Phaotic comma

Interval information

Ratio	256000/255879
Factorization	211 × 3-9 × 53 × 13-1
Monzo	[11 -9 3 0 0 -1⟩
Size in cents	0.818472¢
Names	phaotic comma, phaotisma
FJS name	[math]\displaystyle{ \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
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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.

See also

• Unnoticeable comma