Horwell comma
Ratio | 65625/65536 |
Factorization | 2^{-16} × 3 × 5^{5} × 7 |
Monzo | [-16 1 5 1⟩ |
Size in cents | 2.3494767¢ |
Name | horwell comma |
Color name | Lzy^{5}-2, Lazoquinyo negative 2nd |
FJS name | [math]\text{dd}{-2}^{5,5,5,5,5,7}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 32.002 |
Weil height (log_{2} max(n, d)) | 32.0039 |
Wilson height (sopfr (nd)) | 67 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.42238 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
The horwell comma (monzo: [-16 1 5 1⟩, ratio: 65625/65536) is an unnoticeable 7-limit comma measuring about 2.35 cents. It is the difference between 32/21, the septimal superfifth, and a stack of five 5/4's octave reduced.
Temperaments
Tempering out this comma leads to the horwell temperament, where 32/21 can be found through a stack of five 5/4's and octave reduction. See Horwell family for the rank-3 family where it is tempered out. See Horwell temperaments for a collection of rank-2 temperaments where it is tempered out.
Etymology
This comma was first named as tertiapont by Gene Ward Smith in 2005 as a contraction of tertiaseptal and pontiac^{[1]}. It is not clear how it later became horwell, but the root of horwell is obvious, being a contraction of hemithirds and orwell.