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 amount by which an octave-reduced stack of four [[5/4|just major thirds]] exceeds an octave-reduced stack of nine fifths. Tempering it out leads to the [[tetracot family]] of temperaments. | '''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 amount by which an octave-reduced stack of four [[5/4|just major thirds]] exceeds an octave-reduced stack of nine fifths, or as the difference between two [[81/80|syntonic commas]] and a [[25/24|classic chromatic semitone]]. Tempering it out leads to the [[tetracot family]] of temperaments. | ||
[[Category:tetracot]] | [[Category:tetracot]] | ||
Revision as of 12:00, 8 July 2024
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minimal diesis
20000/19683, the tetracot comma or minimal diesis, is a small 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 amount by which an octave-reduced stack of four just major thirds exceeds an octave-reduced stack of nine fifths, or as the difference between two syntonic commas and a classic chromatic semitone. Tempering it out leads to the tetracot family of temperaments.