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]]. | |||
== See also == | == See also == | ||
* [[Apotome family]] | |||
* [[Apotomic node]] | |||
* [[Gallery of Just Intervals]] | * [[Gallery of Just Intervals]] | ||
* [[Large commas]] | * [[Large commas]] | ||
[[Category: 3-limit]] | [[Category: 3-limit]] | ||
[[Category: Interval]] | [[Category: Interval]] | ||
[[Category: Interval ratio]] | [[Category: Interval ratio]] | ||
[[Category: Pythagorean]] | [[Category: Pythagorean]] | ||
[[Category: Semitone]] | [[Category: Semitone]] | ||
[[Category: Large comma]] | |||
Revision as of 07:25, 8 October 2020
| 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.