1716/1715
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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]\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]\sqrt{nd}[/math])
~1.20773 bits
Comma size
unnoticeable
open this interval in xen-calc
| Interval information |
reduced
(Shannon, [math]\sqrt{nd}[/math])
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.