Tour of regular temperaments: Difference between revisions

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===[[Trienstonic clan|Trienstonic or Zo clan]] (P8, P5) ===

This 2.3.7 clan tempers out the septimal third-tone, [[28/27]], a no-fives comma.

===[[Archytas clan|Archytas or Ru clan]] (P8, P5)===

This 2.3.7 clan tempers out the Archytas comma, [[64/63]], a no-fives comma. The clan consists of rank two temperaments, and should not be confused with the [[Archytas family]] of rank three temperaments.

=== Laru clan (P8, P5) ===

This 2.3.7 clan tempers out [-13 10 0 -1> = 50.7¢. It equates 7/4 to an augmented 6th. It includes as a strong extension Septimal Meantone.

===[[Slendro clan|Slendro or Zozo clan]] (P8, P4/2)===

This 2.3.7 clan tempers out the slendro diesis, [[49/48]], a no-fives comma.

This 2.3.7 clan tempers out the slendro diesis, [[49/48]], a no-fives comma. Generator = 8/7 or 7/6.

===~~[[Archytas~~ clan~~|Archytas or Ru clan]]~~ (P8, P5)===

=== Sasa-zozo clan (P8, P5/2) ===

This 2.3.7 clan tempers out ~~the Archytas comma, [~~[~~64/63]], a no~~-~~fives comma~~. ~~The clan consists of rank two temperaments~~, and ~~should not be confused with~~ the [[~~Archytas family~~]] ~~of rank three temperaments~~.

This 2.3.7 clan tempers out [15 -13 0 2> = 12.2¢, and includes as a strong extension the [[Hemififths]] temperament.

===[[Gamelismic clan|Gamelismic or Latrizo clan]] (P8, P5/3)===

This 2.3.7 clan tempers out the gamelisma, [-10 1 0 3> = 1029/1024, a no-fives comma. Three 8/7 generators equals a 5th. A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72-EDO.

===[[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3)===

=== Latriru clan (P8, P11/3) ===

This 2.3.7 clan tempers out [-9 11 0 -3> = 15.0¢. Generator = 81/56. It includes as a strong extension the [[Liese]] temperament, which is in the Meantone family.

=== Laquadru clan (P8, P11/4) ===

This 2.3.7 clan tempers out [-3 9 0 -4> = 42.3¢. Generator = 9/7. It includes as a strong extension the [[Squares]] temperament, which is in the Meantone family.

=== Saquadru clan (P8, P12/4) ===

This 2.3.7 clan tempers out [16 -3 0 -4> = 18.8¢. Generator = 21/16. It includes as a strong extension the [[Vulture family|Vulture]] temperament, which is in the Vulture family.

=== Saquinzo clan (P8, P12/5) ===

This 2.3.7 clan tempers out [5 -12 0 5> = 20.7¢. It includes as a strong extension the [[Magic]] temperament, which is in the Magic family.

=== Sepru clan (P8, P12/7) ===

This 2.3.7 clan tempers out [7 8 0 -7> = 33.8¢. Generator = 7/6. It includes as a strong extension the [[Orwell]] temperament, which is in the Semicomma family.

=== [[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3) ===

This 2.5.7 clan tempers out the jubilisma, [[50/49]], a no-threes comma which is the difference between 10/7 and 7/5. The pergen's M3 generator equals 5/4. The half-octave period equals 7/5.

@@ Line 160: / Line 160: @@
 ===[[Trienstonic clan|Trienstonic or Zo clan]] (P8, P5) ===
 This 2.3.7 clan tempers out the septimal third-tone, [[28/27]], a no-fives comma.
+===[[Archytas clan|Archytas or Ru clan]] (P8, P5)===
+This 2.3.7 clan tempers out the Archytas comma, [[64/63]], a no-fives comma. The clan consists of rank two temperaments, and should not be confused with the [[Archytas family]] of rank three temperaments.
+=== Laru clan (P8, P5) ===
+This 2.3.7 clan tempers out [-13 10 0 -1> =  50.7¢. It equates 7/4 to an augmented 6th. It includes as a strong extension Septimal Meantone.
 ===[[Slendro clan|Slendro or Zozo clan]] (P8, P4/2)===
-This 2.3.7 clan tempers out the slendro diesis, [[49/48]], a no-fives comma.
+This 2.3.7 clan tempers out the slendro diesis, [[49/48]], a no-fives comma. Generator = 8/7 or 7/6.
-===[[Archytas clan|Archytas or Ru clan]] (P8, P5)===
+=== Sasa-zozo clan (P8, P5/2) ===
-This 2.3.7 clan tempers out the Archytas comma, [[64/63]], a no-fives comma. The clan consists of rank two temperaments, and should not be confused with the [[Archytas family]] of rank three temperaments.
+This 2.3.7 clan tempers out [15 -13 0 2> = 12.2¢, and includes as a strong extension the [[Hemififths]] temperament.
 ===[[Gamelismic clan|Gamelismic or Latrizo clan]] (P8, P5/3)===
 This 2.3.7 clan tempers out the gamelisma, [-10 1 0 3> = 1029/1024, a no-fives comma. Three 8/7 generators equals a 5th. A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72-EDO.
-===[[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3)===
+=== Latriru clan (P8, P11/3) ===
+This 2.3.7 clan tempers out [-9 11 0 -3> = 15.0¢. Generator = 81/56. It includes as a strong extension the [[Liese]] temperament, which is in the Meantone family.
+=== Laquadru clan (P8, P11/4) ===
+This 2.3.7 clan tempers out  [-3 9 0 -4> = 42.3¢. Generator = 9/7. It includes as a strong extension the [[Squares]] temperament, which is in the Meantone family.
+=== Saquadru clan (P8, P12/4) ===
+This 2.3.7 clan tempers out [16 -3 0 -4> = 18.8¢. Generator = 21/16. It includes as a strong extension the [[Vulture family|Vulture]] temperament, which is in the Vulture family.
+=== Saquinzo clan (P8, P12/5) ===
+This 2.3.7 clan tempers out [5 -12 0 5> = 20.7¢. It includes as a strong extension the [[Magic]] temperament, which is in the Magic family.
+=== Sepru clan (P8, P12/7) ===
+This 2.3.7 clan tempers out [7 8 0 -7> = 33.8¢. Generator = 7/6. It includes as a strong extension the [[Orwell]] temperament, which is in the Semicomma family.
+=== [[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3) ===
 This 2.5.7 clan tempers out the jubilisma, [[50/49]], a no-threes comma which is the difference between 10/7 and 7/5. The pergen's M3 generator equals 5/4. The half-octave period equals 7/5.