Horwell comma

Interval information

Ratio	65625/65536
Factorization	2-16 × 3 × 55 × 7
Monzo	[-16 1 5 1⟩
Size in cents	2.349477¢
Name	horwell comma
Color name	Lzy5-2, Lazoquinyo negative 2nd
FJS name	[math]\displaystyle{ \text{dd}{-2}^{5,5,5,5,5,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	32.002
Weil norm (log2 max(n, d))	32.0039
Wilson norm (sopfr(nd))	67
Comma size	unnoticeable
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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. It is also the amount by which the difference between 32/25 and 75/64 falls short of 35/32.

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. It is not clear how it later became horwell, but the root of horwell is obvious, being a contraction of hemithirds and orwell.