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.