Fifive comma

Interval information

Ratio	9765625/9565938
Factorization	2-1 × 3-14 × 510
Monzo	[-1 -14 10⟩
Size in cents	35.76713 ¢
Name	fifive comma
Color name	sy10-2, saquinbiyo negative 2nd
FJS name	[math]\displaystyle{ \text{ddd}{-2}^{5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	46.4088
Weil norm (log2 max(n, d))	46.4386
Wilson norm (sopfr(nd))	94
Comma size	medium
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The fifive comma is a medium 5-limit comma with a width of about a third of a semitone. It is the amount that a stack of five 27/25's falls short of the perfect fifth by, and also the amount by which a stack of ten 5/3's octave-reduced exceeds 81/64.

Temperaments

Tempering out this comma in the 5-limit leads to the fifive temperament, where the perfect fifth is divided into five equal parts and the octave is split in half. 26edo and 34edo are two notable examples of edos that support the basic 5-limit temperament in this family.

See Fifive family for the family of temperaments where it is tempered out.

Etymology

This comma was named by Petr Pařízek in 2011 in terms of the corresponding temperament, fifives, for the temperament splits the perfect fifth in five. It is not clear when it lost an s.