4000/3993
Ratio | 4000/3993 |
Factorization | 2^{5} × 3^{-1} × 5^{3} × 11^{-3} |
Monzo | [5 -1 3 0 -3⟩ |
Size in cents | 3.0323136¢ |
Name | wizardharry comma |
Color name | Triluyo comma |
FJS name | [math]\text{AA1}^{5,5,5}_{11,11,11}[/math] |
Special properties | reduced |
Tenney height (log_{2} n⋅d) | 23.929 |
Weil height (max(n, d)) | 4000 |
Benedetti height (n⋅d) | 15972000 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.43786 bits |
Comma size | unnoticeable |
S-expression | S10 / S11 |
open this interval in xen-calc |
4000/3993, the wizardharry comma, is an unnoticeable 11-limit comma with a size of roughly 3.03 cents. It is the amount by which a stack of three 11/10 submajor seconds falls short of the 4/3 perfect fourth.
In terms of commas, it is the difference between 100/99 and 121/120, and between 540/539 and 9801/9800. It factors into 13-limit commas as (1575/1573)(2080/2079) or (625/624)(6656/6655).
Temperaments
Tempering it out means the fourth is divided into an equal stepped tetrachord, however, it does this by means equating a stack of three 11/10 intervals with 4/3, rather than by equating three 10/9 whole tones with 4/3 as in the porcupine family of temperaments, although 11-limit porcupine does both as 11/10 and 10/9 are equated. Tempering it out along with the schisma results in the rank-2 tertiaschis temperament.