Landscape comma - Revision history

FloraC: + factorization

2026-04-21T13:58:09Z

+ factorization

← Older revision		Revision as of 13:58, 21 April 2026
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	}}		}}

	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]].		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 ==		== Temperaments ==
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	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>.		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~~ ==		== References ==

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

FloraC: +etymology

2024-11-12T18:01:45Z

+etymology

← Older revision		Revision as of 18:01, 12 November 2024
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	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.		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:Landscape]]		[[Category:Landscape]]
	[[Category:Commas ~~with unknown etymology~~]]		[[Category:Commas named for their periods per equave]]

FloraC: Rework

2024-11-12T17:43:44Z

Rework

← Older revision		Revision as of 17:43, 12 November 2024
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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 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.

	[[Category:Landscape]]		[[Category:Landscape]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

BudjarnLambeth at 23:37, 3 November 2024

2024-11-03T23:37:58Z

← Older revision		Revision as of 23:37, 3 November 2024
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	[[Category:Landscape]]		[[Category:Landscape]]
			[[Category:Commas with unknown etymology]]

Fredg999: Small clarification

2023-03-14T04:46:22Z

Small clarification

← Older revision		Revision as of 04:46, 14 March 2023
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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 (41, for example) ~~that isn't threeven~~ cannot temper out the landscape comma.		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.

	== See also ==		== See also ==

TallKite: minor rewrite

2023-01-07T03:10:57Z

minor rewrite

← Older revision		Revision as of 03:10, 7 January 2023
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	\| Ratio = 250047/250000		\| Ratio = 250047/250000
	\| Name = landscape comma		\| Name = landscape comma
	\| Color name = z<sup>3</sup>g<sup>6</sup>3, ~~trizogugu 3rd~~		\| Color name = z<sup>3</sup>g<sup>6</sup>3, Trizogugu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	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. ~~Tempering 63/50 interval into one degree of 3edo (exact 400 cents)~~ is ~~highly characteristic of~~ [[landscape microtemperaments]] – 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''' 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 (41, for example) that isn't threeven cannot temper out the landscape comma.

	== See also ==		== See also ==

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:42:33Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:42, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 250047/250000		\| Ratio = 250047/250000
	~~\| Monzo = -4 6 -6 3~~
	~~\| Cents = 0.32544~~
	\| Name = landscape comma		\| Name = landscape comma
	\| Color name = z<sup>3</sup>g<sup>6</sup>3, trizogugu 3rd		\| Color name = z<sup>3</sup>g<sup>6</sup>3, trizogugu 3rd
	\| ~~FJS name =~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}

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	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]

	~~[[Category:7-limit]]~~
	~~[[Category:Unnoticeable commas]]~~
	[[Category:Landscape]]		[[Category:Landscape]]

Fredg999 category edits: Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

2022-03-20T22:01:54Z

Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

← Older revision		Revision as of 22:01, 20 March 2022
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	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Unnoticeable ~~comma~~]]		[[Category:Unnoticeable commas]]
	[[Category:Landscape]]		[[Category:Landscape]]

TallKite: added the color name

2022-02-13T05:49:34Z

added the color name

← Older revision		Revision as of 05:49, 13 February 2022
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	\| Cents = 0.32544		\| Cents = 0.32544
	\| Name = landscape comma		\| Name = landscape comma
	\| Color name =		\| Color name = z<sup>3</sup>g<sup>6</sup>3, trizogugu 3rd
	\| FJS name =		\| FJS name =
	\| Sound =		\| Sound =

Aura at 15:21, 3 May 2021

2021-05-03T15:21:51Z

← Older revision		Revision as of 15:21, 3 May 2021
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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]], 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. Tempering 63/50 interval into one degree of 3edo (exact 400 cents) is highly characteristic of [[landscape microtemperaments]] – 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''' 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. Tempering 63/50 interval into one degree of 3edo (exact 400 cents) is highly characteristic of [[landscape microtemperaments]] – 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.

	== See also ==		== See also ==