Landscape comma: Difference between revisions
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The '''landscape comma''' is | The '''landscape comma''' ({{monzo|legend=1| -4 6 -6 3 }}, [[ratio]]: 250047/250000) is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] with a size of 0.33 [[cent]]s. It is the amount by which three [[63/50]]'s exceed an [[octave]], the amount by which three [[225/224|septimal kleismas]] fall short of the [[Pythagorean comma]], and also the difference of [[2401/2400]] and [[4375/4374]], the two smallest 7-limit [[superparticular interval|superparticular commas]]. | ||
== | == Temperaments == | ||
[[Tempering out]] this comma results in the [[landscape]] temperament. An octave widened by this comma is {{monzo| -3 6 -6 3 }}, a monzo with four [[threeven]] numbers. Thus landscape temperaments split the octave into three equal parts. It follows that any edo that is not threeven (41, for example) cannot temper out the landscape comma. | |||
See [[Landscape family]] for the rank-3 family of temperaments where it is tempered out. See [[Landscape microtemperaments]] for a collection of rank-2 temperaments where it is tempered out. | |||
[[Category:Landscape]] | [[Category:Landscape]] | ||
[[Category:Commas with unknown etymology]] | [[Category:Commas with unknown etymology]] | ||
Revision as of 17:43, 12 November 2024
| Interval information |
The landscape comma (monzo: [-4 6 -6 3⟩, ratio: 250047/250000) is an unnoticeable 7-limit comma with a size of 0.33 cents. It is the amount by which three 63/50's exceed an octave, the amount by which three septimal kleismas fall short of the Pythagorean comma, and also the difference of 2401/2400 and 4375/4374, the two smallest 7-limit superparticular commas.
Temperaments
Tempering out this comma results in the landscape temperament. An octave widened by this comma is [-3 6 -6 3⟩, a monzo with four threeven numbers. Thus landscape temperaments split the octave into three equal parts. It follows that any edo that is not threeven (41, for example) cannot temper out the landscape comma.
See Landscape family for the rank-3 family of temperaments where it is tempered out. See Landscape microtemperaments for a collection of rank-2 temperaments where it is tempered out.