256/243: Difference between revisions
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The '''Pythagorean limma''', or '''Pythagorean diatonic semitone''', is the interval of size 256/243 = 2<sup>8</sup>/3<sup>5</sup> (about 90.2¢), which is the diatonic semitone in Pythagorean tuning. It can be generated by stacking five [[4/3]] just perfect fourths and octave-reducing the resulting interval. | The '''Pythagorean limma''', or '''Pythagorean diatonic semitone''', is the interval of size 256/243 = 2<sup>8</sup>/3<sup>5</sup> (about 90.2¢), which is the diatonic semitone in [[Pythagorean tuning]]. It can be generated by stacking five [[4/3]] just perfect fourths and octave-reducing the resulting interval. | ||
When this ratio is taken as a comma to be tempered, it produces [[blackwood]] temperament. | == Temperament == | ||
When this ratio is taken as a comma to be tempered, it produces [[blackwood]] temperament. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]]. | |||
== See also == | == See also == | ||
* [[243/128]] – its [[octave complement]] | |||
* [[ | * [[729/512]] – its [[fifth complement]] | ||
* [[Gallery of just intervals]] | |||
* [[ | * [[Medium comma]] | ||
* [[Pythagorean tuning]] | |||
* [[53edo|4\53]] is a very good approximation of the interval | * [[53edo|4\53]] is a very good approximation of the interval | ||
Revision as of 04:34, 13 March 2021
| Interval information |
Pythagorean diatonic semitone
reduced subharmonic
[sound info]
The Pythagorean limma, or Pythagorean diatonic semitone, is the interval of size 256/243 = 28/35 (about 90.2¢), which is the diatonic semitone in Pythagorean tuning. It can be generated by stacking five 4/3 just perfect fourths and octave-reducing the resulting interval.
Temperament
When this ratio is taken as a comma to be tempered, it produces blackwood temperament. Edos tempering it out include 5edo, 10edo, 15edo, 20edo, 25edo and 30edo.
See also
- 243/128 – its octave complement
- 729/512 – its fifth complement
- Gallery of just intervals
- Medium comma
- Pythagorean tuning
- 4\53 is a very good approximation of the interval