Ampersand comma
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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
open this interval in xen-calc
| Interval information |
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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
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