Landscape comma: Difference between revisions

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The '''landscape comma''' is ~~the~~ [[7-limit]] [[~~unnoticeable~~ comma]] with ~~a ratio of '''250047/250000''' and~~ 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 commas. An octave widened by this comma is~~ [~~-3 6 -6 3⟩, a monzo with four~~ [~~[threeven~~]] ~~numbers. Thus [[landscape microtemperaments]] split the octave into three parts. It follows that any edo that isn't threeven (41, for example) cannot temper out the landscape comma~~.

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.

== ~~See also~~ ==

In the [[11-limit]], it factors into ([[9801/9800]])⋅([[151263/151250]]).

* [[Landscape family]]

* [[Landscape microtemperaments]]

== Temperaments ==

* [[~~Unnoticeable~~ comma]]

[[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:Commas named for their periods per equave]]

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-The '''landscape comma''' is the [[7-limit]] [[unnoticeable comma]] with a ratio of '''250047/250000''' and 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 commas. An octave widened by this comma is [-3 6 -6 3⟩, a monzo with four [[threeven]] numbers. Thus [[landscape microtemperaments]] split the octave into three parts. It follows that any edo that isn't threeven (41, for example) cannot temper out the landscape comma.
+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.
-== See also ==
+In the [[11-limit]], it factors into ([[9801/9800]])⋅([[151263/151250]]).
-* [[Landscape family]]
-* [[Landscape microtemperaments]]
+== Temperaments ==
-* [[Unnoticeable comma]]
+[[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:Commas named for their periods per equave]]