Punctisma

Interval information

Ratio	43904/43875
Factorization	27 × 3-3 × 5-3 × 73 × 13-1
Monzo	[7 -3 -3 3 0 -1⟩
Size in cents	1.143913¢
Name	punctisma
Color name	s3uz3g33, sathutrizogu 3rd
FJS name	[math]\text{dd3}^{7,7,7}_{5,5,5,13}[/math]
Special properties	reduced
Tenney height (log2 nd)	30.8432
Weil height (log2 max(n, d))	30.8441
Wilson height (sopfr(nd))	72
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.21131 bits
Comma size	unnoticeable
S-expression	S14 / S15
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The punctisma, with a ratio of 43904/43875, is the difference between three 15/14 semitones and a 16/13 neutral third. It factors into (2401/2400)(4096/4095).

Temperaments

Tempering out this comma is characteristic of the 10n family of edos, including decoid tunings 130edo, 140edo, and 270edo, which approximate both 15/14 and 16/13 to within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as 31edo, 41edo, 99edo, 171edo, 311edo, and 441edo. Perhaps surprisingly, 111edo and 159edo temper it out as well.

Etymology

This comma was named by Jerdle and Aura in 2023, from Latin pūnctum ("point") based on both its relation to the 10n family of edos as well as its small size.