Ampersand comma: Difference between revisions

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Ampersand -> ampersand comma to better distinguish the comma from the temp
-data (addressed in the syntonic-31 continuum)
 
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The '''ampersand comma''', or '''Ampersand's comma''', is the [[comma]] of '''34171875/33554432''' of size 31.567 [[cent]]s. It is the amount by which six [[16/15|classical diatonic semitones (16/15)]] fall short of the [[3/2|perfect fifth (3/2)]]; that is, (3/2)/(16/15)<sup>6</sup>, or the amount by which seven such intervals fall short of the [[8/5|classical minor sixth (8/5)]]. The [[5-limit]] temperament tempering it out gives the 5-limit version of [[Gamelismic clan #Miracle|miracle temperament]]. The ampersand comma was named after [[Paul Rapoport]]'s cat, Ampersand.
The '''ampersand comma''', or '''Ampersand's comma''', is the [[comma]] of '''34171875/33554432''' of size 31.567 [[cent]]s. It is the amount by which six [[16/15|classical diatonic semitones (16/15)]] fall short of the [[3/2|perfect fifth (3/2)]]; that is, (3/2)/(16/15)<sup>6</sup>, or the amount by which seven such intervals fall short of the [[8/5|classical minor sixth (8/5)]]. The [[5-limit]] temperament tempering it out gives the eponymous '''ampersand temperament''', which is the 5-limit version of [[miracle|miracle temperament]]. See [[Syntonic–31 equivalence continuum #Ampersand]] for technical data. The ampersand comma was named after [[Paul Rapoport]]'s cat, Ampersand.
 
== Temperament data ==
 
=== Ampersand ===
{{see also| Gamelismic clan #Miracle }}
 
Subgroup: 2.3.5
 
[[Comma]]: 34171875/33554432
 
[[Mapping]]: [{{Val| 1 1 3 }}, {{Val| 0 6 -7 }}]
 
Optimal tuning ([[CWE]]): ~2 = 1\1, ~16/15 = 116.680
 
Supporting ETs: 31, 10, 41, 72, 21, 11, 103, 113, 51, 52, 134, 175, 154c, 185c
 
[[Badness]] (Sintel): 3.888


[[Category:Miracle]]
[[Category:Commas named after individuals]]
[[Category:Commas named after individuals]]

Latest revision as of 13:41, 6 January 2025

Interval information
Ratio 34171875/33554432
Factorization 2-25 × 37 × 56
Monzo [-25 7 6
Size in cents 31.56729¢
Name ampersand comma
Color name LLy6-3, Lala-tribiyo comma
FJS name [math]\displaystyle{ \text{dddd}{-3}^{5,5,5,5,5,5} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 50.0263
Weil norm (log2 max(n, d)) 50.0526
Wilson norm (sopfr(nd)) 101
Comma size medium
Open this interval in xen-calc

The ampersand comma, or Ampersand's comma, is the comma of 34171875/33554432 of size 31.567 cents. It is the amount by which six classical diatonic semitones (16/15) fall short of the perfect fifth (3/2); that is, (3/2)/(16/15)6, or the amount by which seven such intervals fall short of the classical minor sixth (8/5). The 5-limit temperament tempering it out gives the eponymous ampersand temperament, which is the 5-limit version of miracle temperament. See Syntonic–31 equivalence continuum #Ampersand for technical data. The ampersand comma was named after Paul Rapoport's cat, Ampersand.