250/243

Interval information

Ratio	250/243
Factorization	2 × 3-5 × 53
Monzo	[1 -5 3⟩
Size in cents	49.16614¢
Names	porcupine comma, maximal diesis
Color name	y31, triyo 1sn, y3M, triyoma
FJS name	[math]\displaystyle{ \text{A1}^{5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	15.8906
Weil norm (log2 max(n, d))	15.9316
Wilson norm (sopfr(nd))	32
Comma size	medium
S-expression	S102⋅S11
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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

250/243 is very close to one step of 24edo, which is the quarter tone that is exactly the half of 12edo semitone. Therefore, if 250/243 is not tempered and instead is treated as an identity where it is equated with 1/24th of the octave, it serves as the period in the chromium temperament. (However, note that 24edo itself maps 250/243 inconsistently, and so chromium temperament starts at 72edo.) Thus in the framework of this temperament and the tuning systems associated with it, Eliora proposes the name chromium quartertone.