91/90

Interval information

Ratio	91/90
Factorization	2-1 × 3-2 × 5-1 × 7 × 13
Monzo	[-1 -2 -1 1 0 1⟩
Size in cents	19.12985¢
Names	biome comma, superleap comma
Color name	3ozg2, thozogu 2nd, Thozogu comma
FJS name	[math]\displaystyle{ \text{d2}^{7,13}_{5} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	12.9996
Weil norm (log2 max(n, d))	13.0156
Wilson norm (sopfr(nd))	33
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 10/7, 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

Superleap is a contraction of superpyth and leapday, referring to the two rank-2 temperaments that temper out this comma.

The etymology for biome is unknown, but it is certainly related to biome and the Biosphere, which might be analogous to island temperament and the Archipelago.

See also

• List of superparticular intervals