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
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 (2.3.5.13 subgroup) comma with the ratio 256000/255879, and a size of approximately 0.82 ¢. It separates a stack of two syntonic commas from 40/39, or three 27/20 acute fourths from 16/13 (up an octave). It factors into (4096/4095)(4375/4374) or (6656/6561)(507/500)⁻¹.

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