This page describes [[User:Inthar]]'s approach to [[5L 3s]] (aka oneirotonic).
This page describes [[User:Inthar]]'s approach to [[5L 3s]] (aka oneirotonic).
Now with new theory (thanks in part to tprice and Jaimbee)
== Standing assumptions ==
== Standing assumptions ==
The [[TAMNAMS]] system is used in this article to name 5L 3s intervals and step size ratios and step ratio ranges.
I'll use the [[TAMNAMS]] standard to denote oneirotonic intervals and degrees (independent of their absolute pitch).
The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.
The chain of perfect mosfourths becomes: ... P@ K@ N@ 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.
| | Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
| |Sarnian
| |Sarnathian
|}
|}
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 ===
=== Alterations ===
==== Archeodim ====
==== 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.
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 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:
In [[13edo]], archeodim is a subset of the 9-note [[4L 5s]] MOS generated by the subminor third 3\13.
The cyclic order of archeodim modes are:
# LSLLLSLS is Celdorian
==== Other MODMOSes ====
# SLLLSLSL is Ulphrygian
Other potentially interesting oneirotonic MODMOSes (that do not use half-sharps or half-flats) are:
# LLLSLSLS is Dylydian
* the distorted harmonic minor LSLLSALS (A = aug oneiron2nd = L + chroma)
# LLSLSLSL is Ilarmixian
* the distorted Freygish SASLSLLS
# LSLSLSLL is Mnaeolian
* Celephaïsian &4 &6 LsAsLsLs
# SLSLSLLL is Sarlocrian
# LSLSLLLS is Mnionian
== Hypohard oneiro theory ==
# SLSLLLSL is Sardorian
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.
Notably the cyclic order is almost exactly the "circle" of diatonic modes except the "circle" breaks at Sardorian-Celdorian.
=== 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-Lon2-Pon4-Lon5-Lon7, 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-Lon2-Pon4-Pon6-Lon7 (J-K-M-O-P) can be used for similar effect.
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 minor oneirofifth (instead of the major 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-Lon3-Lon5: Falling Major Triad; Squashed Major Triad
* R-son3-Lon5: Falling Minor Triad; Squashed Minor Triad
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-Lon2-Pon4) and 16:23:30 (R-Lon5-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-Lon2-Pon4), 9:10:11:13 (R-Lon2-Lon3-Lon5), and 8:15:23 (R-Lon7-Lon5)).
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:
In [[18edo]], the augmented 3-mosstep (LLL) is a 600¢ tritone, which can be used as a dissonance.
The 21edo Dylathian mode is close to the /23 JI scale 46:51:56:60:66:73:78:86:92. The other 21edo oneirotonic modes could be tuned to modal rotations of this scale.
The notes 38:41:43:46:48:50:52:54:56:58:60:63:65:68:70:73:76 provide the best low complexity fit to oneirotonic (in particular, 18edo) in the [[prime family]] /19.
* 38:43:45:50:56:58:65:72:76 Novem Bright Celephaïsian
* 38:42:44:49:55:58:65:72:76 Novem Dark Celephaïsian
* 38:43:45:50:56:58:65:68:76 Novem Bright Ultharian
* 38:42:44:49:55:58:65:68:76 Novem Dark Ultharian
=== /23 ===
[https://xenpaper.com/#(bpm%3A110)(osc%3Asawtooth2)%7B18edo%7D%0A%7Br178hz%7D%0A(env%3A1811)%0A%23_0_3_4_7_8_11_12_15_18%0A%5B0_4_7_11_'0_'22%5D-'18-%0A%5B3_7_15_18_'3_'21%5D-'15_'11%0A%5B4_8_12_18_'4_'8%5D-_'15-%0A%5B7_11_15_'0_'7_'11%5D-_'7'12%0A%5B8_12_15_'0_'4_'8%5D'0_'4_'11%0A%5B11_15_18_'3_'11_'15%5D-_'18_'21%0A%5B12_15_18_'7_'12_'22%5D-_'21_'29%0A%5B15_'0_'3_'8_'12_'15_'26%5D_'25_'22_'21%0A%5B0_11_'4_'7_'18%5D- A progression on ascending 18edo Mnaeolian]
23(2:4) has many oneiro pitches, some close to 13edo, and some close to 18edo:
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 4-steps (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. The chord 0-342-629-1085 is delta-rational and is in fact very close to 32:39:46:60.
* [https://xenpaper.com/#(bpm%3A115)%7Br236.960465669hz%7D(osc%3Atriangle)%7B21edo%7D%0A%0A%5B0%2C6%2C8%5D-------%0A%7Br3%7D%5B0%2C3%2C8%5D-------%0A%7Br3%7D%5B0%2C5%2C7%5D-------%0A%7Br5%7D%5B0%2C5%5D---%0A%7Br%6018%7D%5B0%2C5%5D---%0A%7Br%6018%7D%5B0%2C3%2C8%2C13%5D-------%0A%7Br6%7D%5B0%2C2%2C10%5D---%0A%7Br%6018%7D%5B0%2C5%2C10%5D---%0A%7Br%6019%7D%5B0%2C5%2C12%5D-------%0A%7Br%6018%7D%5B0%2C8%2C10%5D--..%7Br%6015%7D0_3_6 Example progression using the above chords]
# '''92''':96:100:'''104''':108:112:'''116''':120:125:130:'''136''':141:146:'''152''':158:164:170:177:184 - 18neji with /13, /17, /19, /23, and /29 prime modes
I'll use the TAMNAMS standard to denote oneirotonic intervals and degrees (independent of their absolute pitch).
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.
Modes
Oneirotonic modes are named after cities in the Dreamlands.
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 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.
21edo has the softoneirotonic (5L 3s) mos with generator 8\21; in addition to the naiadics (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 4-steps (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. The chord 0-342-629-1085 is delta-rational and is in fact very close to 32:39:46:60.