4/5)

: This tempers out the ripple comma, 6561/6250 = {{Monzo| -1 8 -5 }}, which equates a stack of four [[10/9]]'s with [[8/5]]. As one might expect, [[12edo|12EDO]] is about as accurate as it can be.

; [[Passion family|Passion or Saquingu family]] (P8, P4/5)

: This tempers out the passion comma, 262144/253125 = {{monzo| 18 -4 -5 }}, which equates a stack of five [[16/15]]'s with [[4/3]].

; [[Amity family|Amity or Saquinyo family]] (P8, P11/5)

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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.

~~; [[Mutt temperament|Mutt or Trila-septriyo family]] (P8/3, ccP4/7)~~

: This tempers out the [[mutt comma]], {{Monzo|-44 -3 21}}, leading to some strange properties. Seven ~5/4 generators equals a double-compound 4th = ~16/3. The third-octave period is <u>not</u> 5/4, thus the generator is equivalently a period minus ~5/4, only about 14¢. The L/s ratio is very lopsided, and scales resemble a "fuzzy" augmented chord.

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

@@ Line 75: / Line 75: @@
 ; [[Ripple family|Ripple or Quingu family]] (P8, P4/5)
 : This tempers out the ripple comma, 6561/6250 = {{Monzo| -1 8 -5 }}, which equates a stack of four [[10/9]]'s with [[8/5]]. As one might expect, [[12edo|12EDO]] is about as accurate as it can be.
+; [[Passion family|Passion or Saquingu family]] (P8, P4/5)
+: This tempers out the passion comma, 262144/253125 = {{monzo| 18 -4 -5 }}, which equates a stack of five [[16/15]]'s with [[4/3]].
 ; [[Amity family|Amity or Saquinyo family]] (P8, P11/5)
@@ Line 108: / Line 111: @@
 ; [[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.
-; [[Mutt temperament|Mutt or Trila-septriyo family]] (P8/3, ccP4/7)
-: This tempers out the [[mutt comma]], {{Monzo|-44 -3 21}}, leading to some strange properties. Seven ~5/4 generators equals a double-compound 4th = ~16/3. The third-octave period is <u>not</u> 5/4, thus the generator is equivalently a period minus ~5/4, only about 14¢. The L/s ratio is very lopsided, and scales resemble a "fuzzy" augmented chord.
 ; [[Würschmidt family|Würschmidt or Saquadbigu family]] (P8, ccP5/8)