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>. 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 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]].
== 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>.


== See also ==
== See also ==
* [[Negri]]
* [[Medium comma]]
* [[Medium comma]]
== Notes ==


[[Category:Negri]]
[[Category:Negri]]

Revision as of 06:59, 13 June 2023

Interval information
Ratio 16875/16384
Factorization 2-14 × 33 × 54
Monzo [-14 3 4
Size in cents 51.11986¢
Name negri comma
Color name Ly4-2, Laquadyo comma
FJS name [math]\displaystyle{ \text{dd}{-2}^{5,5,5,5} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 28.0426
Weil norm (log2 max(n, d)) 28.0852
Wilson norm (sopfr(nd)) 57
Comma size medium
Open this interval in xen-calc

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 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.

Etymology

The corresponding temperament was discovered first, dubbed negri by Paul Erlich in early 2002[1]. The comma was at one point dubbed negrisma by Gene Ward Smith in late 2002, though it was negri comma that stuck[2][3].

See also

Notes