105/104
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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 (log_{2} nd) | 13.4147 |
Weil height (log_{2} 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.