Misty comma: Difference between revisions
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m put main lemma first (+slight rewording) |
Mention the equivalence continuum |
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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]]) | 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. However, [[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. | ||
[[Category:5-limit]] | [[Category:5-limit]] | ||
[[Category:Small comma]] | [[Category:Small comma]] | ||
[[Category:Misty]] | [[Category:Misty]] | ||
Revision as of 10:10, 11 October 2021
The misty comma, 67108864/66430125 = [26 -12 -3⟩, is an interval of 17.599 cents, that 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. However, 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.