Immunity comma

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 1638400/1594323
Factorization 216 × 3-13 × 52
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 (log2 nd) 41.2484
Weil height (log2 max(n, d)) 41.2877
Wilson height (sopfr (nd)) 81
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.78391 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.


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.


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

See also