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22edo/Unque's compositional approach: Difference between revisions

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{{breadcrumb|22edo}}
{{breadcrumb|22edo}}
'''NOTE: This page is currently under construction, and will be subject to major expansion in the near future.  Come back soon!'''
[[22edo|22 Equal Divisions of the Octave]] is arguably the smallest EDO to support the full 11-limit; it is also the intersection of many popular temperaments such as [[Superpyth]], [[Porcupine]], [[Orwell]], and [[Magic]]. Additionally, fans of 15edo will likely be drawn to 22edo due to the latter being quite useful as an extension of the former that represents many low-complexity intervals with higher accuracy. On this page, I will present my personal experience with 22edo, and hopefully provide a potential framework that others may use to begin their own journeys through the colorful world of 22 Equal Divisions of the Octave.
[[22edo|22 Equal Divisions of the Octave]] is arguably the smallest EDO to support the full 11-limit; it is also the intersection of many popular temperaments such as [[Superpyth]], [[Porcupine]], [[Orwell]], and [[Magic]]. Additionally, fans of 15edo will likely be drawn to 22edo due to the latter being quite useful as an extension of the former that represents many low-complexity intervals with higher accuracy. On this page, I will present my personal experience with 22edo, and hopefully provide a potential framework that others may use to begin their own journeys through the colorful world of 22 Equal Divisions of the Octave.


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| 6\22
| 6\22
| 327.3
| 327.3
| [[6/5]]
| [[6/5]], [[11/9]]
| [[Orgone]]
| [[Orgone]]
| F♭, C𝄪
| F♭, C𝄪
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| 9\22
| 9\22
| 490.9
| 490.9
| [[4/3]]
| [[21/16]], [[4/3]]
| [[Superpyth]]
| [[Superpyth]]
| F
| F
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| 11\22
| 11\22
| 600.0
| 600.0
| [[7/5]], [[10/7]], [[45/32]], [[64/45]]
| [[7/5]], [[45/32]], [[64/45]], [[10/7]]
| [[2edo]]; period for several temps
| [[2edo]]; period for several temps
| E♯, A𝄫
| E♯, A𝄫
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| 13\22
| 13\22
| 709.1
| 709.1
| [[3/2]]
| [[3/2]], [[32/21]]
| Superpyth
| Superpyth
| G
| G
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| Magic
| Magic
| B𝄫, F𝄪
| B𝄫, F𝄪
| This one specific note is very contentious in notation.
| Probably better noted with ups and downs (see below)
|-
|-
| 16\22
| 16\22
| 872.7
| 872.7
| [[5/3]]
| [[18/11]], [[5/3]]
| Orgone
| Orgone
| G♯, C𝄫
| G♯, C𝄫
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22edo has two pairs of thirds: a major/minor pair, and a supermajor/subminor pair; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.
22edo has two pairs of thirds: a major/minor pair, and a supermajor/subminor pair; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.


The subminor third at 5\22 represents 7/6 with moderate accuracy, though it is significantly less consonant than the JI representation. Its fifth complement is the supermajor third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.
The subminor third at 5\22 represents 7/6 with moderate accuracy, though it is often noted to be significantly less concordant than the JI representation. Its fifth complement is the supermajor third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.


The minor third at 6\22 is contentious in its interpretation; it is quite sharp as a representation of 6/5, though not sharp enough to constitute a neutral third. Its fifth complement, the major third at 7\22, is a much clearer 5/4, the two being practically indistinguishable to the untrained ear.
The minor third at 6\22 is contentious in its interpretation; it is quite sharp for a minor third, though not nearly sharp enough to constitute a neutral third; by patent val, it represents 6/5 and 11/9, though in practice it does not accurately represent either of the two. Its fifth complement, the major third at 7\22, is a much clearer 5/4, having a relative error of less than 10%.


== Scales ==
== Scales ==
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Additionally, there are four distinct types of diminished triads that can be formed using the two types of minor thirds; due to the [[225/224|Marvel comma]] being tempered out in 22edo, however, there are only two distinct types of augmented triads that can be formed using the two types of major thirds, as 7 + 7 + 8 = 22.
Additionally, there are four distinct types of diminished triads that can be formed using the two types of minor thirds; due to the [[225/224|Marvel comma]] being tempered out in 22edo, however, there are only two distinct types of augmented triads that can be formed using the two types of major thirds, as 7 + 7 + 8 = 22.


{| class="wikitable"
{| class="wikitable sortable"
|+ style="font-size: 105%;" | Tertiary Chords
|+ style="font-size: 105%;" | Tertiary Chords
|-
|-
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| 25:30:36
| 25:30:36
| 1/(36:30:25)
| 1/(36:30:25)
|-
|Minor Wolf
|c sv
|C - E♭ - vG
|5\22 + 7\22
|24:28:35
|1/(35:30:24)
|-
|Major Wolf
|C v
|C - E - vG
|7\22 + 5\22
|24:30:35
|1/(35:28:24)
|-
|-
| Marvel
| Marvel
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|-
|-
| Marvel (1st inv.)
| Marvel (1st inv.)
| vE+/C
| vG♯+/C
| C - vE - vG♯
| C - vE - vG♯
| 7\22 + 8\22
| 7\22 + 8\22
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|-
|-
| Marvel (2nd inv.)
| Marvel (2nd inv.)
| vG♯+/C
| E+/C
| C - E - vG♯
| C - E - vG♯
| 8\22 + 7\22
| 8\22 + 7\22
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| C - E - G♯
| C - E - G♯
| 8\22 + 8\22
| 8\22 + 8\22
| 21:27:35
| 11:14:18
| 1/(45:35:27)
| 1/(18:14:11)
|-
|Sensa (1st inv.)
|^G×/C
|C - E - ^G
|8\22 + 6\22
|7:9:11
|1/(14:11:9)
|-
|Sensa (2nd inv.)
|E♭×/C
|C - E♭ - ^G
|6\22 + 8\22
|9:11:14
|1/(11:9:7)
|}
|}


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! 7-limit JI
! 7-limit JI
|-
|-
| 2{{pipe}}0
| <nowiki>2|0</nowiki>
| C<sup>4</sup>
| C<sup>4</sup>
| C - F - B♭
| C - F - B♭
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| 16:21:28
| 16:21:28
|-
|-
| 1{{pipe}}1
| <nowiki>1|1</nowiki>
| Csus4
| Csus4
| C - F - G
| C - F - G
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| 16:21:24
| 16:21:24
|-
|-
| 0{{pipe}}2
| <nowiki>0|2</nowiki>
| Csus2
| Csus2
| C - D - G
| C - D - G
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