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]\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{nd}[/math])	~3.63932 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 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.

See also

• List of superparticular intervals

Todo: research, add etymology Add etymology for “biome”.