26-comma

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]\text{ddd}{-2}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	82.209
Weil height (log2 max(n, d))	82.4181
Wilson height (sopfr(nd))	160
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.22806 bits
Comma size	large
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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.