2187/2048: Difference between revisions

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{{Infobox Interval

| Name = apotome, Pythagorean chromatic semitone

| Name = apotome, Pythagorean chroma, Pythagorean chromatic semitone, whitewood comma

| Color name = Lw1, lawa unison

| Sound = jid_2187_2048_pluck_adu_dr220.mp3

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'''2187/2048''', the '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean ~~major semitone~~''', is the chromatic semitone in the [[Pythagorean tuning]]. It is the [[3-limit]] interval between seven perfect just fifths ([[3/2]]) and four octaves ([[2/1]]): 37/211 = 2187/2048, and measures about 113.7¢. Unlike the situation in [[meantone]] tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of [[256/243]].

'''2187/2048''', the '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean chroma''', is the [[chromatic semitone]] in the [[Pythagorean tuning]]. It is the [[3-limit]] interval between seven perfect just fifths ([[3/2]]) and four octaves ([[2/1]]): 37/211 = 2187/2048, and measures about 113.7¢. Unlike the situation in [[meantone]] tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of [[256/243]].

== ~~Temperament~~ ==

== Approximation ==

When ~~treated~~ as a comma to be tempered ~~out~~, it ~~leads to~~ [[apotome family]] ~~of temperaments~~.

This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, [[53edo|4\53]] is a very good approximation.

== Temperaments ==

When this ratio is taken as a comma to be tempered in the 5-limit, it produces the [[whitewood]] temperament, and it may be called the '''whitewood comma'''. See [[apotome family]] for extensions thereof.

== See also ==

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* [[Gallery of just intervals]]

* [[Large comma]]

* [[53edo|5\53]] is a very good approximation of the interval

* [[25/24]] – classic chromatic semitone

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[[Category:Semitone]]

[[Category:Chroma]]

[[Category:~~Apotomic~~]]

[[Category:Whitewood]]

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 {{Infobox Interval
-| Name = apotome, Pythagorean chromatic semitone
+| Name = apotome, Pythagorean chroma, Pythagorean chromatic semitone, whitewood comma
 | Color name = Lw1, lawa unison
 | Sound = jid_2187_2048_pluck_adu_dr220.mp3
@@ Line 7: / Line 7: @@
 {{Wikipedia|Semitone#Pythagorean tuning}}
-'''2187/2048''', the '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean major semitone''', is the chromatic semitone in the [[Pythagorean tuning]]. It is the [[3-limit]] interval between seven perfect just fifths ([[3/2]]) and four octaves ([[2/1]]): 3<sup>7</sup>/2<sup>11</sup> = 2187/2048, and measures about 113.7¢. Unlike the situation in [[meantone]] tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of [[256/243]].
+'''2187/2048''', the '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean chroma''', is the [[chromatic semitone]] in the [[Pythagorean tuning]]. It is the [[3-limit]] interval between seven perfect just fifths ([[3/2]]) and four octaves ([[2/1]]): 3<sup>7</sup>/2<sup>11</sup> = 2187/2048, and measures about 113.7¢. Unlike the situation in [[meantone]] tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of [[256/243]].
-== Temperament ==
+== Approximation ==
-When treated as a comma to be tempered out, it leads to [[apotome family]] of temperaments.
+This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, [[53edo|4\53]] is a very good approximation.
+== Temperaments ==
+When this ratio is taken as a comma to be tempered in the 5-limit, it produces the [[whitewood]] temperament, and it may be called the '''whitewood comma'''. See [[apotome family]] for extensions thereof.
 == See also ==
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 * [[Gallery of just intervals]]
 * [[Large comma]]
-* [[53edo|5\53]] is a very good approximation of the interval
 * [[25/24]] – classic chromatic semitone
@@ Line 22: / Line 24: @@
 [[Category:Semitone]]
 [[Category:Chroma]]
-[[Category:Apotomic]]
+[[Category:Whitewood]]