Phaotic comma
Jump to navigation
Jump to search
Ratio | 256000/255879 |
Factorization | 2^{11} × 3^{-9} × 5^{3} × 13^{-1} |
Monzo | [11 -9 3 0 0 -1⟩ |
Size in cents | 0.81847204¢ |
Names | phaotic comma, phaotisma |
Color name | s3uy^{3}1, Sathutriyo comma |
FJS name | [math]\text{A1}^{5,5,5}_{13}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 35.9309 |
Weil height (log_{2} max(n, d)) | 35.9316 |
Wilson height (sopfr (nd)) | 77 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.40034 bits |
Comma size | unnoticeable |
S-expression | S79 * S80^{2} |
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.