Misty comma: Difference between revisions

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The '''misty comma''', '''67108864/66430125''' = {{monzo| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents, which 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, which can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). It is the amount by which 3 [[512/405]] major thirds exceed the octave. 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 ==

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-The '''misty comma''', '''67108864/66430125''' = {{monzo| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents, which 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, which can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). It is the amount by which 3 [[512/405]] major thirds exceed the octave. 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 ==