Amity comma
Ratio | 1600000/1594323 |
Factorization | 2^{9} × 3^{-13} × 5^{5} |
Monzo | [9 -13 5⟩ |
Size in cents | 6.1535581¢ |
Name | amity comma |
Color name | sy^{5}1, Saquinyo comma |
FJS name | [math]\text{A1}^{5,5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 41.2142 |
Weil height (log_{2} max(n, d)) | 41.2193 |
Wilson height (sopfr (nd)) | 82 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.59778 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]}.