Ampersand comma

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]\text{dddd}{-3}^{5,5,5,5,5,5}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	50.0263
Weil height (log2 max(n, d))	50.0526
Wilson height (sopfr(nd))	101
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.48007 bits
Comma size	medium
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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.