26-comma

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information

Ratio	2541865828329/2199023255552
Factorization	2-41 × 326
Monzo	[-41 26⟩
Size in cents	250.83 ¢
Names	26-comma, Pythagorean inverse triple-diminished second
Color name	Wa-26, L4w-2
FJS name	[math]\displaystyle{ \text{ddd}{-2} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	82.209
Weil norm (log2 max(n, d))	82.4181
Wilson norm (sopfr(nd))	160
Comma size	large
Open this interval in xen-calc

The 26-comma is a 3-limit semifourth that acts as a comma in certain temperaments. It is the difference between 26 perfect fifths and 15 octaves, as well as being two Pythagorean commas sharp of 9/8.

While it is exceptionally large for a comma (two of them make a near-perfect fourth, off by the small 53-comma), it is tempered out in 26edo, because of that temperament's narrow fifths.

Used as an interval in its own right, it is the Pythagorean inverse triple-diminished second. It approximates intervals like 15/13, and is the simplest Pythagorean interval of this size. As such, it could also be known as the Pythagorean semifourth.