250/243: Difference between revisions

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{{Infobox Interval

~~| Ratio = 250/243~~

| Name = porcupine comma, maximal diesis

~~| Monzo = 1 -5 3~~

| Color name = y31, triyo 1sn, y3M, triyoma

~~| Cents = 49.16614~~

| Comma = yes

| Name = porcupine comma, ~~ ~~maximal diesis

| Color name = y31, ~~Triyo comma~~

~~| FJS name =~~

| ~~Sound~~ =

}}

'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9|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 [[2187/2048|Pythagorean apotome]], putting it on the [[Syntonic–chromatic equivalence continuum]].

~~'''250/243''' is known as~~ the ~~'''~~porcupine ~~comma''' or '''maximal diesis'''~~. ~~Measuring about 49{{cent}}, it is a~~ [[~~medium comma~~]]. It is ~~the amount by which two~~ [[~~10/9|minor whole tones~~]] ~~exceed a minor third~~, that is, ~~(10~~/~~9)2~~/(6/~~5). Tempering it out leads to~~ [[~~5-limit~~]] [[~~Porcupine family|porcupine temperament~~]].

== 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''.

~~[[Category:5-limit]]~~

~~[[Category:Medium commas]]~~

[[Category:Porcupine]]

[[Category:Commas named after compositions]]

~~{{todo|improve layout}}~~

@@ Line 6: / Line 6: @@
 }}
 {{Infobox Interval
-| Ratio = 250/243
+| Name = porcupine comma, maximal diesis
-| Monzo = 1 -5 3
+| Color name = y<sup>3</sup>1, triyo 1sn,<br>y<sup>3</sup>M, triyoma
-| Cents = 49.16614
+| Comma = yes
-| Name = porcupine comma, <br>maximal diesis
-| Color name = y<sup>3</sup>1, Triyo comma
-| FJS name =
-| Sound =
 }}
+'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(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 [[2187/2048|Pythagorean apotome]], putting it on the [[Syntonic&ndash;chromatic equivalence continuum]].
-'''250/243''' is known as the '''porcupine comma''' or '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). Tempering it out leads to [[5-limit]] [[Porcupine family|porcupine temperament]].
+== 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 ==
+/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:5-limit]]
-[[Category:Medium commas]]
 [[Category:Porcupine]]
+[[Category:Commas named after compositions]]
-{{todo|improve layout}}