22edo/Eliora's approach
Theory
This notation assumes naming the 22 notes after the Major Arcana in Tarot, with the base note being 0 or 22 = The Fool. There are no sharps or flats, as the notation is bijective.
Table of intervals
| Degree | Cents | Major Arcana Notation |
|---|---|---|
| 0 | 0.000 | The Fool |
| 1 | 54.545 | The Magician |
| 2 | 109.091 | The High Priestess |
| 3 | 163.636 | The Empress |
| 4 | 218.182 | The Emperor |
| 5 | 272.737 | The Hierophant |
| 6 | 327.273 | The Lovers |
| 7 | 381.818 | The Chariot |
| 8 | 436.364 | Justice |
| 9 | 490.909 | The Hermit |
| 10 | 545.455 | Wheel of Fortune |
| 11 | 600.000 | Strength |
| 12 | 654.545 | The Hanged Man |
| 13 | 709.091 | Death |
| 14 | 763.636 | Temperance |
| 15 | 818.182 | The Devil |
| 16 | 872.727 | The Tower |
| 17 | 927.273 | The Star |
| 18 | 981.818 | The Moon |
| 19 | 1036.364 | The Sun |
| 20 | 1090.909 | Judgement |
| 21 | 1145.455 | The World |
| 22 | 1200.000 | The Fool (2/1) |
Base chord into which everything resolves
The conventional approach would be to take the "just" triad 4:5:6 and its inversion, which would result in 0–7–13 and 0–6–13 chords, respectively. However, The Lovers are sharp of just 6/5, making them neutralized or superminor. This is in contrast to the 12edo, where minor third is flat of 6/5, which creates a lower brightness and aligns with the feeling of minor.
As such, 4:5:6 triad is not consonant in this approach. Below some of the variant triads are shown.
5:6:7 triad
A triad which makes more sense to take as the main one would be 5:6:7, represented as 0–6–11, thus meaning it's subtended by a 600 cent tritone representing 7/5. The "major" version of this would be quite stretched, so it would align with feeling "major" by tonal brightness.
This triad can be used in any period-2 temperament that 22edo provides. In addition, it doubles the property of the tritone being consonant in this instance.
14:18:21 triad
The 1/1–9/7–3/2 triad uses the 9/7 interval as the major third, and arises from the 4414441 superpyth scale. This is the more diatonic-normative approach.
In this case, since minor version is otonal (6:7:9), it is consonant, as opposed to the inversion of 4:5:6.
Orwell tetrad
0–5–10–15 is the equidistant chord that is associated with the orwell temperament, which 22edo supports. As such, it can be used as well.
Rank-2 temperaments
Orson
In this approach, Orson will refer to not just 5-limit orwell, but also the way of playing orwell that favors the 0–6–13 and 0–7–13 triads as the main resolution destinations, as opposed to the 0–5–10–15 triad.
Hedgehog
Hedgehog is to be used with the 5:6:7 triad, which it contains on the brightest mode in the Hedgehog[8] scale.