Tetracot comma
| Ratio | 20000/19683 |
| Factorization | 25 × 3-9 × 54 |
| Monzo | [5 -9 4⟩ |
| Size in cents | 27.659848¢ |
| Names | tetracot comma, minimal diesis |
| Color name | sy41, Saquadyo comma |
| FJS name | [math]\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 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.37587 bits |
| Comma size | small |
| open this interval in xen-calc | |
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.