Linus comma
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Ratio | 578509309952/576650390625 |
Factorization | 2^{11} × 3^{-10} × 5^{-10} × 7^{10} |
Monzo | [11 -10 -10 10⟩ |
Size in cents | 5.5719174¢ |
Name | linus comma |
Color name | sz^{10}g^{10}8, 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 (log_{2} nd) | 78.1425 |
Weil height (log_{2} 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^{[1]}^{[2]}.
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.