Fifive comma: Difference between revisions

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The '''fifive comma''' is a [[medium comma|medium]] [[5-limit]] [[comma]] with a width of about a third of a semitone. It is the amount that a stack of five [[27/25]]'s falls short of [[3/2]] by, and also the amount by which a stack of ten [[5/3]]'s [[octave reduction|octave-reduced]] exceeds [[81/64]].

~~The '''fifive comma''' is a~~ [[~~5-limit~~]] interval ~~with a width of about a third of a semitone. It is~~ the ~~amount that a stack of 5~~ [[~~27/25~~]]~~s exceeds~~ [[3/2]] ~~by,~~ and ~~also~~ the ~~amount by which a stack~~ of 10 [[5/3]]~~s exceeds harmonic 162~~.

== Temperaments ==

[[Tempering out]] this interval leads to the [[fifive family]] of temperaments, where the [[3/2|perfect fifth]] is divided into five equal parts and the octave is split in half. [[26edo]] and [[34edo]] are two notable examples of [[edo]]s that support the basic 5-limit temperament in this family, simply known as [[fifive]].

~~Tempering out this interval leads to the~~ [[~~Fifive family|fifive family~~]] of ~~temperaments~~, ~~where~~ the perfect fifth ~~is divided into 5 equal parts and the octave is split~~ in ~~half. [[26edo]] and [[34edo]] are two notable examples of [[EDO|edo]]s that support the basic 5-limit temperament in this family, simply known as~~ [[Fifive family~~#Fifive|fifive~~]].

== Etymology ==

This comma was named by [[Petr Pařízek]] in 2011 in terms of the corresponding temperament, ''fifives'', for the temperament splits the perfect fifth in five<ref>See [[Fifive family]] for sources. </ref>. It is not clear when it lost an ''s''.

== Notes ==

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+The '''fifive comma''' is a [[medium comma|medium]] [[5-limit]] [[comma]] with a width of about a third of a semitone. It is the amount that a stack of five [[27/25]]'s falls short of [[3/2]] by, and also the amount by which a stack of ten [[5/3]]'s [[octave reduction|octave-reduced]] exceeds [[81/64]].
-The '''fifive comma''' is a [[5-limit]] interval with a width of about a third of a semitone. It is the amount that a stack of 5 [[27/25]]s exceeds [[3/2]] by, and also the amount by which a stack of 10 [[5/3]]s exceeds harmonic 162.
+== Temperaments ==
+[[Tempering out]] this interval leads to the [[fifive family]] of temperaments, where the [[3/2|perfect fifth]] is divided into five equal parts and the octave is split in half. [[26edo]] and [[34edo]] are two notable examples of [[edo]]s that support the basic 5-limit temperament in this family, simply known as [[fifive]].
-Tempering out this interval leads to the [[Fifive family|fifive family]] of temperaments, where the perfect fifth is divided into 5 equal parts and the octave is split in half. [[26edo]] and [[34edo]] are two notable examples of [[EDO|edo]]s that support the basic 5-limit temperament in this family, simply known as [[Fifive family#Fifive|fifive]].
+== Etymology ==
+This comma was named by [[Petr Pařízek]] in 2011 in terms of the corresponding temperament, ''fifives'', for the temperament splits the perfect fifth in five<ref>See [[Fifive family]] for sources. </ref>. It is not clear when it lost an ''s''.
+== Notes ==