5L 3s/Inthar's approach

From Xenharmonic Wiki
Jump to navigation Jump to search

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

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.


Oneirotonic modes are named after cities in the Dreamlands.

Mode UDP Name Former names
LLsLLsLs 7|0 Dylian Dylathian
LLsLsLLs 6|1 Ilarnekian
LsLLsLLs 5|2 Celephaïsian
LsLLsLsL 4|3 Ultharian
LsLsLLsL 3|4 Mnarian
sLLsLLsL 2|5 Kadian Kadathian
sLLsLsLL 1|6 Hlanian Hlanithian
sLsLLsLL 0|7 Sarnian Sarnathian



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.

Mode UDP Name
LLLsLsLs 7|0 &4 Dylydian (Dylathian #4)
LLsLsLsL 6|1 @8 Ilarmixian (Ilarnekian 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:

  1. LSLLLSLS is Celdorian
  2. SLLLSLSL is Ulphrygian
  3. LLLSLSLS is Dylydian
  4. LLSLSLSL is Ilarmixian
  5. LSLSLSLL is Mnaeolian
  6. SLSLSLLL is Sarlocrian
  7. LSLSLLLS is Mnionian
  8. 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 chordal theory

Main article: 13edo/Inthar's approach

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.

A progression on ascending 18edo Mnaeolian

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. The chord 0-342-629-1085 is delta-rational and is in fact very close to 32:39:46:60.

  • 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


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


Modal studies