From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 1331/1296
Factorization 2-4 × 3-4 × 113
Monzo [-4 -4 0 0 3
Size in cents 46.133824¢
Names Alpharabian parachromatic semilimma,
Alpharabian semilimmic ultraprime
Color name 1o31, trilo 1sn, Trilo comma
FJS name [math]\text{d1}^{11,11,11}[/math]
Special properties reduced
Tenney height (log2 nd) 20.7181
Weil height (log2 max(n, d)) 20.7566
Wilson height (sopfr (nd)) 53
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.78055 bits
open this interval in xen-calc

1331/1296, the Alpharabian parachromatic semilimma or Alpharabian semilimmic ultraprime, is a quartertone in the 11-limit, specifically the 2.3.11 subgroup, that differs from the simpler 33/32 by the rastma, and is also the interval separating 81/64 and 1331/1024. It is of further note that this interval is only just slightly more than half of 256/243- the Pythagorean limma- being separated from the nearby 4096/3993, the interval forming the other part of the Pythagorean limma, by the nexus comma.