Quintile family: Difference between revisions

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The '''~~pental~~ family''' tempers out the [[~~pental~~ comma]], 847288609443/838860800000 = {{monzo| -28 25 -5 }}.

The '''quintile family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[quintile comma]] ([[ratio]]: 847288609443/838860800000, {{monzo|legend=1| -28 25 -5 }}.

== ~~Pental~~ ==

== Quintile ==

~~The 5-limit version of pental~~ reaches the interval class of 5 by 5 perfect fifths (i.e. a major seventh) plus two periods of 1/5-octave. ~~This~~ temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the ~~[[syntonic-diatonic equivalence~~ continuum]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group | ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012 by [[Petr Pařízek]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group | ''2D temperaments, part II -- new 5-limit temperaments'']</ref>.

Quintile reaches the interval class of 5 by five perfect fifths (i.e. a major seventh) plus two periods of 1/5-octave. It is a member of the [[syntonic–diatonic equivalence continuum]] with {{nowrap| ''n'' {{=}} 5 }}, so it equates a [[256/243|Pythagorean limma]] with a stack of five [[81/80|syntonic commas]].

The temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the continuum mentioned above<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group | ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012, when [[Petr Pařízek]] called it ''pental''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group | ''2D temperaments, part II -- new 5-limit temperaments'']</ref>. In 2024, the community has decided to rename it for fear of confusion.

[[Subgroup]]: 2.3.5

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== Pentacloud ==

~~The pentacloud (formerly ''septimal pental'') temperament~~ can be described as 5&~~amp;~~60 temperament, tempering out the [[cloudy comma]] 16807/16384 and the [[245/243|sensamagic comma]] 245/243 in the 7-limit.

Pentacloud can be described as the 5 & 60 temperament. It identifies the period as ~8/7, tempering out the [[cloudy comma]] 16807/16384 and the [[245/243|sensamagic comma]] 245/243 in the 7-limit.

[[Subgroup]]: 2.3.5.7

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Badness: 0.067549

== ~~Hemipental~~ ==

== Hemiquintile ==

~~The~~ ''hemipental'' ~~temperament (~~125 &~~amp;~~ 130) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 ([[~~Hewuermera~~ temperaments|hewuermera]], satribiru-agu) and 5250987/5242880 ([[~~Mitonismic~~ temperaments|mitonisma]], laquadzo-agu).

Hemiquintile (formerly ''hemipental'') can be described as 125 & 130 and tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 ([[hewuermera temperaments|hewuermera]], satribiru-agu) and 5250987/5242880 ([[mitonismic temperaments|mitonisma]], laquadzo-agu).

[[Subgroup]]: 2.3.5.7

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Badness: 0.047624

==== ~~Hemipent~~ ====

==== Hemiquint ====

Subgroup: 2.3.5.7.11.13

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Badness: 0.041043

==== ~~Hemipentalis~~ ====

==== Hemiquintilis ====

Subgroup: 2.3.5.7.11.13

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Badness: 0.033542

== ~~Decal~~ ==

== Decile ==

~~The~~ decal ~~temperament (~~130 &~~amp;~~ 190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 ([[2460375/2458624|breeze comma]], laquadru-atriyo), and the [[~~15/14 equal-step tuning|~~linus comma]], {{monzo| 11 -10 -10 10 }}.

Decile (formerly ''decal'') can be described as 130 & 190 and tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 ([[2460375/2458624|breeze comma]], laquadru-atriyo), and the [[linus comma]], {{monzo| 11 -10 -10 10 }}.

[[Subgroup]]: 2.3.5.7

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[[Category:Temperament families]]

[[Category:~~Pental~~ family| ]]

[[Category:Quintile family| ]]

[[Category:~~Pental~~| ]]

[[Category:Quintile| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
-The '''pental family''' tempers out the [[pental comma]], 847288609443/838860800000 = {{monzo| -28 25 -5 }}.
+The '''quintile family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[quintile comma]] ([[ratio]]: 847288609443/838860800000, {{monzo|legend=1| -28 25 -5 }}.
-== Pental ==
+== Quintile ==
-The 5-limit version of pental reaches the interval class of 5 by 5 perfect fifths (i.e. a major seventh) plus two periods of 1/5-octave. This temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the [[syntonic-diatonic equivalence continuum]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group | ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012 by [[Petr Pařízek]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group | ''2D temperaments, part II -- new 5-limit temperaments'']</ref>.
+Quintile reaches the interval class of 5 by five perfect fifths (i.e. a major seventh) plus two periods of 1/5-octave. It is a member of the [[syntonic–diatonic equivalence continuum]] with {{nowrap| ''n'' {{=}} 5 }}, so it equates a [[256/243|Pythagorean limma]] with a stack of five [[81/80|syntonic commas]].
+The temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the continuum mentioned above<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group | ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012, when [[Petr Pařízek]] called it ''pental''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group | ''2D temperaments, part II -- new 5-limit temperaments'']</ref>. In 2024, the community has decided to rename it for fear of confusion.
 [[Subgroup]]: 2.3.5
@@ Line 19: / Line 21: @@
 == Pentacloud ==
-The pentacloud (formerly ''septimal pental'') temperament can be described as 5&amp;60 temperament, tempering out the [[cloudy comma]] 16807/16384 and the [[245/243|sensamagic comma]] 245/243 in the 7-limit.
+Pentacloud can be described as the 5 & 60 temperament. It identifies the period as ~8/7, tempering out the [[cloudy comma]] 16807/16384 and the [[245/243|sensamagic comma]] 245/243 in the 7-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 59: / Line 61: @@
 Badness: 0.067549
-== Hemipental ==
+== Hemiquintile ==
-The ''hemipental'' temperament (125 &amp; 130) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 ([[Hewuermera temperaments|hewuermera]], satribiru-agu) and 5250987/5242880 ([[Mitonismic temperaments|mitonisma]], laquadzo-agu).
+Hemiquintile (formerly ''hemipental'') can be described as 125 & 130 and tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 ([[hewuermera temperaments|hewuermera]], satribiru-agu) and 5250987/5242880 ([[mitonismic temperaments|mitonisma]], laquadzo-agu).
 [[Subgroup]]: 2.3.5.7
@@ Line 89: / Line 91: @@
 Badness: 0.047624
-==== Hemipent ====
+==== Hemiquint ====
 Subgroup: 2.3.5.7.11.13
@@ Line 102: / Line 104: @@
 Badness: 0.041043
-==== Hemipentalis ====
+==== Hemiquintilis ====
 Subgroup: 2.3.5.7.11.13
@@ Line 115: / Line 117: @@
 Badness: 0.033542
-== Decal ==
+== Decile ==
-The decal temperament (130 &amp; 190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 ([[2460375/2458624|breeze comma]], laquadru-atriyo), and the [[15/14 equal-step tuning|linus comma]], {{monzo| 11 -10 -10 10 }}.
+Decile (formerly ''decal'') can be described as 130 & 190 and tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 ([[2460375/2458624|breeze comma]], laquadru-atriyo), and the [[linus comma]], {{monzo| 11 -10 -10 10 }}.
 [[Subgroup]]: 2.3.5.7
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 [[Category:Temperament families]]
-[[Category:Pental family| ]] <!-- main article -->
+[[Category:Quintile family| ]] <!-- main article -->
-[[Category:Pental| ]] <!-- key article -->
+[[Category:Quintile| ]] <!-- key article -->
+[[Category:Rank 2]]