343/324
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Ratio
343/324
Factorization
2-2 × 3-4 × 73
Monzo
[-2 -4 0 3⟩
Size in cents
98.65772¢
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
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
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.
Temperaments
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.