Phaotic comma: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 256000/255879

~~| Monzo = 11 -9 3 0 0 1~~

| Name = phaotic comma, phaotisma

~~| Cents = 0.81847~~

| Color name = s3uy31, Sathutriyo comma

| Name = phaotic comma, ~~ ~~ phaotisma

| Comma = yes

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

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]])−1}}.

== 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 ==

* [[Unnoticeable comma]]

~~[[Category:13-limit]]~~

~~[[Category:Unnoticeable commas]]~~

[[Category:Phaotismic]]

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

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 256000/255879
-| Monzo = 11 -9 3 0 0 1
+| Name = phaotic comma, phaotisma
-| Cents = 0.81847
+| Color name = s3uy<sup>3</sup>1, Sathutriyo comma
-| Name = phaotic comma, <br> phaotisma
+| Comma = yes
-| Color name =
-| FJS name =
-| Sound =
 }}
-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 ==
 * [[Unnoticeable comma]]
-[[Category:13-limit]]
-[[Category:Unnoticeable commas]]
 [[Category:Phaotismic]]
+[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named by translating something into another language]]