27edo: Difference between revisions

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Its step, as well as the octave-inverted and octave-equivalent versions of it, has some of the highest [[harmonic entropy]] possible and thus is, in theory, one of the most dissonant intervals possible, assuming the relatively common values of {{nowrap|''a'' {{=}} 2}} and {{nowrap|''s'' {{=}} 1%}}. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.

Its step of 44.4{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having very [[harmonic entropy]] and thus is, in theory, the third-most dissonant (third-closest to the peak at 46.4{{c}}, after neighboring [[26edo]] and its neighbor [[25edo]]), assuming the relatively common values of ''a'' = 2 and ''s'' = 1.01. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 27 factors into primes as 3<sup>3</sup>, 27edo contains [[3edo]] and [[9edo]] as subsets.

Since 27 factors into primes as 3<sup>3</sup>, 27edo contains [[3edo]] and [[9edo]] as subsets. Multiplying it by 3 gives [[81edo]], which is a good [[meantone]] tuning.

== Intervals ==

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 Its step, as well as the octave-inverted and octave-equivalent versions of it, has some of the highest [[harmonic entropy]] possible and thus is, in theory, one of the most dissonant intervals possible, assuming the relatively common values of {{nowrap|''a'' {{=}} 2}} and {{nowrap|''s'' {{=}} 1%}}. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
+Its step of 44.4{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having very [[harmonic entropy]] and thus is, in theory, the third-most dissonant (third-closest to the peak at 46.4{{c}}, after neighboring [[26edo]] and its neighbor [[25edo]]), assuming the relatively common values of ''a'' = 2 and ''s'' = 1.01. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
 === Odd harmonics ===
@@ Line 18: / Line 20: @@
 === Subsets and supersets ===
-Since 27 factors into primes as 3<sup>3</sup>, 27edo contains [[3edo]] and [[9edo]] as subsets.
+Since 27 factors into primes as 3<sup>3</sup>, 27edo contains [[3edo]] and [[9edo]] as subsets.  Multiplying it by 3 gives [[81edo]], which is a good [[meantone]] tuning.
 == Intervals ==