Negri comma
| Ratio | 16875/16384 |
| Factorization | 2-14 × 33 × 54 |
| Monzo | [-14 3 4⟩ |
| Size in cents | 51.119858¢ |
| Name | negri comma |
| Color name | Ly4-2, Laquadyo comma |
| FJS name | [math]\text{dd}{-2}^{5,5,5,5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 28.0426 |
| Weil height (log2 max(n, d)) | 28.0852 |
| Wilson height (sopfr (nd)) | 57 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.77901 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