Hypovishnuzma

Interval information

Ratio	254803968/244140625
Factorization	220 × 35 × 5-12
Monzo	[20 5 -12⟩
Size in cents	74.01044¢
Name	hypovishnuzma
Color name	saquadtrigu 4th, sg124
FJS name	[math]\text{6d4}_{5,5,5,5,5,5,5,5,5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	55.7879
Weil height (log2 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.