Immunity comma
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Ratio
1638400/1594323
Factorization
216 × 3-13 × 52
Monzo
[16 -13 2⟩
Size in cents
47.21242¢
Name
immunity comma
Color name
ssyy2, Sasa-yoyo comma
FJS name
[math]\text{m2}^{5,5}[/math]
Special properties
reduced
Tenney height (log2 nd)
41.2484
Weil height (log2 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
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
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