Kwadransma - Revision history

Xenllium at 10:36, 10 April 2025

2025-04-10T10:36:08Z

← Older revision		Revision as of 10:36, 10 April 2025
Line 2:		Line 2:
	\| Ratio = 279936/279841		\| Ratio = 279936/279841
	\| Name = kwadransma		\| Name = kwadransma
	\| Color name = ~~Laquadtwethu comma~~		\| Color name = Quadtwethu negative 3rd
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''279936/279841''', the '''kwadransma''', is a [[23-limit]] and 2.3.23 subgroup comma of about 0.59 cents. It is expressible as (6<sup>7</sup>)/(23<sup>4</sup>), therefore being the difference between [[6/1]] and four intervals of [[36/23]] - the small size of this comma representing the extreme accuracy of the 23rd harmonic in [[4ed6]] - or between [[8/3]] and four [[23/18]] thirds. This should be mentioned in relation to [[skwares]], which tempers out the comma [[19683/19208]], equating 8/3 to four intervals of [[9/7]]; tempering out 279936/279841 instead provides a far more accurate interpretation of the skwares generator (9/7[[~]][[14/11]]) as 23/18. In terms of [[S-expression]]s, it is expressible as [[2401/2400\|S49]]/([[25921/25920\|S161 = S46/S48]])<sup>2</sup>; in the 2.3.13.23 subgroup it factorizes into superparticulars as ([[3888/3887]])([[12168/12167]]).		'''279936/279841''', the '''kwadransma''' is a [[23-limit]] and 2.3.23 subgroup comma of about 0.59 cents. It is expressible as (6<sup>7</sup>)/(23<sup>4</sup>), therefore being the difference between [[6/1]] and four intervals of [[36/23]] - the small size of this comma representing the extreme accuracy of the 23rd harmonic in [[4ed6]] - or between [[8/3]] and four [[23/18]] thirds. This should be mentioned in relation to [[skwares]], which tempers out the comma [[19683/19208]], equating 8/3 to four intervals of [[9/7]]; tempering out 279936/279841 instead provides a far more accurate interpretation of the skwares generator (9/7[[~]][[14/11]]) as 23/18. In terms of [[S-expression]]s, it is expressible as [[2401/2400\|S49]]/([[25921/25920\|S161 = S46/S48]])<sup>2</sup>; in the 2.3.13.23 subgroup it factorizes into superparticulars as ([[3888/3887]])([[12168/12167]]).

	== Etymology ==		== Etymology ==

Lériendil at 05:14, 11 November 2024

2024-11-11T05:14:09Z

← Older revision		Revision as of 05:14, 11 November 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''279936/279841''', the '''kwadransma''', is a [[23-limit]] and 2.3.23 subgroup comma of about 0.59 cents. It is expressible as (6<sup>7</sup>)/(23<sup>4</sup>), therefore being the difference between [[6/1]] and four intervals of [[36/23]] - the small size of this comma representing the extreme accuracy of the 23rd harmonic in [[4ed6]] - or between [[8/3]] and four [[23/18]] thirds. This should be mentioned in relation to [[skwares]], which tempers out the comma [[19683/19208]], equating 8/3 to four intervals of [[9/7]]; tempering out 279936/279841 instead provides a far more accurate interpretation of the skwares generator (9/7[[~]][[14/11]]) as 23/18. In terms of [[S-expression]]s, it is expressible as [[2401/2400\|S49]]/([[25921/25920\|S161 = S46/S48]])<sup>2</sup>.		'''279936/279841''', the '''kwadransma''', is a [[23-limit]] and 2.3.23 subgroup comma of about 0.59 cents. It is expressible as (6<sup>7</sup>)/(23<sup>4</sup>), therefore being the difference between [[6/1]] and four intervals of [[36/23]] - the small size of this comma representing the extreme accuracy of the 23rd harmonic in [[4ed6]] - or between [[8/3]] and four [[23/18]] thirds. This should be mentioned in relation to [[skwares]], which tempers out the comma [[19683/19208]], equating 8/3 to four intervals of [[9/7]]; tempering out 279936/279841 instead provides a far more accurate interpretation of the skwares generator (9/7[[~]][[14/11]]) as 23/18. In terms of [[S-expression]]s, it is expressible as [[2401/2400\|S49]]/([[25921/25920\|S161 = S46/S48]])<sup>2</sup>; in the 2.3.13.23 subgroup it factorizes into superparticulars as ([[3888/3887]])([[12168/12167]]).

	== Etymology ==		== Etymology ==

Lériendil: Lériendil moved page 279936/279841 to Kwadransma

2024-11-10T09:27:27Z

Lériendil moved page 279936/279841 to Kwadransma

← Older revision	Revision as of 09:27, 10 November 2024
(No difference)

Lériendil: Created page with "{{Infobox Interval | Ratio = 279936/279841 | Name = kwadransma | Color name = Laquadtwethu comma | Comma = yes }} '''279936/279841''', the '''kwadransma''', is a 23-limit..."

2024-11-10T09:18:42Z

Created page with "{{Infobox Interval | Ratio = 279936/279841 | Name = kwadransma | Color name = Laquadtwethu comma | Comma = yes }} '''279936/279841''', the '''kwadransma''', is a 23-limit..."

New page

{{Infobox Interval
| Ratio = 279936/279841
| Name = kwadransma
| Color name = Laquadtwethu comma
| Comma = yes
}}
'''279936/279841''', the '''kwadransma''', is a [[23-limit]] and 2.3.23 subgroup comma of about 0.59 cents. It is expressible as (67)/(234), therefore being the difference between [[6/1]] and four intervals of [[36/23]] - the small size of this comma representing the extreme accuracy of the 23rd harmonic in [[4ed6]] - or between [[8/3]] and four [[23/18]] thirds. This should be mentioned in relation to [[skwares]], which tempers out the comma [[19683/19208]], equating 8/3 to four intervals of [[9/7]]; tempering out 279936/279841 instead provides a far more accurate interpretation of the skwares generator (9/7[[~]][[14/11]]) as 23/18. In terms of [[S-expression]]s, it is expressible as [[2401/2400|S49]]/([[25921/25920|S161 = S46/S48]])2.

== Etymology ==
This comma was named by Lériendil in 2024, with the root "quadrans" coming from the property of splitting 6/1 into fourths, and the spelling with <kw> being a deliberate reference to skwares, as kwadrans provides the skwares structure with much less damage at the price of a sparser subgroup.

== Temperaments ==
Tempering this out in the full 23-limit would lead to the rank-8 kwadransmic temperament, and in the 2.3.23 subgroup leads to the rank-2 '''kwadrans''' temperament.

== See also ==
* [[Squares]]
* [[Würschmidt]]

[[Category:Commas named for their regular temperament properties]]