2187/2048: Difference between revisions
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{{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 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]]. | ||
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* [[Large comma]] | * [[Large comma]] | ||
* [[53edo|5\53]] is a very good approximation of the interval | * [[53edo|5\53]] is a very good approximation of the interval | ||
* [[25/24 | * [[25/24]] – classic chromatic semitone | ||
[[Category:3-limit]] | [[Category:3-limit]] | ||
[[Category: | [[Category:Second]] | ||
[[Category: | [[Category:Semitone]] | ||
[[Category:Large comma]] | [[Category:Large comma]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Apotomic]] | [[Category:Apotomic]] | ||
[[Category:Octave-reduced harmonics]] | |||
Revision as of 18:11, 15 December 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
- 4096/2187 – its octave complement
- Gallery of just intervals
- Large comma
- 5\53 is a very good approximation of the interval
- 25/24 – classic chromatic semitone