Skwares comma

Interval information

Ratio	19683/19208
Factorization	2-3 × 39 × 7-4
Monzo	[-3 9 0 -4⟩
Size in cents	42.29138¢
Name	skwares comma
Color name	Laquadru comma
FJS name	[math]\text{dd}{-3}_{7,7,7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	28.4941
Weil height (log2 max(n, d))	28.5293
Wilson height (sopfr(nd))	61
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.51414 bits
Comma size	medium
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19683/19208, the skwares comma, is a 7-limit and 2.3.7 subgroup comma of about 42 cents. It can be defined as the difference between a perfect eleventh (8/3) and a stack of four 9/7 supermajor thirds. In the 2.3.7.11 subgroup, it decomposes into (99/98)² × 243/242, and in the full 7-limit, it decomposes as (81/80)²/(2401/2400).

In the 2.3.7 subgroup, this comma defines skwares temperament, whose obvious extensions to primes 5 (squares) and 11 are dictated by the above decompositions.

See also

• Squares