Punctisma

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Interval information
Ratio 43904/43875
Factorization 27 × 3-3 × 5-3 × 73 × 13-1
Monzo [7 -3 -3 3 0 -1
Size in cents 1.1439134¢
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{n\cdot d}[/math])
~2.44793 bits
Comma size unnoticeable
S-expression S14 / S15
open this interval in xen-calc

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, 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 41edo, 171edo, and 311edo. Perhaps surprisingly, 159edo tempers 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.