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Interval information
Ratio 91/90
Factorization 2-1 × 3-2 × 5-1 × 7 × 13
Monzo [-1 -2 -1 1 0 1
Size in cents 19.129853¢
Names biome comma,
superleap comma
Color name 3ozg2, thozogu 2nd,
Thozogu comma
FJS name [math]\text{d2}^{7,13}_{5}[/math]
Special properties superparticular,
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 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).


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 subgroup results in the sengic temperament.


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

See also