Linus comma

Interval information

Ratio	578509309952/576650390625
Factorization	211 × 3-10 × 5-10 × 710
Monzo	[11 -10 -10 10⟩
Size in cents	5.5719174¢
Name	linus comma
Color name	sz10g108, saquinbizogu octave
FJS name	[math]\text{10d8}^{7,7,7,7,7,7,7,7,7,7}_{5,5,5,5,5,5,5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	78.1425
Weil height (log2 max(n, d))	78.1471
Wilson height (sopfr(nd))	172
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.48456 bits
Comma size	small
open this interval in xen-calc

The linus comma (monzo: [11 -10 -10 10⟩) is a small 7-limit comma measuring about 5.57 ¢. It is the difference between a stack of 10 15/14's and the octave.

Temperaments

Tempering out this comma alone in the 7-limit results in the rank-3 linus temperament. Edos not divisible by 10 cannot temper it out. For technical details see Kalismic temperaments #Linus.

Etymology

The name linus was given by Gene Ward Smith in 2011, referring to the fact that it is a "line comma" since the simplest comma pump will simply march along a line of the tetrad lattice.

A 2016 article on this wiki by Mason Green, not aware of this comma already having been named, dubbed it the higherlovesma, and the corresponding rank-3 temperament winwood.