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 about 0.325 [[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]] commas. | ||
== | In the [[11-limit]], it factors into ([[9801/9800]])⋅([[151263/151250]]). | ||
== 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. | |||
== Etymology == | |||
This comma was named by [[Yahya Abdal-Aziz]] in 2005, referring to landscape painting where there is a three-layer technique, which in turn was a reference to [[Gene Ward Smith]]'s description of the comma as the ''three-layer comma''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_58180.html#58217 Yahoo! Tuning Group | ''Common commas and 768'']</ref>. | |||
== References == | |||
[[Category:Landscape]] | [[Category:Landscape]] | ||
[[Category:Commas named for their periods per equave]] | |||
Latest revision as of 13:58, 21 April 2026
| Interval information |
The landscape comma (monzo: [-4 6 -6 3⟩, ratio: 250047/250000) is an unnoticeable 7-limit comma with a size of about 0.325 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.
In the 11-limit, it factors into (9801/9800)⋅(151263/151250).
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.
Etymology
This comma was named by Yahya Abdal-Aziz in 2005, referring to landscape painting where there is a three-layer technique, which in turn was a reference to Gene Ward Smith's description of the comma as the three-layer comma[1].