Quintile comma: Difference between revisions

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The '''quintile comma''' ({{monzo|legend=1| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000) is a [[small comma|small]] [[5-limit]] [[comma]] of about 17.306 [[cent]]s. It is the amount by which a stack of five grave fourths of [[320/243]] falls short of two [[octave]]s, or the amount by which a stack of five acute fifths of [[243/160]] exceeds three octaves. It is also the amount by which a stack of five [[81/80|syntonic commas]] ~~exceed~~ a [[256/243|Pythagorean limma]].

The '''quintile comma''' ({{monzo|legend=1| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000) is a [[small comma|small]] [[5-limit]] [[comma]] of about 17.306 [[cent]]s. It is the amount by which a stack of five grave fourths of [[320/243]] falls short of two [[octave]]s, or the amount by which a stack of five acute fifths of [[243/160]] exceeds three octaves. It is also the amount by which a stack of five [[81/80|syntonic commas]] exceeds a [[256/243|Pythagorean limma]].

== Temperaments ==

Tempering out this comma leads to the [[quintile family]] of temperaments.

== Etymology ==

The corresponding temperament was discovered first, called ''pental'' by [[Petr Pařízek]] in 2012 for the fact that it splits the octave in five equal parts. In 2024, the community has decided to rename it to ''quintile'' for fear of confusion with the more common usage of the term ''pental'' to refer to the 5-limit.

[[Category:Commas named for their periods per equave]]

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-The '''quintile comma''' ({{monzo|legend=1| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000) is a [[small comma|small]] [[5-limit]] [[comma]] of about 17.306 [[cent]]s. It is the amount by which a stack of five grave fourths of [[320/243]] falls short of two [[octave]]s, or the amount by which a stack of five acute fifths of [[243/160]] exceeds three octaves. It is also the amount by which a stack of five [[81/80|syntonic commas]] exceed a [[256/243|Pythagorean limma]].
+The '''quintile comma''' ({{monzo|legend=1| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000) is a [[small comma|small]] [[5-limit]] [[comma]] of about 17.306 [[cent]]s. It is the amount by which a stack of five grave fourths of [[320/243]] falls short of two [[octave]]s, or the amount by which a stack of five acute fifths of [[243/160]] exceeds three octaves. It is also the amount by which a stack of five [[81/80|syntonic commas]] exceeds a [[256/243|Pythagorean limma]].
 == Temperaments ==
 Tempering out this comma leads to the [[quintile family]] of temperaments.
+== Etymology ==
+The corresponding temperament was discovered first, called ''pental'' by [[Petr Pařízek]] in 2012 for the fact that it splits the octave in five equal parts. In 2024, the community has decided to rename it to ''quintile'' for fear of confusion with the more common usage of the term ''pental'' to refer to the 5-limit.
 [[Category:Commas named for their periods per equave]]