Passion comma

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Interval information
Ratio 262144/253125
Factorization 218 × 3-4 × 5-5
Monzo [18 -4 -5
Size in cents 60.611427¢
Name passion comma
Color name saquingu 3rd, sg53
FJS name [math]\text{ddd3}_{5,5,5,5,5}[/math]
Special properties reduced
Tenney height (log2 nd) 35.9495
Weil height (log2 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.

Notes