Amity comma: Difference between revisions

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Use a simpler approach and add explanation thru the syntonic-chromatic equivalence continuum
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The '''amity comma''', 1600000/1594323 = {{monzo|9 -13 5}}, is an interval of 6.154 cents, the amount by which five [[10/9|minor whole tones]] and an octave exceed three fifths; that is, 2 × (10/9)<sup>5</sup>/(3/2)<sup>3</sup>. Tempering it out leads to [[Amity|amity temperament]].
The '''amity comma''', 1600000/1594323 = {{monzo| 9 -13 5 }}, is an interval of 6.154 cents, the amount by which five [[10/9|minor whole tones (10/9)]] exceed the [[27/16|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 comma]]s ((2187/2048)/(81/80)<sup>3</sup>), or in terms of classic chromatic semitone, between a classic chromatic semitone and a stack of three syntonic commas ((25/24)/(81/80)<sup>3</sup>). Tempering it out leads to the [[amity family]] of temperaments.


== See also ==
== See also ==
* [[Comma]]
* [[Amity family]]
* [[Small comma]]


[[Category:5-limit]]
[[Category:5-limit]]
[[Category:Small comma]]
[[Category:Small comma]]
[[Category:Amity]]
[[Category:Amity]]

Revision as of 04:33, 7 December 2020

The amity comma, 1600000/1594323 = [9 -13 5, 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)3), or in terms of classic chromatic semitone, between a classic chromatic semitone and a stack of three syntonic commas ((25/24)/(81/80)3). Tempering it out leads to the amity family of temperaments.

See also