Negri comma
| Interval information |
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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. 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