Immunity comma: Difference between revisions

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 norm (log2 nd)	41.2484
Weil norm (log2 max(n, d))	41.2877
Wilson norm (sopfr(nd))	81
Comma size	medium
	Open this interval in xen-calc

Latest revision as of 08:07, 3 November 2024

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.

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

@@ Line 5: / Line 5: @@
 | Comma = yes
 }}
-The '''immunity comma''' ({{monzo|legend=1| 16 -13 2 }}, [[ratio]]: 1638400/1594323) is a [[Medium comma|medium]] [[5-limit]] [[comma]] of about 47.2 [[cent]]s. It is the difference between the [[256/243|Pythagorean diatonic semitone (256/243)]] and a stack of two [[syntonic comma]]s.
+The '''immunity comma''' ({{monzo|legend=1| 16 -13 2 }}, [[ratio]]: 1638400/1594323) is a [[Medium comma|medium]] [[5-limit]] [[comma]] of about 47.2 [[cent]]s. It is the difference between the [[256/243|Pythagorean diatonic semitone (256/243)]] and a stack of two [[syntonic comma]]s, or between a [[25/24|diptolemaic chromatic semitone (25/24)]] and a [[Pythagorean comma]].
 == Temperaments ==
@@ Line 22: / Line 22: @@
 [[Category:Immunity]]
+[[Category:Commas named for their regular temperament properties]]