Tour of regular temperaments: Difference between revisions

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; [[Ditonmic family]] (P8, c4P4/13)

: This tempers out the [[ditonma]], {{monzo| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti.

; [[Parakleismic family]] (P8, c3P4/13)

: This tempers out the [[parakleisma]], {{monzo| 8 14 -13 }} (1224440064/1220703125). The generator is a slightly sharpened ~5/3 major sixth. Thirteen generators minus three octaves equal ~4/3, and fourteen generators minus three octaves equal ~8/5.

; [[Luna family]] (P8, ccP4/15)

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

: The gammic family tempers out the [[gammic comma]], {{monzo| -29 -11 20 }}. Nine generators of about 35{{c}} 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 the [[neptune]] temperament. Its color name is Laquinquadyoti.

: The gammic family tempers out the [[gammic comma]], {{monzo| -29 -11 20 }}. Nine generators of about 35{{c}} 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 the [[Neptune (temperament)|neptune]] temperament. Its color name is Laquinquadyoti.

=== Clans defined by a 2.3.7 comma ===

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; [[Garischismic clan]] (P8, P5)

: This clan tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} (33554432/33480783). It equates 8/7 to two apotomes ({{monzo| -~~11 7~~ }}, 2187/2048) and 7/4 to a double-diminished octave {{monzo| 23 -14 }}. This clan includes [[~~vulture~~ family #~~Vulture~~|~~vulture~~]], [[~~breedsmic temperaments~~ #Newt|newt]], [[~~schismatic family~~ #~~Garibaldi~~|~~garibaldi~~]], [[~~landscape microtemperaments~~ #~~Sextile~~|~~sextile~~]], and [[~~canousmic temperaments~~ #~~Satin~~|~~satin~~]]. Its color name is Sasaruti.

: This clan tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} (33554432/33480783). It equates 8/7 to two apotomes ({{monzo| -22 14 }}, (2187/2048)<sup>2</sup>) and 7/4 to a double-diminished octave {{monzo| 23 -14 }}. This clan includes [[schismatic family #Garibaldi|garibaldi]], [[garischismic clan #Newt|newt]], [[garischismic clan #Satin|satin]], [[vulture family #Vulture|vulture]], and [[garischismic clan #Sextile|sextile]]. Its color name is Sasaruti.

; Sasazoti clan (P8, P5)

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: These temper out the [[avicennma]], {{monzo| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti.

; Sengic temperaments

; [[Sengic temperaments]]

: Sengic rank-2 temperaments temper out the [[senga]], {{monzo| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti.

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: Cataharry rank-2 temperaments temper out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} (19683/19600). Its color name is Labiruguti.

; [[~~Canousmic~~ temperaments]]

; [[Cathartic temperaments]]

: ~~Canousmic~~ rank-2 temperaments temper out the [[~~canousma~~]], {{monzo| 4 -14 3 4 }} (4802000/4782969). Its color name is Saquadzo-atriyoti.

: Cathartic rank-2 temperaments temper out the [[cathartic comma]], {{monzo| 4 -14 3 4 }} (4802000/4782969). Its color name is Saquadzo-atriyoti.

; [[Triwellismic temperaments]]

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: The gariboh family of rank-3 temperaments tempers out the gariboh comma, {{monzo| 0 -2 5 -3 }} (3125/3087). Three ~25/21 generators equal the pergen's downmajor sixth of ~5/3. Its color name is Triru-aquinyoti.

; [[~~Canou~~ family]] (P8, P5, vm6/3)

; [[Cathartic family]] (P8, P5, vm6/3)

: The ~~canou~~ family of rank-3 temperaments tempers out the ~~canousma~~, {{monzo| 4 -14 3 4 }} (4802000/4782969). Three ~81/70 generators equal the pergen's downminor sixth of ~14/9. Its color name is Saquadzo-atriyoti.

: The cathartic family of rank-3 temperaments tempers out the cathartic comma, {{monzo| 4 -14 3 4 }} (4802000/4782969). Three ~81/70 generators equal the pergen's downminor sixth of ~14/9. Its color name is Saquadzo-atriyoti.

; [[Dimcomp family]] (P8/4, P5, ^1)

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: These temper out the [[4000/3993|wizardharry comma]], {{monzo| 5 -1 3 0 -3 }} (4000/3993), and split the fourth in three. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Triluyoti.

; [[~~Semicanousmic~~ clan]] (P8, P5, ^1)

; [[Semicathartismic clan]] (P8, P5, ^1)

: These temper out the [[~~semicanousma~~]], {{monzo| -2 -6 -1 0 4 }} (14641/14580). 5/4 is equated to a 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Quadlo-aguti.

: These temper out the [[semicathartisma]], {{monzo| -2 -6 -1 0 4 }} (14641/14580). 5/4 is equated to a 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Quadlo-aguti.

; [[Semiporwellismic clan]] (P8, P5, ^1)

@@ Line 154: / Line 154: @@
 ; [[Ditonmic family]] (P8, c4P4/13)
 : This tempers out the [[ditonma]], {{monzo| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti.
+; [[Parakleismic family]] (P8, c3P4/13)
+: This tempers out the [[parakleisma]], {{monzo| 8 14 -13 }} (1224440064/1220703125). The generator is a slightly sharpened ~5/3 major sixth. Thirteen generators minus three octaves equal ~4/3, and fourteen generators minus three octaves equal ~8/5.
 ; [[Luna family]] (P8, ccP4/15)
@@ Line 171: / Line 174: @@
 ; [[Gammic family]] (P8, P5/20)
-: The gammic family tempers out the [[gammic comma]], {{monzo| -29 -11 20 }}. Nine generators of about 35{{c}} 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 the [[neptune]] temperament. Its color name is Laquinquadyoti.
+: The gammic family tempers out the [[gammic comma]], {{monzo| -29 -11 20 }}. Nine generators of about 35{{c}} 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 the [[Neptune (temperament)|neptune]] temperament. Its color name is Laquinquadyoti.
 === Clans defined by a 2.3.7 comma ===
@@ Line 188: / Line 191: @@
 ; [[Garischismic clan]] (P8, P5)
-: This clan tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} (33554432/33480783). It equates 8/7 to two apotomes ({{monzo| -11 7 }}, 2187/2048) and 7/4 to a double-diminished octave {{monzo| 23 -14 }}. This clan includes [[vulture family #Vulture|vulture]], [[breedsmic temperaments #Newt|newt]], [[schismatic family #Garibaldi|garibaldi]], [[landscape microtemperaments #Sextile|sextile]], and [[canousmic temperaments #Satin|satin]]. Its color name is Sasaruti.
+: This clan tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} (33554432/33480783). It equates 8/7 to two apotomes ({{monzo| -22 14 }}, (2187/2048)<sup>2</sup>) and 7/4 to a double-diminished octave {{monzo| 23 -14 }}. This clan includes [[schismatic family #Garibaldi|garibaldi]], [[garischismic clan #Newt|newt]], [[garischismic clan #Satin|satin]], [[vulture family #Vulture|vulture]], and [[garischismic clan #Sextile|sextile]]. Its color name is Sasaruti.
 ; Sasazoti clan (P8, P5)
@@ Line 341: / Line 344: @@
 : These temper out the [[avicennma]], {{monzo| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti.
-; Sengic temperaments
+; [[Sengic temperaments]]
 : Sengic rank-2 temperaments temper out the [[senga]], {{monzo| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti.
@@ Line 410: / Line 413: @@
 : Cataharry rank-2 temperaments temper out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} (19683/19600). Its color name is Labiruguti.
-; [[Canousmic temperaments]]
+; [[Cathartic temperaments]]
-: Canousmic rank-2 temperaments temper out the [[canousma]], {{monzo| 4 -14 3 4 }} (4802000/4782969). Its color name is Saquadzo-atriyoti.
+: Cathartic rank-2 temperaments temper out the [[cathartic comma]], {{monzo| 4 -14 3 4 }} (4802000/4782969). Its color name is Saquadzo-atriyoti.
 ; [[Triwellismic temperaments]]
@@ Line 594: / Line 597: @@
 : The gariboh family of rank-3 temperaments tempers out the gariboh comma, {{monzo| 0 -2 5 -3 }} (3125/3087). Three ~25/21 generators equal the pergen's downmajor sixth of ~5/3. Its color name is Triru-aquinyoti.
-; [[Canou family]] (P8, P5, vm6/3)
+; [[Cathartic family]] (P8, P5, vm6/3)
-: The canou family of rank-3 temperaments tempers out the canousma, {{monzo| 4 -14 3 4 }} (4802000/4782969). Three ~81/70 generators equal the pergen's downminor sixth of ~14/9. Its color name is Saquadzo-atriyoti.
+: The cathartic family of rank-3 temperaments tempers out the cathartic comma, {{monzo| 4 -14 3 4 }} (4802000/4782969). Three ~81/70 generators equal the pergen's downminor sixth of ~14/9. Its color name is Saquadzo-atriyoti.
 ; [[Dimcomp family]] (P8/4, P5, ^1)
@@ Line 625: / Line 628: @@
 : These temper out the [[4000/3993|wizardharry comma]], {{monzo| 5 -1 3 0 -3 }} (4000/3993), and split the fourth in three. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Triluyoti.
-; [[Semicanousmic clan]] (P8, P5, ^1)
+; [[Semicathartismic clan]] (P8, P5, ^1)
-: These temper out the [[semicanousma]], {{monzo| -2 -6 -1 0 4 }} (14641/14580). 5/4 is equated to a 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Quadlo-aguti.
+: These temper out the [[semicathartisma]], {{monzo| -2 -6 -1 0 4 }} (14641/14580). 5/4 is equated to a 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Quadlo-aguti.
 ; [[Semiporwellismic clan]] (P8, P5, ^1)