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 height (log2 nd)	46.4088
Weil height (log2 max(n, d))	46.4386
Wilson height (sopfr(nd))	94
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.52137 bits
Comma size	medium
Open this interval in xen-calc

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 3/2 by, and also the amount by which a stack of ten 5/3's octave-reduced exceeds 81/64.

Temperaments

Tempering out this interval leads to the fifive family of temperaments, 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, simply known as fifive.

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.