729/728

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 729/728
Factorization 2-3 × 36 × 7-1 × 13-1
Monzo [-3 6 0 -1 0 -1
Size in cents 2.376437¢
Name squbema
Color name L3ur-2, lathuru negative 2nd
FJS name [math]\text{d}{-2}_{7,13}[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 19.0176
Weil height (log2 max(n, d)) 19.0196
Wilson height (sopfr (nd)) 44
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.42293 bits
Comma size unnoticeable
S-expression S27
open this interval in xen-calc

The squbema, 729/728, is a 13-limit superparticular comma measuring about 2.4 ¢. It often arises as the difference between simpler commas: (225/224)/(325/324), (243/242)/(364/363), (351/350)/(676/675), (540/539)/(2080/2079). It factors into (1575/1573)(9801/9800) as well as (2200/2197)(123201/123200).

Tempering out this comma in the 13-limit leads to the rank-5 squbemic temperament, and enables squbemic chords. It is tempered out by several notable edos including 41edo, 72edo and 313edo among others, as well as by the 13-limit amity temperament.