|
|
| Line 836: |
Line 836: |
| | +5 | | | +5 |
| |} | | |} |
| -->
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|
| |
|
| == Key signatures == | | == Key signatures == |
| Line 864: |
Line 863: |
| ** Enharmonic with K@ Oneirominor, M@ Oneiromajor in 13edo | | ** Enharmonic with K@ Oneirominor, M@ Oneiromajor in 13edo |
|
| |
|
| == Modes ==
| | --> |
| Oneirotonic modes are named after cities in the Dreamlands.
| | == Approaches == |
| {| class="wikitable"
| | * [[5L 3s/Inthar's approach]] |
| |-
| | * [[5L 3s/Primodal theory]] |
| | colspan=2 style="text-align:center;" | '''Mode'''
| | * [[5L 3s/Temperaments]] |
| | style="text-align:center;" | [[Modal UDP Notation|'''UDP''']]
| |
| | style="text-align:center;" | '''Name'''
| |
| |-
| |
| | rowspan=4 bgcolor="#ffeaea" | '''Ana'''
| |
| | | LLsLLsLs
| |
| | style="text-align:center;" | 7|0
| |
| | | Dylathian (də-LA(H)TH-iən)
| |
| |-
| |
| | | LLsLsLLs
| |
| | style="text-align:center;" | 6|1
| |
| | | Illarnekian (ill-ar-NEK-iən)
| |
| |-
| |
| | | LsLLsLLs
| |
| | style="text-align:center;" | 5|2
| |
| | | Celephaïsian (kel-ə-FAY-zhən)
| |
| |-
| |
| | | LsLLsLsL
| |
| | style="text-align:center;" | 4|3
| |
| | | Ultharian (ul-THA(I)R-iən)
| |
| |-
| |
| | rowspan=4 bgcolor="#eaeaff" | '''Kata'''
| |
| | | LsLsLLsL
| |
| | style="text-align:center;" | 3|4
| |
| | | Mnarian (mə-NA(I)R-iən)
| |
| |-
| |
| | | sLLsLLsL
| |
| | style="text-align:center;" | 2|5
| |
| | | Kadathian (kə-DA(H)TH-iən)
| |
| |-
| |
| | | sLLsLsLL
| |
| | style="text-align:center;" | 1|6
| |
| | | Hlanithian (lə-NITH-iən)
| |
| |-
| |
| | | sLsLLsLL
| |
| | style="text-align:center;" | 0|7
| |
| | | Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
| |
| |}
| |
| | |
| We call modes with a major mos5th ''ana modes'' (from Greek for 'up'), because the sharper 5th degree functions as a flattened melodic fifth when moving from the tonic up. The ana modes of the MOS are the 4 brightest modes, namely Dylathian, Illarnekian, Celephaïsian and Ultharian.
| |
| We call modes with a minor mos5th ''kata modes'' (from Greek for 'down'). The kata modes of the MOS are the 4 darkest modes, namely Mnarian, Kadathian, Hlanithian and Sarnathian. In kata modes, the melodically squashed fifth from the tonic downwards is the flatter 5th degree. Kata modes could be used to distort diatonic tropes that start from the tonic and work downwards or work upwards towards the tonic from below it. For example:
| |
| * Mnarian (LSLSLLSL) and Kadathian (SLLSLLSL) are kata-Mixolydians
| |
| * Hlanithian (SLLSLSLL) is a kata-melodic major (the 4th degree sounds like a major third; it's actually a perfect mosfourth.)
| |
| * Sarnathian (SLSLLSLL) is a kata-melodic minor (When starting from the octave above, the 4th degree sounds like a minor third; it's actually a diminished mosfourth.)
| |
| | |
| === Functional tonalities ===
| |
| For classical-inspired functional harmony, we use the terms ''(Functional) Oneiromajor'' and ''(Functional) Oneirominor'': Oneiromajor for Illarnekian where the 6th degree (the rising fifth) can be sharpened, and Oneirominor for Ultharian where the 8th degree (the leading tone) can be sharpened. The respective purposes of these alterations are:
| |
| # in Oneiromajor, to have both major (requiring a sharpened 6th degree) on the flat fourth "subdominant" and the sharp fifth as "dominant"
| |
| # in Oneirominor, to have both the flat 8th degree as the dominant of the "mediant" (relative major) and the sharp 8th degree as leading tone
| |
| | |
| In key signatures, Oneirominor should be treated as Ultharian and Oneiromajor should be treated as Illarnekian. Note that Oneiromajor and Oneirominor still have the relative major-minor relationship; they are related by a major mosthird, just like diatonic major/minor.
| |
| | |
| === Alterations ===
| |
| ==== Archeodim ====
| |
| We call the LSLLLSLS pattern (independently of modal rotation) '''archeodim''', because the "LLL" resembles the [[archeotonic]] scale in 13edo and the "LSLSLS" resembles the diminished scale. Archeodim is the most important oneirotonic [[MODMOS]] pattern (a MODMOS is a MOS with one or more alterations), because it allows one to evoke certain ana or kata diatonic modes where three whole steps in a row are important (Dorian, Phrygian, Lydian or Mixo) in an octatonic context. The MOS would not always be able to do this because it has at most two consecutive large steps. Archeodim modes exist in all oneirotonic tunings, since they use the same large and small steps as the oneirotonic scale itself.
| |
| | |
| As with the MOS, archeodim has four ana and four kata rotations:
| |
| | |
| {| class="wikitable"
| |
| |-
| |
| | colspan=2 style="text-align:center;" | '''Mode'''
| |
| | style="text-align:center;" | [[Modal UDP Notation|'''UDP''']]
| |
| | style="text-align:center;" | '''Name'''
| |
| |-
| |
| | rowspan=4 bgcolor="#ffeaea" | '''Ana'''
| |
| | | LLLsLsLs
| |
| | style="text-align:center;" | 7|0 &4
| |
| | | Dylydian (Dylathian &4)
| |
| |-
| |
| | | LLsLsLsL
| |
| | style="text-align:center;" | 6|1 @8
| |
| | | Illarmixian (Illarnekian @8)
| |
| |-
| |
| | | LsLLLsLs
| |
| | style="text-align:center;" | 5|2 &6
| |
| | | Celdorian (Celephaïsian &6)
| |
| |-
| |
| | | sLLLsLsL
| |
| | style="text-align:center;" | 4|3 @2
| |
| | | Ulphrygian (Ultharian @2)
| |
| |-
| |
| | rowspan=4 bgcolor="#eaeaff" | '''Kata'''
| |
| | | LsLsLLLs
| |
| | style="text-align:center;" | 3|4 &8
| |
| | | Mnionian (Mnarian &8)
| |
| |-
| |
| | | sLsLLLsL
| |
| | style="text-align:center;" | 0|7 &7
| |
| | | Sardorian (Sarnathian &7)
| |
| |-
| |
| | | LsLsLsLL
| |
| | style="text-align:center;" | 3|4 @7
| |
| | | Mnaeolian (Mnarian @7)
| |
| |-
| |
| | | sLsLsLLL
| |
| | style="text-align:center;" | 0|7 @6
| |
| | | Sarlocrian (Sarnathian @6)
| |
| |}
| |
| | |
| In [[13edo]], archeodim is a subset of the 9-note [[4L 5s]] MOS generated by the subminor third 3\13.
| |
| | |
| ==== Other MODMOSes ====
| |
| Other potentially interesting oneirotonic MODMOSes (that do not use half-sharps or half-flats) are:
| |
| * the distorted harmonic minor LSLLSALS (A = aug oneiro2nd = L + chroma)
| |
| * the distorted Freygish SASLSLLS
| |
| * Celephaïsian &4 &6 LsAsLsLs
| |
| | |
| == Hypohard oneiro theory ==
| |
| Oneirotonic is often used as distorted diatonic. Because distorted diatonic modal harmony and functional harmony both benefit from a recognizable major third, the following theory essentially assumes a hypohard tuning, i.e. an oneirotonic tuning with generator between 5\13 and 7\18 (or possibly an approximation of such a tuning, such as a [[neji]]). The reader is encouraged to experiment and see what ideas work for other oneirotonic tunings.
| |
| === Ana modes ===
| |
| The ana modes have squashed versions of the classical major and minor pentachords R-M2-M3-P4-P5 and R-M2-m3-P4-P5 and can be viewed as providing a distorted version of classical 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.
| |
| | |
| In pseudo-classical functional harmony, the 6th scale degree (either an augmented mossixth or a perfect mossixth) could be treated as mutable. The perfect mossixth would be used when invoking the diatonic V-to-I trope by modulating by a perfect mosfourth from the sixth degree "dominant". The augmented mossixth would be used when a major key needs to be used on the fourth degree "subdominant".
| |
| | |
| ==== Pentatonic subsets ====
| |
| The ''Oneiro Falling Suspended Pentatonic'', i.e. R-Lo2-Po4-Lo5-Lo7, is also an important subset in ana modes: it roughly implies the "least" tonality (In particular, it only implies ana-ness, not major or minor tonality), and it sounds floaty, and suspended, much like suspended and quartal chords do in diatonic contexts. The ''Oneiro Rising Suspended Pentatonic'' R-Lo2-Po4-Po6-Lo7 (J-K-M-O-P) can be used for similar effect.
| |
| | |
| Modes of the oneiro-pentatonic MOS:
| |
| # R-Lo2-Po4-Lo5-Lo7 Oneiro Falling Suspended Pentatonic
| |
| # R-Lo2-Po4-Po6-Lo7 Oneiro Rising Suspended Pentatonic
| |
| # R-so3-Po4-Po6-Lo7 Oneiro Symmetrical Pentatonic
| |
| # R-so3-Po4-Po6-so8 Oneiro Expanding Quartal Pentatonic
| |
| # R-so3-so5-Po6-so8 Oneiro Diminished Pentatonic
| |
| | |
| ==== Functional harmony ====
| |
| Oneiro has at least two different types of "V-to-I" resolution because of the two fifth sizes:
| |
| # One uses the sharp fifth as the "V" and uses a true major third. The sharp "V" voiceleads naturally to the flat fifth in the resolved falling tonic triad on the I: e.g. P6-M8-P2 > M5-P1-(M/m)3.
| |
| # One uses the flat fifth as the "V" and the chord on the "V" is a "false major triad" R-P4-P6 (root-falling 4th-rising 5th).
| |
| | |
| Some suggested basic ana functional harmony progressions are listed below, outlined very roughly. Note that VI, VII and VIII are sharp 5th, 6th-like and 7th-like degrees respectively. A Roman numeral without maj or min means either major or minor. The "Natural" Roman numerals follow the Illarnekian mode.
| |
| | |
| * I-IVmin-VImaj-I
| |
| * Imaj-VIImin-IVmin-Imaj
| |
| * Imin-@IIImaj-VImaj-Imaj
| |
| * Imin-@IIImaj-Vdim-VImaj-Imin
| |
| * Imin-@VIIImin-IIImaj-VImaj-Imin
| |
| * Imin-IVmin-@VIIImin-@IIImaj-VImaj-Imin
| |
| * Imin-IVmin-IIdim-VImaj-Imin
| |
| * Imin-IVmin-IIdim-@IIImaj-Imin
| |
| * I-VIImin-IImin-VImaj-I
| |
| * Imaj-VIImin-IVmin-VImaj-Imaj
| |
| * Modulations by major mos2nd:
| |
| ** I-IV-VII-II
| |
| ** I-IVmaj-II
| |
| ** I-VIImin-II
| |
| * Modulations by major mos3rd:
| |
| ** Modulate up major mos2nd twice
| |
| ** Imin-VImin-III (only in 13edo)
| |
| ** Imaj-&VImin-III (only in 13edo)
| |
| * Modulations by minor mos3rd:
| |
| ** I-VI-@III
| |
| ** I-IVmin-VImin-@VIIImaj-@III
| |
| | |
| Another Western-classical-influenced approach to oneirotonic chord progressions is to let the harmony emerge from counterpoint. This would allow, for example, using the perfect oneirofourth and small oneirofifth (instead of the large oneirothird and the perfect oneirofourth) as stand-ins for major thirds and fourths in neobaroque contexts (this adds some dissonance which might be what you want sometimes, e.g. in a chord that is supposed to resolve to a more consonant chord).
| |
| ===== Samples =====
| |
| [[File:Oneiro Baroque Exercises 13edo.mp3]]
| |
| | |
| (A short contrapuntal 13edo keyboard exercise, meant to be played in all 13 keys. The first part is in Oneiromajor, i.e. Illarnekian with mutable 6th degree, and the second part is in Oneirominor, i.e. Celephaïsian with mutable 7th degree.)
| |
| | |
| [[File:Oneiro Baroque Exercises 18edo.mp3]]
| |
| | |
| ([[18edo]])
| |
| | |
| [[File:Oneiro Baroque Exercises 31edo.mp3]]
| |
| | |
| ([[31edo]])
| |
| | |
| [[File:Oneiro Classical Exercises 21edo.mp3]]
| |
| | |
| ([[21edo]] for comparison)
| |
| | |
| [[File:Oneirotonic 3 part sample.mp3]]
| |
| | |
| (A rather classical-sounding 3-part harmonization of the ascending J Illarnekian scale; tuning is 13edo)
| |
| | |
| === Kata modes ===
| |
| When used in an "ana" way, the kata modes are radically different in character than the ana modes. Particularly in 13edo and tunings close to it, the fifth and seventh scale degrees become the more concordant 11/8 and quasi-13/8 respectively, so they may sound more like stable scale functions. Hlanithian, in particular, may be like a more stable version of the Locrian mode in diatonic.
| |
| | |
| === Chords and extended harmony ===
| |
| Chords are given in oneirotonic MOS interval notation. For example, M5 means major mosfifth (squashed fifth).
| |
| | |
| "Rising" means that a triad uses the perfect mos6th (major 5th); "falling" means that a triad uses a major mos5th (minor 5th)
| |
| | |
| * R-Lo3-Lo5: Falling Major Triad; Squashed Major Triad
| |
| * R-so3-Lo5: Falling Minor Triad; Squashed Minor Triad
| |
| * R-so3-so5: Squashed Dim Triad
| |
| * R-Lo3-Ao5: Squashed Aug Triad
| |
| * R-Lo3-Lo5-Ao6: Falling Major Triad Add6
| |
| * R-so3-Lo5-Ao6: Falling Minor Triad Add6
| |
| * R-Lo3-Lo5-Lo7: Falling Major Tetrad
| |
| * R-so3-Lo5-Lo7: Falling Minor Tetrad
| |
| * R-so3-so5-Lo7: Oneiro Half-Diminished Tetrad
| |
| * R-so3-so5-so7: Orwell Tetrad, Oneiro Diminished Tetrad
| |
| * R-Lo3-Ao6: Squashed 1st Inversion Minor Triad; Sephiroth Triad (approximates 8:10:13 in 13edo and 31edo) | |
| * R-Lo3-Ao6-Lo8: Sephiroth Triad Add7
| |
| * R-Lo3-Ao6-(Mo2)-(Po4): Sephiroth Tetrad Add9
| |
| * R-Lo3-Ao6-(mo2)-(Po4): Sephiroth Tetrad Addm9
| |
| * R-Lo3-Ao6-(Po4): Sephiroth Tetrad
| |
| * R-so3-Po6: Rising Minor Triad; Squashed 1st Inversion Major Triad
| |
| * R-Lo3-Po6: Rising Major Triad
| |
| * R-so3-Lo7: Minor add6 no5
| |
| * R-so3-so7: Minor addm6 no5
| |
| * R-so5-Lo7: Falling no3 add6
| |
| * R-so5-so7: Falling no3 add6
| |
| * R-Lo3-Lo8: Major 7th no5
| |
| * R-so3-Lo8: Minor Major 7th no5
| |
| * R-Lo3-Lo5-Lo8: Falling Major Seventh Tetrad
| |
| * R-so3-Lo5-Lo8: Falling Minor Major Seventh Tetrad
| |
| * R-Lo3-Lo7-Lo8: no5 Major Seventh Add6
| |
| * R-so3-Lo7-Lo8: no5 Minor Major Seventh Add6
| |
| * R-Lo3-Po6-Lo8: Rising Major Seventh
| |
| * R-so3-Po6-Lo8: Rising Oneiro Minor Major Seventh
| |
| * R-Lo3-(Mo2): Oneiro Major Add9
| |
| * R-so3-(Mo2): Oneiro Minor Add9
| |
| * R-Lo3-Lo5-(Mo2): Falling Major Triad Add9
| |
| * R-so3-Lo5-(Mo2): Falling Minor Triad Add9
| |
| * R-Lo3-(Mo2)-(Po4): no5 Major Add9 Sub11
| |
| * R-so3-(Mo2)-(Po4): no5 Minor Add9 sub11
| |
| * R-Lo2-Po4: Sus24 No5
| |
| * R-Lo2-Lo5: Falling Sus2 Triad
| |
| * R-Po4-Lo5: Falling Sus4 Triad
| |
| * R-Lo2-Po4-Lo5: Falling Sus24
| |
| * R-Po4-Lo7: Oneiro Quartal Triad
| |
| * R-Po4-Lo7-(Mo2): Oneiro Quartal Tetrad, Core Tetrad
| |
| * R-Po4-Lo7-(Mo2)-(Mo5): Oneiro Quartal Pentad, Core Pentad
| |
| * R-Po4-Lo7-(Mo2)-(Mo5)-(Mo8): Oneiro Quartal Hexad
| |
| * R-Po4-Lo7-Lo8: Oneiro Quartal Seventh Tetrad
| |
| * R-Po4-so8: Expanding Quartal Triad
| |
| * R-Lo2-Po4-so8: Expanding Quartal Triad add2
| |
| * R-so3-Po4-so8: Expanding Quartal Triad Addm3
| |
| * R-so5-so8: Contracting Quartal Triad
| |
| * R-so5-so7-so8: Contracting Quartal Triad Addm7
| |
| * R-Lo3-Lo5-so8: Falling Major Triad addm7
| |
| | |
| == Hyposoft oneiro theory ==
| |
| 21edo has the [[Step ratio|soft]] [[oneirotonic]] (5L 3s) MOS with generator 8\21; in addition to the [[naiadic]]s (457.14¢) and extremely sharp fifths (742.85¢) that generate it, it has neutral thirds (instead of major thirds as in [[13edo]] oneirotonic), neogothic minor thirds, and meantone-like diatonic semitones. The oneirofifths (4-step intervals) are more tritone-like than fifth-like, unlike in 13edo, although they do have a consonant, even JI-like quality to them. In terms of JI, it mainly approximates 5:9:11:13 (R-so8-Lo2-Po4) and 16:23:30 (R-Lo5-Lo8). Importantly, the sharp fifth is now harmonically much more fifth-like than the flat fifth, unlike in [[13edo]] and harder tunings. Rather than squashed tertian triads, it may be preferable to use triads with sharp fifths, quartal harmony, stacks of seconds and thirds, third+sixth and third+seventh chords, and using the JI approximations (subsets of 5:9:11:13 (R-so8-Lo2-Po4), 9:10:11:13 (R-Lo2-Lo3-Lo5), and 8:15:23 (R-Lo7-Lo5)).
| |
| | |
| 34edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like, and it is a bit more optimized for the 5:9:11:13 approximation.
| |
| | |
| Approximate low-complexity JI chords in the JKLMNOPQ = Ultharian mode:
| |
| * sus24 no5 ≈ 5:11:13, 10:11:13: J-K-M, L-M-O, M-N-P, O-P-J, Q-J-L
| |
| * sus24 no5 addmin7 ≈ 5:9:11:13: J-Q-K-M, M-L-N-P
| |
| * falling fifth addmaj7 ≈ 16:23:30: O-K-N, L-P-K, Q-M-P
| |
| * Falling Major Triad ≈ 9:11:13: Q-K-M, L-N-P
| |
| * 16:23:29 (in 21edo): J-N-Q
| |
| Other chords:
| |
| * Quartal Tetrad (≈ 10:11:13:17?): Q-J-L-O, L-M-O-J, O-P-J-M, J-K-M-P, M-N-P-K
| |
| * Quartal Pentad: L-M-O-P-J, O-P-J-K-M, J-K-M-N-P, M-N-P-Q-K
| |
| * Falling Minor Triad (≈ 11:13:16?): J-L-N, O-Q-K
| |
| * squashed diminished: M-O-Q, P-J-L, K-M-O, N-P-J | |
| | |
| == Primodal theory ==
| |
| :''Main article: [[5L 3s/Primodal theory]]''
| |
| | |
| == Temperaments ==
| |
| :''Main article: [[5L 3s/Temperaments]]''
| |
|
| |
|
| == Samples == | | == Samples == |