Tetracot comma

Interval information

Ratio	20000/19683
Factorization	25 × 3-9 × 54
Monzo	[5 -9 4⟩
Size in cents	27.65985¢
Names	tetracot comma, minimal diesis
Color name	sy41, Saquadyo comma
FJS name	[math]\displaystyle{ \text{A1}^{5,5,5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	28.5524
Weil height (log2 max(n, d))	28.5754
Wilson height (sopfr(nd))	57
Comma size	small
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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 octave-reduced difference between four just major thirds and nine just perfect fifths, between four syntonic commas and a Pythagorean apotome, or between two syntonic commas and a classic chromatic semitone. Tempering it out leads to the tetracot family of temperaments.