4000/3993

Interval information

Ratio	4000/3993
Factorization	25 × 3-1 × 53 × 11-3
Monzo	[5 -1 3 0 -3⟩
Size in cents	3.032314¢
Name	wizardharry comma
Color name	1u3y31, triluyo unison, Triluyo comma
FJS name	[math]\displaystyle{ \text{AA1}^{5,5,5}_{11,11,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	23.929
Weil norm (log2 max(n, d))	23.9316
Wilson norm (sopfr(nd))	61
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.