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]].

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.

== Temperaments ==

Tempering it out leads to the '''[[Thuja]]''' temperament. {{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 ==~~

* [[High badness temperaments#Hypovishnu]].

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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]].
-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.
+== Temperaments ==
+Tempering it out leads to the '''[[Thuja]]''' temperament. {{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 ==
-* [[High badness temperaments#Hypovishnu]].