Ragismic microtemperaments: Difference between revisions

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This is a collection of [[~~Rank~~-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the ragisma, [[4375/4374]] = {{monzo| -1 -7 4 1 }}. The ragisma is the smallest [[7-limit]] [[superparticular ratio]].

This is a collection of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] the ragisma, [[4375/4374]] ({{monzo| -1 -7 4 1 }}). The ragisma is the smallest [[7-limit]] [[superparticular ratio]].

Since (10/9)<sup>4</sup> = 4375/4374 × 32/21, the minor tone 10/9 tends to be an interval of relatively low [[complexity]] in temperaments tempering out the ragisma, though when looking at [[microtemperament]]s the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 × (27/25)<sup>2</sup>, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.

Microtemperaments considered below are ~~ennealimmal,~~ supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, quatracot, moulin, and palladium. Some near-microtemperaments are appended as octoid, parakleismic, counterkleismic, quincy, sfourth, and trideci. Discussed elsewhere are:

Microtemperaments considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, quatracot, moulin, and palladium. Some near-microtemperaments are appended as octoid, parakleismic, counterkleismic, quincy, sfourth, and trideci. Discussed elsewhere are:

* ''[[Hystrix]]'' (+36/35) → [[Porcupine family #Hystrix|Porcupine family]]

* ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros|Unicorn family]]

* ''[[Crepuscular]]'' (+50/49) → ~~[[Jubilismic clan #Crepuscular|Jubilismic clan]] and~~ [[Fifive family #Crepuscular|Fifive family]]

* ''[[Crepuscular]]'' (+50/49) → [[Fifive family #Crepuscular|Fifive family]]

* ''[[Modus]]'' (+64/63) → [[Tetracot family #Modus|Tetracot family]]

* ''[[Flattone]]'' (+81/80) → [[Meantone family #Flattone|Meantone family]]

* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi|Sensipent family~~]] and [[Sensamagic clan #Sensi|Sensamagic clan~~]]

* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi|Sensipent family]]

* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]]

* [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]]

* ''[[Quartonic]]'' (+1728/1715 or 4000/3969) → [[Quartonic family]]

* ''[[Srutal]]'' (+2048/2025) → [[Diaschismic family #Srutal|Diaschismic family]]

* [[Ennealimmal]] (+2401/2400) → [[~~Tritrizo~~ clan #Ennealimmal|~~Tritrizo~~ clan]]

* [[Ennealimmal]] (+2401/2400) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]

* ''[[Maja]]'' (+2430/2401 or 3125/3087) → [[Maja family #Septimal maja|Maja family]]

* [[Amity]] (+5120/5103) → [[Amity family #Septimal amity|Amity family]]

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* ''[[Vacuum]]'' (+{{monzo| -68 18 17 }}) → [[Vavoom family #Vacuum|Vavoom family]]

* ''[[Unlit]]'' (+{{monzo| 41 -20 -4 }}) → [[Undim family #Unlit|Undim family]]

* ''[[Chlorine]]'' (+{{monzo| -52 -17 34}}) → [[17th-octave temperaments#Chlorine|17th-octave temperaments]]

* ''[[Chlorine]]'' (+{{monzo| -52 -17 34}}) → [[17th-octave temperaments #Chlorine|17th-octave temperaments]]

* ''[[Quindro]]'' (+{{monzo| 56 -28 -5 }}) → [[Quindromeda family #Quindro|Quindromeda family]]

* ''[[Dzelic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments#Dzelic|37th-octave temperaments]]

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-This is a collection of [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the ragisma, [[4375/4374]] = {{monzo| -1 -7 4 1 }}. The ragisma is the smallest [[7-limit]] [[superparticular ratio]].
+This is a collection of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] the ragisma, [[4375/4374]] ({{monzo| -1 -7 4 1 }}). The ragisma is the smallest [[7-limit]] [[superparticular ratio]].
 Since (10/9)<sup>4</sup> = 4375/4374 × 32/21, the minor tone 10/9 tends to be an interval of relatively low [[complexity]] in temperaments tempering out the ragisma, though when looking at [[microtemperament]]s the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 × (27/25)<sup>2</sup>, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.
-Microtemperaments considered below are ennealimmal, supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, quatracot, moulin, and palladium. Some near-microtemperaments are appended as octoid, parakleismic, counterkleismic, quincy, sfourth, and trideci. Discussed elsewhere are:
+Microtemperaments considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, quatracot, moulin, and palladium. Some near-microtemperaments are appended as octoid, parakleismic, counterkleismic, quincy, sfourth, and trideci. Discussed elsewhere are:
 * ''[[Hystrix]]'' (+36/35) → [[Porcupine family #Hystrix|Porcupine family]]
 * ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros|Unicorn family]]
-* ''[[Crepuscular]]'' (+50/49) → [[Jubilismic clan #Crepuscular|Jubilismic clan]] and [[Fifive family #Crepuscular|Fifive family]]
+* ''[[Crepuscular]]'' (+50/49) → [[Fifive family #Crepuscular|Fifive family]]
 * ''[[Modus]]'' (+64/63) → [[Tetracot family #Modus|Tetracot family]]
 * ''[[Flattone]]'' (+81/80) → [[Meantone family #Flattone|Meantone family]]
-* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi|Sensipent family]] and [[Sensamagic clan #Sensi|Sensamagic clan]]
+* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi|Sensipent family]]
 * [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]]
 * [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]]
 * ''[[Quartonic]]'' (+1728/1715 or 4000/3969) → [[Quartonic family]]
 * ''[[Srutal]]'' (+2048/2025) → [[Diaschismic family #Srutal|Diaschismic family]]
-* [[Ennealimmal]] (+2401/2400) → [[Tritrizo clan #Ennealimmal|Tritrizo clan]]
+* [[Ennealimmal]] (+2401/2400) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
 * ''[[Maja]]'' (+2430/2401 or 3125/3087) → [[Maja family #Septimal maja|Maja family]]
 * [[Amity]] (+5120/5103) → [[Amity family #Septimal amity|Amity family]]
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 * ''[[Vacuum]]'' (+{{monzo| -68 18 17 }}) → [[Vavoom family #Vacuum|Vavoom family]]
 * ''[[Unlit]]'' (+{{monzo| 41 -20 -4 }}) → [[Undim family #Unlit|Undim family]]
-* ''[[Chlorine]]'' (+{{monzo| -52 -17 34}}) → [[17th-octave temperaments#Chlorine|17th-octave temperaments]]
+* ''[[Chlorine]]'' (+{{monzo| -52 -17 34}}) → [[17th-octave temperaments #Chlorine|17th-octave temperaments]]
 * ''[[Quindro]]'' (+{{monzo| 56 -28 -5 }}) → [[Quindromeda family #Quindro|Quindromeda family]]
 * ''[[Dzelic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments#Dzelic|37th-octave temperaments]]