2187/2048: Difference between revisions

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~~The~~ '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean major semitone''', is the interval 37/211 = 2187/2048 ~~which is the chromatic semitone in the [[Pythagorean tuning|Pythagorean]] ([[3-limit]]) version of the diatonic scale~~. 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]]~~. It measures about 113.7¢ and can be generated by stacking seven [[3/2]] perfect fifths and octave-reducing the resulting interval~~.

'''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]].

== See also ==

* [[Apotome family]]

* [[Apotomic node]]

* [[Gallery of Just Intervals]]

* [[Large commas]]

[[Category: 3-limit]]

~~[[Category: Large comma]]~~

[[Category: Interval]]

[[Category: Interval ratio]]

[[Category: Pythagorean]]

[[Category: Semitone]]

[[Category: Large comma]]

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 }}
-The '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean major semitone''', is the interval 3<sup>7</sup>/2<sup>11</sup> = 2187/2048 which is the chromatic semitone in the [[Pythagorean tuning|Pythagorean]] ([[3-limit]]) version of the diatonic scale. 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]]. It measures about 113.7¢ and can be generated by stacking seven [[3/2]] perfect fifths and octave-reducing the resulting interval.
+'''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]].
 == See also ==
+* [[Apotome family]]
+* [[Apotomic node]]
 * [[Gallery of Just Intervals]]
 * [[Large commas]]
 [[Category: 3-limit]]
-[[Category: Large comma]]
 [[Category: Interval]]
 [[Category: Interval ratio]]
 [[Category: Pythagorean]]
 [[Category: Semitone]]
+[[Category: Large comma]]