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. | ||
== Approximation == | |||
[[53edo|4\53]] is a very good approximation of the interval. | |||
== Temperament == | == Temperament == | ||
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* [[16/15]] - the classic (5-limit) diatonic semitone | * [[16/15]] - the classic (5-limit) diatonic semitone | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Limma family]], where it is tempered out | |||
* [[Medium comma]] | * [[Medium comma]] | ||
* [[Pythagorean tuning]] | * [[Pythagorean tuning]] | ||
[[Category: 3-limit]] | [[Category:3-limit]] | ||
[[Category: Interval]] | [[Category:Interval]] | ||
[[Category: Interval ratio]] | [[Category:Interval ratio]] | ||
[[Category: Pythagorean]] | [[Category:Pythagorean]] | ||
[[Category: Second]] | [[Category:Second]] | ||
[[Category: Semitone]] | [[Category:Semitone]] | ||
Revision as of 11:33, 26 September 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.
Approximation
4\53 is a very good approximation of the interval.
Temperament
When this ratio is taken as a comma to be tempered (and the starting JI subgroup is the 5-limit), 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
- 16/15 - the classic (5-limit) diatonic semitone
- Gallery of just intervals
- Limma family, where it is tempered out
- Medium comma
- Pythagorean tuning