Phaotic comma

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Interval information
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,
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{n\cdot d}[/math])
~2.40034 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 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.


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 subgroup.

See also