Kwadransma: Difference between revisions
m Lériendil moved page 279936/279841 to Kwadransma |
No edit summary |
||
| 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 == | ||
Revision as of 05:14, 11 November 2024
| Interval information |
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-expressions, it is expressible as S49/(S161 = S46/S48)2; in the 2.3.13.23 subgroup it factorizes into superparticulars as (3888/3887)(12168/12167).
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.