4000/3993

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Interval information
Ratio 4000/3993
Factorization 25 × 3-1 × 53 × 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 (log2 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.