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. 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 [[ | 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 == | == Etymology == | ||
Latest revision as of 16:16, 10 December 2024
| Interval information |
Sasatrigu comma
reduced subharmonic
The misty comma, 67108864/66430125 = [26 -12 -3⟩, is a small comma of 17.599 cents. It is the amount by which a stack of three 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[1].