250/243: Difference between revisions

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<~~span style~~=~~"display: block; text-align: right;">~~[[~~:de:250~~/~~243 Deutsch~~]]</~~span~~>

{{Interwiki

| de = 250/243

| en = 250/243

| es =

| ja =

}}

{{Infobox Interval

| Name = porcupine comma, maximal diesis

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

| Comma = yes

}}

'''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''', known as~~ the ~~'''porcupine~~ [[~~Comma|comma~~]]~~''' or maximal diesis, is an interval of size 49~~.~~166~~ [[~~cent|cents~~]]. 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|5-limit~~]] [[~~Porcupine_family|porcupine temperament~~]].

== Temperaments ==

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

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.

[[Category:~~comma~~]]

[[Category:~~porcupine~~]]

== 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:Porcupine]]

[[Category:Commas named after compositions]]

@@ Line 1: / Line 1: @@
-<span style="display: block; text-align: right;">[[:de:250/243 Deutsch]]</span>
+{{Interwiki
+| de = 250/243
+| en = 250/243
+| es =
+| ja =
+}}
+{{Infobox Interval
+| Name = porcupine comma, maximal diesis
+| Color name = y<sup>3</sup>1, triyo 1sn,<br>y<sup>3</sup>M, triyoma
+| Comma = yes
+}}
+'''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''', known as the '''porcupine [[Comma|comma]]''' or maximal diesis, is an interval of size 49.166 [[cent|cents]]. 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|5-limit]] [[Porcupine_family|porcupine temperament]].
+== Temperaments ==
-[[Category:5-limit]]
+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.
-[[Category:comma]]
-[[Category:porcupine]]
+== 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:Porcupine]]
+[[Category:Commas named after compositions]]