Amity comma

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Interval information
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{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].

See also

Notes