Oneirotonic: Difference between revisions
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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) | # 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) | ||
# 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) | # 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== | == Notation== | ||
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: | 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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== Oneirotonic key signatures == | == Oneirotonic key signatures == | ||
Flat keys: | Flat keys: | ||
*Jb Celephaisian, Lb Dylathian = Qb, Nb, Kb, Pb, Mb, Jb, Ob, Lb | * Jb Celephaisian, Lb Dylathian = Qb, Nb, Kb, Pb, Mb, Jb, Ob, Lb | ||
*Mb Celephaisian, Ob Dylathian = Qb, Nb, Kb, Pb, Mb, Jb, Ob | * Mb Celephaisian, Ob Dylathian = Qb, Nb, Kb, Pb, Mb, Jb, Ob | ||
*Pb Celephaisian, Jb Dylathian = Qb, Nb, Kb, Pb, Mb, Jb | * Pb Celephaisian, Jb Dylathian = Qb, Nb, Kb, Pb, Mb, Jb | ||
*Kb Celephaisian, Mb Dylathian = Qb, Nb, Kb, Pb, Mb | * Kb Celephaisian, Mb Dylathian = Qb, Nb, Kb, Pb, Mb | ||
*Nb Celephaisian, Pb Dylathian = Qb, Nb, Kb, Pb | * Nb Celephaisian, Pb Dylathian = Qb, Nb, Kb, Pb | ||
*Qb Celephaisian, Kb Dylathian = Qb, Nb, Kb | * Qb Celephaisian, Kb Dylathian = Qb, Nb, Kb | ||
*L Celephaisian, Nb Dylathian = Qb, Nb | * L Celephaisian, Nb Dylathian = Qb, Nb | ||
*O Celephaisian, Qb Dylathian = Qb | * O Celephaisian, Qb Dylathian = Qb | ||
All-natural key signature: | All-natural key signature: | ||
*J Celephaisian, L Dylathian = no sharps or flats | * J Celephaisian, L Dylathian = no sharps or flats | ||
Sharp keys: | Sharp keys: | ||
*M Celephaisian, O Dylathian = L# | * M Celephaisian, O Dylathian = L# | ||
*P Celephaisian, J Dylathian = L#, O# | * P Celephaisian, J Dylathian = L#, O# | ||
*K Celephaisian, M Dylathian = L#, O#, J# | * K Celephaisian, M Dylathian = L#, O#, J# | ||
*N Celephaisian, P Dylathian = L#, O#, J#, M# | * N Celephaisian, P Dylathian = L#, O#, J#, M# | ||
*Q Celephaisian, K Dylathian = L#, O#, J#, M#, P# | * Q Celephaisian, K Dylathian = L#, O#, J#, M#, P# | ||
**Enharmonic with Jb Celeph., Lb Dylath. in [[13edo]] | ** Enharmonic with Jb Celeph., Lb Dylath. in [[13edo]] | ||
*L# Celephaisian, N Dylathian = L#, O#, J#, M#, P#, K# | * L# Celephaisian, N Dylathian = L#, O#, J#, M#, P#, K# | ||
**Enharmonic with Mb Celeph., Ob Dylath. in 13edo | ** Enharmonic with Mb Celeph., Ob Dylath. in 13edo | ||
*O# Celephaisian, Q Dylathian = L#, O#, J#, M#, P#, K#, N# | * O# Celephaisian, Q Dylathian = L#, O#, J#, M#, P#, K#, N# | ||
**Enharmonic with Pb Celeph., Jb Dylath. in 13edo | ** Enharmonic with Pb Celeph., Jb Dylath. in 13edo | ||
*J# Celephaisian, L# Dylathian = L#, O#, J#, M#, P#, K#, N#, Q# | * J# Celephaisian, L# Dylathian = L#, O#, J#, M#, P#, K#, N#, Q# | ||
**Enharmonic with Kb Celeph., Mb Dylath. in 13edo | ** Enharmonic with Kb Celeph., Mb Dylath. in 13edo | ||
== Modal harmony == | == Modal harmony == | ||
Oneirotonic modes are named after cities in the Dreamlands. | Oneirotonic modes are named after cities in the Dreamlands. | ||
#Dylathian: LLsLLsLs (major with hints of Mixolydian and "#5") | # Dylathian: LLsLLsLs (major with hints of Mixolydian and "#5") | ||
#Ilarnekian: LLsLsLLs (major with hints of "b6") | # Ilarnekian: LLsLsLLs (major with hints of "b6") | ||
#Celephaïsian: LsLLsLLs (the oneirotonic melodic minor. Very classical-sounding; Easley Blackwood's 13-note etude uses this as its home mode.) | # Celephaïsian: LsLLsLLs (the oneirotonic melodic minor. Very classical-sounding; Easley Blackwood's 13-note etude uses this as its home mode.) | ||
#Ultharian: LsLLsLsL (A Dorian analogue. Another Dorian analogue is the MODMOS LsLLLsLs) | # Ultharian: LsLLsLsL (A Dorian analogue. Another Dorian analogue is the MODMOS LsLLLsLs) | ||
#Mnarian: LsLsLLsL | # Mnarian: LsLsLLsL | ||
#Kadathian: sLLsLLsL (another "Locrian") | # Kadathian: sLLsLLsL (another "Locrian") | ||
#Hlanithian: sLLsLsLL (closest Locrian analogue) | # Hlanithian: sLLsLsLL (closest Locrian analogue) | ||
#Sarnathian: sLsLLsLL (Darkest but ironically the most consonant. Here be dragons.) | # Sarnathian: sLsLLsLL (Darkest but ironically the most consonant. Here be dragons.) | ||
The modes in 13edo edo steps and C-H notation: | The modes in 13edo edo steps and C-H notation: | ||
[[File:Oneirotonic.png|alt=Oneirotonic.png|Oneirotonic.png]] | [[File:Oneirotonic.png|alt=Oneirotonic.png|Oneirotonic.png]] | ||
===Modes with sharp tritone === | |||
=== 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). | 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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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. | 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== | == A-Team (13&18, 4:5:9:(11:13):21) interpretation == | ||
EDOs that support A-Team include [[13edo]], [[18edo]], [[31edo]] and [[44edo]]. | EDOs that support A-Team include [[13edo]], [[18edo]], [[31edo]] and [[44edo]]. | ||
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! Size in 31edo | ! Size in 31edo | ||
! Note name on L | ! Note name on L | ||
!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> | ! 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> | ||
! #Gens up | ! #Gens up | ||
|- | |- | ||
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<references/> | <references/> | ||
==Petrtri (13&21, 4:5:9:11:13:17) interpretation== | == 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 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,....) | 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,....) | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
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! Size in 34edo | ! Size in 34edo | ||
! Note name on L | ! Note name on L | ||
!class="unsortable"| Approximate ratios | ! class="unsortable"| Approximate ratios | ||
! #Gens up | ! #Gens up | ||
|- | |- | ||
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<references/> | <references/> | ||
===Chords=== | === 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. | 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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*/17 chords occur on Hlanithian and Kadathian | */17 chords occur on Hlanithian and Kadathian | ||
==Samples == | == Samples == | ||
[[File:Oneirotonic 3 part sample.mp3]] | [[File:Oneirotonic 3 part sample.mp3]] | ||
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(by [[Igliashon Jones]], 13edo, J Celephaïsian) | (by [[Igliashon Jones]], 13edo, J Celephaïsian) | ||
[[Category:Scales]] | [[Category:Scales]] | ||
[[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A --> | [[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A --> | ||
[[Category:Mos]] | [[Category:Mos]] | ||
[[Category:MOS scales]] | [[Category:MOS scales]] | ||