13edo scales
Both archaeotonic and oneirotonic modes are partly analogous to diatonic modes, though many of them sound more like combinations of different diatonic modes.
Archaeotonic
The archaeotonic scale is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics, and extremely dissonant intervals such as 16/11 and 32/21 are less common.
Scales
The position of the small step determines the sound of the 7-note MOSes.
- Ryonian: Whole tone with a leading tone up to the tonic
- Karakaliaan: Bright whole tone major with a bit of Mixolydian
- Lobonian: Bright with a bit of natural minor
- Horthathian: The true Lydian equivalent? + Locrian
- Oukranian: Ironically the most major scale-like of them all?
- Tamashian: The true "minor" equivalent
- Zo-Kalarian: The Phrygian equivalent
Harmony
Oneirotonic
The darker, damper, more "minory" cousin of archaeotonic. Only 2 out of 8 oneirotonic modes (Dylathian and Ilarnekian) are "major" in the sense of having a major third, and both sound pretty bittersweet.
The names I use for the oneirotonic interval classes are borrowed from diatonic interval categories: "second", "third", "fourth", "tritone" (4-step intervals), "fifth" (5-step intervals), "sixth" (6-step intervals), "seventh" (7-step intervals) and octave. You just have to remember that there's an extra category between fourths and fifths and that fourths and fifths are dissonant.
Like in archaeotonic, seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly sixths and sevenths are similar to diatonic sixths and sevenths. Perfect fourths (21/16) are dissonant, but they work a lot like diatonic perfect fourths do e.g. in "sus24" chords that resolve down to thirds, and can also be spread out to make convincing 4:9:21 chords which are common in oneirotonic.
Minor tritones (approximating 11/8) work like tritones and they like to resolve inward to a third. Major tritones (16/11) are the opposite: they like to resolve outward to a sixth. Unlike in 12edo, fourths and tritones, and their octave inversions are very different in quality. Perfect fourths and minor tritones are more consonant than their inversions major tritones and perfect fifths; they can also both be spread out to make them more consonant, whereas their inversions cannot.
The diminished fourth can work either like the diatonic diminished fourth, or (uniquely in 13edo) serve as an extra 5/4 in the scale and can be part of extra consonant chords (such as O-J-K-M, representing both 8:10:11:13 and 13:16:18:21, but it only represents 13:16:18:21 in other oneirotonic-supporting tunings such as 31edo).
Basic chord progressions can move by perfect fourths or major seconds: J major-M minor-P minor-Ob major-J major (in Ilarnekian) or J major-K major-O major-M major-J major (in Dylathian)
You can also view oneirotonic as scales made of two tetrachords each spanning a 21/16 and one trichord spanning a 7/6. This will let you build 13edo "tetrachordal" scales with a similar structure that is not one of the 8 modes, with tetrachord structures similar to 12edo ones. For example:
- [2 1 1] [2 1] [1 3 1] is a kind of harmonic minor (also obtained by lowering the 7th degree of the Celephaïsian mode)
- [1 3 1] [2 1] [1 2 2] is a kind of Phrygian dominant scale (which also contains 1 3 1 2 2 2 2, a chromatic modification of the Zo-Kalarian mode of the archeotonic scale). This will give you an 8:9:13 over the first degree and an 8:9:11 over the second degree.
Samples
(A rather classical-sounding 3-part harmonization of the ascending J Ilarnekian scale (base pitch: J = 180 Hz))
Chords
Oneirotonic provides Orwell tetrads, made of three stacked minor thirds making one minor sixth. We get them by taking every second degree of the scale, JLNP or KMOQ. They sound like squashed diminished chords. One could use it to play an earbending trick where a movement up a major third and up 3 minor thirds will get you back to where you started unlike in 12edo.
J-L-K (4:5:9) and its minor counterpart J-Lb-K work well with an added sixth or seventh, even when the resulting chord does not approximate an obvious JI chord.
todo: try added fifths or tritones, describe chords with two additions or more