250/243: Difference between revisions
start by mentioning first how 250/243 is close to 24edo step, then explain chromium |
→Approximation: 24edo itself does not qualify as a chromium tuning |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = porcupine comma, maximal diesis | | Name = porcupine comma, maximal diesis | ||
| Color name = y<sup>3</sup>1, triyo 1sn,<br> | | Color name = y<sup>3</sup>1, triyo 1sn,<br>y<sup>3</sup>M, triyoma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
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== Approximation == | == 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''. | 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''. | ||
[[Category:Porcupine]] | [[Category:Porcupine]] | ||
[[Category:Commas named after compositions]] | [[Category:Commas named after compositions]] | ||
Latest revision as of 02:17, 28 May 2026
| Interval information |
maximal diesis
y3M, triyoma
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.