Phaotic comma: Difference between revisions

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The '''phaotic comma''', or '''phaotisma''' ~~(from Ancient Greek ''pháos'' 'light')~~, is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (~~also~~ 2.3.5.13 subgroup) comma with a ratio of '''256000/255879''', and a size of approximately 0.82 [[cent~~]]s~~. It ~~is significant in that it is the interval separating~~ a stack of two [[81/80|~~meantone~~ commas]] from [[40/39]], ~~as well as the interval separating an octave-reduced stack of~~ three ~~instances of~~ [[27/20]] from [[16/13]].

The '''phaotic comma''', or '''phaotisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] ([[2.3.5.13 subgroup]]) comma with the ratio '''256000/255879''', and a size of approximately 0.82{{cent}}. It separates a stack of two [[81/80|syntonic commas]] from [[40/39]], or three [[27/20]] acute fourths from [[16/13]] (up an octave). It factors into {{nowrap|([[4096/4095]])([[4375/4374]])}} or {{nowrap|([[6656/6561]])([[507/500]])<sup>−1</sup>}}.

== Temperaments ==

Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of '''phaotismic temperament''' in the full 13-limit and '''phaotic temperament''' in the 2.3.5.13 subgroup.

== Etymology ==

This comma was finally named by [[Aura]] in 2021 after several failed attempts. Its name comes from the Ancient Greek word [[Wiktionary: φάος #Ancient Greek|''pháos'']] ("light")- a name that was chosen in part to reflect [https://discord.com/channels/332357996569034752/780300193110818826/829357139398361118 an association of certain intervals involved with brightness] on the part of [[User:Godtone|Osmium]].

== See also ==

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[[Category:Phaotismic]]

[[Category:Commas named for their regular temperament properties]]

[[Category:Commas named by translating something into another language]]

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-The '''phaotic comma''', or '''phaotisma''' (from Ancient Greek ''pháos'' 'light'), is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (also 2.3.5.13 subgroup) comma with a ratio of '''256000/255879''', and a size of approximately 0.82 [[cent]]s. It is significant in that it is the interval separating a stack of two [[81/80|meantone commas]] from [[40/39]], as well as the interval separating an octave-reduced stack of three instances of [[27/20]] from [[16/13]].
+The '''phaotic comma''', or '''phaotisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] ([[2.3.5.13 subgroup]]) comma with the ratio '''256000/255879''', and a size of approximately 0.82{{cent}}. It separates a stack of two [[81/80|syntonic commas]] from [[40/39]], or three [[27/20]] acute fourths from [[16/13]] (up an octave). It factors into {{nowrap|([[4096/4095]])([[4375/4374]])}} or {{nowrap|([[6656/6561]])([[507/500]])<sup>&minus;1</sup>}}.
 == Temperaments ==
 Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of '''phaotismic temperament''' in the full 13-limit and '''phaotic temperament''' in the 2.3.5.13 subgroup.
+== Etymology ==
+This comma was finally named by [[Aura]] in 2021 after several failed attempts.  Its name comes from the Ancient Greek word [[Wiktionary: φάος #Ancient Greek|''pháos'']] ("light")- a name that was chosen in part to reflect [https://discord.com/channels/332357996569034752/780300193110818826/829357139398361118 an association of certain intervals involved with brightness] on the part of [[User:Godtone|Osmium]].
 == See also ==
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 [[Category:Phaotismic]]
+[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named by translating something into another language]]