Ampersand comma: Difference between revisions

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The '''ampersand''', or '''Ampersand's [[comma]]''', is the interval of '''34171875/33554432''' ([[monzo]]: {{Monzo| -25 7 6 }}), of size 31.567 [[cent]]s. It is the amount by which six [[16/15|diatonic semitones]] fall short of a fifth; that is, (3/2)/(16/15)^6. 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.
{{Infobox Interval
| JI glyph =
| Ratio = 34171875/33554432
| Monzo = -25 7 6
| Cents = 31.567
| Name = ampersand
| Color name =
| FJS name =
| Sound =
}}


The '''ampersand''', or '''Ampersand's [[comma]]''', is the interval of '''34171875/33554432''' of size 31.567 [[cent]]s. It is the amount by which six [[16/15|classic diatonic semitones (16/15)]] fall short of a fifth; that is, (3/2)/(16/15)<sup>6</sup>. 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.
[[Category:5-limit]]
[[Category:Small comma]]
[[Category:Small comma]]
[[Category:Medium comma]]
[[Category:Medium comma]]
[[Category:Todo:expand]]

Revision as of 08:27, 19 December 2020

Interval information
Ratio 34171875/33554432
Factorization 2-25 × 37 × 56
Monzo [-25 7 6⟩
Size in cents 31.56729¢
Name ampersand
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
Open this interval in xen-calc

The ampersand, or Ampersand's comma, is the interval of 34171875/33554432 of size 31.567 cents. It is the amount by which six classic diatonic semitones (16/15) fall short of a fifth; that is, (3/2)/(16/15)6. The 5-limit temperament tempering it out gives the 5-limit version of miracle temperament. The Ampersand's comma was named after Paul Rapoport's cat, Ampersand.

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