Negri comma
Ratio | 16875/16384 |
Factorization | 2^{-14} × 3^{3} × 5^{4} |
Monzo | [-14 3 4⟩ |
Size in cents | 51.119858¢ |
Name | negri comma |
Color name | Ly^{4}-2, Laquadyo comma |
FJS name | [math]\text{dd}{-2}^{5,5,5,5}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 28.0426 |
Weil height (log_{2} max(n, d)) | 28.0852 |
Wilson height (sopfr (nd)) | 57 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.46216 bits |
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 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