Immunity comma

Interval information

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]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.48976 bits
Comma size	medium
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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.

Perhaps "Immunity," because it's a counterpart to Amity or something like that.

—Mike Battaglia

See also

• Syntonic-diatonic equivalence continuum