105/104

Interval information

Ratio	105/104
Factorization	2-3 × 3 × 5 × 7 × 13-1
Monzo	[-3 1 1 1 0 -1⟩
Size in cents	16.56696¢
Names	animist comma, small tridecimal comma
Color name	3uzy1, thuzoyo unison, Thuzoyo comma
FJS name	[math]\displaystyle{ \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
Comma size	small
S-expression	S14 × S15
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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

• List of superparticular intervals