22edo: Difference between revisions

Line 27:

=== Subsets and supersets ===

As 22 is divisible by 11, a 22edo instrument can play any music in 11edo, in the same way that [[12edo]] can play [[6edo]] (the whole tone scale). 11edo is interesting for sounding melodically very similar to 12edo (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to [[24edo]] as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In [[Sagittal notation]], 11 can be notated as every other note of 22.

=== Stretched and compressed tunings ===

The [[The Riemann zeta function and tuning|local zeta peak]] around 22, '''80zpi''', is located at 22.025147, which has the octave [[Stretched and compressed tuning|compressed]] by 1.37{{c}}. The octave of 123ed48 comes quite close, differing by only 0.09{{c}}. This improves the tuning of primes 3 and 7, but worsens that of primes 5 and 11, so this compromise may be considered when treating 22edo as a tuning of [[archy]] (2.3.7 superpyth).

{{Harmonics in equal|123|48|1|intervals=prime|columns=11|collapsed=true}}

== Defining features ==

@@ Line 27: / Line 27: @@
 === Subsets and supersets ===
 As 22 is divisible by 11, a 22edo instrument can play any music in 11edo, in the same way that [[12edo]] can play [[6edo]] (the whole tone scale). 11edo is interesting for sounding melodically very similar to 12edo (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to [[24edo]] as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In [[Sagittal notation]], 11 can be notated as every other note of 22.
+=== Stretched and compressed tunings ===
+The [[The Riemann zeta function and tuning|local zeta peak]] around 22, '''80zpi''', is located at 22.025147, which has the octave [[Stretched and compressed tuning|compressed]] by 1.37{{c}}. The octave of 123ed48 comes quite close, differing by only 0.09{{c}}. This improves the tuning of primes 3 and 7, but worsens that of primes 5 and 11, so this compromise may be considered when treating 22edo as a tuning of [[archy]] (2.3.7 superpyth).
+{{Harmonics in equal|123|48|1|intervals=prime|columns=11|collapsed=true}}
 == Defining features ==