User:Inthar/5L 3s
This page describes User:Inthar's approach to 5L 3s (aka oneirotonic).
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, unless specified otherwise. We denote raising and lowering by a chroma (L − s) by # and b.
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 3-steps becomes: ... Pb Kb Nb Q L O J M P K N Q# L# O# ...
Thus the 13edo gamut is as follows:
J/Q# J#/Kb K/Lb L/K# L#/Mb M M#/Nb N/Ob O/N# O#/Pb P Q Q#/Jb J
The 18edo gamut is notated as follows:
J Q#/Kb J#/Lb K L K#/Mb L# M Nb M#/Ob N O Pb O# P Q P#/Jb Qb J
The 21edo gamut:
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
Modes
Oneirotonic modes are named after cities in the Dreamlands.
| Mode | UDP | Name |
| LLsLLsLs | 7|0 | Dylathian (də-LA(H)TH-iən) |
| LLsLsLLs | 6|1 | Illarnekian (ill-ar-NEK-iən) |
| LsLLsLLs | 5|2 | Celephaïsian (kel-ə-FAY-zhən) |
| LsLLsLsL | 4|3 | Ultharian (ul-THA(I)R-iən) |
| LsLsLLsL | 3|4 | Mnarian (mə-NA(I)R-iən) |
| sLLsLLsL | 2|5 | Kadathian (kə-DA(H)TH-iən) |
| sLLsLsLL | 1|6 | Hlanithian (lə-NITH-iən) |
| sLsLLsLL | 0|7 | Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn" |
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.
Todo: chord progs
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 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:
| Mode | UDP | Name |
| LLLsLsLs | 7|0 &4 | Dylydian (Dylathian #4) |
| LLsLsLsL | 6|1 @8 | Illarmixian (Illarnekian b8) |
| LsLLLsLs | 5|2 &6 | Celdorian (Celephaïsian #6) |
| sLLLsLsL | 4|3 @2 | Ulphrygian (Ultharian b2) |
| LsLsLLLs | 3|4 &8 | Mnionian (Mnarian #8) |
| sLsLLLsL | 0|7 &7 | Sardorian (Sarnathian #7) |
| LsLsLsLL | 3|4 @7 | Mnaeolian (Mnarian b7) |
| sLsLsLLL | 0|7 @6 | Sarlocrian (Sarnathian b6) |
The cyclic order of archeodim modes are:
- LSLLLSLS is Celdorian
- SLLLSLSL is Ulphrygian
- LLLSLSLS is Dylydian
- LLSLSLSL is Illarmixian
- LSLSLSLL is Mnaeolian
- SLSLSLLL is Sarlocrian
- LSLSLLLS is Mnionian
- SLSLLLSL is Sardorian
Notably the cyclic order is almost exactly the "circle" of diatonic modes except the "circle" breaks at Sardorian-Celdorian.
In 18edo, the augmented 3-mosstep (LLL) is a 600¢ tritone, which can be used as a dissonance.
Other modmosses
- LSLSLSAS Harmonic Mnarian
13edo oneiro theory
Favorite modes: Dylathian (22122121), Illarnekian (22121221), Celephaisian (21221221), Ultharian (21221212), Celdorian (21222121)
(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: major 0-185-369-646 and minor 0-277-738-923. 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.
On O Celephaisian:
- O: 0 277 738 923 (O Q L M)
- P: 0 277 738 923 (P J M N)
- Q: 0 185 369 646 (Q J K M)
- J: 0 277 738 923 (J L O P)
- K: 0 277 738 1015 (K M P J)
- L: 0 185 369 646 (L M N P)
- M: 0 277 738 923 (M O J K)
- N: 0 277 738 1015 (N P K M)
- O: 0 277 738 923 (O Q L M)
On M Mnionian (Melodic Mnarian):
- M: 0 277 738 923 (M O J K)
- N: 0 277 738 923 (N P K L#)
- O: 0 277 831 (O Q L#)?
- P: 0 277 738 923 (P J M N)
- Q: 0 185 369 646 (Q J K M)
- J: 0 185 369 646 (J K L# N)
- K: 0 277 738 1015 (K N P J)
- L#: 0 369 646 (L# O Q) ("misspelled"); 0 277 553 (L# N P); 0 277 831 (L# N J)
Adding 923 to chords works well, and for jazzy extensions one can add 185, 461, and 646 to the upper octave.
Some more dissonant sonorities are 0 277 646 923.
18edo oneiro theory
Favorite modes: Mnionian (31313331), Mnaeolian (31313133), Ulphrygian (13331313), Celdorian (31333131), Sardorian (13133313)
The biggest difference from 13edo oneiro is that the P0ms-M2ms-m4ms chord (0 400 667) is now dissonant.
21edo oneiro theory
Favorite modes: Dylathian (33233232), Sarn (23233233)
21edo has the soft oneirotonic (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. In terms of JI, it mainly approximates 16:23:30 (R-Lmos5-L7ms). Importantly, the sharp fifth is now harmonically much more fifth-like than the flat fifth, unlike in 13edo and harder tunings. The main consonances are now chords using seconds and sevenths (in addition to thirds and sixths). The relatively consonant 114¢ and 1086¢ intervals may help to mask some of the more dissonant sonorities such as the naiadic and the sharp fifth, and work for chill and lo-fi styles.
- 0-342-629: buzzy with sine-like timbres
- 0-343-457
- 0-171-457
- 0-286-400
- 0-171-457-743
- 0-114-571
- 0-286-571
- 0-286-686
- 0-457-571
Seconds, tritones and sevenths are consonances in addition to thirds and sixths. The naiadic is a semiconsonance. The sharp fifth is fifth-like but is still dissonant. The triad root-third-629 can resolve to a more consonant chord such as 0-343-457.
It is suggested to use R-2ms-mos5-6ms carefully in 21edo oneiro - it sounds more like a dissonant, unstable 12edo diminished 7th, unlike in 13edo and harder oneiro tunings where they have a more discernible (though complex) identity.
Nejis
A curated list of nejis.
- 26:29:32:34:38:42:44:49:52 Tridecimal Dylathian
- 26:29:30:34:38:42:44:49:52 Tridecimal Celdorian