Negri comma: Difference between revisions

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'''16875/16384''' is the 51.120 [[cent]] interval called the '''negri comma''' or double augmentation diesis. It is the amount by which four major thirds exceed three fourths, that is, ([[5/4]])4/([[4/3]])3, and is also the amount by which three [[16/15|diatonic semitones (16/15)]] fall short of a major third, that is, (5/4)/(16/15)3. It factors into simpler commas as ([[81/80]])([[3125/3072]]), the syntonic comma and the magic comma. Tempering it out leads to [[5-limit]] [[negri]] temperament, which is closely associated with [[19edo]].

'''16875/16384''' is the 51.120 [[cent]] interval called the '''negri comma''' or double augmentation diesis. It is the amount by which four classical major thirds exceed three fourths, that is, ([[5/4]])4/([[4/3]])3, and is also the amount by which three [[16/15|diatonic semitones (16/15)]] fall short of a classical major third, that is, (5/4)/(16/15)3. Another characterization of this comma is the difference between the [[256/243|Pythagorean limma (256/243)]] and a stack of two [[25/24|classical chromas (25/24)]].

It factors into simpler commas as ([[81/80]])⋅([[3125/3072]]), the syntonic comma and the magic comma. In the [[7-limit]], it factors into ([[225/224]])⋅([[525/512]]), (225/224)2⋅([[49/48]]), or (225/224)3⋅([[686/675]]).

== Temperaments ==

Tempering it out leads to [[5-limit]] [[negri]] temperament, which is closely associated with [[19edo]].

== Etymology ==

The corresponding temperament was discovered first, dubbed ''negri'' by [[Paul Erlich]] in ~~early 2002~~<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning~~-math~~/~~topicId_3774~~.html#~~3813~~ Yahoo! Tuning Group | ''~~25 best weighted generator steps 5~~-limit ~~temperaments~~'']</ref>. The comma was at one point dubbed ''negrisma'' by [[Gene Ward Smith]] in late 2002, though it was ''negri comma'' that stuck<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.

The corresponding temperament was discovered first, dubbed ''negri'' by [[Paul Erlich]] in late 2001<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_31054.html#31065 Yahoo! Tuning Group | ''The grooviest linear temperaments for 7-limit music'']</ref> after John Negri's 10-out-of-19 maximally even scale<ref>"The Nineteen-Tone System as Ten Plus Nine". [https://interval.xentonic.org/tables-of-contents.html ''Interval, Journal of Music Research and Development''], pp. 11–13 of Volume 5, Number 3 (Winter 1986–1987). John Negri. </ref>. The comma was at one point dubbed ''negrisma'' by [[Gene Ward Smith]] in late 2002, though it was ''negri comma'' that stuck<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.

== See also ==

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[[Category:Negri]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

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-'''16875/16384''' is the 51.120 [[cent]] interval called the '''negri comma''' or double augmentation diesis. It is the amount by which four major thirds exceed three fourths, that is, ([[5/4]])<sup>4</sup>/([[4/3]])<sup>3</sup>, and is also the amount by which three [[16/15|diatonic semitones (16/15)]] fall short of a major third, that is, (5/4)/(16/15)<sup>3</sup>. It factors into simpler commas as ([[81/80]])([[3125/3072]]), the syntonic comma and the magic comma. Tempering it out leads to [[5-limit]] [[negri]] temperament, which is closely associated with [[19edo]].
+'''16875/16384''' is the 51.120 [[cent]] interval called the '''negri comma''' or double augmentation diesis. It is the amount by which four classical major thirds exceed three fourths, that is, ([[5/4]])<sup>4</sup>/([[4/3]])<sup>3</sup>, and is also the amount by which three [[16/15|diatonic semitones (16/15)]] fall short of a classical major third, that is, (5/4)/(16/15)<sup>3</sup>. Another characterization of this comma is the difference between the [[256/243|Pythagorean limma (256/243)]] and a stack of two [[25/24|classical chromas (25/24)]].
+It factors into simpler commas as ([[81/80]])⋅([[3125/3072]]), the syntonic comma and the magic comma. In the [[7-limit]], it factors into ([[225/224]])⋅([[525/512]]), (225/224)<sup>2</sup>⋅([[49/48]]), or (225/224)<sup>3</sup>⋅([[686/675]]).
+== Temperaments ==
+Tempering it out leads to [[5-limit]] [[negri]] temperament, which is closely associated with [[19edo]].
 == Etymology ==
-The corresponding temperament was discovered first, dubbed ''negri'' by [[Paul Erlich]] in early 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3774.html#3813 Yahoo! Tuning Group | ''25 best weighted generator steps 5-limit temperaments'']</ref>. The comma was at one point dubbed ''negrisma'' by [[Gene Ward Smith]] in late 2002, though it was ''negri comma'' that stuck<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.
+The corresponding temperament was discovered first, dubbed ''negri'' by [[Paul Erlich]] in late 2001<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_31054.html#31065 Yahoo! Tuning Group | ''The grooviest linear temperaments for 7-limit music'']</ref> after John Negri's 10-out-of-19 maximally even scale<ref>"The Nineteen-Tone System as Ten Plus Nine". [https://interval.xentonic.org/tables-of-contents.html  ''Interval, Journal of Music Research and Development''], pp. 11–13 of Volume 5, Number 3 (Winter 1986–1987). John Negri. </ref>. The comma was at one point dubbed ''negrisma'' by [[Gene Ward Smith]] in late 2002, though it was ''negri comma'' that stuck<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.
 == See also ==
@@ Line 16: / Line 21: @@
 [[Category:Negri]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]