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5L 3s has a pentatonic MOS subset [[3L 2s]] (SLSLL). (Note: [[3L 5s]] scales also have 3L 2s subsets.)
5L 3s has a pentatonic MOS subset [[3L 2s]] (SLSLL). (Note: [[3L 5s]] scales also have 3L 2s subsets.)


== Standing assumptions ==
== Name ==
The [[TAMNAMS]] system is used in this article to name 5L 3s intervals and step size ratios and step ratio ranges.
[[TAMNAMS]] suggests the name '''oneirotonic''' (/oʊnaɪrəˈtɒnɪk/ ''oh-ny-rə-TON-ik'' or /ənaɪrə-/ ''ə-ny-rə-'') or 'oneiro' for short. The name ''oneirotonic'' (from Greek ''oneiros'' 'dream') is coined after the Dreamlands in H.P. Lovecraft's Dream Cycle mythos.  


== Names ==
'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L 2s]].
The [[TAMNAMS]] system suggests the name '''oneirotonic''' (/oʊnaɪrəˈtɒnɪk/ ''oh-ny-rə-TON-ik'' or /ənaɪrə-/ ''ə-ny-rə-'') or 'oneiro' for short. The name ''oneirotonic'' (from Greek ''oneiros'' 'dream') is coined after the Dreamlands in H.P. Lovecraft's Dream Cycle mythos.  


'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L 2s]].
== Scale properties ==
{{TAMNAMS use}}


== Intervals ==
=== Intervals ===
The table of oneirotonic intervals below takes the flat fourth as the generator. Given the size of the subfourth generator ''g'', any oneirotonic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number ''k'' of generators it takes to reach the interval and reducing mod 1200 if necessary (so you can use "''k''*''g'' % 1200" for search engines, for plugged-in values of ''k'' and ''g''). For example, since the major 2-step is reached by six subfourth generators, [[18edo]]'s major 2-step is 6*466.67 mod 1200 = 2800 mod 1200 = 400¢, same as the [[12edo]] major third.
{{MOS intervals}}


Note: In TAMNAMS, a k-step interval class in oneirotonic may be called a "k-step", "k-mosstep", or "k-oneirostep". We discourage using 1-indexed terms such as "mos(k+1)th" for non-diatonic mosses in TAMNAMS.
=== Modes ===
{{MOS mode degrees}}
====Proposed Names====
Oneirotonic modes are named after cities in the Dreamlands.
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
!  
! Mode
![[TAMNAMS]] name
![[Modal UDP Notation|UDP]]
!In L's and s's
! Name
!# generators up
! [[TAMNAMS]] name
!In L's and s's
|-
|-
| colspan="6" style="text-align:center" |The 8-note MOS has the following intervals (from some root):
| LLsLLsLs
|<nowiki>7|0</nowiki>
| Dylathian
|-
|-
| 0
| LLsLsLLs
| perfect unison
|<nowiki>6|1</nowiki>
| 0L + 0s
| Ilarnekian
| 0
| octave
| 5L + 3s
|-
|-
| 1
| LsLLsLLs
| perfect 3-step
| |<nowiki>5|2</nowiki>
| 2L + 1s
| Celephaïsian
| -1
| perfect 5-step
| 3L + 2s
|-
|-
| 2
| LsLLsLsL
| major 6-step
|<nowiki>4|3</nowiki>
| 4L + 2s
| Ultharian
| -2
| minor 2-step
| 1L + 1s
|-
|-
| 3
| LsLsLLsL
| major (1-)step
|<nowiki>3|4</nowiki>
| 1L + 0s
| Mnarian
| -3
| minor 7-step
| 4L + 3s
|-
|-
| 4
| sLLsLLsL
| major 4-step
|<nowiki>2|5</nowiki>
| 3L + 1s
| Kadathian
| -4
| minor 4-step
| 2L + 2s
|-
|-
| 5
| sLLsLsLL
| major 7-step
|<nowiki>1|6</nowiki>
| 5L + 2s
| Hlanithian
| -5
| minor (1-)step
| 0L + 1s
|-
|-
| 6
| sLsLLsLL
| major 2-step
|<nowiki>0|7</nowiki>
| 2L + 0s
| Sarnathian
| -6
| minor 6-step
| 3L + 3s
|-
| 7
| augmented 5-step
| 4L + 1s
| -7
| diminished 3-step
| 1L + 2s
|-
| colspan="6" style="text-align:center" |The chromatic 13-note MOS (either [[5L 8s]], [[8L 5s]], or [[13edo]]) also has the following intervals (from some root):
|-
| 8
| augmented 0-step (aka moschroma)
| 1L - 1s
| -8
| diminished 8-step (aka diminished mosoctave)
| 4L + 4s
|-
| 9
| augmented 3-step
| 3L + 0s
| -9
| diminished 5-step
| 2L + 3s
|-
| 10
| augmented 6-step
| 5L + 1s
| -10
| diminished 2-step
| 0L + 2s
|-
| 11
| augmented 1-step
| 2L - 1s
| -11
| diminished 7-step
| 3L + 4s
|-
| 12
| augmented 4-step
| 4L + 0s
| -12
| diminished 4-step
| 1L + 3s
|}
|}


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|}
|}


== Modes ==
== Approaches ==
{{MOS mode degrees}}
===Proposed Names===
Oneirotonic modes are named after cities in the Dreamlands.
{| class="wikitable center-all"
|-
! Mode
! [[Modal UDP Notation|UDP]]
! Name
|-
| LLsLLsLs
| <nowiki>7|0</nowiki>
| Dylathian
|-
| LLsLsLLs
| <nowiki>6|1</nowiki>
| Ilarnekian
|-
| LsLLsLLs
| |<nowiki>5|2</nowiki>
| Celephaïsian
|-
| LsLLsLsL
| <nowiki>4|3</nowiki>
| Ultharian
|-
| LsLsLLsL
| <nowiki>3|4</nowiki>
| Mnarian
|-
| sLLsLLsL
| <nowiki>2|5</nowiki>
| Kadathian
|-
| sLLsLsLL
| <nowiki>1|6</nowiki>
| Hlanithian
|-
| sLsLLsLL
| <nowiki>0|7</nowiki>
| Sarnathian
|}
 
==Approaches==
* [[5L 3s/Temperaments]]
* [[5L 3s/Temperaments]]


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