1716/1715
Jump to navigation
Jump to search
| Ratio | 1716/1715 |
| Factorization | 22 × 3 × 5-1 × 7-3 × 11 × 13 |
| Monzo | [2 1 -1 -3 1 1⟩ |
| Size in cents | 1.0091717¢ |
| 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{n\cdot d}[/math]) |
~2.40185 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
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.