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| | {{breadcrumb|5L 3s}} |
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| This page describes [[User:Inthar]]'s approach to [[5L 3s]] (aka oneirotonic). | | This page describes [[User:Inthar]]'s approach to [[5L 3s]] (aka oneirotonic). |
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| Now with new theory (thanks to tprice and Jaimbee) | | Now with new theory (thanks in part to tprice and Jaimbee) |
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| == Standing assumptions == | | == Standing assumptions == |
| The Fox-Raven absolute pitch system is used in this article to name 5L 3s pitches: The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz. I denote raising and lowering by a chroma (L − s) by # and b.
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| I'll use the [[TAMNAMS]] standard to denote oneirotonic intervals and degrees (independent of their absolute pitch). | | I'll use the [[TAMNAMS]] standard to denote oneirotonic intervals and degrees (independent of their absolute pitch). |
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| The chain of perfect 3-steps becomes: ... Pb Kb Nb Q L O J M P K N Q# L# O# ...
| | Todo: In the following, I will use the [[diamond-mos notation]] standard to discuss oneirotonic harmony. JKLMNOPQ will refer to the mode being discussed, if the mode is unaltered. |
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| Thus the [[13edo]] gamut is as follows:
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| '''J/Q#''' J#/Kb '''K/Lb''' '''L/K#''' L#/Mb '''M''' M#/Nb '''N/Ob''' '''O/N#''' O#/Pb '''P''' '''Q''' Q#/Jb '''J'''
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| The [[18edo]] gamut is notated as follows:
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| '''J''' Q#/Kb J#/Lb '''K''' '''L''' K#/Mb L# '''M''' Nb M#/Ob '''N''' '''O''' Pb O# '''P''' '''Q''' P#/Jb Qb '''J'''
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| The [[21edo]] gamut:
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| '''J''' J# Kb '''K''' K#/Lb '''L''' L# Mb '''M''' M# Nb '''N''' N#/Ob '''O''' O# Pb '''P''' P#/Qb '''Q''' Q# Jb '''J'''
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| == Modes == | | == Modes == |
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| {| class="wikitable" | | {| class="wikitable" |
| |- | | |- |
| | style="text-align:center;" | '''Mode''' | | | style="text-align:center;" |'''Mode''' |
| | style="text-align:center;" | [[Modal UDP Notation|'''UDP''']] | | | style="text-align:center;" |[[Modal UDP Notation|'''UDP''']] |
| | style="text-align:center;" | '''Name''' | | | style="text-align:center;" |'''Name''' |
| | |'''Former names''' |
| |- | | |- |
| | | LLsLLsLs | | | |LLsLLsLs |
| | style="text-align:center;" | 7|0 | | | style="text-align:center;" |<nowiki>7|0</nowiki> |
| | | Dylathian (də-LA(H)TH-iən) | | | |Dylian |
| | | |Dylathian |
| |- | | |- |
| | | LLsLsLLs | | | |LLsLsLLs |
| | style="text-align:center;" | 6|1 | | | style="text-align:center;" |<nowiki>6|1</nowiki> |
| | | Illarnekian (ill-ar-NEK-iən) | | | |Ilarnekian |
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| |- | | |- |
| | | LsLLsLLs | | | |LsLLsLLs |
| | style="text-align:center;" | 5|2 | | | style="text-align:center;" |<nowiki>5|2</nowiki> |
| | | Celephaïsian (kel-ə-FAY-zhən) | | | |Celephaïsian |
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| |- | | |- |
| | | LsLLsLsL | | | |LsLLsLsL |
| | style="text-align:center;" | 4|3 | | | style="text-align:center;" |<nowiki>4|3</nowiki> |
| | | Ultharian (ul-THA(I)R-iən) | | | |Ultharian |
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| |- | | |- |
| | | LsLsLLsL | | | |LsLsLLsL |
| | style="text-align:center;" | 3|4 | | | style="text-align:center;" |<nowiki>3|4</nowiki> |
| | | Mnarian (mə-NA(I)R-iən) | | | |Mnarian |
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| |- | | |- |
| | | sLLsLLsL | | | |sLLsLLsL |
| | style="text-align:center;" | 2|5 | | | style="text-align:center;" |<nowiki>2|5</nowiki> |
| | | Kadathian (kə-DA(H)TH-iən) | | | |Kadian |
| | | |Kadathian |
| |- | | |- |
| | | sLLsLsLL | | | |sLLsLsLL |
| | style="text-align:center;" | 1|6 | | | style="text-align:center;" |<nowiki>1|6</nowiki> |
| | | Hlanithian (lə-NITH-iən) | | | |Hlanian |
| | | |Hlanithian |
| |- | | |- |
| | | sLsLLsLL | | | |sLsLLsLL |
| | style="text-align:center;" | 0|7 | | | style="text-align:center;" |<nowiki>0|7</nowiki> |
| | | Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn" | | | |Sarnian |
| | | |Sarnathian |
| |} | | |} |
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| === Alterations === | | === Alterations === |
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| | | LLsLsLsL | | | | LLsLsLsL |
| | style="text-align:center;" | 6|1 @8 | | | style="text-align:center;" | 6|1 @8 |
| | | Illarmixian (Illarnekian b8) | | | | Ilarmixian (Ilarnekian b8) |
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| | | LsLLLsLs | | | | LsLLLsLs |
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| # SLLLSLSL is Ulphrygian | | # SLLLSLSL is Ulphrygian |
| # LLLSLSLS is Dylydian | | # LLLSLSLS is Dylydian |
| # LLSLSLSL is Illarmixian | | # LLSLSLSL is Ilarmixian |
| # LSLSLSLL is Mnaeolian | | # LSLSLSLL is Mnaeolian |
| # SLSLSLLL is Sarlocrian | | # SLSLSLLL is Sarlocrian |
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| == 13edo oneiro chordal theory == | | == 13edo oneiro chordal theory == |
| Favorite modes: Dylathian (22122121), Illarnekian (22121221), Celephaisian (21221221), Mnionian (21212221), Dylydian (22212121), Harmonic Mnarian (21212131)?
| | {{main|13edo/Inthar's approach}} |
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| We will primarily discuss functional harmony using [[delta-rational chord]]s, treating these separately from counterpoint. h/t to tprice and Jaimbee for the delta-rational chords presented here and for other discussions.
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| 13edo oneiro enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("delta-rational major triad" or just "major"/"Maj") and 0-277-738-923 ("delta-rational minor tetrad" or just "minor"/"min"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "minor triad" or "mintri", and 0-277-646-923 will be called "minor diminished" or "mindim". | |
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| [https://xenpaper.com/#(bpm%3A60)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br179hz%7D%0A(env%3A1811)%0A%23_0_2_3_5_7_8_10_12_13%0A%5B%600_%608_3_8_10_'0%5D-%0A%5B%602_5_10_12_'2%5D-%0A%5B%603_5_7_10_'0_'3%5D-%0A%5B%605_8_13_'2_'5%5D-%0A%5B%607_10_13_'3_'7%5D-%0A%5B%608_10_12_'2_'8%5D-%0A%5B%6010_'0_'5_'7_'10%5D-%0A%5B%6012_'2_'5_'8_'12%5D-%0A%5B0_'3_8_10_'13%5D- A progression on the ascending Celephaïsian scale]
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| [https://xenpaper.com/#(bpm%3A60)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br274.988hz%7D%0A(env%3A1811)%0A%23_0_2_3_5_6_8_10_12_13%0A%5B%600_%608_0_3_10_%270%5D-%0A%5B%602_%6010_2_5_10%5D12%0A%5B%603_0_3_6_13_%273%5D-%0A%5B%605_2_8_13_15_%278%5D%275%0A%5B%606_0_3_8_10_%276%5D-%0A%5B%608_2_5_10_%275%5D-%0A%5B%6010_0_6_8_%273%5D-%0A%5B%6012_5_8_12_%272%5D-%0A%5B0_3_8_10_12_13%5D- A progression on the ascending Melodic Mnarian scale]
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| Adding 923 and 1108 to chords works well, and for jazzy extensions one can add 185, 461, and 646 to the upper octave.
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| [https://xenpaper.com/#(bpm%3A240)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br360hz%7D%0A(env%3A1847)%0A%23_0_2_3_5_6_8_10_11~12_13%0A%5B%600_%608_0%5D_3_6_8-----........%0A%5B%600_%608_0%5D_3_8_10-----.......13%0A%5B%60%608_%608_11%5D_%6011_2_3---6_3-2-3-5-%0A%5B%605_5_8_11_13_8%5D-_11_13----_13_'2------%0A%5B%600_%608_0%5D_3_6_8-----........%0A%5B%600_%608_0%5D_3_8_10-----.....'3'2'0%0A%5B%603_3_6_8_0_11%5D-13_%5B%602_5_8%5D-_11-_8_%5B0_10%5D-_%5B%6011_8%5D_%5B%6010_6%5D-%5B%6011_8%5D_%5B%6010_6%5D_%5B%608_5%5D%0A%5B%603_%606_%6011_3%5D-_%5B%602_5%5D-_%5B%600_3%5D-.._%0A%5B%608_%608_%6010_%6012_2%5D_%608_%6010_%6012---- A Mnarian loop with an &8 leading tone at the end]
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| [https://xenpaper.com/#(bpm%3A30)(osc%3Asawtooth2)%0A%7Br200Hz%7D%7B13edo%7D%0A(env%3A1846)%0A%5B0_4_7_10_%272_%276_%279_%2712%5D-.._%23_Dylydian%0A%5B0_5_9_%270_%272_%274_%277_%2710_%2712%5D-.._%23_Dylathian%0A%5B0_5_8_10_%270_%272_%274_%277_%2712%5D-.._%23_Illarnekian%0A%5B0_3_8_10_%272_%275_%277_%2712%5D-.._%23_Celepha%C3%AFsian%0A%5B0_5_9_%273_%277_%2710_%2712_%27%272%5D-.._%23_Celdorian%0A%5B0_3_6_8_%2711_%272_%275_10%5D-.._%23_Mnarian%0A%5B0_3_6_8_10_%272_%275_%2712%5D-.._%23_Mnionian Some motherchords of oneiro modes]
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| === Functional chords on each degree ===
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| Celephaisian
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| * 0d: minor
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| * 1d: minor
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| * 2d: major
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| * 3d: minor, mindim
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| * 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 5d: major
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| * 6d: minor
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| * 7d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| Mnionian (Melodic Mnarian)
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| * 0d: minor
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| * 1d: minor
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| * 2d: mindim
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| * 3d: minor, mindim
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| * 4d: major, augmented 3ms
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| * 5d: major, minor 7ms
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| * 6d: minor triad, minor 6ms, minor 7ms
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| * 7d: "diminished triad", diminished 5ms, minor 6ms, minor 7ms
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| === Progressions ===
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| kd(maj) means the triad 0 369 646 on kd, kd(min) means the tetrad 0 277 738 923 on kd
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| Common motions:
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| * 0d(maj or min) → M1d(min)
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| * 0d(maj or min) → 4d(min) (when ending on 0d this sounds like diatonic V to I)
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| * 0d(maj or min) → m6d(min)
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| * 0d(maj) → 5d(maj), 0d(min) → 5d(maj or min) (when ending on 0d this is a "dominant to tonic" motion)
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| * 0d(maj) → M3d(maj)
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| * 2d(min) → m1d(maj) → 0d(maj) (pseudo tritone sub)
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| === Modal harmony ===
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| Modes can be grouped by their functional properties.
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| * Dual-fifth: Illarnekian, Celephaïsian, Ultharian; Illarmixian, Ulphrygian
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| * Dual-fourth: Mnarian, Kadathian, Hlanithian; Mnionian, Mnaeolian
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| * Major pJI chord on root: Dylathian, Illarnekian; Dylydian, Illarmixian
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| * Minor pJI chord on root: Celephaïsian, Ultharian, Mnarian, Kadathian; Mnionian, Sardorian, Ulphrygian
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| * Lower leading tone: Dylathian, Illarnekian, Celephaïsian; Dylydian, Mnionian
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| * "Neoclassical functional modes" (loose grouping): Dylathian, Illarnekian, Celephaïsian, Ultharian; Mnionian, Mnaeolian(?)
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| * Upper leading tone: Kadathian, Hlanithian, Sarnathian, Sardorian, Sarlocrian
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| * Minor 6-mosstep: Hlanithian, Sarnathian, Mnaeolian, Sarlocrian
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| * 0 462 831 delta-rational chord on root: Dylathian, Dylydian, Hlanithian, Mnaeolian
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| * "Dorian-like", i.e. no leading tone, 5d is minor, and m7d is major: Ultharian, Mnarian
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| * 7d is minor: Kadathian, Hlanithian
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| We'll call degrees that don't have the major delta-rational or the minor delta-rational chord ''dissonant degrees'' (keeping in mind that dissonance is a feature a chord has in a musical language rather than a purely psychoacoustic property).
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| ==== Celephaïsian ====
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| Functional chords on each degree:
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| * 0d: min
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| * 1d: min
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| * 2d: Maj
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| * 3d: min
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| * 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 5d: Maj
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| * 6d: min
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| * 7d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| The main resolving degrees (analogues to dominant in diatonic) are 3d and 5d because of their leading tones.
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| Motherchord: 0d-m2d-P5d-M6d-(M7d)-M1d-P3d-M5d-(M7d)
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| Progressions:
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| * 0d(min) 1d(min) 3d(min or mindim) 0d(min)
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| * 0d(min) 1d(min) 6d(min) 3d(min or mindim) 0d(min)
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| * 0d(min) 6d(min) 3d(min or mindim) 0d(min)
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| * 0d(min) 2d(Maj) 3d(min or mindim) 0d(min)
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| * 0d(min) 4d(min7) 5d(Maj)/3d(min or mindim) 0d(min)
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| * 0d(min) 6d(min) 5d(Maj) 0d(min)
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| Secondary modes:
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| * 3d Ultharian
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| * 2d Dylathian
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| * 5d illarnekian
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| ==== Ultharian ====
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| * 0d: min
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| * 1d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 2d: Maj
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| * 3d: min
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| * 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 5d: min
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| * 6d: min
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| * 7d: Maj
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| Ultharian and Mnarian often behave like Dorian because they lack a leading tone. Resolving degrees: 3d(min), 5d(min), 7d(Maj)
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| ==== Mnarian ====
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| * 0d: min
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| * 1d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 2d: min
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| * 3d: min
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| * 4d: Maj
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| * 5d: min
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| * 6d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 7d: Maj
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| Resolving degrees: 3d(min), 5d(min), 7d(Maj)
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| ==== Kadathian ====
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| * 0d: min
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| * 1d: Maj
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| * 2d: min
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| * 3d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 4d: Maj
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| * 5d: min
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| * 6d: minor triad, minor 4ms, minor 6ms, minor 7ms
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| * 7d: min
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| Resolving degrees: 2d(min)?, 4d(Maj), 5d(min), 7d(min)
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| ==== Hlanithian and Sarn ====
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| Main tonic chord is 0-3-8-11\13 (min7), works well with m6d(maj) and m7d(min7).
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| === Alterations ===
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| === Modulations ===
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| == 18edo oneiro theory == | | == 18edo oneiro theory == |
| Favorite modes: Mnionian (31313331), Mnaeolian (31313133), Ulphrygian (13331313), Celdorian (31333131), Sardorian (13133313) | | Favorite modes: Mnionian (31313331), Mnaeolian (31313133), Ulphrygian (13331313), Celdorian (31333131), Sardorian (13133313) |
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| * 26:29:32:34:38:42:44:49:52 Tridecimal Dylathian | | * 26:29:32:34:38:42:44:49:52 Tridecimal Dylathian |
| * 26:29:30:34:38:42:44:49:52 Tridecimal Celdorian | | * 26:29:30:34:38:42:44:49:52 Tridecimal Celdorian |
| | == Samples == |
| | === Modal studies === |
| | [[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3|thumb|center|Dylathian study]] |
| | [[Category:Oneirotonic]] |
| | [[Category:13edo]] |
| | [[Category:18edo]] |
| | [[Category:21edo]] |
| | [[Category:Method]] |
| | [[Category:Approaches to tuning systems]] |