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| The term '''oneirotonic''' (/oʊnaɪrəˈtɒnɪk/ ''oh-ny-rə-TON-ik'' or /ənaɪrə-/ ''ə-ny-rə-'') 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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| 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. [[13edo]] is the smallest edo with a (non-degenerate) 5L3s oneirotonic scale and thus is the most commonly used oneirotonic tuning.
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| In terms of [[regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic. [[13edo]] represents both temperaments.
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| # 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)
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| # 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)
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| == Notation==
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| The notation used in this article is J Celephaïsian (LsLLsLLs) = JKLMNOPQJ (with J ≈ 180 Hz), unless specified otherwise. So the [[13edo]] gamut is as follows:
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| '''J''' J#/Kb '''K''' '''L''' L#/Mb '''M''' M#/Nb '''N''' '''O''' O#/Pb '''P''' P#/Qb '''Q''' '''J'''
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| Note: N is close to standard C, since the reference pitche 180 Hz for J was chosen to be nearly a pure 11/8 above standard 12edo C.
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| == Intervals ==
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| {| class="wikitable center-all"
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| |-
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| ! Generators
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| ! Notation (1/1 = J)
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| ! Octatonic interval category name
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| ! Generators
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| ! Notation of 2/1 inverse
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| ! Octatonic interval category name
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| |-
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| | colspan="6" style="text-align:left" | The "diatonic" 8-note scale has the following intervals (from some root):
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| |-
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| | 0
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| | J
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| | perfect unison
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| | 0
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| | J
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| | octave
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| |-
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| | 1
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| | M
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| | perfect mosfourth
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| | -1
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| | O
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| | perfect mossixth
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| |-
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| | 2
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| | P
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| | major mosseventh
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| | -2
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| | L
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| | minor mosthird
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| |-
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| | 3
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| | K
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| | major mossecond
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| | -3
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| | Qb
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| | minor moseighth
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| |-
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| | 4
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| | N
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| | major mosfifth
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| | -4
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| | Nb
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| | minor mosfifth
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| |-
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| | 5
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| | Q
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| | major moseighth
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| | -5
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| | Kb
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| | minor mossecond
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| |-
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| | 6
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| | L#
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| | major mosthird
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| | -6
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| | Pb
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| | minor mosseventh
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| |-
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| | 7
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| | O#
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| | augmented sixth
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| | -7
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| | Mb
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| | diminished fourth
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| |-
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| | colspan="6" style="text-align:left" | The "chromatic" 13-note scale also has the following intervals (from some root):
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| |-
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| | 8
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| | J#
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| | augmented unison
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| | -8
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| | Jb
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| | diminished octave
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| |-
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| | 9
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| | M#
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| | augmented mosfourth
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| | -9
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| | Ob
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| | diminished mossixth
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| |-
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| | 10
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| | P#
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| | augmented mosseventh
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| | -10
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| | Lb
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| | diminished mosthird
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| |-
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| | 11
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| | K#
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| | augmented mossecond
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| | -11
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| | Qbb
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| | diminished moseighth
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| |-
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| | 12
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| | N#
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| | augmented mosfifth
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| | -12
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| | Nbb
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| | diminished mosfifth
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| |}
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| == Oneirotonic key signatures ==
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| Flat keys:
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| * Jb Celephaisian, Lb Dylathian = Qb, Nb, Kb, Pb, Mb, Jb, Ob, Lb
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| * Mb Celephaisian, Ob Dylathian = Qb, Nb, Kb, Pb, Mb, Jb, Ob
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| * Pb Celephaisian, Jb Dylathian = Qb, Nb, Kb, Pb, Mb, Jb
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| * Kb Celephaisian, Mb Dylathian = Qb, Nb, Kb, Pb, Mb
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| * Nb Celephaisian, Pb Dylathian = Qb, Nb, Kb, Pb
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| * Qb Celephaisian, Kb Dylathian = Qb, Nb, Kb
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| * L Celephaisian, Nb Dylathian = Qb, Nb
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| * O Celephaisian, Qb Dylathian = Qb
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| All-natural key signature:
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| * J Celephaisian, L Dylathian = no sharps or flats
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| Sharp keys:
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| * M Celephaisian, O Dylathian = L#
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| * P Celephaisian, J Dylathian = L#, O#
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| * K Celephaisian, M Dylathian = L#, O#, J#
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| * N Celephaisian, P Dylathian = L#, O#, J#, M#
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| * Q Celephaisian, K Dylathian = L#, O#, J#, M#, P#
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| ** Enharmonic with Jb Celeph., Lb Dylath. in [[13edo]]
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| * L# Celephaisian, N Dylathian = L#, O#, J#, M#, P#, K#
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| ** Enharmonic with Mb Celeph., Ob Dylath. in 13edo
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| * O# Celephaisian, Q Dylathian = L#, O#, J#, M#, P#, K#, N#
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| ** Enharmonic with Pb Celeph., Jb Dylath. in 13edo
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| * J# Celephaisian, L# Dylathian = L#, O#, J#, M#, P#, K#, N#, Q#
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| ** Enharmonic with Kb Celeph., Mb Dylath. in 13edo
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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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| The modes in 13edo edo steps and C-H notation:
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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. 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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| EDOs that support A-Team include [[13edo]], [[18edo]], [[31edo]] and [[44edo]].
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| It is possible to tune A-Team by ear, by tuning a chain of pure harmonic sevenths and taking every other note. This corresponds to using a generator of 64/49 = 462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS.
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| The sizes of the generator, large step and small step of oneirotonic are as follows in various A-Team tunings.
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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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| ! 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 L
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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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| | L
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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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| | M
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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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| | N
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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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| | O
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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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| | P
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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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| | Q
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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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| | J
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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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| | K
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| | +5
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| |}
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| <references/>
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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 Petrtri tunings. (Golden oneirotonic uses 1200*(2-φ) = 458.3592135¢ as generator and has L/s = φ; it is the limit of taking generators in Fibonacci number edos 5\13, 8\21, 13\34, 21\55, 34\89,....)
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| {| class="wikitable right-2 right-3 right-4"
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| |-
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| !
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| ! [[13edo]]
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| ! [[21edo]]
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| ! [[34edo]]
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| ! Golden oneirotonic
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| ! JI intervals represented (2.5.9.11.13.17 subgroup)
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| |-
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| | generator (g)
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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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| | 458.36
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| | 13/10, 17/13, 22/17
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| |-
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| | L (3g - octave)
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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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| | 175.08
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| | 10/9, 11/10
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| |-
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| | s (-5g + 2 octaves)
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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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| | 108.20
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| | 18/17, 17/16
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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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| ! 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 L
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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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| | L
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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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| | M
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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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| | N
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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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| | O
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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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| | P
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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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| | Q
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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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| | J
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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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| | K
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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-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.
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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-M8 "9:10:17" occurs 3x
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| *P1-M3-M5 "9:11:13" occurs 2x
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| *P1-M3-M8 "9:11:17" occurs 2x
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| *P1-M5-M8 "9:13:17" occurs 3x
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| All 8 modes provide chords in various prime families (list of modes is non-exhaustive):
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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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| (13edo, first 30 seconds is in J Celephaïsian)
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| [[File:A Moment of Respite.mp3]]
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| (13edo, L Ilarnekian)
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| [[File:Lunar Approach.mp3]]
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| (by [[Igliashon Jones]], 13edo, J Celephaïsian)
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| [[Category:Scales]]
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| [[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A -->
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| [[Category:Mos]]
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| [[Category:MOS scales]]
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