Immunity comma
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| 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{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