Kwadransma

Interval information

Ratio	279936/279841
Subgroup monzo	2.3.23 [7 7 -4⟩
Size in cents	0.587617¢
Name	kwadransma
Color name	Laquadtwethu comma
FJS name	[math]\text{dd3}_{23,23,23,23}[/math]
Special properties	reduced
Tenney height (log2 nd)	36.189
Weil height (log2 max(n, d))	36.1895
Wilson height (sopfr(nd))	127
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20143 bits
Comma size	unnoticeable
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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-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.

See also

• Squares
• Würschmidt