Wizma
(Redirected from 420175/419904)
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| 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{nd}[/math]) |
~1.21075 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.