User:Unque/22edo Composition Theory
NOTE: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!
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.
As always, this page will be full of personal touches that may not reflect an objective truth or even wide consensus about how to use 15edo; I encourage learning musicians to experiment with different ideas and develop styles that best suit their own needs, rather than to take my word (or anyone else's for that matter) at face value as a great truth of music.
Intervals
22edo is often regarded as a full 11-limit system or some subgroup thereof; I will here prioritize intervals of the 7-limit, as they better describe the harmony of 22edo, but 11-limit intervals will additionally be used where applicable.
| Interval | Cents | JI Intervals | As a generator | Notation | Notes |
|---|---|---|---|---|---|
| 0\22 | 0 | 1/1 | C | ||
| 1\22 | 54.5 | 36/35, 28/27, 25/24 | Escapade | D♭, A𝄪 | |
| 2\22 | 109.1 | 16/15 | 11edo | B♯, E𝄫 | |
| 3\22 | 163.6 | 10/9 | Porcupine | C♯, F𝄫 | |
| 4\22 | 218.2 | 9/8, 8/7 | Wizard | D | |
| 5\22 | 272.7 | 7/6 | Orwell | E♭, B𝄪 | Often considered more dissonant than a true 7/6. |
| 6\22 | 327.3 | 6/5 | Orgone (actually in 11edo) | F♭, C𝄪 | Somewhat contentious JI interpretation (see below). |
| 7\22 | 381.8 | 5/4 | Magic | D♯, G𝄫 | |
| 8\22 | 436.3 | 9/7, 14/11 | Sensamagic | E | |
| 9\22 | 490.9 | 4/3 | Superpyth | F | |
| 10\22 | 545.5 | 15/11, 11/8 | Unnamed Balzano temp | G♭, D𝄪 | Somewhat contentious JI interpretation. |
| 11\22 | 600.0 | 45/32, 64/45 | 2edo; period for several temps | E♯, A𝄫 | |
| 12\22 | 654.5 | 16/11, 22/15 | Unnamed Balzano temp | F♯ | |
| 13\22 | 709.1 | 3/2 | Superpyth | G | |
| 14\22 | 763.6 | 14/9, 11/7 | Sensamagic | A♭, E𝄪 | |
| 15\22 | 818.2 | 8/5 | Magic | B𝄫, F𝄪 | This one specific note is very contentious in notation. |
| 16\22 | 872.7 | 5/3 | Orgone (actually in 11edo) | G♯, C𝄫 | |
| 17\22 | 927.3 | 12/7 | Orwell | A | |
| 18\22 | 981.8 | 7/4, 16/9 | Jubilic | B♭ | |
| 19\22 | 1036.3 | 9/5 | Porcupine | C♭, G𝄪 | |
| 20\22 | 1090.9 | 15/8 | 11edo | A♯, D𝄫 | |
| 21\22 | 1145.5 | 48/25, 27/14, 35/18 | Escapade | B | |
| 22\22 | 1200.0 | 2/1 | C |
The thirds of 22edo
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 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.
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Scales
5L 2s
The 5L 2s scale is one of two types of Diatonic scales represented in 22edo, and represents 2.3.7 subgroup shade of Diatonic popularized by the Greek mathematician Archytas.