105/104

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Interval information
Ratio 105/104
Factorization 2-3 × 3 × 5 × 7 × 13-1
Monzo [-3 1 1 1 0 -1
Size in cents 16.566959¢
Names animist comma,
small tridecimal comma
Color name 3uzy1, thuzoyo unison,
Thuzoyo comma
FJS name [math]\text{A1}^{5,7}_{13}[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 13.4147
Weil height (log2 max(n, d)) 13.4285
Wilson height (sopfr (nd)) 34
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~3.23913 bits
Comma size small
S-expression S14 × S15
open this interval in xen-calc

105/104, the animist comma, is a 13-limit small comma. It arises in several places in 13-limit just intonation, most notably as the difference between 15/8 and 13/7, between 8/5 and 21/13, between 8/7 and 15/13, and between 21/16 and 13/10 (and their octave complements, i.e. between 16/15 and 14/13, between 5/4 and 26/21, between 7/4 and 26/15, and between 32/21 and 20/13).

Being a triangle superparticular, it factors neatly into (196/195)(225/224).

Temperaments

Tempering out this comma leads to a form of animist temperament. An obvious further temperament is to temper out 196/195 and/or 225/224, equating 15/14 with 14/13~16/15. This in the 2.3.5.7.13 subgroup is an extension of marvel and a restriction of tripod.

See also