Ampersand comma

Interval information

Ratio	34171875/33554432
Factorization	2-25 × 37 × 56
Monzo	[-25 7 6⟩
Size in cents	31.56729¢
Name	ampersand
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, 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's 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: [⟨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