Diminished family: Difference between revisions

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The '''~~dimipent~~ family''' tempers out the major diesis ~~aka~~ diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].

The '''diminished family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the major diesis a.k.a. diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].

== ~~Dimipent~~ ==

== Diminished ==

The [[generator]] of diminished can be taken as a fifth or a semitone, and 12edo, with its excellent fifth, is an obvious tuning, though a flatter fifth might be preferred to go with the flat minor third. Its [[ploidacot]] is tetraploid monocot.

[[Subgroup]]: 2.3.5

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[[Badness]] (Sintel): 1.11

== ~~Diminished~~ ==

== Septimal diminished ==

~~<div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>~~

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=== Cohedim ===

This ~~temperament~~ has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[~~Dimipent family~~ #Hemidim|11-limit 4e &~~amp;~~ 24 and 13-limit 4ef &~~amp;~~ 24]]. For 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense.

This extension has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[#Hemidim|11-limit 4e & 24 and 13-limit 4ef & 24]]. For the 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense. Its ploidacot is tetraploid alpha-dicot.

Subgroup: 2.3.5.7.11

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== Hemidim ==

Hemidim tempers out 49/48 and may be described as the {{nowrap| 4 & 24 }} temperament. Its ploidcot is tetraploid dicot.

[[Subgroup]]: 2.3.5.7

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Comma list: 49/48, 77/75, 243/242

Mapping: {{mapping| 4 0 3 8 -2 | 0 2 2 1 5}}

Mapping: {{mapping| 4 0 3 8 -2 | 0 2 2 1 5 }}

Optimal tunings:

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== Octonion ==

It was formerly known as "semidim" but renamed to avoid confusion with another temperament of the same name.

Octonion tempers out 245/243, and may be described as the {{nowrap| 8d & 24 }} temperament. Its ploidacot is octoploid monocot.

It was formerly known as ''semidim'' but renamed to avoid confusion with another temperament of the same name.

[[Subgroup]]: 2.3.5.7

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[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:~~Dimipent~~ family| ]]

[[Category:Diminished family| ]]

[[Category:Diminished| ]]

[[Category:Rank 2]]

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 {{Technical data page}}
-The '''dimipent family''' tempers out the major diesis aka diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].
+The '''diminished family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the major diesis a.k.a. diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].
-== Dimipent ==
+== Diminished ==
 {{Main| Diminished (temperament) }}
+The [[generator]] of diminished can be taken as a fifth or a semitone, and 12edo, with its excellent fifth, is an obvious tuning, though a flatter fifth might be preferred to go with the flat minor third. Its [[ploidacot]] is tetraploid monocot.
 [[Subgroup]]: 2.3.5
@@ Line 21: / Line 23: @@
 [[Badness]] (Sintel): 1.11
-== Diminished ==
+== Septimal diminished ==
-<div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
 {{Main| Diminished (temperament) }}
@@ Line 88: / Line 88: @@
 === Cohedim ===
-This temperament has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[Dimipent family #Hemidim|11-limit 4e &amp; 24 and 13-limit 4ef &amp; 24]]. For 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense.
+This extension has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[#Hemidim|11-limit 4e & 24 and 13-limit 4ef & 24]]. For the 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense. Its ploidacot is tetraploid alpha-dicot.
 Subgroup: 2.3.5.7.11
@@ Line 122: / Line 122: @@
 == Hemidim ==
+Hemidim tempers out 49/48 and may be described as the {{nowrap| 4 & 24 }} temperament. Its ploidcot is tetraploid dicot.
 [[Subgroup]]: 2.3.5.7
@@ Line 145: / Line 147: @@
 Comma list: 49/48, 77/75, 243/242
-Mapping: {{mapping| 4 0 3 8 -2 | 0 2 2 1 5}}
+Mapping: {{mapping| 4 0 3 8 -2 | 0 2 2 1 5 }}
 Optimal tunings:
@@ Line 171: / Line 173: @@
 == Octonion ==
-It was formerly known as "semidim" but renamed to avoid confusion with another temperament of the same name.
+Octonion tempers out 245/243, and may be described as the {{nowrap| 8d & 24 }} temperament. Its ploidacot is octoploid monocot.
+It was formerly known as ''semidim'' but renamed to avoid confusion with another temperament of the same name.
 [[Subgroup]]: 2.3.5.7
@@ Line 223: / Line 227: @@
 [[Category:Temperament families]]
 [[Category:Pages with mostly numerical content]]
-[[Category:Dimipent family| ]] <!-- main article -->
+[[Category:Diminished family| ]] <!-- main article -->
 [[Category:Diminished| ]] <!-- key article -->
 [[Category:Rank 2]]