Misty comma: Difference between revisions

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67108864/66430125 = |26 -12 -3~~>~~, ~~the misty~~ comma of 17.599 cents, can be written as (81/80)/(32805/32768)^2, (2048/2025)/(32805/32768), (128/125)/(531441/524288) ~~and 393216/390625 * 1600000/1594323~~. Since these are commas of [[12edo~~|12et~~]], so is the misty comma. However, [[~~Misty_family|~~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|~~87edo]] and [[99edo|~~99edo~~]].

{{Infobox Interval

| Ratio = 67108864/66430125

| Name = misty comma

|Color name = ssg33, sasatrigu 3rd, Sasatrigu comma

| Comma = yes

}}

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]])2, ([[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]]

@@ Line 1: / Line 1: @@
-67108864/66430125 = |26 -12 -3&gt;, the misty comma of 17.599 cents, can be written as (81/80)/(32805/32768)^2, (2048/2025)/(32805/32768), (128/125)/(531441/524288) and 393216/390625 * 1600000/1594323. Since these are commas of [[12edo|12et]], so is the misty comma. However, [[Misty_family|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|87edo]] and [[99edo|99edo]].
+{{Infobox Interval
+| Ratio = 67108864/66430125
+| Name = misty comma
+|Color name = ssg<sup>3</sup>3, sasatrigu 3rd,<br>Sasatrigu comma
+| Comma = yes
+}}
+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]]