From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 343/324
Factorization 2-2 × 3-4 × 73
Monzo [-2 -4 0 3
Size in cents 98.657716¢
Name gamelismic minor second
Color name z33, trizo 3rd
FJS name [math]\text{d3}^{7,7,7}[/math]
Special properties reduced
Tenney height (log2 nd) 16.7619
Weil height (log2 max(n, d)) 16.8441
Wilson height (sopfr (nd)) 37
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.29401 bits
Comma size medium
S-expression S72 × S8
open this interval in xen-calc

343/324 is a semitone-sized interval, defined as the difference between a stack of two 7/6 subminor thirds and a 9/7 supermajor third, making it a form of septimal diminished third. It is a gamelisma (1029/1024) above the Pythagorean minor second of 256/243, and is extremely close to 18/17, differing from it by the unnoticeable comma of 5832/5831.


Tempering it out equates a stack of three 7/6 subminor thirds with a 3/2 perfect fifth. While this is an unusual comma to temper, being nearly 100 cents in size, it is tempered out in blacksmith.

See also