Misty comma: Difference between revisions

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The '''misty comma''', '''67108864/66430125''' = {{monzo|26 -12 -3}}, is ~~an interval~~ of 17.599 cents~~, that~~ can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[~~schismic-Pythagorean~~ equivalence continuum]], with ''n'' = 3.

The '''misty comma''', '''67108864/66430125''' = {{monzo| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents. It is the amount by which a stack of three [[512/405|ptolemaic diminished fourths (512/405)]] exceed the [[octave]]. It can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic–Pythagorean equivalence continuum]], with ''n'' = 3.

== Etymology ==

The misty comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that [[Carl Lumma]] "missed" this comma in a 5-limit comma search<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.

== Notes ==

[[Category:Misty]]

[[Category:Commas named following events]]

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-The '''misty comma''', '''67108864/66430125''' = {{monzo|26 -12 -3}}, is an interval of 17.599 cents, that can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.
+The '''misty comma''', '''67108864/66430125''' = {{monzo| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents. It is the amount by which a stack of three [[512/405|ptolemaic diminished fourths (512/405)]] exceed the [[octave]]. It can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic–Pythagorean equivalence continuum]], with ''n'' = 3.
+== Etymology ==
+The misty comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that [[Carl Lumma]] "missed" this comma in a 5-limit comma search<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.
+== Notes ==
 [[Category:Misty]]
+[[Category:Commas named following events]]