Hypovishnuzma
Ratio | 254803968/244140625 |
Factorization | 2^{20} × 3^{5} × 5^{-12} |
Monzo | [20 5 -12⟩ |
Size in cents | 74.010438¢ |
Name | hypovishnuzma |
Color name | saquadtrigu 4th, sg^{12}4 |
FJS name | [math]\text{6d4}_{5,5,5,5,5,5,5,5,5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 55.7879 |
Weil height (log_{2} max(n, d)) | 55.8496 |
Wilson height (sopfr (nd)) | 115 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.34143 bits |
Comma size | medium |
open this interval in xen-calc |
The hypovishnuzma (ratio: 254803968/244140625, monzo: [20 5 -12⟩) is a medium 5-limit comma, which is the difference between a stack of six classic chromatic semitones (25/24) and a perfect fourth (4/3), that is, (4/3)/(25/24)^{6}, or simply the octave-reduced difference between five 3/2 perfect fifths and twelve 5/4 major thirds. In terms of commas, it is the difference between a stack of two dieses (128/125) and a kleisma (15625/15552). This comma is larger than 25/24 itself, but if one more 25/24 is removed from the hypovishnuzma, we get the regular vishnuzma.
Temperaments
Tempering it out in the 5-limit and 7-limit leads to the Thuja temperament. 15, 28, 43, 58, 73, and 101 are the only edos that temper out this comma whose patent vals are unenfactored. Although 129edo inherits its patent val from 43edo (thus enfactored), 129 is the last integer patent val to temper out the hypovishnuzma, and curiously, also the last integer patent val to temper out 81/80, the syntonic comma.