Quartisma

The quartisma is an unnoticeable 11-limit comma with a ratio of 117440512/117406179 and a value of approximately 0.5 cents. It is significant on account of it being the interval between a stack of five 33/32 quartertones and one 7/6 subminor third in just intonation – this significance in relation to quartertones being the source of its name.

Interval information

Ratio	117440512/117406179
Factorization	224 × 3-6 × 7 × 11-5
Monzo	[24 -6 0 1 -5⟩
Size in cents	0.5061895¢
Name	quartisma
Color name	Saquinlu-azo comma
FJS name	[math]\displaystyle{ \text{m3}^{7}_{11,11,11,11,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	53.6143
Weil norm (log2 max(n, d))	53.6147
Wilson norm (sopfr(nd))	128
Comma size	unnoticeable
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Temperaments

Tempering out this comma in the 11-limit leads to the quartismic temperament (→ Catalog of rank-4 temperaments #Quartismic (117440512/117406179)), or in the 2.3.7.11 subgroup, the quartic temperament. For a list of temperaments that temper it out, see The Quartercache.

Etymology

This comma was named by Aura in 2020.