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| The term '''oneirotonic''' 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]]).
| | #redirect [[5L 3s]] |
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| In terms of [[regular temperament]]s, there are two melodically viable ways to interpret oneirotonic:
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| # [[A-Team]] (13&18, a 4:5:9:21 or 2.9.5.21 temperament)
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| # [[Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)
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| == Intervals ==
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| 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 archeotonic you can change the perception of an interval by approaching it from different directions, but in oneirotonic it will change what diatonic interval class you hear it as: say, as both a third and a fourth, rather than both a major and a minor third.
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| == Modal harmony ==
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| Oneirotonic modes are named after cities in the Dreamlands.
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| #Dylathian: LLsLLsLs (major with hints of Mixolydian and "#5")
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| #Ilarnekian: LLsLsLLs (major with hints of "b6")
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| #Celephaïsian: LsLLsLLs (the oneirotonic melodic minor. Very classical-sounding; Easley Blackwood's 13-note etude uses this as its home mode.)
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| #Ultharian: LsLLsLsL (A Dorian analogue. Another Dorian analogue is the MODMOS LsLLLsLs)
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| #Mnarian: LsLsLLsL
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| #Kadathian: sLLsLLsL (another "Locrian")
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| #Hlanithian: sLLsLsLL (closest Locrian analogue)
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| #Sarnathian: sLsLLsLL (Darkest but ironically the most consonant. Here be dragons.)
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| [[File:Oneirotonic.png|alt=Oneirotonic.png|Oneirotonic.png]]
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| ===Modes with sharp tritone ===
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| 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).
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| === Modes with flat tritone ===
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| The darker modes are radically different in character than the brighter modes. In A-team tunings, because of the consonant 11/8 minor tritone and the 13/8 minor sixth, the flat tritone sounds more like a stable scale function.
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| ==A-Team (13&18, 4:5:9:(11:13):21) interpretation==
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| The sizes of the generator, large step and small step of oneirotonic are as follows in various edos:
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| {| class="wikitable right-2 right-3 right-4 right-5"
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| |-
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| ! style="text-align:right" |
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| ! 13edo
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| ! 18edo
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| ! 31edo
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| ! 64/49 generator
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| ! JI intervals represented (2.9.5.21 subgroup)
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| |-
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| | generator
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| | 5\13, 461.54
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| | 7\18, 466.67
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| | 12\31, 464.52
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| | 462.35
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| | 21/16
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| |-
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| | L
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| | 2\13, 184.62
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| | 3\18, 200.00
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| | 5\31, 193.55
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| | 187.04
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| | 9/8, 10/9
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| |-
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| | s
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| | 1\13, 92.31
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| | 1\18, 66.66
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| | 2\31, 77.42
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| | 88.26
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| | 21/20
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| |}
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| === Intervals ===
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| Sortable table of Dylathian, the brightest mode:
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| {| class="wikitable right-2 right-3 right-4 sortable"
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| |-
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| ! style="text-align:right" | Degree
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| ! Size in 13edo
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| ! Size in 18edo
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| ! Size in 31edo
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| ! Note name on J
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| !class="unsortable"| Approximate ratios<ref>The harmonics over 1/1 are in bold. The ratio interpretations that are not valid for 18edo are italicized.</ref>
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| ! #Gens up
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| |-
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| | 1
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| | 0\13, 0.00
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| | 0\18, 0.00
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| | 0\31, 0.00
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| | J
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| | '''1/1'''
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| | 0
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| |-
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| | 2
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| | 2\13, 184.62
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| | 3\18, 200.00
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| | 5\31, 193.55
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| | K
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| | '''9/8''', 10/9
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| | +3
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| |-
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| | 3
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| | 4\13, 369.23
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| | 6\18, 400.00
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| | 10\31, 387.10
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| | L
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| | '''5/4'''
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| | +6
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| |-
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| | 4
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| | 5\13, 461.54
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| | 7\18, 466.67
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| | 12\31, 464.52
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| | M
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| | '''21/16''', ''13/10''
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| | +1
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| |-
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| | 5
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| | 7\13, 646.15
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| | 10\18, 666.66
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| | 17\31, 658.06
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| | N
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| | ''13/9'', ''16/11''
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| | +4
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| |-
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| | 6
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| | 9\13, 830.77
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| | 13\18, 866.66
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| | 22\31, 851.61
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| | O
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| | '''''13/8''''', ''18/11''
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| | +7
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| |-
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| | 7
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| | 10\13, 923.08
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| | 14\18, 933.33
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| | 24\31, 929.03
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| | P
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| | 12/7
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| | +2
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| |-
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| | 8
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| | 12\13, 1107.69
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| | 17\18, 1133.33
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| | 29\31, 1122.58
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| | Q
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| | +5
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| |}
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| <references/>
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| === Chords ===
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| 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.
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| ==Petrtri (13&21, 4:5:9:11:13:17) interpretation==
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| The sizes of the generator, large step and small step of oneirotonic are as follows in various edos: [TODO: Golden father]
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| {| class="wikitable right-2 right-3 right-4"
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| |-
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| ! style="text-align:right" |
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| ! 13edo
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| ! 21edo
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| ! 34edo
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| ! JI intervals represented (2.9/5.11/5.13/5.17/5 subgroup)
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| |-
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| | generator
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| | 5\13, 461.54
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| | 8\21, 457.14
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| | 13\34, 458.824
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| | 13/10, 17/13, 22/17
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| |-
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| | L
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| | 2\13, 184.62
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| | 3\21, 171.43
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| | 5\34, 176.47
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| | 10/9, 11/10
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| |-
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| | s
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| | 1\13, 92.31
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| | 2\21, 114.29
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| | 3\34, 105.88
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| | 18/17
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| |}
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| === Intervals ===
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| Sortable table of Dylathian, the brightest mode:
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| {| class="wikitable right-2 right-3 right-4 sortable"
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| |-
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| ! style="text-align:right" | Degree
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| ! Size in 13edo
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| ! Size in 21edo
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| ! Size in 34edo
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| ! Note name on J
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| !class="unsortable"| Approximate ratios
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| ! #Gens up
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| |-
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| | 1
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| | 0\13, 0.00
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| | 0\21, 0.00
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| | 0\34, 0.00
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| | J
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| | 1/1
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| | 0
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| |-
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| | 2
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| | 2\13, 184.62
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| | 3\21, 171.43
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| | 5\34, 176.47
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| | K
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| | 10/9, 11/10
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| | +3
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| |-
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| | 3
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| | 4\13, 369.23
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| | 6\21, 342.86
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| | 10\34, 352.94
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| | L
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| | 11/9, 16/13
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| | +6
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| |-
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| | 4
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| | 5\13, 461.54
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| | 8\21, 457.14
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| | 13\34, 458.82
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| | M
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| | 13/10, 17/13, 22/17
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| | +1
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| |-
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| | 5
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| | 7\13, 646.15
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| | 11\21, 628.57
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| | 18\34, 635.294
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| | N
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| | 13/9, 16/11
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| | +4
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| |-
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| | 6
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| | 9\13, 830.77
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| | 14\21, 800.00
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| | 23\34, 811.77
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| | O
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| | 8/5
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| | +7
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| |-
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| | 7
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| | 10\13, 923.08
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| | 16\21, 914.29
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| | 26\34, 917.65
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| | P
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| | 17/10
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| | +2
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| |-
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| | 8
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| | 12\13, 1107.69
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| | 19\21, 1085.71
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| | 31\34, 1094.12
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| | Q
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| | 17/9, 32/17
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| | +5
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| |}
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| <references/>
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| ===Chords===
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| The pentad P1-m7-M9-m11-M13 "5:9:11:13:17" occurs twice in the 8 note mos of 13edo and 21edo's father[8], hence this forms the basis for 13&21 temperament. 4:5:9:11:13:17 occurs once.
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| Triad occurrences:
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| *P1-M2-M3 "9:10:11" occurs 2x
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| *P1-M2-m5 "9:10:13" occurs 3x
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| *P1-M2-M7 "9:10:17" occurs 3x
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| *P1-M3-m5 "9:11:13" occurs 2x
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| *P1-M3-M7 "9:11:17" occurs 2x
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| *P1-m5-M7 "9:13:17" occurs 3x
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| All 8 modes provide chords in various prime families:
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| */2 chords occur on Sarnathian
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| */5 chords occur on Ultharian and Mnarian
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| */9 chords occur on Dylathian and Ilarnekian
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| */11 chords occur on Hlanithian and Sarnathian
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| */13 chords occur on Mnarian and Kadathian
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| */17 chords occur on Hlanithian and Kadathian
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| ==Samples ==
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| [[File:Oneirotonic 3 part sample.mp3]]
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| (A rather classical-sounding 3-part harmonization of the ascending J Ilarnekian scale; tuning is 13edo)
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| [[File:13edo_1MC.mp3]]
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| (First 30 seconds is in Celephaïsian mode)
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| [[Category:Scales]]
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| [[Category:Oneirotonic|*]]
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| [[Category:Mos]]
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