91/90: Difference between revisions

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The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma]] of about 19 cents.
The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of about 19 [[cent]]s. 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 complement]]s, 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]]).  


For temperaments eliminating this comma, see also [[The Biosphere]].
== Temperaments ==
For temperaments eliminating this comma, see [[The Biosphere]].
 
== See also ==
* [[List of superparticular intervals]]

Revision as of 04:49, 13 March 2024

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 height (log2 nd) 12.9996
Weil height (log2 max(n, d)) 13.0156
Wilson height (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 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).

Temperaments

For temperaments eliminating this comma, see The Biosphere.

See also