2187/2048: Difference between revisions
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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]]): 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 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]]. | ||
== Temperament == | |||
When treated as a comma to be tempered out, it leads to [[apotome family]] of temperaments. | |||
== See also == | == See also == | ||
* [[Gallery of just intervals]] | |||
* [[Large comma]] | |||
* [[Gallery of | |||
* [[Large | |||
* [[53edo|5\53]] is a very good approximation of the interval | * [[53edo|5\53]] is a very good approximation of the interval | ||
[[Category:3-limit]] | [[Category:3-limit]] | ||
Revision as of 04:41, 13 March 2021
| Interval information |
Pythagorean chromatic semitone
reduced harmonic
[sound info]
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.
Temperament
When treated as a comma to be tempered out, it leads to apotome family of temperaments.
See also
- Gallery of just intervals
- Large comma
- 5\53 is a very good approximation of the interval