Vishnu comma: Difference between revisions

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The '''vishnuzma''' or '''semisuper comma''' ([[ratio]]: ~~6115295232~~/~~6103515625~~, [[monzo]]: {{monzo| 23 6 -14 }}) of 3.~~338~~ [[cent]]s, is the amount by which seven [[25/24|classical chromatic semitones]] ~~fall~~ short of a ~~just perfect fourth and also by which fourteen~~ [[5/4~~|classical major thirds]] miss the [[729~~/~~512~~|~~pythagorean augmented~~ fourth]]; in other words the interval (4/3)/(25/24)<sup>7</sup>.

The '''vishnu comma''', '''vishnuzma''' or '''semisuper comma''' ([[ratio]]: 6 115 295 232 / 6 103 515 625, [[monzo]]: {{monzo| 23 6 -14 }}), is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 3.34 [[cent]]s. It is the amount by which a stack of seven [[25/24|classical chromatic semitones]] falls short of a [[4/3|just perfect fourth]], in other words the interval (4/3)/(25/24)<sup>7</sup>. Equivalently, it is the amount by which a stack of fourteen [[5/4|classical major thirds]] misses the [[729/512|Pythagorean augmented fourth]].

== Temperaments ==

Tempering out this comma leads to ~~temperaments of~~ the [[~~vishnuzmic~~ family]].

[[Tempering out]] this comma leads to the 5-limit [[vishnu]] temperament.

See [[Vishnu family]] for the [[family]] of rank-2 temperaments where it is tempered out.

== Etymology ==

This comma was named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''semisuper'', for one possible generator of the temperament was a "semisuper fourth"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>. ''Semisuper comma'' appeared shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>. It is yet ~~to be found out~~ how and why the later ~~name~~ ''vishnuzma'' ~~was~~ added.

This comma was first named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''semisuper'', for one possible generator of the temperament was a "semisuper fourth"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>. ''Semisuper comma'' appeared shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>. It is not clear yet how and why the later names ''vishnu'' (for the temperament) and ''vishnuzma'' (for the comma) were added.

== ~~Notes~~ ==

== References ==

[[Category:~~Vishnuzmic~~]]

[[Category:Vishnu]]

[[Category:Commas with unknown etymology]]

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 | Comma = yes
 }}
-The '''vishnuzma''' or '''semisuper comma''' ([[ratio]]: 6115295232/6103515625, [[monzo]]: {{monzo| 23 6 -14 }}) of 3.338 [[cent]]s, is the amount by which seven [[25/24|classical chromatic semitones]] fall short of a just perfect fourth and also by which fourteen [[5/4|classical major thirds]] miss the [[729/512|pythagorean augmented fourth]]; in other words the interval (4/3)/(25/24)<sup>7</sup>.
+The '''vishnu comma''', '''vishnuzma''' or '''semisuper comma''' ([[ratio]]: 6 115 295 232 / 6 103 515 625, [[monzo]]: {{monzo| 23 6 -14 }}), is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 3.34 [[cent]]s. It is the amount by which a stack of seven [[25/24|classical chromatic semitones]] falls short of a [[4/3|just perfect fourth]], in other words the interval (4/3)/(25/24)<sup>7</sup>.  Equivalently, it is the amount by which a stack of fourteen [[5/4|classical major thirds]] misses the [[729/512|Pythagorean augmented fourth]].
 == Temperaments ==
-Tempering out this comma leads to temperaments of the [[vishnuzmic family]].
+[[Tempering out]] this comma leads to the 5-limit [[vishnu]] temperament.
+See [[Vishnu family]] for the [[family]] of rank-2 temperaments where it is tempered out.
 == Etymology ==
-This comma was named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''semisuper'', for one possible generator of the temperament was a "semisuper fourth"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>. ''Semisuper comma'' appeared shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>. It is yet to be found out how and why the later name ''vishnuzma'' was added.
+This comma was first named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''semisuper'', for one possible generator of the temperament was a "semisuper fourth"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>. ''Semisuper comma'' appeared shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>. It is not clear yet how and why the later names ''vishnu'' (for the temperament) and ''vishnuzma'' (for the comma) were added.
-== Notes ==
+== References ==
-[[Category:Vishnuzmic]]
+[[Category:Vishnu]]
 [[Category:Commas with unknown etymology]]