Ragismic microtemperaments: Difference between revisions

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* ''[[Quindro]]'', {4375/4374, {{monzo| 56 -28 -5 }}} → [[Quindromeda family #Quindro|Quindromeda family]]

Considered below are ennealimmal, gamera, supermajor, ~~enneadeca~~, decal, sfourth, abigail, semidimi, brahmagupta, quasithird, semidimfourth, acrokleismic, seniority, orga, quatracot, octoid, amity, parakleismic, counterkleismic, quincy, chlorine, palladium, and monzism.

Considered below are ennealimmal, gamera, supermajor, enneadecal, decal, sfourth, abigail, semidimi, brahmagupta, quasithird, semidimfourth, acrokleismic, seniority, orga, quatracot, octoid, amity, parakleismic, counterkleismic, quincy, trideci, chlorine, palladium, and monzism.

== Ennealimmal ==

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== Sfourth ==

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sfourth]].''

Subgroup: 2.3.5.7

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== Semidimi ==

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semidimi]].''

The generator of semidimi temperament is a semi-diminished fourth interval tuned between 162/125 and 35/27. It tempers out 5-limit {{monzo|-12 -73 55}} and 7-limit 3955078125/3954653486, as well as 4375/4374.

~~Subgroup: 2.3.5~~

~~[[Comma]]: {{monzo|-12 -73 55}}~~

~~[[Mapping]]: [{{val|1 36 48}}, {{val|0 -55 -73}}]~~

~~[[POTE generator]]: ~162/125 = 449.1269~~

~~{{Val list|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}~~

~~[[Badness]]: 0.754866~~

~~=== 7-limit ===~~

Subgroup: 2.3.5.7

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== Semidimfourth ==

~~The~~ ''~~'semidimifourth''' temperament is featured by a semi-diminished fourth inverval which is [[128/125]] above~~ the ~~pythagorean major third [[81/64]]. In the 7~~-limit, this temperament ~~tempers out the ragisma and the triwellisma~~, ~~235298/234375~~.

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semidimfourth]].''

~~Subgroup: 2~~.3.5

The '''semidimfourth''' temperament is featured by a semi-diminished fourth inverval which is [[128/125]] above the pythagorean major third [[81/64]]. In the 7-limit, this temperament tempers out the ragisma and the triwellisma, 235298/234375.

~~[[Comma]]: {{monzo|7 41 -31}}~~

~~[[Mapping]]: [{{val|1 21 28}}, {{val|0 -31 -41}}]~~

~~[[POTE generator]]: ~162/125 = 448.449~~

~~{{Val list|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}~~

~~[[Badness]]: 0.233376~~

~~=== 7-limit ===~~

Subgroup: 2.3.5.7

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== Counterkleismic ==

{{see also|~~Syntonic-enneadecal equivalence continuum~~ #Counterhanson}}

In the 5-limit, the counterhanson temperament tempers out the counterhanson (quinquinyo) comma, {{monzo|-20 -24 25}}, the amount by which six [[648/625|major dieses (648/625)]] fall short of the [[5/4|classic major third (5/4)]]. It can be described as 19&224 temperament (''counterkleismic'', named by analogy to [[catakleismic]] and parakleismic), tempering out the ragisma and 158203125/157351936 (laquadru-atritriyo comma).

Subgroup: 2.3.5.7

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 * ''[[Quindro]]'', {4375/4374, {{monzo| 56 -28 -5 }}} → [[Quindromeda family #Quindro|Quindromeda family]]
-Considered below are ennealimmal, gamera, supermajor, enneadeca, decal, sfourth, abigail, semidimi, brahmagupta, quasithird, semidimfourth, acrokleismic, seniority, orga, quatracot, octoid, amity, parakleismic, counterkleismic, quincy, chlorine, palladium, and monzism.
+Considered below are ennealimmal, gamera, supermajor, enneadecal, decal, sfourth, abigail, semidimi, brahmagupta, quasithird, semidimfourth, acrokleismic, seniority, orga, quatracot, octoid, amity, parakleismic, counterkleismic, quincy, trideci, chlorine, palladium, and monzism.
 == Ennealimmal ==
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 == Sfourth ==
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sfourth]].''
 Subgroup: 2.3.5.7
@@ Line 620: / Line 622: @@
 == Semidimi ==
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semidimi]].''
 The generator of semidimi temperament is a semi-diminished fourth interval tuned between 162/125 and 35/27. It tempers out 5-limit {{monzo|-12 -73 55}} and 7-limit 3955078125/3954653486, as well as 4375/4374.
-Subgroup: 2.3.5
-[[Comma]]: {{monzo|-12 -73 55}}
-[[Mapping]]: [{{val|1 36 48}}, {{val|0 -55 -73}}]
-[[POTE generator]]: ~162/125 = 449.1269
-{{Val list|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
-[[Badness]]: 0.754866
-=== 7-limit ===
 Subgroup: 2.3.5.7
@@ Line 749: / Line 740: @@
 == Semidimfourth ==
-The '''semidimifourth''' temperament is featured by a semi-diminished fourth inverval which is [[128/125]] above the pythagorean major third [[81/64]]. In the 7-limit, this temperament tempers out the ragisma and the triwellisma, 235298/234375.
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semidimfourth]].''
-Subgroup: 2.3.5
+The '''semidimfourth''' temperament is featured by a semi-diminished fourth inverval which is [[128/125]] above the pythagorean major third [[81/64]]. In the 7-limit, this temperament tempers out the ragisma and the triwellisma, 235298/234375.
-[[Comma]]: {{monzo|7 41 -31}}
-[[Mapping]]: [{{val|1 21 28}}, {{val|0 -31 -41}}]
-[[POTE generator]]: ~162/125 = 448.449
-{{Val list|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}
-[[Badness]]: 0.233376
-=== 7-limit ===
 Subgroup: 2.3.5.7
@@ Line 1,486: / Line 1,466: @@
 == Counterkleismic ==
-{{see also|Syntonic-enneadecal equivalence continuum #Counterhanson}}
+{{see also| High badness temperaments #Counterhanson}}
 In the 5-limit, the counterhanson temperament tempers out the counterhanson (quinquinyo) comma, {{monzo|-20 -24 25}}, the amount by which six [[648/625|major dieses (648/625)]] fall short of the [[5/4|classic major third (5/4)]]. It can be described as 19&amp;224 temperament (''counterkleismic'', named by analogy to [[catakleismic]] and parakleismic), tempering out the ragisma and 158203125/157351936 (laquadru-atritriyo comma).
 Subgroup: 2.3.5.7