22edo: Difference between revisions
m →Porcupine notation: Fix wording to make it fit better with the Ups and Downs section above |
m →Stretched and compressed tunings: Temporary improvement until the roll out of the standard |
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=== Subsets and supersets === | === 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. | 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 step size of [[APS|1ed54.5c]] differs from 22edo by only 0.05{{c}}. It improves the tuning of primes 3 and 7, but worsens that of primes 5 and 11, so it may be considered when treating 22edo as a tuning of [[archy]] (2.3.7 superpyth). | |||
{{Harmonics in cet|54.5|intervals=prime|columns=11|collapsed=true}} | |||
== Defining features == | == Defining features == | ||
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! Cents | ! Cents | ||
! Approximate Ratios<ref group="note">{{sg|limit=2.3.5.7.11.17 subgroup}}</ref> | ! Approximate Ratios<ref group="note">{{sg|limit=2.3.5.7.11.17 subgroup}}</ref> | ||
! colspan="3" | [[Ups and | ! colspan="3" | [[Ups and downs notation|Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and ^^d2) | ||
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(K {{=}} 1)}} | ! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(K {{=}} 1)}} | ||
! Audio | ! Audio | ||
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! rowspan="2" | [[Degree]] | ! rowspan="2" | [[Degree]] | ||
! rowspan="2" | [[Cent]]s | ! rowspan="2" | [[Cent]]s | ||
! colspan="2" | [[Ups and downs notation|Ups and | ! colspan="2" | [[Ups and downs notation|Ups and downs notation]] | ||
|- | |- | ||
! [[5L 2s|Diatonic Interval Names]] | ! [[5L 2s|Diatonic Interval Names]] | ||
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|} | |} | ||
Treating [[Ups and | Treating [[Ups and downs notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately: | ||
[[File:Tibia_22edo_ups_and_downs_guide_1.png|alt=Tibia 22edo ups and downs guide 1.png|800x147px|Tibia 22edo ups and downs guide 1.png]] | [[File:Tibia_22edo_ups_and_downs_guide_1.png|alt=Tibia 22edo ups and downs guide 1.png|800x147px|Tibia 22edo ups and downs guide 1.png]] | ||
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=== Interval mappings === | === Interval mappings === | ||
{{Q-odd-limit intervals|22}} | {{Q-odd-limit intervals|22}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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== Scales == | == Scales == | ||
{{Main|22edo modes}} | |||
{{See also|List of MOS scales in 22edo}} | |||
== Tetrachords == | == Tetrachords == | ||
{{Main|22edo tetrachords}} | |||
== | == Chords == | ||
{{Main|22edo chords}} | |||
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors: | Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors: | ||
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* 0-5-11 = C Eb ^Gb = Cd(^5) | * 0-5-11 = C Eb ^Gb = Cd(^5) | ||
* 0-5-12 = C Eb vG = Cm(v5) | * 0-5-12 = C Eb vG = Cm(v5) | ||
== Instruments == | == Instruments == | ||
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A potential layout for a 22edo keyboard with both split black and white keys. | A potential layout for a 22edo keyboard with both split black and white keys. | ||
[[Lumatone mapping for 22edo|Lumatone mappings for 22edo]] are available. | |||
== Music == | == Music == | ||
{{Main| 22edo/Music }} | {{Main| 22edo/Music }} | ||
{{Catrel|22edo tracks}} | {{Catrel|22edo tracks}} | ||
== | == See also == | ||
* [[User:Unque/22edo Composition Theory|Unque's approach]] | * [[User:Unque/22edo Composition Theory|Unque's approach]] | ||
* [[William Lynch's thoughts on septimal harmony and 22edo|William Lynch's approach]] | * [[William Lynch's thoughts on septimal harmony and 22edo|William Lynch's approach]] | ||