From Xenharmonic Wiki
(Redirected from 420175/419904)
Jump to navigation Jump to search
Interval information
Ratio 420175/419904
Factorization 2-6 × 3-8 × 52 × 75
Monzo [-6 -8 2 5
Size in cents 1.1169532¢
Name wizma
Color name z5yy3, quinzo-ayoyo 3rd
FJS name [math]\text{d3}^{5,5,7,7,7,7,7}[/math]
Special properties reduced
Tenney height (log2 nd) 37.3603
Weil height (log2 max(n, d)) 37.3613
Wilson height (sopfr (nd)) 81
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.40283 bits
Comma size unnoticeable
open this interval in xen-calc

The wizma (monzo[-6 -8 2 5, ratio: 420175/419904) is an unnoticeable 7-limit comma measuring about 1.12 ¢. In terms of other commas, it is the difference between 245/243 and 1728/1715, and it is the sum of 2401/2400 and 4375/4374, the two smallest 7-limit superparticular commas.


Tempering out this comma alone in the 7-limit leads to the rank-3 wizmic temperament, where the septimal comma (64/63) is split into two equal parts, each for 245/243~1728/1715.

See Wizmic microtemperaments for a collection of rank-2 temperaments where it is tempered out.