256/243: Difference between revisions
Jump to navigation
Jump to search
m +link |
m Misc. edits, categories |
||
| Line 7: | Line 7: | ||
| FJS name = m2 | | FJS name = m2 | ||
}} | }} | ||
{{Wikipedia|Semitone#Pythagorean tuning}} | |||
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 reduction|octave-reducing]] the resulting interval. | ||
== Approximation == | == Approximation == | ||
| Line 26: | Line 27: | ||
[[Category:3-limit]] | [[Category:3-limit]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Medium comma]] | |||
[[Category:Pages with internal sound examples]] | |||
Revision as of 19:29, 15 December 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