1716/1715

Interval information

Ratio	1716/1715
Factorization	22 × 3 × 5-1 × 7-3 × 11 × 13
Monzo	[2 1 -1 -3 1 1⟩
Size in cents	1.009172¢
Name	lummic comma
Color name	3o1or3g-2, tholotriru-agu negative 2nd
FJS name	[math]\displaystyle{ \text{M}{-2}^{11,13}_{5,7,7,7} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	21.4888
Weil height (log2 max(n, d))	21.4897
Wilson height (sopfr(nd))	57
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.20773 bits
Comma size	unnoticeable
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The lummic comma, 1716/1715, is a 13-limit superparticular comma measuring about 1.0 ¢. It often arises as the difference between simpler commas: (176/175)/(196/195), (351/350)/(441/440), (1573/1568)/(385/384), (540/539)/(1575/1573), and (1001/1000)/(2401/2400). It factors into (2080/2079)(9801/9800).

Tempering it out leads to the rank-5 lummic temperament. It is tempered out by several notable edos including 72edo, 270edo and 400edo among others.

Etymology

This comma was named after Carl Lumma. Perhaps interestingly, a lummisma was first proposed by Gene Ward Smith in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better", which might ultimately led to this comma being named so.