343/324: Difference between revisions

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


== See also ==
== See also ==

Latest revision as of 15:16, 11 September 2025

Interval information
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]\displaystyle{ \text{d3}^{7,7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 16.7619
Weil norm (log2 max(n, d)) 16.8441
Wilson norm (sopfr(nd)) 37
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.

Temperaments

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

See also