Oneirotonic

Pseudo-diatonic theory

Oneirotonic is often used as distorted diatonic. Because distorted diatonic modal harmony and functional harmony both benefit from a recognizable major third, the following theory essentially assumes an A-Team tuning, i.e. an oneirotonic tuning with generator between 5\13 and 7\18 (or possibly an approximation of such a tuning, such as a neji). The reader should experiment and see how well these ideas work in other oneirotonic tunings.

Ana modes

We call modes with a major mos5th ana modes (from Greek for 'up'), because the sharper 5th degree functions as a flattened melodic fifth when moving from the tonic up. The ana modes of the MOS are the 4 brightest modes, namely Dylathian, Ilarnekian, Celephaïsian and Ultharian.

The ana modes have squashed versions of the classical major and minor pentachords R-M2-M3-P4-P5 and R-M2-m3-P4-P5 and can be viewed as providing a distorted version of classical diatonic functional harmony and counterpoint. For example, in the Dylathian mode, the 4:5:9 triad on the sixth degree can sound like both "V" and "III of iv" depending on context.

In pseudo-classical functional harmony, the 6th scale degree (either an augmented mossixth or a perfect mossixth) could be treated as mutable. The perfect mossixth would be used when invoking the diatonic V-to-I trope by modulating by a perfect mosfourth from the sixth degree. The augmented mossixth would be used when a major key needs to be used on the fourth degree.

Progressions

Some suggested basic ana functional harmony progressions, outlined very roughly (note: VI is the sharp 5th, etc.). "I" means either Imaj or Imin. "Natural" Roman numerals follow the Ilarnekian mode.

• I-IVmin-VImaj-I
• Imaj-VIImin-IVmaj-Imaj
• Imin-@IIImaj-VImaj-Imaj
• Imin-@IIImaj-Vdim-VImaj-Imin
• Imin-@VIIImin-IIImaj-VImaj-Imin
• Imin-IVmin-@VIIImin-@IIImaj-VImaj-Imin
• Imin-IVmin-IIdim-VImaj-Imin
• Imin-IVmin-IIdim-@IIImaj-Imin
• I-VIImin-IImin-VImaj-I
• Imaj-VIImin-IVmin-VImaj-Imaj
• Modulations by major mos2nd:
  • I-IV-VII-II
  • I-IVmaj-II
  • I-VIImin-II
• Modulations by major mos3rd:
  • Modulate up major mos2nd twice
  • Imin-VImin-III (only in 13edo)
  • Imaj-&VImin-III (only in 13edo)
• Modulations by minor mos3rd:
  • I-VI-@III
  • I-IVmin-VImin-@VIIImaj-@III

Another approach to oneirotonic chord progressions is to let the harmony emerge from counterpoint.

Kata modes

We call modes with a minor mos5th kata modes (from Greek for 'down'). The kata modes of the MOS are the 4 darkest modes, namely Mnarian, Kadathian, Hlanithian and Sarnathian. In kata modes, the melodically squashed fifth from the tonic downwards is the flatter 5th degree. Kata modes could be used to distort diatonic tropes that start from the tonic and work downwards or work upwards towards the tonic from below it. For example:

• Mnarian (LSLSLLSL) and Kadathian (SLLSLLSL) are kata-Mixolydians
• Hlanithian (SLLSLSLL) is a kata-melodic major (the 4th degree sounds like a major third; it's actually a perfect mosfourth.)
• Sarnathian (SLSLLSLL) is a kata-melodic minor (When starting from the octave above, the 4th degree sounds like a minor third; it's actually a diminished mosfourth.)

When used in an "ana" way, the kata modes are radically different in character than the brighter modes. Because the fifth and seventh scale degrees become the more consonant minor tritone and the minor sixth respectively, the flat tritone sounds more like a stable scale function. Hlanithian, in particular, is a lot like a more stable version of the Locrian mode in diatonic.

MODMOSes

The most important oneirotonic MODMOS is LSLLLSLS (and its rotations), because it allows one to evoke certain ana or kata diatonic modes where three whole steps in a row are important (Dorian, Phrygian, Lydian or Mixo) in an octatonic context. The MOS would not always be able to do this because it has at most two consecutive large steps.

As with the MOS, this MODMOS has four ana and four kata rotations:

• LLLSLSLS: Dylathian &4: an ana-Lydian
• LLSLSLSL: Ilarnekian @8: an ana-Mixolydian
• LSLLLSLS: Celephaïsian &6: an ana-Dorian
• SLLLSLSL: Ultharian @2: an ana-Phrygian
• SLSLSLLL: Sarnathian @6: a kata-Locrian
• SLSLLLSL: Sarnathian &6: a kata-Dorian
• LSLSLLLS: Mnarian &8: a kata-Ionian
• LSLSLSLL: Hlanithian &2: a kata-Aeolian

Other potentially interesting oneirotonic MODMOSes (that do not use half-sharps or half-flats) are:

• the distorted harmonic minor LSLSLLSAS (A = aug 2nd = L + chroma)
• the distorted Freygish SASLSLLS

Chords

Chords are given in oneirotonic MOS interval notation. For example, M5 means major mosfifth (squashed fifth).

• R-M3-M5: Squashed Major Triad
• R-m3-M5: Squashed Minor Triad
• R-m3-m5: Squashed Dim Triad
• R-M3-A5: Squashed Aug Triad
• R-M3-M5-A6: Squashed Major Triad Add6
• R-m3-M5-A6: Squashed Minor Triad Add6
• R-M3-M5-M7: Oneiro Major Tetrad
• R-m3-M5-M7: Oneiro Minor Tetrad
• R-m3-m5-M7: Oneiro Half-Diminished Tetrad
• R-m3-m5-m7: Orwell Tetrad, Oneiro Diminished Tetrad
• R-M3-A6: Squashed 1st Inversion Minor Triad
• R-m3-P6: Squashed 1st Inversion Major Triad
• R-M3-M7: 1st Inversion Squashed Minor Triad (note the order of terms!)
• R-m3-m7: 1st Inversion Squashed Major Triad
• R-m5-M7: 2nd Inversion Squashed Major Triad
• R-m5-m7: 2nd Inversion Squashed Minor Triad
• R-M3-M8: Oneiro Major Seventh
• R-m3-M8: Oneiro Minor Major Seventh
• R-M3-(M2): Oneiro Major Add9
• R-m3-(M2): Oneiro Minor Add9
• R-M3-(M2)-(P4): Oneiro Major Add9 Sub11
• R-m3-(M2)-(P4): Oneiro Minor Add9 Sub11
• R-M2-P4: Oneiro Sus2 Sus4
• R-P4-M7: Oneiro Quartal Triad
• R-P4-M7-(M2): Oneiro Quartal Tetrad, Core Tetrad
• R-P4-M7-(M2)-(M5): Oneiro Quartal Pentad, Core Pentad
• R-P4-M7-(M2)-(M5)-(M8): Oneiro Quartal Hexad
• R-P4-M7-M8: Oneiro Quartal Seventh Tetrad
• R-M3-m7: Sephiroth Triad (approximates 8:10:13 in 13edo)
• R-M3-m7-m2-(P4): Sephiroth Triad Addmin9 Sub11
• R-M3-m7-(P4): Sephiroth Triad Sub11
• R-P4-m8
• R-m3-P4-m8
• R-m5-m8
• R-m5-m7-m8

"Oneirotonic maqam"

"Oneirotonic maqam" is based on the idea "If maqam is loosely an extension of diatonic that uses neutral intervals, what is the oneirotonic counterpart that uses oneirotonic neutral intervals?" or "What if we distorted maqam scales similarly to how oneirotonic distorts diatonic scales?" The following assumes an edo with A-Team oneirotonic scales and neutral mosseconds (i.e. half of an oneirotonic minor mosthird) such as 18edo and 26edo. In rank-2 temperament terms, this requires a loosely 18&26 structure.

• 26edo can be used if you want neutral mosseconds and minor mosthirds closer to their 24edo counterparts. In 26edo these are 138c and 277c respectively, but in 18edo these are 133c and 267c.
• 18edo can be used if you want neutral mosthirds (neutral mos2nd + major mos2nd) closer to conventional neutral thirds. The neutral mos3rd is 333c in 18edo and 323c in 26edo.

Zheanist theory

A-Team oneirotonic may be a particularly good place to bring to bear Zheanism's high harmonic chords, as A-Team temperament doesn't yield many low-complexity chords.

18edo may be a better basis for a style of oneirotonic Zheanism using comma sharp and comma flat fifths than 13edo (in particular diesis sharp and diesis flat fifths; diesis is a category with a central region of 32 to 40c). In 18edo both the major fifth (+31.4c) and the minor fifth (-35.3) are about a diesis off from a just perfect fifth. In 13edo only the major fifth is a diesis sharp, and it is +36.5c off from just; so there's less wiggle room for a neji if you want every major fifth to be at most a diesis sharp).

31nejis and 34nejis also provide opportunities to use dieses directly, since 1\31 (38.71c) and 1\34 (35.29c) are both dieses.

Primodal chords

These are just oneirotonic-inspired chords, they aren't guaranteed to fit in your neji.

/13

• 13:16:19 Tridecimal Squashed Major Triad
• 13:17:19 Tridecimal Naiadic Maj2
• 13:17:20 Tridecimal Squashed 2nd Inversion Minor Triad
• 13:17:21 Tridecimal Squashed 2nd Inversion Major Triad
• 13:16:19:22 Tridecimal Oneiro Major Tetrad

/17

• 17:20:25 Septen Squashed Minor Triad
• 17:20:26 Septen Squashed 1st Inversion Major Triad
• 17:20:25:29 Septen Minor Oneiro Tetrad
• 17:21:25:29 Septen Major Oneiro Tetrad
• 17:20:26:29 Septen Squashed 1st Inversion Major Triad addM6
• 34:40:47:55 Septen Orwell Tetrad
• 34:40:52:58:76:89:102:129 (Celephaïsian + P5; R-min3-sup5-M6-M9-sub11-P12(fc)-M14)
• 34:40:52:58:76:89:102:110:129 (Celephaïsian + P5; R-min3-sup5-M6-M9-sub11-P12(fc)-supmin13-M14)
• 34:40:50:58:89:102:129 (R-min3-sub5-M6-M9-sub11-P12(rc)-M14)
• 34:40:50:58:89:102:110:129 (R-min3-sub5-M6-M9-sub11-P12(rc)-supmin13-M14)
• 34:40:50:58:76:89:110:129 (R-m3-sub5-M6-M9-sub11-supm13-M7)
• 34:40:50:58:76:89:102:110:129:208 (R-m3-sub5-M6-M9-sub11-P12(rc)-supm13-M14-sup19(rc^2))

/23

• 23:27:30 Vice Squashed Min4
• 23:27:30:35:44 Vice Squashed Min4 addM5,M7
• 23:27:37 Vice Orwell Tetrad no5
• 46:54:63:76 Vice Orwell Tetrad
• 46:54:67:78 Vice Minor Oneiro Tetrad
• 46:54:60:67:78 Vice Min4 Oneiro Pentad

/29

• 29:34:38 Vicenon Squashed Sus4
• 29:34:42 Vicenon Squashed Minor Triad
• 29:36:42 Vicenon Squashed Major Triad
• 29:34:40:47 Vicenon Orwell Tetrad
• 29:38:65:84:99 Vicenon Oneiro Core Pentad
• 29:38:65:84:99:110 Vicenon Oneiro Core Hexad
• 58:65:72:80:84:94:99:110:116 Vicenon Dylathian &4
• 58:65:72:76:84:94:99:110:116 Vicenon Dylathian
• 58:65:72:76:84:89:99:110:116 Vicenon Ilarnekian
• 58:65:72:76:84:89:99:104:116 Vicenon Ilarnekian @8
• 58:65:68:76:84:94:99:110:116 Vicenon Celephaïsian &6
• 58:65:68:76:84:89:99:110:116 Vicenon Celephaïsian
• 58:65:68:76:84:89:99:104:116 Vicenon Ultharian
• 58:65:68:76:80:89:99:104:116 Vicenon Mnarian
• 58:65:68:76:80:89:99:110:116 Vicenon Mnarian &8
• 58:65:68:76:80:89:94:104:116 Vicenon Hlanithian &2
• 58:61:68:76:80:89:99:104:116 Vicenon Kadathian
• 58:61:68:76:84:89:99:104:116 Vicenon Ultharian @2
• 58:61:68:76:80:89:94:104:116 Vicenon Hlanithian
• 58:61:68:72:80:89:99:104:116 Vicenon Sarnathian &6
• 58:61:68:72:80:89:94:104:116 Vicenon Sarnathian
• 58:61:68:72:80:84:94:104:116 Vicenon Sarnathian @6

Some oneirotonic nejis

• 58:61:65:68:72:76:80:84:89:94:99:104:110:116 A very low-complexity 13neji; not optimized for transposability.

Rank-2 temperaments

A-Team (13&18, 4:5:9:21)

Sortable table of intervals in the Dylathian mode and their A-Team interpretations:

Degree	Size in 13edo	Size in 18edo	Size in 31edo	Note name on L	Approximate ratios	#Gens up
1	0\13, 0.00	0\18, 0.00	0\31, 0.00	L	1/1	0
2	2\13, 184.62	3\18, 200.00	5\31, 193.55	M	9/8, 10/9	+3
3	4\13, 369.23	6\18, 400.00	10\31, 387.10	N	5/4	+6
4	5\13, 461.54	7\18, 466.67	12\31, 464.52	O	21/16, 13/10	+1
5	7\13, 646.15	10\18, 666.66	17\31, 658.06	P	13/9, 16/11	+4
6	9\13, 830.77	13\18, 866.66	22\31, 851.61	Q	13/8, 18/11	+7
7	10\13, 923.08	14\18, 933.33	24\31, 929.03	J	12/7	+2
8	12\13, 1107.69	17\18, 1133.33	29\31, 1122.58	K		+5

Petrtri (13&21, 4:5:9:11:13:17)

Intervals

Sortable table of intervals in the Dylathian mode and their Petrtri interpretations:

Degree	Size in 13edo	Size in 21edo	Size in 34edo	Size in POTE tuning	Note name on L	Approximate ratios	#Gens up
1	0\13, 0.00	0\21, 0.00	0\34, 0.00	0.00	L	1/1	0
2	2\13, 184.62	3\21, 171.43	5\34, 176.47	177.45	M	10/9, 11/10	+3
3	4\13, 369.23	6\21, 342.86	10\34, 352.94	354.90	N	11/9, 16/13	+6
4	5\13, 461.54	8\21, 457.14	13\34, 458.82	459.15	O	13/10, 17/13, 22/17	+1
5	7\13, 646.15	11\21, 628.57	18\34, 635.294	636.60	P	13/9, 16/11	+4
6	9\13, 830.77	14\21, 800.00	23\34, 811.77	814.05	Q	8/5	+7
7	10\13, 923.08	16\21, 914.29	26\34, 917.65	918.30	J	17/10	+2
8	12\13, 1107.69	19\21, 1085.71	31\34, 1094.12	1095.75	K	17/9, 32/17	+5

Samples

‎(A rather classical-sounding 3-part harmonization of the ascending J Ilarnekian scale; tuning is 13edo)

(13edo, first 30 seconds is in J Celephaïsian)

(13edo, L Ilarnekian)

(by Igliashon Jones, 13edo, J Celephaïsian)