Immunity comma: Difference between revisions

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The '''immunity comma''' ('''1638400/1594323''' = {{monzo| 16 -13 2 }}) is a 5-limit [[medium comma]] of about 47.2 [[cent]]s. [[Tempering out]] this comma leads to the [[immunity family]] of temperaments.
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.
 
== Temperaments ==
[[Tempering out]] this comma leads to the [[immunity family]] of temperaments. These temperaments offer [[interseptimal interval|hemifourths and hemitwelfths]] as a result of dividing the diatonic semitone in equal halves.  


== Etymology ==
== Etymology ==
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<blockquote>Perhaps "Immunity," because it's a counterpart to Amity or something like that. </blockquote>
<blockquote>Perhaps "Immunity," because it's a counterpart to Amity or something like that. </blockquote>
—Mike Battaglia
—Mike Battaglia
== See also ==
* [[Syntonic-diatonic equivalence continuum]]


== Notes ==
== Notes ==


[[Category:Immunity]]
[[Category:Immunity]]

Revision as of 11:47, 26 August 2023

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

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.

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

See also

Notes