256/243: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = Pythagorean limma, Pythagorean diatonic semitone | | Name = Pythagorean limma, Pythagorean diatonic semitone, blackwood comma | ||
| Color name = sw2, sawa 2nd | | Color name = sw2, sawa 2nd | ||
| Sound = jid_256_243_pluck_adu_dr220.mp3 | | Sound = jid_256_243_pluck_adu_dr220.mp3 | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
{{Wikipedia|Semitone#Pythagorean tuning}} | {{Wikipedia| Semitone #Pythagorean tuning }} | ||
The interval '''256/243''', the '''Pythagorean limma''', or '''Pythagorean diatonic semitone''' factors as 2<sup>8</sup>/3<sup>5</sup>, is about 90.2 [[cent]]s in size, and 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. | The interval '''256/243''', the '''Pythagorean limma''', or '''Pythagorean diatonic semitone''' factors as 2<sup>8</sup>/3<sup>5</sup>, is about 90.2 [[cent]]s in size, and 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 == | ||
[[53edo|4\53]] is a very good approximation | This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, [[53edo|4\53]] is a very good approximation. | ||
== | == Temperaments == | ||
When this ratio is taken as a comma to be tempered | When this ratio is taken as a comma to be tempered in the [[5-limit]], it produces the [[blackwood]] temperament, and it may be called the '''blackwood comma'''. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]]. See [[limmic temperaments]] for a number of other temperaments where it is tempered out. | ||
== See also == | == See also == | ||
* [[243/128]] – its [[octave complement]] | * [[243/128]] – its [[octave complement]] | ||
* [[729/512]] – its [[fifth complement]] | * [[729/512]] – its [[fifth complement]] | ||
* [[16/15]] | * [[16/15]] – the classic (5-limit) diatonic semitone | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Medium comma]] | * [[Medium comma]] | ||
* [[Pythagorean tuning]] | * [[Pythagorean tuning]] | ||
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[[Category:Second]] | [[Category:Second]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Blackwood]] | |||