Phaotic comma
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| Ratio | 256000/255879 |
| Factorization | 211 × 3-9 × 53 × 13-1 |
| Monzo | [11 -9 3 0 0 -1⟩ |
| Size in cents | 0.81847204¢ |
| Names | phaotic comma, phaotisma |
| Color name | s3uy31, Sathutriyo comma |
| FJS name | [math]\text{A1}^{5,5,5}_{13}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 35.9309 |
| Weil height (log2 max(n, d)) | 35.9316 |
| Wilson height (sopfr(nd)) | 77 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20606 bits |
| Comma size | unnoticeable |
| S-expression | S79 * S802 |
| open this interval in xen-calc | |
The phaotic comma, or phaotisma (from Ancient Greek pháos 'light'), is an unnoticeable 13-limit (also 2.3.5.13 subgroup) comma with a ratio of 256000/255879, and a size of approximately 0.82 cents. It is significant in that it is the interval separating a stack of two meantone commas from 40/39, as well as the interval separating an octave-reduced stack of three instances of 27/20 from 16/13.
Temperaments
Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of phaotismic temperament in the full 13-limit and phaotic temperament in the 2.3.5.13 subgroup.