250/243
Ratio | 250/243 |
Factorization | 2 × 3^{-5} × 5^{3} |
Monzo | [1 -5 3⟩ |
Size in cents | 49.166137¢ |
Names | porcupine comma, maximal diesis |
Color name | y^{3}1, triyo 1sn, Triyo comma |
FJS name | [math]\text{A1}^{5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 15.8906 |
Weil height (log_{2} max(n, d)) | 15.9316 |
Wilson height (sopfr (nd)) | 32 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.47692 bits |
Comma size | medium |
S-expression | S10^{2} × S11 |
open this interval in xen-calc |
250/243 is known as the porcupine comma or the maximal diesis. Measuring about 49 ¢, it is a medium comma. It is the amount by which two minor whole tones exceed a minor third, that is, (10/9)^{2}/(6/5). It is also the difference between 25/24 and 81/80, the two smallest 5-limit superparticular ratios, and between three syntonic commas and the Pythagorean apotome, putting it on the Syntonic-chromatic equivalence continuum.
Temperaments
Tempering it out leads to the 5-limit porcupine temperament. See porcupine family for the family of rank-2 temperaments where it is tempered out.
Approximation
If we do not temper out this interval and instead use it as an identity of some sort, it serves as the period in the chromium temperament, where it is mapped to 1/24th of the octave. Thus Eliora proposes the name chromium quartertone.