Wizma
(Redirected from 420175/419904)
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Ratio | 420175/419904 |
Factorization | 2^{-6} × 3^{-8} × 5^{2} × 7^{5} |
Monzo | [-6 -8 2 5⟩ |
Size in cents | 1.1169532¢ |
Name | wizma |
Color name | z^{5}yy3, quinzo-ayoyo 3rd |
FJS name | [math]\text{d3}^{5,5,7,7,7,7,7}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 37.3603 |
Weil height (log_{2} 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.
Temperaments
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.