22edo/Eliora's approach: Difference between revisions
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'''Main article: [[22edo]]''' | '''Main article: [[22edo]]''' | ||
== Theory | == 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. | 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 == | |||
{| class="wikitable center-all right-2 left-3" | {| class="wikitable center-all right-2 left-3" | ||
|- | |- | ||
| Line 8: | Line 10: | ||
!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) | ||
|} | |} | ||
== 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. | |||