Ampersand comma: Difference between revisions

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

Revision as of 13:37, 6 January 2025

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 5-limit version of miracle temperament. The ampersand comma was named after Paul Rapoport's cat, Ampersand.

See also: Gamelismic clan § Miracle

Subgroup: 2.3.5

Comma: 34171875/33554432

Mapping: [⟨1 1 3], ⟨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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 34171875/33554432
-| Name = ampersand
+| Name = ampersand comma
 | Color name = LLy<sup>6</sup>-3, Lala-tribiyo comma
 | Comma = yes
 }}
-The '''ampersand''', 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's 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 5-limit version of [[Gamelismic clan #Miracle|miracle temperament]]. The ampersand comma was named after [[Paul Rapoport]]'s cat, Ampersand.
 == Temperament data ==