343/324
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Ratio | 343/324 |
Factorization | 2^{-2} × 3^{-4} × 7^{3} |
Monzo | [-2 -4 0 3⟩ |
Size in cents | 98.657716¢ |
Name | gamelismic minor second |
Color name | z^{3}3, trizo 3rd |
FJS name | [math]\text{d3}^{7,7,7}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 16.7619 |
Weil height (log_{2} 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 | S7^{2} × 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.
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.