33698267/33554432

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information

Ratio	33698267/33554432
Subgroup monzo	2.17.19 [-25 3 3⟩
Size in cents	7.405277¢
Name	sylvisma
Color name	latrinoso 3rd, L19o317o33
FJS name	[math]\displaystyle{ \text{ddd3}^{17,17,17,19,19,19} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	50.0062
Weil norm (log2 max(n, d))	50.0123
Wilson norm (sopfr(nd))	158
Comma size	small
Open this interval in xen-calc

}} 33698267/33554432, or the sylvisma^{[idiosyncratic term]}, is a small 19-limit comma of about 7.4 cents that is the difference between the stacking of three 323/256 major thirds and an octave. It is notably tempered out in 12edo and arsenic temperament.

Etymology

The name was coined by Zeta Function from the mineral sylvite, which is made of potassium chloride. Chloride is element 17, and potassium is element 19, so the name thus reflects in a roundabout way the prime factors that make up this comma.