Tetracot comma
(Redirected from 20000/19683)
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Ratio | 20000/19683 |
Factorization | 2^{5} × 3^{-9} × 5^{4} |
Monzo | [5 -9 4⟩ |
Size in cents | 27.659848¢ |
Names | tetracot comma, minimal diesis |
Color name | sy^{4}1, Saquadyo comma |
FJS name | [math]\text{A1}^{5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 28.5524 |
Weil height (log_{2} max(n, d)) | 28.5754 |
Wilson height (sopfr (nd)) | 57 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.37587 bits |
Comma size | small |
open this interval in xen-calc |
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.