Immunity comma
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Ratio | 1638400/1594323 |
Factorization | 2^{16} × 3^{-13} × 5^{2} |
Monzo | [16 -13 2⟩ |
Size in cents | 47.212416¢ |
Name | immunity comma |
Color name | ssyy2, Sasa-yoyo comma |
FJS name | [math]\text{m2}^{5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 41.2484 |
Weil height (log_{2} max(n, d)) | 41.2877 |
Wilson height (sopfr (nd)) | 81 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.48976 bits |
Comma size | medium |
open this interval in xen-calc |
The immunity comma (monzo: [16 -13 2⟩, ratio: 1638400/1594323) is a medium 5-limit comma of about 47.2 cents. It is the difference between the Pythagorean diatonic semitone (256/243) and a stack of two syntonic commas, or between a diptolemaic chromatic semitone (25/24) and a Pythagorean comma.
Temperaments
Tempering out this comma leads to the immunity family of temperaments. These temperaments offer hemifourths and hemitwelfths as a result of dividing the diatonic semitone in equal halves.
Etymology
This comma was named by Mike Battaglia in 2011 such that the corresponding temperament is paired with amity^{[1]}^{[2]}.
Perhaps "Immunity," because it's a counterpart to Amity or something like that.
—Mike Battaglia