5th-octave temperaments: Difference between revisions

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{{Infobox fractional-octave|5}}[[5edo]] is the smallest xenharmonic system, as 1edo, 2edo, 3edo and 4edo are all subsets of [[12edo]].

The most notable 5th-octave family is [[~~limmic temperaments~~]] – [[tempering out]] [[256/243]] and associates 3\5 to [[3/2]] as well as 1\5 to [[9/8]], producing temperaments like [[blackwood]]. Equally notable among small equal divisions are the [[Cloudy ~~clan~~|cloudy temperaments]] – identifying [[8/7]] with one step of 5edo.

The most notable 5th-octave family is [[blackwood family]] – [[tempering out]] [[256/243]] and associates 3\5 to [[3/2]] as well as 1\5 to [[9/8]], producing temperaments like [[blackwood]]. Equally notable among small equal divisions are the [[Cloudy comma #Temperaments|cloudy temperaments]] – identifying [[8/7]] with one step of 5edo.

Other families of 5-limit 5th-octave commas are:

* [[Quintile family~~|Quintile temperaments~~]] - tempers out the {{monzo|-28 25 -5}} comma which improves the 3/2 mapping for 5edo, producing a temperament with 3/2 as a generator and 1\5 as a period.

* [[Quintile family]] – tempers out the {{monzo|-28 25 -5}} comma which improves the 3/2 mapping for 5edo, producing a temperament with 3/2 as a generator and 1\5 as a period.

* [[Quintosec family~~|Quintosec temperaments~~]]

* [[Quintosec family]]

* [[Trisedodge family~~|Trisedodge temperaments~~]]

* [[Trisedodge family]]

== Slendroschismic ==

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 {{Infobox fractional-octave|5}}[[5edo]] is the smallest xenharmonic system, as 1edo, 2edo, 3edo and 4edo are all subsets of [[12edo]].
-The most notable 5th-octave family is [[limmic temperaments]] – [[tempering out]] [[256/243]] and associates 3\5 to [[3/2]] as well as 1\5 to [[9/8]], producing temperaments like [[blackwood]]. Equally notable among small equal divisions are the [[Cloudy clan|cloudy temperaments]] – identifying [[8/7]] with one step of 5edo.
+The most notable 5th-octave family is [[blackwood family]] – [[tempering out]] [[256/243]] and associates 3\5 to [[3/2]] as well as 1\5 to [[9/8]], producing temperaments like [[blackwood]]. Equally notable among small equal divisions are the [[Cloudy comma #Temperaments|cloudy temperaments]] – identifying [[8/7]] with one step of 5edo.
 Other families of 5-limit 5th-octave commas are:
-* [[Quintile family|Quintile temperaments]] - tempers out the {{monzo|-28 25 -5}} comma which improves the 3/2 mapping for 5edo, producing a temperament with 3/2 as a generator and 1\5 as a period.
+* [[Quintile family]] – tempers out the {{monzo|-28 25 -5}} comma which improves the 3/2 mapping for 5edo, producing a temperament with 3/2 as a generator and 1\5 as a period.
-* [[Quintosec family|Quintosec temperaments]]
+* [[Quintosec family]]
-* [[Trisedodge family|Trisedodge temperaments]]
+* [[Trisedodge family]]
 == Slendroschismic ==
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 {{Navbox fractional-octave}}
+{{Todo| review | cleanup }}