Hypovishnuzma: Difference between revisions
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The '''hypovishnuzma''' ([[ratio]]: 254803968/244140625, {{monzo|legend=1| 20 5 -12 }}) is a [[medium comma|medium]] [[5-limit]] [[comma]], which is the difference between a stack of six [[25/24|classic chromatic semitones (25/24)]] and a [[4/3|perfect fourth (4/3)]], that is, (4/3)/(25/24)<sup>6</sup>, 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 [[128/125|dieses (128/125)]] and a [[15625/15552|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]]. | The '''hypovishnuzma''' ([[ratio]]: 254803968/244140625, {{monzo|legend=1| 20 5 -12 }}) is a [[medium comma|medium]] [[5-limit]] [[comma]], which is the difference between a stack of six [[25/24|classic chromatic semitones (25/24)]] and a [[4/3|perfect fourth (4/3)]], that is, (4/3)/(25/24)<sup>6</sup>, 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 [[128/125|dieses (128/125)]] and a [[15625/15552|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]]. | ||
Tempering it out leads to a temperament known as ''' | Tempering it out leads to a temperament known as '''[[Thuja]]'''. {{EDOs|15, 28, 43, 58, 73, and 101}} are the only [[edo]]s that temper out this comma whose [[patent val]]s are [[enfactoring|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. | ||
== See also == | == See also == | ||
* [[High badness temperaments#Hypovishnu]]. | * [[High badness temperaments#Hypovishnu]]. | ||
Revision as of 18:10, 1 June 2024
| Interval information |
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.
Tempering it out leads to a temperament known as Thuja. 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.