91/90
| Interval information |
superleap comma
Thozogu comma
reduced
(Shannon, [math]\sqrt{nd}[/math])
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
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Todo: research, add etymology Add etymology for “biome”. |