91/90
| Ratio | 91/90 |
| Factorization | 2-1 × 3-2 × 5-1 × 7 × 13 |
| Monzo | [-1 -2 -1 1 0 1⟩ |
| Size in cents | 19.129853¢ |
| Names | biome comma, superleap comma |
| Color name | 3ozg2, thozogu 2nd, Thozogu comma |
| FJS name | [math]\text{d2}^{7,13}_{5}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 12.9996 |
| Weil height (log2 max(n, d)) | 13.0156 |
| Wilson height (sopfr (nd)) | 33 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~3.60893 bits |
| Comma size | small |
| S-expression | S13 × S14 |
| open this interval in xen-calc | |
The superparticular interval 91/90, the biome comma or superleap comma, is a small 13-limit comma of about 19 cents. It arises in several places in 13-limit just intonation, most notably as the difference between 13/12 and 15/14, between 13/9 and 7/5, between 7/6 and 15/13, and between 9/7 and 13/10 (and their octave complements, i.e. between 24/13 and 28/15, between 18/13 and 10/7, between 12/7 and 26/15, and between 14/9 and 20/13).
Being a triangle superparticular, it factors neatly into (169/168)(196/195).
Temperaments
Tempering out this comma in the full 13-limit results in the rank-5 biosphere temperament. See The Biosphere. An obvious further temperament is to temper out 169/168 and/or 196/195, equating 14/13 with 13/12~15/14. This in the 2.3.5.7.13 subgroup results in the sengic temperament.
Etymology
Observably, superleap is a contraction of superpyth and leapday, referring to the two rank-2 temperaments that temper out this comma.