Negri comma
(Redirected from 16875/16384)
Jump to navigation
Jump to search
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} n⋅d) | 28.0426 |
Weil height (max(n, d)) | 16875 |
Benedetti height (n⋅d) | 276480000 |
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.