22edo: Difference between revisions
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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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The keyboard runs {{nowrap|D * * E * * F * * G * * * A * * B * * C * * D}}. | The keyboard runs {{nowrap|D * * E * * F * * G * * * A * * B * * C * * D}}. | ||
A score video demonstrating this type of notation using redefined sharp and flat symbols is available: [https://www.youtube.com/watch?v=se79rdp705Y ''Study #1 in Porcupine Temperament: "Flying Straight Down" (Microtonal/Xenharmonic)''] (2020) by [[John Moriarty]]. Note that the sharp of one note is lower than the flat of the next note, in contrast to sharps and flats in the diatonic notation with ups and downs described above. | |||
=== Pentatonic notation === | === Pentatonic notation === | ||
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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]] | ||