Ampersand comma
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| Ratio | 34171875/33554432 |
| Factorization | 2-25 × 37 × 56 |
| Monzo | [-25 7 6⟩ |
| Size in cents | 31.567289¢ |
| 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 | |
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