Oneirotonic

The term oneirotonic /oʊnaɪrəˈtɒnɪk/ oh-ny-rə-TON-ik is used for the 8-note MOS structure 5L 3s, whose brightest mode is LLsLLsLs. The name "oneirotonic" was coined by Cryptic Ruse after the Dreamlands in H.P. Lovecraft's Dream Cycle mythos. Oneirotonic is a distorted diatonic, because it has one extra small step compared to diatonic (5L 2s).

The generator size ranges from 450¢ (3\8) to 480¢ (2\5). Hence any edo with an interval between 450¢ and 480¢ has an oneirotonic scale.

In terms of regular temperaments, there are at least two melodically viable ways to interpret oneirotonic:

1. When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): A-Team (13&18, a 4:5:9:21 or 2.9.5.21 temperament)
2. When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): Petrtri (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)

Notation

The notation used in this article is LLsLLsLs = JKLMNOPQJ (with J ≈ 180 Hz), unless specified otherwise.

Intervals

Generators	Notation (1/1 = J)	Octatonic interval category name	Generators	Notation of 2/1 inverse	Octatonic interval category name
The "diatonic" 8-note scale has the following intervals (from some root):
0	J	perfect unison	0	J	octave
1	M	perfect mosfourth	-1	Ob	perfect mossixth
2	P	major mosseventh	-2	Lb	minor mosthird
3	K	major mossecond	-3	Qb	minor moseighth
4	N	major mosfifth	-4	Nb	minor mosfifth
5	Q	major moseighth	-5	Kb	minor mossecond
6	L	major mosthird	-6	Pb	minor mosseventh
7	O	augmented sixth	-7	Mb	diminished fourth
The "chromatic" 13-note scale also has the following intervals (from some root):
8	J#	augmented unison	-8	Jb	diminished octave
9	M#	augmented mosfourth	-9	Obb	diminished mossixth
10	P#	augmented mosseventh	-10	Lbb	diminished mosthird
11	K#	augmented mossecond	-11	Qbb	diminished moseighth
12	N#	augmented mosfifth	-12	Nbb	diminished mosfifth

Modal harmony

Oneirotonic modes are named after cities in the Dreamlands.

1. Dylathian: LLsLLsLs (major with hints of Mixolydian and "#5")
2. Ilarnekian: LLsLsLLs (major with hints of "b6")
3. Celephaïsian: LsLLsLLs (the oneirotonic melodic minor. Very classical-sounding; Easley Blackwood's 13-note etude uses this as its home mode.)
4. Ultharian: LsLLsLsL (A Dorian analogue. Another Dorian analogue is the MODMOS LsLLLsLs)
5. Mnarian: LsLsLLsL
6. Kadathian: sLLsLLsL (another "Locrian")
7. Hlanithian: sLLsLsLL (closest Locrian analogue)
8. Sarnathian: sLsLLsLL (Darkest but ironically the most consonant. Here be dragons.)

The modes in 13edo edo steps and C-H notation:

Modes with sharp tritone

At least in A-Team, the brighter modes can be viewed as providing a distorted version of diatonic functional harmony. 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. Basic chord progressions can move by minor fourths, thirds, or major seconds: for example, 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).

Modes with flat tritone

The darker modes are radically different in character than the brighter modes. Because of the consonant 11/8 minor tritone and the 13/8 minor sixth, the flat tritone sounds more like a stable scale function.

A-Team (13&18, 4:5:9:(11:13):21) interpretation

The sizes of the generator, large step and small step of oneirotonic are as follows in various edos:

	13edo	18edo	31edo	64/49 generator	JI intervals represented (2.9.5.21 subgroup)
generator	5\13, 461.54	7\18, 466.67	12\31, 464.52	462.35	21/16
L	2\13, 184.62	3\18, 200.00	5\31, 193.55	187.04	9/8, 10/9
s	1\13, 92.31	1\18, 66.66	2\31, 77.42	88.26	21/20

Intervals

Sortable table of Dylathian, the brightest mode:

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

Chords

Despite being melodically familiar, oneirotonic is harmonically complex in that it doesn't represent many lower-complexity JI triads other than 4:9:21, 9:10:13, and the occasional 4:5:9. Hence oneirotonic may especially benefit from either using inharmonic timbres in addition to harmonic ones or using a well-tempered version of 13edo adopted for this scale. The availability of certain consonances also varies greatly by mode: for example, only Dylathian, Ilarnekian and Sarnathian have a 5/4 on the tonic, and only Mnarian, Kadathian, Hlanithian and Sarnathian have an 11/8 on the tonic.

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

The sizes of the generator, large step and small step of oneirotonic are as follows in various edos: [TODO: Golden father]

	13edo	21edo	34edo	JI intervals represented (2.5.9.11.13.17 subgroup)
generator	5\13, 461.54	8\21, 457.14	13\34, 458.824	13/10, 17/13, 22/17
L	2\13, 184.62	3\21, 171.43	5\34, 176.47	10/9, 11/10
s	1\13, 92.31	2\21, 114.29	3\34, 105.88	18/17, 17/16

Intervals

Sortable table of Dylathian, the brightest mode:

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

Chords

The pentad P1-m8-M10-m12-M16 "5:9:11:13:17" occurs twice in the 8 note mos of 13edo and 21edo's father[8]. The pentad P1-M3-M4-m6-m9 "4:5:11:13:17" occurs once.

Triad occurrences:

• P1-M2-M3 "9:10:11" occurs 2x
• P1-M2-M5 "9:10:13" occurs 3x
• P1-M2-M8 "9:10:17" occurs 3x
• P1-M3-M5 "9:11:13" occurs 2x
• P1-M3-M8 "9:11:17" occurs 2x
• P1-M5-M8 "9:13:17" occurs 3x

All 8 modes provide chords in various prime families (list of modes is non-exhaustive):

• /2 chords occur on Sarnathian
• /5 chords occur on Ultharian and Mnarian
• /9 chords occur on Dylathian and Ilarnekian
• /11 chords occur on Hlanithian and Sarnathian
• /13 chords occur on Mnarian and Kadathian
• /17 chords occur on Hlanithian and Kadathian

Samples

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

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

(by Igliashon Jones, 13edo)