Passion comma
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Ratio | 262144/253125 |
Factorization | 2^{18} × 3^{-4} × 5^{-5} |
Monzo | [18 -4 -5⟩ |
Size in cents | 60.611427¢ |
Name | passion comma |
Color name | saquingu 3rd, sg^{5}3 |
FJS name | [math]\text{ddd3}_{5,5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 35.9495 |
Weil height (log_{2} max(n, d)) | 36 |
Wilson height (sopfr (nd)) | 73 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.39146 bits |
Comma size | medium |
open this interval in xen-calc |
The passion comma (ratio: 262144/253125, monzo: [18 -4 -5⟩, is a medium 5-limit comma measuring about 60.6 cents. It is the amount by which a stack of five classical minor seconds (16/15) exceeds the perfect fourth (4/3). According to an analysis in The Harmonic Experience by W. A. Mathieu, Beethoven's Appassionata sonata pumps this comma, leading to its name passion as was given by Paul Erlich in 2004^{[1]}^{[2]}.
Temperaments
Tempering out this comma leads to the 5-limit passion temperament. See Passion family for the family of rank-2 temperaments where it is tempered out.