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, Triyo comma
FJS name	[math]\displaystyle{ \text{A1}^{5,5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	15.8906
Weil height (log2 max(n, d))	15.9316
Wilson height (sopfr(nd))	32
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.47692 bits
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. Thus in the framework of this temperament and the tuning systems associated with it, Eliora proposes the name chromium quartertone.