Amity comma

Interval information

Ratio	1600000/1594323
Factorization	29 × 3-13 × 55
Monzo	[9 -13 5⟩
Size in cents	6.153558¢
Name	amity comma
Color name	sy51, Saquinyo comma
FJS name	[math]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~1.5462 bits
Comma size	small
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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 and named by Gene Ward Smith as acute minor third or amt in 2001–2002. 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.

See also

• Small comma