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 to tprice and Jaimbee)
Now with new theory (thanks in part to tprice and Jaimbee)
== 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.
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).
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.
We will primarily discuss functional harmony using pseudo-JI chords, treating these separately from counterpoint. h/t to tprice and Jaimbee for the pseudo-JI chords presented here and for other discussions.
13edo oneiro enjoys two main (rooted) pseudo-JI sonorities analogous to major and minor triads: 0-(185)-369-646 ("pseudo-JI major triad" or just "major"/"Maj") and 0-277-738-923 ("pseudo-JI 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".
[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]
[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]
Adding 923 and 1108 to chords works well, and for jazzy extensions one can add 185, 461, and 646 to the upper octave.
[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]
=== Functional chords on each degree ===
Celephaisian
* 0d: minor
* 1d: minor
* 2d: major
* 3d: minor, mindim
* 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 5d: major
* 6d: minor
* 7d: minor triad, minor 4ms, minor 6ms, minor 7ms
Mnionian (Melodic Mnarian)
* 0d: minor
* 1d: minor
* 2d: mindim
* 3d: minor, mindim
* 4d: major, augmented 3ms
* 5d: major, minor 7ms
* 6d: minor triad, minor 6ms, minor 7ms
* 7d: "diminished triad", diminished 5ms, minor 6ms, minor 7ms
=== Progressions ===
kd(maj) means the triad 0 369 646 on kd, kd(min) means the tetrad 0 277 738 923 on kd
Common motions:
* 0d(maj or min) → M1d(min)
* 0d(maj or min) → 4d(min) (when ending on 0d this sounds like diatonic V to I)
* 0d(maj or min) → m6d(min)
* 0d(maj) → 5d(maj), 0d(min) → 5d(maj or min) (when ending on 0d this is a "dominant to tonic" motion)
* "Dorian-like", i.e. no leading tone, 5d is minor, and m7d is major: Ultharian, Mnarian
* 7d is minor: Kadathian, Hlanithian
We'll call degrees that don't have the major pseudo-JI or the minor pseudo-JI chord ''dissonant degrees'' (keeping in mind that dissonance is a feature a chord has in a musical language rather than a purely psychoacoustic property).
==== Celephaïsian ====
* 0d: min
* 1d: min
* 2d: Maj
* 3d: min
* 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 5d: Maj
* 6d: min
* 7d: minor triad, minor 4ms, minor 6ms, minor 7ms
The main resolving degrees (analogues to dominant in diatonic) are 3d and 5d because of their leading tones.
Progressions:
* 0d(min) 1d(min) 3d(min or mindim) 0d(min)
* 0d(min) 1d(min) 6d(min) 3d(min or mindim) 0d(min)
* 0d(min) 6d(min) 3d(min or mindim) 0d(min)
* 0d(min) 2d(Maj) 3d(min or mindim) 0d(min)
* 0d(min) 4d(min7) 5d(Maj)/3d(min or mindim) 0d(min)
* 0d(min) 6d(min) 5d(Maj) 0d(min)
Secondary modes:
* 3d Ultharian
* 2d Dylathian
* 5d illarnekian
==== Ultharian ====
* 0d: min
* 1d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 2d: Maj
* 3d: min
* 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 5d: min
* 6d: min
* 7d: Maj
Ultharian and Mnarian often behave like Dorian because they lack a leading tone. Resolving degrees: 3d(min), 5d(min), 7d(Maj)
==== Mnarian ====
* 0d: min
* 1d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 2d: min
* 3d: min
* 4d: Maj
* 5d: min
* 6d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 7d: Maj
Resolving degrees: 3d(min), 5d(min), 7d(Maj)
==== Kadathian ====
* 0d: min
* 1d: Maj
* 2d: min
* 3d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 4d: Maj
* 5d: min
* 6d: minor triad, minor 4ms, minor 6ms, minor 7ms
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 pseudo-JI and is in fact very close to 32:39:46:60.
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.
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.