13/12
(Redirected from 13 12)
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| Ratio | 13/12 |
| Factorization | 2-2 × 3-1 × 13 |
| Monzo | [-2 -1 0 0 0 1⟩ |
| Size in cents | 138.57266¢ |
| Name | (lesser) tridecimal neutral second |
| Color name | 3o2, tho 2nd |
| FJS name | [math]\text{m2}^{13}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 7.2854 |
| Weil height (log2 max(n, d)) | 7.40088 |
| Wilson height (sopfr (nd)) | 20 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.60326 bits |
[sound info] | |
| open this interval in xen-calc | |
In 13-limit just intonation, 13/12 is the (lesser) tridecimal neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).
The neutral second in 17edo is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.