Amity comma
| Ratio | 1600000/1594323 |
| Factorization | 29 × 3-13 × 55 |
| Monzo | [9 -13 5⟩ |
| Size in cents | 6.1535581¢ |
| Name | amity comma |
| Color name | sy51, Saquinyo comma |
| FJS name | [math]\text{A1}^{5,5,5,5,5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 41.2142 |
| Weil height (log2 max(n, d)) | 41.2193 |
| Wilson height (sopfr(nd)) | 82 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.5462 bits |
| Comma size | small |
| open this interval in xen-calc | |
The amity comma ([9 -13 5⟩ = 1600000/1594323) is an interval of 6.154 cents, the amount by which five minor whole tones (10/9) exceed the Pythagorean major sixth (27/16). It belongs to the syntonic-chromatic equivalence continuum and is equal to the difference between an apotome and a stack of five syntonic commas ((2187/2048)/(81/80)5), or in terms of classic chromatic semitone, between a classic chromatic semitone and a stack of three syntonic commas ((25/24)/(81/80)3).
Temperaments
Tempering it out leads to the amity family of temperaments.
Etymology
The corresponding temperament was discovered first, known as amt (for acute minor third) no later than early 2002[1]. The temperament was renamed to amity, and the comma was at one point dubbed amitisma, both by Gene Ward Smith in late 2002, though it was amity comma that stuck[2][3].