22edo/Eliora's approach: Difference between revisions
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== Theory == | == Theory == | ||
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{| class="wikitable center-all right-2 left-3" | {| class="wikitable center-all right-2 left-3" | ||
|- | |- | ||
!Degree | ! Degree | ||
!Cents | ! Cents | ||
!Major Arcana Notation | ! Major Arcana Notation | ||
|- | |- | ||
|0 | | 0 | ||
|0.000 | | 0.000 | ||
|The Fool | | The Fool | ||
|- | |- | ||
|1 | | 1 | ||
|54.545 | | 54.545 | ||
|The Magician | | The Magician | ||
|- | |- | ||
|2 | | 2 | ||
|109.091 | | 109.091 | ||
|The High Priestess | | The High Priestess | ||
|- | |- | ||
|3 | | 3 | ||
|163.636 | | 163.636 | ||
|The Empress | | The Empress | ||
|- | |- | ||
|4 | | 4 | ||
|218.182 | | 218.182 | ||
|The Emperor | | The Emperor | ||
|- | |- | ||
|5 | | 5 | ||
|272.737 | | 272.737 | ||
|The Hierophant | | The Hierophant | ||
|- | |- | ||
|6 | | 6 | ||
|327.273 | | 327.273 | ||
|The Lovers | | The Lovers | ||
|- | |- | ||
|7 | | 7 | ||
|381.818 | | 381.818 | ||
|The Chariot | | The Chariot | ||
|- | |- | ||
|8 | | 8 | ||
|436.364 | | 436.364 | ||
|Justice | | Justice | ||
|- | |- | ||
|9 | | 9 | ||
|490.909 | | 490.909 | ||
|The Hermit | | The Hermit | ||
|- | |- | ||
|10 | | 10 | ||
|545.455 | | 545.455 | ||
|Wheel of Fortune | | Wheel of Fortune | ||
|- | |- | ||
|11 | | 11 | ||
|600.000 | | 600.000 | ||
|Strength | | Strength | ||
|- | |- | ||
|12 | | 12 | ||
|654.545 | | 654.545 | ||
|The Hanged Man | | The Hanged Man | ||
|- | |- | ||
|13 | | 13 | ||
|709.091 | | 709.091 | ||
|Death | | Death | ||
|- | |- | ||
|14 | | 14 | ||
|763.636 | | 763.636 | ||
|Temperance | | Temperance | ||
|- | |- | ||
|15 | | 15 | ||
|818.182 | | 818.182 | ||
|The Devil | | The Devil | ||
|- | |- | ||
|16 | | 16 | ||
|872.727 | | 872.727 | ||
|The Tower | | The Tower | ||
|- | |- | ||
|17 | | 17 | ||
|927.273 | | 927.273 | ||
|The Star | | The Star | ||
|- | |- | ||
|18 | | 18 | ||
|981.818 | | 981.818 | ||
|The Moon | | The Moon | ||
|- | |- | ||
|19 | | 19 | ||
|1036.364 | | 1036.364 | ||
|The Sun | | The Sun | ||
|- | |- | ||
|20 | | 20 | ||
|1090.909 | | 1090.909 | ||
|Judgement | | Judgement | ||
|- | |- | ||
|21 | | 21 | ||
|1145.455 | | 1145.455 | ||
|The World | | The World | ||
|- | |- | ||
|22 | | 22 | ||
|1200.000 | | 1200.000 | ||
|The Fool (2/1) | | The Fool (2/1) | ||
|} | |} | ||
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== Rank-2 temperaments == | == Rank-2 temperaments == | ||
=== Orson === | === 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. | 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. | ||
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=== Hedgehog === | === Hedgehog === | ||
Hedgehog is to be used with the 5:6:7 triad, which it contains on the brightest mode in the Hedgehog[8] scale. | Hedgehog is to be used with the 5:6:7 triad, which it contains on the brightest mode in the Hedgehog[8] scale. | ||
[[Category:22edo]] | [[Category:22edo]] | ||
Revision as of 17:57, 7 October 2024
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.