Kwadransma: Difference between revisions

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'''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.

'''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; in the 2.3.13.23 subgroup it factorizes into superparticulars as ([[3888/3887]])([[12168/12167]]).

== Etymology ==

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-'''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 ==