Vishnu comma

The vishnu comma, vishnuzma or semisuper comma (ratio: 6 115 295 232 / 6 103 515 625, monzo: [23 6 -14⟩), is an unnoticeable 5-limit comma measuring about 3.34 cents. It is the amount by which a stack of seven classical chromatic semitones falls short of a just perfect fourth, in other words the interval (4/3)/(25/24)⁷. Equivalently, it is the amount by which a stack of fourteen classical major thirds misses the Pythagorean augmented fourth.

Interval information

Ratio	6115295232/6103515625
Factorization	223 × 36 × 5-14
Monzo	[23 6 -14⟩
Size in cents	3.338011¢
Names	vishnu comma, vishnuzma, semisuper comma
Color name	sg144, sasepbigu 4th
FJS name	[math]\displaystyle{ \text{7d4}_{5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	65.0168
Weil norm (log2 max(n, d))	65.0196
Wilson norm (sopfr(nd))	134
Comma size	unnoticeable
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Temperaments

Tempering out this comma leads to the 5-limit vishnu temperament.

See Vishnu family for the family of rank-2 temperaments where it is tempered out.

Etymology

This comma was first named by Gene Ward Smith in 2001 in terms of the corresponding temperament, semisuper, for one possible generator of the temperament was a "semisuper fourth". Semisuper comma appeared shortly after. It is not clear yet how and why the later names vishnu (for the temperament) and vishnuzma (for the comma) were added.