Tetracot comma: Difference between revisions

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~~'''20000/19683''', the~~ '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9|minor whole tones]] exceed a [[3/2|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4|just major thirds]] and nine just perfect fifths, between four [[81/80|syntonic commas]] and a [[2187/2048|Pythagorean apotome]], ~~or between~~ two syntonic commas ~~and~~ a [[25/24|~~classic chromatic semitone~~]]. Tempering it out leads to the [[tetracot family]] of temperaments.

The '''tetracot comma''' ({{monzo|legend=1| 5 -9 4 }}, [[ratio]]: 20000/19683), or '''minimal diesis''', is a [[small comma|small]] [[5-limit]] [[comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9|minor whole tones]] exceed a [[3/2|fifth]]; that is, (10/9)<sup>4</sup>/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4|just major thirds]] and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four [[81/80|syntonic commas]] and a [[2187/2048|Pythagorean apotome]], making the corresponding temperament a member of the [[syntonic–chromatic equivalence continuum]]. Since an apotome minus two syntonic commas is a [[25/24|classical chroma]], the comma can be expressed as the difference between an apotome and a stack of two classical chromas, or between a classical chroma and a stack of two syntonic commas.

== Temperaments ==

Tempering out this comma leads to the [[tetracot family]] of temperaments.

[[Category:Tetracot]]

[[Category:Commas named for ~~their regular temperament properties~~]]

[[Category:Commas named for how they divide the fifth]]

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-'''20000/19683''', the '''tetracot comma''' or '''minimal diesis''', is a [[small comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9|minor whole tones]] exceed a [[3/2|fifth]]; that is, (10/9)^4/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4|just major thirds]] and nine just perfect fifths, between four [[81/80|syntonic commas]] and a [[2187/2048|Pythagorean apotome]], or between two syntonic commas and a [[25/24|classic chromatic semitone]]. Tempering it out leads to the [[tetracot family]] of temperaments.
+The '''tetracot comma''' ({{monzo|legend=1| 5 -9 4 }}, [[ratio]]: 20000/19683), or '''minimal diesis''', is a [[small comma|small]] [[5-limit]] [[comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9|minor whole tones]] exceed a [[3/2|fifth]]; that is, (10/9)<sup>4</sup>/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4|just major thirds]] and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four [[81/80|syntonic commas]] and a [[2187/2048|Pythagorean apotome]], making the corresponding temperament a member of the [[syntonic&ndash;chromatic equivalence continuum]]. Since an apotome minus two syntonic commas is a [[25/24|classical chroma]], the comma can be expressed as the difference between an apotome and a stack of two classical chromas, or between a classical chroma and a stack of two syntonic commas.
+== Temperaments ==
+Tempering out this comma leads to the [[tetracot family]] of temperaments.
 [[Category:Tetracot]]
-[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named for how they divide the fifth]]