Tetracot comma: Difference between revisions
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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. | |||
[[Category: | == Temperaments == | ||
Tempering out this comma leads to the [[tetracot family]] of temperaments. | |||
[[Category:Tetracot]] | |||
[[Category:Commas named for how they divide the fifth]] | |||
Latest revision as of 01:55, 4 December 2024
| Interval information |
minimal diesis
The tetracot comma (monzo: [5 -9 4⟩, ratio: 20000/19683), or minimal diesis, is a small 5-limit comma of 27.660 cents which is the amount by which four minor whole tones exceed a fifth; that is, (10/9)4/(3/2). It can also be expressed as the octave-reduced difference between four just major thirds and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four syntonic commas and a Pythagorean apotome, making the corresponding temperament a member of the syntonic–chromatic equivalence continuum. Since an apotome minus two syntonic commas is a 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.