22edo: Difference between revisions

Line 10:

== Theory ==

=== Prime harmonics ===

=== History ===

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist {{w|Robert Holford Macdowall Bosanquet|R. H. M. Bosanquet}}. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosanquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.

Line 19:

Line 22:

Since 22et's fifth is sharp of just by approximately one-quarter of the septimal comma ([[64/63]]), and since it tunes the septimal supermajor third ([[9/7]]) almost exactly just, it is equivalent for all practical purposes to an extended "quarter-comma archy", in the same way that 31edo is practically idential to quarter-comma meantone.

=== 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.

== Intervals ==

@@ Line 10: / Line 10: @@
 == Theory ==
+=== Prime harmonics ===
+{{Harmonics in equal|22|columns=11}}
 === History ===
 The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist {{w|Robert Holford Macdowall Bosanquet|R. H. M. Bosanquet}}. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosanquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.
@@ Line 19: / Line 22: @@
 Since 22et's fifth is sharp of just by approximately one-quarter of the septimal comma ([[64/63]]), and since it tunes the septimal supermajor third ([[9/7]]) almost exactly just, it is equivalent for all practical purposes to an extended "quarter-comma archy", in the same way that 31edo is practically idential to quarter-comma meantone.
+=== 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.
 == Intervals ==