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]])<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>. Tempering it out leads to [[5-limit]] [[negri]] temperament, which is closely associated with [[19edo]]. | {{Infobox Interval | ||
| Ratio = 16875/16384 | |||
| Name = negri comma | |||
| Color name = Ly<sup>4</sup>-2, Laquadyo comma | |||
| Comma = yes | |||
}} | |||
'''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 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 == | == See also == | ||
* [[Medium comma]] | * [[Medium comma]] | ||
== Notes == | |||
[[Category:Negri]] | [[Category:Negri]] | ||
[[Category:Commas named after composers]] | |||
[[Category:Commas named after music theorists]] | |||
Latest revision as of 10:15, 13 April 2026
| Interval information |
reduced harmonic
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 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 Pythagorean limma (256/243) and a stack of two 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 late 2001[1] after John Negri's 10-out-of-19 maximally even scale[2]. The comma was at one point dubbed negrisma by Gene Ward Smith in late 2002, though it was negri comma that stuck[3][4].
See also
Notes
- ↑ Yahoo! Tuning Group | The grooviest linear temperaments for 7-limit music
- ↑ "The Nineteen-Tone System as Ten Plus Nine". Interval, Journal of Music Research and Development, pp. 11–13 of Volume 5, Number 3 (Winter 1986–1987). John Negri.
- ↑ Yahoo! Tuning Group | 5-limit comma names
- ↑ Yahoo! Tuning Group | Ultimate 5-limit comma list