Canousma

Interval information

Ratio	4802000/4782969
Factorization	24 × 3-14 × 53 × 74
Monzo	[4 -14 3 4⟩
Size in cents	6.874755¢
Name	canousma
Color name	sz4y33, saquadzo-atriyo 3rd
FJS name	[math]\text{d3}^{5,5,5,7,7,7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	44.3847
Weil height (log2 max(n, d))	44.3904
Wilson height (sopfr(nd))	93
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.62813 bits
Comma size	small
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The canousma (monzo: [4 -14 3 4⟩, ratio: 4802000/4782969) is a 7-limit comma measuring about 6.9 cents. It is notable as the amount by which a stack of three instances of 81/70 falls short of 14/9. It is also the interval separating the syntonic comma (81/80) from a stack of two sensamagic commas (245/243).

Temperaments

Tempering it out leads to the canou family of rank-3 temperaments, which splits the syntonic comma into two equal parts, each representing 245/243. It also splits 5/4 (classic major third) into two equal parts, each representing 2450/2187~2187/1960. It is similar to hemimean in that regard. Tempering out both equates 245/243 with 126/125 (septimal semicomma) and 225/224 (septimal kleisma) leads to parakleismic.

See Canou family for the rank-3 family where it is tempered out. See Canousmic temperaments for a collection of rank-2 temperaments where it is tempered out.

Etymology

This comma was named by Flora Canou in 2020 after herself.

See also

• Small comma