Negri comma

From Xenharmonic Wiki
(Redirected from 16875/16384)
Jump to navigation Jump to search
Interval information
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,
reduced harmonic
Tenney height (log2 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.

See also