Punctisma
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Ratio | 43904/43875 |
Factorization | 2^{7} × 3^{-3} × 5^{-3} × 7^{3} × 13^{-1} |
Monzo | [7 -3 -3 3 0 -1⟩ |
Size in cents | 1.1439134¢ |
Name | punctisma |
Color name | s3uz^{3}g^{3}3, sathutrizogu 3rd |
FJS name | [math]\text{dd3}^{7,7,7}_{5,5,5,13}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 30.8432 |
Weil height (log_{2} 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 |
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.