Horwell comma
| Ratio | 65625/65536 |
| Factorization | 2-16 × 3 × 55 × 7 |
| Monzo | [-16 1 5 1⟩ |
| Size in cents | 2.3494767¢ |
| Name | horwell comma |
| Color name | Lzy5-2, Lazoquinyo negative 2nd |
| FJS name | [math]\text{dd}{-2}^{5,5,5,5,5,7}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 32.002 |
| Weil height (log2 max(n, d)) | 32.0039 |
| Wilson height (sopfr(nd)) | 67 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.25051 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.