Landscape comma: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 250047/250000

~~| Monzo = -4 6 -6 3~~

~~| Cents = 0.32544~~

| Name = landscape comma

| Color name =

| Color name = z<sup>3</sup>g<sup>6</sup>3, Trizogugu comma

| ~~FJS name =~~

| Comma = yes

~~| Sound~~ =

}}

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]] ~~intervals~~ exceed an [[octave]], ~~and is also~~ the amount by which ~~a stack of~~ three [[225/224|septimal kleismas]] ~~falls~~ short of the [[Pythagorean comma]]~~. Tempering 63/50 interval into one degree of 3edo (exact 400 cents) is highly characteristic of '''landscape temperament'''- any tuning system (41edo~~, ~~for example) in which~~ the ~~number of divisions~~ of the ~~octave is not a multiple of 3 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 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]].

== ~~See also~~ ==

== Temperaments ==

* [[Landscape family]]

[[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.

* [[Landscape microtemperaments]]

* [[~~Unnoticeable~~ 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>.

== Notes ==

~~[[Category:7-limit]]~~

~~[[Category:Unnoticeable comma]]~~

[[Category:Landscape]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 250047/250000
-| Monzo = -4 6 -6 3
-| Cents = 0.32544
 | Name = landscape comma
-| Color name =
+| Color name = z<sup>3</sup>g<sup>6</sup>3, Trizogugu comma
-| FJS name =
+| Comma = yes
-| Sound =
 }}
-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]] intervals exceed an [[octave]], and is also the amount by which a stack of three [[225/224|septimal kleismas]] falls short of the [[Pythagorean comma]]. Tempering 63/50 interval into one degree of 3edo (exact 400 cents) is highly characteristic of '''landscape temperament'''- any tuning system (41edo, for example) in which the number of divisions of the octave is not a multiple of 3 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 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]].
-== See also ==
+== Temperaments ==
-* [[Landscape family]]
+[[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.
-* [[Landscape microtemperaments]]
-* [[Unnoticeable 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>.
+== Notes ==
-[[Category:7-limit]]
-[[Category:Unnoticeable comma]]
 [[Category:Landscape]]
+[[Category:Commas named for their periods per equave]]