Tour of regular temperaments: Difference between revisions

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: The sensipent family tempers out the [[sensipent comma]], 78732/78125 ({{monzo| 2 9 -7 }}), also known as the medium semicomma. Its generator is {{nowrap| ~162/125 {{=}} ~443{{c}} }}. Seven generators equals a double-compound fifth of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo]], [[19edo]], [[46edo]], and [[65edo]]. Its color name is Sepguti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.

; [[~~Vishnuzmic~~ family]] (P8/2, P4/7)

; [[Vishnu 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. Its color name is Sasepbiguti.

: This tempers out the [[vishnu comma]], {{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. Its color name is Sasepbiguti.

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

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: This tempers out the [[vavoom comma]], {{monzo| -68 18 17 }}. The generator is {{nowrap| ~16/15 {{=}} ~111.9{{c}} }}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators. Its color name is Quinla-seyoti.

; [[~~Minortonic~~ family]] (P8, ccP5/17)

; [[Minortone family]] (P8, ccP5/17)

: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is ~~minortonic temperament~~, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.

: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is minortone, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.

; [[Maja family]] (P8, c6P4/17)

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; Sasazoti clan (P8, P5)

: This clan tempers out the [[leapfrog comma]], {{monzo| 21 -15 0 1 }} (14680064/14348907). It equates 7/6 to two apotomes and 7/4 to double augmented fifth. This clan includes [[~~hemifamity~~ temperaments #Leapday|leapday]], [[sensamagic clan #Leapweek|leapweek]] and [[diaschismic family #Srutal|srutal]].

: This clan tempers out the [[leapfrog comma]], {{monzo| 21 -15 0 1 }} (14680064/14348907). It equates 7/6 to two apotomes and 7/4 to double augmented fifth. This clan includes [[aberschismic temperaments #Leapday|leapday]], [[sensamagic clan #Leapweek|leapweek]] and [[diaschismic family #Srutal|srutal]].

; Laruruti clan (P8/2, P5)

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: This 3.5.7 clan tempers out the [[gariboh comma]] {{monzo| 0 -2 5 -3 }} (3125/3087). The generator is ~25/21, two generators equals ~7/5, and three generators equals the classical major sixth (~5/3). Its color name is Triru-aquinyoti Noca.

; [[~~Mirkwai~~ clan]] (P12, cm7/5)

; [[Canopic clan]] (P12, cm7/5)

: This 3.5.7 clan tempers out the [[~~mirkwai~~ comma]], {{monzo| 0 3 4 -5 }} (16875/16807). The generator is ~7/5, four generators equals ~27/7, and five generators equals the classical compound minor seventh (~27/5). Its color name is Quinru-aquadyoti Noca.

: This 3.5.7 clan tempers out the [[canopic comma]], {{monzo| 0 3 4 -5 }} (16875/16807). The generator is ~7/5, four generators equals ~27/7, and five generators equals the classical compound minor seventh (~27/5). Its color name is Quinru-aquadyoti Noca.

; Sasepzo-atriguti Noca clan (P12, m7/7)

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: Hemimage rank-2 temperaments temper out the [[hemimage comma]], {{monzo| 5 -7 -1 3 }} (10976/10935). Its color name is Satrizo-aguti.

; [[~~Hemifamity~~ temperaments]]

; [[Aberschismic temperaments]]

: ~~Hemifamity~~ rank-2 temperaments temper out the [[~~hemifamity comma~~]], {{monzo| 10 -6 1 -1 }} (5120/5103). Its color name is Saruyoti.

: Aberschismic rank-2 temperaments temper out the [[aberschisma]], {{monzo| 10 -6 1 -1 }} (5120/5103). Its color name is Saruyoti.

; [[Parkleiness temperaments]]

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: These temper out the nuwell comma, {{monzo| 1 5 1 -4 }} (2430/2401). In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Quadru-ayoti.

; [[~~Ragisma~~ family]] (P8, P5, ^1)

; [[Ragismic family]] (P8, P5, ^1)

: The 7-limit rank-3 microtemperament which tempers out the ragisma, {{monzo| -1 -7 4 1 }} (4375/4374), extends to various higher-limit rank-3 temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Zoquadyoti.

; [[~~Hemifamity~~ family]] (P8, P5, ^1)

; [[Aberschismic family]] (P8, P5, ^1)

: The ~~hemifamity~~ family of rank-3 temperaments tempers out the ~~hemifamity comma~~, {{monzo| 10 -6 1 -1 }} (5120/5103), which divides 10/7 into three 9/8's. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Saruyoti.

: The aberschismic family of rank-3 temperaments tempers out the aberschisma, {{monzo| 10 -6 1 -1 }} (5120/5103), which divides 10/7 into three 9/8's. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Saruyoti.

; [[Horwell family]] (P8, P5, ^1)

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: The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, {{monzo| -1 -4 8 -4 }} (390625/388962). In the pergen, the 1/4-octave period is ~25/21, and {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Quadruyoyoti.

; [[~~Mirkwai~~ family]] (P8, P5, c^M7/4)

; [[Canopic family]] (P8, P5, c^M7/4)

: The ~~mirkwai~~ family of rank-3 temperaments tempers out the ~~mirkwai~~ comma, {{monzo| 0 3 4 -5 }} (16875/16807). Four ~7/5 generators equal the pergen's compound upmajor seventh of ~27/7. Its color name is Quinru-aquadyoti.

: The canopic family of rank-3 temperaments tempers out the canopic comma, {{monzo| 0 3 4 -5 }} (16875/16807). Four ~7/5 generators equal the pergen's compound upmajor seventh of ~27/7. Its color name is Quinru-aquadyoti.

=== Temperaments defined by an 11-limit comma ===

@@ Line 128: / Line 128: @@
 : The sensipent family tempers out the [[sensipent comma]], 78732/78125 ({{monzo| 2 9 -7 }}), also known as the medium semicomma. Its generator is {{nowrap| ~162/125 {{=}} ~443{{c}} }}. Seven generators equals a double-compound fifth of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo]], [[19edo]], [[46edo]], and [[65edo]]. Its color name is Sepguti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.
-; [[Vishnuzmic family]] (P8/2, P4/7)
+; [[Vishnu 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)<sup>7</sup>. The period is ~{{monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.
+: This tempers out the [[vishnu comma]], {{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)<sup>7</sup>. The period is ~{{monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.
 ; [[Unicorn family]] (P8, P4/8)
@@ Line 161: / Line 161: @@
 : This tempers out the [[vavoom comma]], {{monzo| -68 18 17 }}. The generator is {{nowrap| ~16/15 {{=}} ~111.9{{c}} }}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators. Its color name is Quinla-seyoti.
-; [[Minortonic family]] (P8, ccP5/17)
+; [[Minortone family]] (P8, ccP5/17)
-: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is minortonic temperament, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.
+: This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is minortone, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.
 ; [[Maja family]] (P8, c<sup>6</sup>P4/17)
@@ Line 191: / Line 191: @@
 ; Sasazoti clan (P8, P5)
-: This clan tempers out the [[leapfrog comma]], {{monzo| 21 -15 0 1 }} (14680064/14348907). It equates 7/6 to two apotomes and 7/4 to double augmented fifth. This clan includes [[hemifamity temperaments #Leapday|leapday]], [[sensamagic clan #Leapweek|leapweek]] and [[diaschismic family #Srutal|srutal]].
+: This clan tempers out the [[leapfrog comma]], {{monzo| 21 -15 0 1 }} (14680064/14348907). It equates 7/6 to two apotomes and 7/4 to double augmented fifth. This clan includes [[aberschismic temperaments #Leapday|leapday]], [[sensamagic clan #Leapweek|leapweek]] and [[diaschismic family #Srutal|srutal]].
 ; Laruruti clan (P8/2, P5)
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 : This 3.5.7 clan tempers out the [[gariboh comma]] {{monzo| 0 -2 5 -3 }} (3125/3087). The generator is ~25/21, two generators equals ~7/5, and three generators equals the classical major sixth (~5/3). Its color name is Triru-aquinyoti Noca.
-; [[Mirkwai clan]] (P12, cm7/5)
+; [[Canopic clan]] (P12, cm7/5)
-: This 3.5.7 clan tempers out the [[mirkwai comma]], {{monzo| 0 3 4 -5 }} (16875/16807). The generator is ~7/5, four generators equals ~27/7, and five generators equals the classical compound minor seventh (~27/5). Its color name is Quinru-aquadyoti Noca.
+: This 3.5.7 clan tempers out the [[canopic comma]], {{monzo| 0 3 4 -5 }} (16875/16807). The generator is ~7/5, four generators equals ~27/7, and five generators equals the classical compound minor seventh (~27/5). Its color name is Quinru-aquadyoti Noca.
 ; Sasepzo-atriguti Noca clan (P12, m7/7)
@@ Line 422: / Line 422: @@
 : Hemimage rank-2 temperaments temper out the [[hemimage comma]], {{monzo| 5 -7 -1 3 }} (10976/10935). Its color name is Satrizo-aguti.
-; [[Hemifamity temperaments]]
+; [[Aberschismic temperaments]]
-: Hemifamity rank-2 temperaments temper out the [[hemifamity comma]], {{monzo| 10 -6 1 -1 }} (5120/5103). Its color name is Saruyoti.
+: Aberschismic rank-2 temperaments temper out the [[aberschisma]], {{monzo| 10 -6 1 -1 }} (5120/5103). Its color name is Saruyoti.
 ; [[Parkleiness temperaments]]
@@ Line 549: / Line 549: @@
 : These temper out the nuwell comma, {{monzo| 1 5 1 -4 }} (2430/2401). In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Quadru-ayoti.
-; [[Ragisma family]] (P8, P5, ^1)
+; [[Ragismic family]] (P8, P5, ^1)
 : The 7-limit rank-3 microtemperament which tempers out the ragisma, {{monzo| -1 -7 4 1 }} (4375/4374), extends to various higher-limit rank-3 temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Zoquadyoti.
-; [[Hemifamity family]] (P8, P5, ^1)
+; [[Aberschismic family]] (P8, P5, ^1)
-: The hemifamity family of rank-3 temperaments tempers out the hemifamity comma, {{monzo| 10 -6 1 -1 }} (5120/5103), which divides 10/7 into three 9/8's. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Saruyoti.
+: The aberschismic family of rank-3 temperaments tempers out the aberschisma, {{monzo| 10 -6 1 -1 }} (5120/5103), which divides 10/7 into three 9/8's. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Saruyoti.
 ; [[Horwell family]] (P8, P5, ^1)
@@ Line 603: / Line 603: @@
 : The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, {{monzo| -1 -4 8 -4 }} (390625/388962). In the pergen, the 1/4-octave period is ~25/21, and {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Quadruyoyoti.
-; [[Mirkwai family]] (P8, P5, c^M7/4)
+; [[Canopic family]] (P8, P5, c^M7/4)
-: The mirkwai family of rank-3 temperaments tempers out the mirkwai comma, {{monzo| 0 3 4 -5 }} (16875/16807). Four ~7/5 generators equal the pergen's compound upmajor seventh of  ~27/7. Its color name is Quinru-aquadyoti.
+: The canopic family of rank-3 temperaments tempers out the canopic comma, {{monzo| 0 3 4 -5 }} (16875/16807). Four ~7/5 generators equal the pergen's compound upmajor seventh of  ~27/7. Its color name is Quinru-aquadyoti.
 === Temperaments defined by an 11-limit comma ===