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{{Interwiki
:''For the tritave-equivalent MOS structure with the same step pattern, see [[5L 3s (tritave-equivalent)]].''
| en = 5L 3s
| de =
| es =
| ja =
| ko = 5L3s (Korean)
}}
{{Infobox MOS
{{Infobox MOS
| Name = oneirotonic
| Neutral = 2L 6s
| Periods = 1
| nLargeSteps = 5
| nSmallSteps = 3
| Equalized = 3
| Paucitonic = 2
| Pattern = LLsLLsLs
}}
}}
'''5L 3s''' or '''oneirotonic''' (/oʊnaɪrəˈtɒnɪk/ ''oh-ny-rə-TON-ik'' or /ənaɪrə-/ ''ə-ny-rə-'') refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 2\5 (two degrees of [[5edo]] = 480¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The name ''oneirotonic'' (from Greek ''oneiros'' 'dream') was coined by [[Cryptic Ruse]] after the Dreamlands in H.P. Lovecraft's Dream Cycle mythos.  
: ''For the tritave-equivalent MOS structure with the same step pattern, see [[5L 3s (3/1-equivalent)]].''
{{MOS intro}}
5L 3s can be seen as a [[Warped diatonic|warped diatonic scale]], because it has one extra small step compared to diatonic ([[5L 2s]]).


Oneirotonic is a distorted diatonic, because it has one extra small step compared to diatonic ([[5L 2s]]): for example, the Ionian diatonic mode LLsLLLs can be distorted to the Dylathian oneirotonic mode LLsLLsLs.
== Name ==
{{TAMNAMS name}} 'Oneiro' is sometimes used as a shortened form.


Any edo with an interval between 450¢ and 480¢ has an oneirotonic scale. [[13edo]] is the smallest edo with a (non-degenerate) 5L3s oneirotonic scale and thus is the most commonly used oneirotonic tuning.
'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]].


5L 3s has a pentatonic MOS subset [[3L 2s]] (SLSLL), and in this context we call this the ''oneiro-pentatonic''. When viewed as a chord (with undetermined voicing) we call it the Oneiro Core Pentad. (Note: [[3L 5s]] scales also have 3L 2s subsets.)
== Scale properties ==


== Notation==
=== Intervals ===
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.
{{MOS intervals}}


The chain of oneirofourths becomes: ... P@ K@ N@ Q L O J M P K N Q& L& O& ...
=== Generator chain ===
{{MOS genchain}}


Thus the [[13edo]] gamut is as follows:
=== Modes ===
{{MOS mode degrees}}


'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M''' M&/N@ '''N/O@''' '''O/N&''' O&/P@ '''P''' '''Q''' Q&/J@ '''J'''
==== Proposed mode names ====
 
The following names have been proposed for the modes of 5L 3s, and are named after cities in the Dreamlands.
The [[18edo]] gamut is notated as follows:
{{MOS modes
| Mode Names=
Dylathian $
Ilarnekian $
Celephaïsian $
Ultharian $
Mnarian $
Kadathian $
Hlanithian $
Sarnathian $
| Collapsed=1
}}


'''J''' Q&/K@ J&/L@ '''K''' '''L''' K&/M@ L& '''M''' N@ M&/O@ '''N''' '''O''' P@ O& '''P''' '''Q''' P&/J@ Q@ '''J'''
== Tunings==
=== Simple tunings ===
The simplest tuning for 5L 3s correspond to 13edo, 18edo, and 21edo, with step ratios 2:1, 3:1, and 3:2, respectively.


The [[21edo]] gamut:
{{MOS tunings|JI Ratios=Int Limit: 30; Prime Limit: 19; Tenney Height: 7.7}}


'''J''' J& K@ '''K''' K&/L@ '''L''' L& M@ '''M''' M& N@ '''N''' N&/O@ '''O''' O& P@ '''P''' P&/Q@ '''Q''' Q& J@ '''J'''
=== Hypohard tunings ===
[[Hypohard]] oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic", sharing the following features with [[meantone]] diatonic tunings:
* The large step is a "meantone", around the range of [[10/9]] to [[9/8]].
* The major 2-mosstep is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third.


== Tuning ranges ==
With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to [[7/6]].
=== Hypohard ===
[[Hypohard]] oneirotonic tunings (with generator between 5\13 and 7\18) have step ratios between 2/1 and 3/1.  


Hypohard oneirotonic can be considered "meantone oneirotonic". This is because these tunings share the following features with [[meantone]] diatonic tunings:
EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]], and are associated with [[5L 3s/Temperaments#A-Team|A-Team]] temperament.
* The large step is a "meantone", somewhere between near-10/9 (as in [[13edo]]) and near-9/8 (as in [[18edo]]).
* 13edo has characteristically small 1-mossteps of about 185{{c}}. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings.
* The major mosthird (made of two large steps) is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third.
* 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3{{c}}, a perfect 5-mosstep) and falling fifths (666.7{{c}}, a major 4-mosstep) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* 31edo can be used to make the major 2-mosstep a near-just 5/4.
* [[44edo]] (generator {{nowrap|17\44 {{=}} 463.64{{c}}}}), [[57edo]] (generator {{nowrap|22\57 {{=}} 463.16{{c}}}}), and [[70edo]] (generator 27\70 {{=}} 462.857{{c}}}}) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8.


EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]].
{{MOS tunings|Step Ratios=Hypohard|JI Ratios=Subgroup: 2.5.9.21; Int Limit:40; Complements Only: 1|Tolerance=15}}
* 13edo has characteristically small major mosseconds of about 185c. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings.
* 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3c, a perfect mossixth) and falling fifths (666.7c, a major mosfifth) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* 31edo  can be used to make the major mos3rd a near-just 5/4.
* [[44edo]] (generator 17\44 = 463.64¢), [[57edo]] (generator 22\57 = 463.16¢), and [[70edo]] (generator 27\70 = 462.857¢) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8.


The sizes of the generator, large step and small step of oneirotonic are as follows in various hypohard oneiro tunings.
=== Hyposoft tunings ===
{| class="wikitable right-2 right-3 right-4 right-5"
[[Hyposoft]] oneirotonic tunings have step ratios between 3:2 and 2:1, which remains relatively unexplored. In these tunings,
|-
* The large step of oneirotonic tends to be intermediate in size between [[10/9]] and [[11/10]]; the small step size is a semitone close to [[17/16]], about 92{{c}} to 114{{c}}.
!
* The major 2-mosstep (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342{{c}}) to 4\13 (369{{c}}).
! [[13edo]]
! [[18edo]]
! [[31edo]]
|-
| generator (g)
| 5\13, 461.54
| 7\18, 466.67
| 12\31, 464.52
|-
| L (3g - octave)
| 2\13, 184.62
| 3\18, 200.00
| 5\31, 193.55
|-
| s (-5g + 2 octaves)
| 1\13, 92.31
| 1\18, 66.67
| 2\31, 77.42
|}


==== Intervals ====
* [[21edo]]'s P1-L1ms-L2ms-L4ms approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71{{c}}) and Baroque diatonic semitones (114.29{{c}}, close to quarter-comma meantone's 117.11{{c}}).
Sortable table of intervals in the Dylathian mode in hypohard oneiro tunings:
 
{| class="wikitable right-2 right-3 right-4 sortable"
|-
! Degree
! Size in 13edo
! Size in 18edo
! Size in 31edo
! Note name on Q
! class="unsortable"| Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! #Gens up
|-
| 1
| 0\13, 0.00
| 0\18, 0.00
| 0\31, 0.00
| Q
| 1/1
| 0
|-
| 2
| 2\13, 184.62
| 3\18, 200.00
| 5\31, 193.55
| J
| 9/8, 10/9
| +3
|-
| 3
| 4\13, 369.23
| 6\18, 400.00
| 10\31, 387.10
| K
| 5/4
| +6
|-
| 4
| 5\13, 461.54
| 7\18, 466.67
| 12\31, 464.52
| L
| 21/16, ''13/10''
| +1
|-
| 5
| 7\13, 646.15
| 10\18, 666.66
| 17\31, 658.06
| M
| ''13/9'', ''16/11''
| +4
|-
| 6
| 9\13, 830.77
| 13\18, 866.66
| 22\31, 851.61
| N
| ''13/8'', ''18/11''
| +7
|-
| 7
| 10\13, 923.08
| 14\18, 933.33
| 24\31, 929.03
| O
| 12/7
| +2
|-
| 8
| 12\13, 1107.69
| 17\18, 1133.33
| 29\31, 1122.58
| P
|
| +5
|}
<references/>
 
=== Hyposoft ===
[[Hyposoft]] oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of oneirotonic tunings remains relatively unexplored. In these tunings,
* the large step of oneirotonic tends to be intermediate in size between [[10/9]] and [[11/10]]; the small step size is a semitone close to [[17/16]], about 92¢ to 114¢.
* The major mosthird (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342¢) to 4\13 (369¢).
 
* [[21edo]]'s P1-M2-M3-M5 (in oneiro interval classes) approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71¢) and Baroque diatonic semitones (114.29¢, close to quarter-comma meantone's 117.11¢).
* [[34edo]]'s 9:10:11:13 is even better.
* [[34edo]]'s 9:10:11:13 is even better.


The sizes of the generator, large step and small step of oneirotonic are as follows in various hyposoft oneiro tunings.
This set of JI identifications is associated with [[5L 3s/Temperaments#Petrtri|petrtri]] temperament. (P1-M1ms-P3ms could be said to approximate 5:11:13 in all soft-of-basic tunings, which is what "basic" [[petrtri]] temperament is.)
{| class="wikitable right-2 right-3 right-4 right-5"
|-
!
! [[13edo]]
! [[21edo]]
! [[34edo]]
|-
| generator (g)
| 5\13, 461.54
| 8\21, 457.14
| 13\34, 458.82
|-
| L (3g - octave)
| 2\13, 184.62
| 3\21, 171.43
| 5\34, 176.47
|-
| s (-5g + 2 octaves)
| 1\13, 92.31
| 2\21, 114.29
| 3\34, 105.88
|}


==== Intervals ====
{{MOS tunings
Sortable table of intervals in the Dylathian mode in hyposoft tunings:
| Step Ratios = Hyposoft
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
| JI Ratios =  
|-
1/1;
! Degree
16/15;
! Size in 13edo
10/9; 11/10;
! Size in 21edo
13/11; 20/17;
! Size in 34edo
11/9;
! Note name on Q
5/4;
! class="unsortable"| Approximate ratios
13/10;
! #Gens up
18/13; 32/23;
|-
13/9; 23/16;
| 1
20/13;
| 0\13, 0.00
8/5;
| 0\21, 0.00
18/11;
| 0\34, 0.00
22/13; 17/10;
| Q
9/5;
| 1/1
15/8;
| 0
2/1
|-
}}
| 2
| 2\13, 184.62
| 3\21, 171.43
| 5\34, 176.47
| J
| 10/9, 11/10
| +3
|-
| 3
| 4\13, 369.23
| 6\21, 342.86
| 10\34, 352.94
| K
| 11/9, 16/13
| +6
|-
| 4
| 5\13, 461.54
| 8\21, 457.14
| 13\34, 458.82
| L
| 13/10, 17/13, 22/17
| +1
|-
| 5
| 7\13, 646.15
| 11\21, 628.57
| 18\34, 635.294
| M
| 13/9, 16/11, 23/16 (esp. 21edo)
| +4
|-
| 6
| 9\13, 830.77
| 14\21, 800.00
| 23\34, 811.77
| N
| 8/5
| +7
|-
| 7
| 10\13, 923.08
| 16\21, 914.29
| 26\34, 917.65
| O
| 17/10
| +2
|-
| 8
| 12\13, 1107.69
| 19\21, 1085.71
| 31\34, 1094.12
| P
| 17/9, 32/17, 15/8
| +5
|}
=== Parasoft to ultrasoft tunings ===
Oneirotonic tunings of step ratio between 6/5 and 3/2 (thus in the [[parasoft]] to [[ultrasoft]] range) equate three oneirotonic large steps to a diatonic perfect fourth, i.e. they equate the oneirotonic large step to a [[porcupine]] generator. [This identification may come in handy since many altered oneirotonic modes have three consecutive large steps.]


The sizes of the generator, large step and small step of oneirotonic are as follows in various tunings in this range.
=== Parasoft and ultrasoft tunings ===
{| class="wikitable right-2 right-3 right-4 right-5"
The range of oneirotonic tunings of step ratio between 6:5 and 3:2 is closely related to [[porcupine]] temperament; these tunings equate three oneirotonic large steps to a diatonic perfect fourth, i.e. they equate the oneirotonic large step to a [[porcupine]] generator. The chord 10:11:13 is very well approximated in 29edo.
|-
!
! [[29edo]]
! [[37edo]]
|-
| generator (g)
| 11\29, 455.17
| 14\37, 454.05
|-
| L (3g - octave)
| 4\29, 165.52
| 5\37, 162.16
|-
| s (-5g + 2 octaves)
| 3\29, 124.14
| 4\37, 129.73
|}
==== Intervals ====
The sizes of the generator, large step and small step of oneirotonic are as follows in these tunings.
{| class="wikitable right-2 right-3 right-4 sortable"
|-
! Degree
! Size in 29edo
! Size in 37edo
! Note name on Q
! class="unsortable"| Approximate ratios
! #Gens up
|-
| 1
| 0\29, 0.00
| 0\37, 0.00
| Q
| 1/1
| 0
|-
| 2
| 4\29, 165.52
| 5\37, 163.16
| J
| 11/10
| +3
|-
| 3
| 8\29, 331.03
| 10\37, 324.32
| K
|
| +6
|-
| 4
| 11\29, 455.17
| 14\37, 454.05
| L
| 13/10
| +1
|-
| 5
| 15\29, 620.69
| 19\37, 616.22
| M
| 10/7
| +4
|-
| 6
| 19\29, 786.21
| 23\37, 778.38
| N
| 11/7
| +7
|-
| 7
| 22\29, 910.34
| 28\37, 908.11
| O
| 22/13
| +2
|-
| 8
| 26\29, 1075.86
| 33\37, 1070.27
| P
| 13/7
| +5
|}
<!--=== Buzzard ===
Buzzard is an oneirotonic rank-2 temperament in the [[Step ratio|pseudopaucitonic]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum.


In the broad sense, [[Buzzard]] can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into it's own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well.
{{MOS tunings
| Step Ratios = 6/5; 3/2; 4/3
| JI Ratios =
1/1;
14/13;
11/10;
9/8;
15/13;
13/11;
14/11;
13/10;
4/3;
15/11;
7/5;
10/7;
22/15;
3/2;
20/13;
11/7;
22/13;
26/15;
16/9;
20/11;
13/7;
2/1
}}


Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.
=== Parahard tunings ===
23edo oneiro combines the sound of neogothic tunings like [[46edo]] and the sounds of "superpyth" and "semaphore" scales. This is because 23edo oneirotonic has a large step of 208.7¢, same as [[46edo]]'s neogothic major second, and is both a warped [[22edo]] [[superpyth]] [[diatonic]] and a warped [[24edo]] [[semaphore]] [[semiquartal]] (and both nearby scales are [[superhard]] MOSes).


The sizes of the generator, large step and small step of oneirotonic are as follows in various buzzard tunings.
{{MOS tunings
{| class="wikitable right-2 right-3 right-4 right-5"
| JI Ratios =  
|-
1/1;
!
21/17;
! [[38edo]]
17/16;
! [[53edo]]
14/11;
! [[63edo]]
6/5;
! Optimal ([[POTE]]) Buzzard tuning
21/16;
! JI intervals represented (2.3.5.7.13 subgroup)
21/17;
|-
34/21;
| generator (g)
32/21;
| 15\38, 473.68
5/3;
| 21\53, 475.47
11/7;
| 25\63, 476.19
32/17;
| 475.69
34/21;
| 3/2 21/16
2/1
|-
| Step Ratios = 4/1
| L (3g - octave)
}}
| 7/38, 221.04
| 10/53, 226.41
| 12/63, 228.57
| 227.07
| 8/7
|-
| s (-5g + 2 octaves)
| 1/38 31.57
| 1/53 22.64
| 1/63 19.05
| 21.55
| 55/54 81/80 91/90
|}


==== Intervals ====
=== Ultrahard tunings ===
Sortable table of intervals in the Dylathian mode and their Buzzard interpretations:
{{Main|5L&nbsp;3s/Temperaments#Buzzard}}


{| class="wikitable right-2 right-3 right-4 right-5 sortable"
[[Buzzard]] is a rank-2 temperament in the [[Step ratio|pseudocollapsed]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum.
|-
! Degree
! Size in 38edo
! Size in 53edo
! Size in 63edo
! Size in POTE tuning
! Note name on Q
! class="unsortable"| Approximate ratios
! #Gens up
|-
| 1
| 0\38, 0.00
| 0\53, 0.00
| 0\63, 0.00
| 0.00
| Q
| 1/1
| 0
|-
| 2
| 7\38, 221.05
| 10\53, 226.42
| 12\63, 228.57
| 227.07
| J
| 8/7
| +3
|-
| 3
| 14\38, 442.10
| 20\53, 452.83
| 24\63, 457.14
| 453.81
| K
| 13/10, 9/7
| +6
|-
| 4
| 15\38, 473.68
| 21\53, 475.47
| 25\63, 476.19
| 475.63
| L
| 21/16
| +1
|-
| 5
| 22\38, 694.73
| 31\53, 701.89
| 37\63, 704.76
| 702.54
| M
| 3/2
| +4
|-
| 6
| 29\38, 915.78
| 41\53, 928.30
| 49\63, 933.33
| 929.45
| N
| 12/7, 22/13
| +7
|-
| 7
| 30\38, 947.36
| 42\53, 950.94
| 50\63, 952.38
| 951.27
| O
| 26/15
| +2
|-
| 8
| 37\38, 1168.42
| 52\53, 1177.36
| 62\63, 1180.95
| 1178.18
| P
| 108/55, 160/81
| +5
|}
-->


== Intervals ==
In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into its own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well.
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 of generators it takes to reach the interval and reducing mod 1200 if necessary. For example, since the major oneirothird is reached by six subfourth generators, [[18edo]]'s major oneirothird is 6*466.67 mod 1200 = 2800 mod 1200 = 400¢, same as the [[12edo]] major third.
{| class="wikitable center-all"
|-
! Generators
! Notation (1/1 = J)
! Octatonic interval category name
! Generators
! Notation of 2/1 inverse
! Octatonic interval category name
|-
| colspan="6" style="text-align:left" | The 8-note MOS has the following intervals (from some root):
|-
| 0
| J
| perfect unison
| 0
| J
| octave
|-
| 1
| M
| perfect oneirofourth (aka minor fourth, falling fourth)
| -1
| O
| perfect oneirosixth (aka major fifth, rising fifth)
|-
| 2
| P
| major oneiroseventh
| -2
| L
| minor oneirothird
|-
| 3
| K
| major oneirosecond
| -3
| Q
| minor oneiroeighth
|-
| 4
| N
| major oneirofifth (aka minor fifth, falling fifth)
| -4
| N@
| minor oneirofifth (aka major fourth, rising fourth)
|-
| 5
| Q&
| major oneiroeighth
| -5
| K@
| minor oneirosecond
|-
| 6
| L&
| major oneirothird
| -6
| P@
| minor oneiroseventh
|-
| 7
| O&
| augmented oneirosixth
| -7
| M@
| diminished oneirofourth
|-
| colspan="6" style="text-align:left" | The chromatic 13-note MOS (either [[5L 8s]] or [[8L 5s]]) also has the following intervals (from some root):
|-
| 8
| J&
| augmented unison
| -8
| J@
| diminished octave
|-
| 9
| M&
| augmented oneirofourth
| -9
| O@
| diminished oneirosixth
|-
| 10
| P&
| augmented oneiroseventh
| -10
| L@
| diminished oneirothird
|-
| 11
| K&
| augmented oneirosecond
| -11
| Q@
| diminished oneiroeighth
|-
| 12
| N&
| augmented oneirofifth
| -12
| N@@
| diminished oneirofifth
|}


== Key signatures ==
Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.
Flat keys:
* J@ Oneirominor, L@ Oneiromajor = N@, K@, P@, M@, J@, O@, L@, Q@
* M@ Oneirominor, O@ Oneiromajor = N@, K@, P@, M@, J@, O@, L@
* P@ Oneirominor, J@ Oneiromajor = N@, K@, P@, M@, J@, O@
* K@ Oneirominor, M@ Oneiromajor = N@, K@, P@, M@, J@
* N@ Oneirominor, P@ Oneiromajor = N@, K@, P@, M@
* Q Oneirominor, K@ Oneiromajor = N@, K@, P@
* L Oneirominor, N@ Oneiromajor = N@, K@
* O Oneirominor, Q Oneiromajor = N@
All-natural key signature:
* J Oneirominor, L Oneiromajor = no sharps or flats
Sharp keys:
* M Oneirominor, O Oneiromajor = Q&
* P Oneirominor, J Oneiromajor = Q&, L&
* K Oneirominor, M Oneiromajor = Q&, L&, O&
* N Oneirominor, P Oneiromajor = Q&, L&, O&, J&
* Q& Oneirominor, K Oneiromajor = Q&, L&, O&, J&, M&
** Enharmonic with J@ Oneirominor, L@ Oneiromajor in [[13edo]]
* L& Oneirominor, N Oneiromajor = Q&, L&, O&, J&, M&, P&
** Enharmonic with M@ Oneirominor, O@ Oneiromajor in 13edo
* O& Oneirominor, Q& Oneiromajor = Q&, L&, O&, J&, M&, P&, K&
** Enharmonic with P@ Oneirominor, J@ Oneiromajor in 13edo
* J& Oneirominor, L& Oneiromajor = Q&, L&, O&, J&, M&, P&, K&, N&
** Enharmonic with K@ Oneirominor, M@ Oneiromajor in 13edo


== Modes ==
{{MOS tunings
Oneirotonic modes are named after cities in the Dreamlands. (The names are by Cryptic Ruse.)
| JI Ratios =  
1/1;
8/7;
13/10;
21/16;
3/2;
12/7, 22/13;
26/15;
49/25, 160/81;
2/1
| Step Ratios = 7/1; 10/1; 12/1
| Tolerance = 30
}}


# Dylathian (də-LA(H)TH-iən): LLSLLSLS
== Approaches ==
# Illarnekian (ill-ar-NEK-iən): LLSLSLLS
* [[5L&nbsp;3s/Temperaments]]
# Celephaïsian (kel-ə-FAY-zhən): LSLLSLLS
# Ultharian (ul-THA(I)R-iən): LSLLSLSL
# Mnarian (mə-NA(I)R-iən): LSLSLLSL
# Kadathian (kə-DA(H)TH-iən): SLLSLLSL
# Hlanithian (lə-NITH-iən): SLLSLSLL
# Sarnathian (sar-NA(H)TH-iən): SLSLLSLL


The modes on the white keys JKLMNOPQJ are:
== Samples ==
* J Ultharian
[[File:The Angels' Library edo.mp3]] [[:File:The Angels' Library edo.mp3|The Angels' Library]] by [[Inthar]] in the Sarnathian (23233233) mode of 21edo oneirotonic ([[:File:The Angels' Library Score.pdf|score]])
* K Hlanithian
* L Illarnekian
* M Mnarian
* N Sarnathian
* O Celephaïsian
* P Kadathian
* Q Dylathian
 
{| class="wikitable"
|-
|+ Table of modes (based on J, from brightest to darkest)
|-
! Mode
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! (9)
|-
| Dylathian
| J
| K
| L&
| M
| N
| O&
| P
| Q&
| (J)
|-
| Illarnekian
| J
| K
| L&
| M
| N
| O
| P
| Q&
| (J)
|-
| Celephaïsian
| J
| K
| L
| M
| N
| O
| P
| Q&
| (J)
|-
| Ultharian
| J
| K
| L
| M
| N
| O
| P
| Q
| (J)
|-
| Mnarian
| J
| K
| L
| M
| N@
| O
| P
| Q
| (J)
|-
| Kadathian
| J
| K@
| L
| M
| N@
| O
| P
| Q
| (J)
|-
| Hlanithian
| J
| K@
| L
| M
| N@
| O
| P@
| Q
| (J)
|-
| Sarnathian
| J
| K@
| L
| M@
| N@
| O
| P@
| Q
| (J)
|}
 
For classical-inspired functional harmony, we propose 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 ===
==== 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.
 
As with the MOS, archeodim has four ana and four kata rotations:
* Ana:
** LLLSLSLS: Dylathian &4, Dylydian
** LLSLSLSL: Illarnekian @8, Illarmixian
** LSLLLSLS: Celephaïsian &6, Celdorian
** SLLLSLSL: Ultharian @2, Ulphrygian
* Kata:
** LSLSLLLS: Mnarian &8, Mnionian
** SLSLLLSL: Sarnathian &7, Sardorian
** LSLSLSLL: Mnarian @7, Mnaeolian
** SLSLSLLL: Sarnathian @6, Sarlocrian
 
{| class="wikitable"
|-
|+ Table of archeodim modes (based on J)
|-
! Mode
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! (9)
|-
| Dylydian
| J
| K
| L&
| M&
| N
| O&
| P
| Q&
| (J)
|-
| Illarmixian
| J
| K
| L&
| M
| N
| O
| P
| Q
| (J)
|-
| Celdorian
| J
| K
| L
| M
| N
| O&
| P
| Q&
| (J)
|-
| Ulphrygian
| J
| K@
| L
| M
| N
| O
| P
| Q
| (J)
|-
| Mnionian
| J
| K
| L
| M
| N@
| O
| P
| Q&
| (J)
|-
| Sardorian
| J
| K@
| L
| M@
| N@
| O
| P
| Q
| (J)
|-
| Mnaeolian
| J
| K
| L
| M
| N@
| O
| P@
| Q
| (J)
|-
| Sarlocrian
| J
| K@
| L
| M@
| N@
| O@
| P@
| Q
| (J)
|}
 
==== Other MODMOSes ====
Other potentially interesting oneirotonic MODMOSes (that do not use half-sharps or half-flats) are:
* the distorted harmonic minor LSLLSALS (A = aug 2nd = L + chroma)
* the distorted Freygish SASLSLLS
* Celephaïsian &4 &6 LsAsLsLs
 
== Hypohard oneiro theory ==
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.
=== Ana modes ===
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.
 
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. P1-M2-P4-M5-M7 (on J, J-K-M-N-P), 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'' P1-M2-P4-P6-M7 (J-K-M-O-P) can be used for similar effect.
 
Modes of the oneiro-pentatonic MOS:
# P1-M2-P4-M5-M7 Oneiro Falling Suspended Pentatonic
# P1-M2-P4-P6-M7 Oneiro Rising Suspended Pentatonic
# P1-m3-P4-P6-M7 Oneiro Symmetrical Pentatonic
# P1-m3-P4-P6-m8 Oneiro Expanding Quartal Pentatonic
# P1-m3-m5-P6-m8 Oneiro Diminished Pentatonic
 
==== Functional harmony ====
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.
===== 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 ===
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.)
 
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-M3-M5: Falling Major Triad; Squashed Major Triad
* R-m3-M5: Falling Minor Triad; Squashed Minor Triad
* R-m3-m5: Squashed Dim Triad
* R-M3-A5: Squashed Aug Triad
* R-M3-M5-A6: Falling Major Triad Add6
* R-m3-M5-A6: Falling Minor Triad Add6
* R-M3-M5-M7: Falling Major Tetrad
* R-m3-M5-M7: Falling Minor Tetrad
* R-m3-m5-M7: Half-Diminished Tetrad
* R-m3-m5-m7: Orwell Tetrad, Diminished Tetrad
* R-M3-A6: Squashed 1st Inversion Minor Triad; Sephiroth Triad (approximates 8:10:13 in 13edo and 31edo)
* R-M3-A6-M8: Sephiroth Triad Add7
* R-M3-A6-(M2)-(P4): Sephiroth Triad Add9 Sub11
* R-M3-A6-(m2)-(P4): Sephiroth Triad Addm9 Sub11
* R-M3-A6-(P4): Sephiroth Triad Sub11
* R-m3-P6: Rising Minor Triad; Squashed 1st Inversion Major Triad
* R-M3-P6: Rising Major Triad
* R-m3-M7: Minor add6 no5
* R-m3-m7: Minor addm6 no5
* R-m5-M7: Falling no3 add6
* R-m5-m7: Falling no3 add6
* R-M3-M8: Major 7th no5
* R-m3-M8: Minor Major 7th no5
* R-M3-M5-M8: Falling Major Seventh Tetrad
* R-m3-M5-M8: Falling Minor Major Seventh Tetrad
* R-M3-M7-M8: no5 Major Seventh Add6
* R-m3-M7-M8: no5 Minor Major Seventh Add6
* R-M3-P6-M8: Rising Major Seventh
* R-m3-P6-M8: Rising Oneiro Minor Major Seventh
* R-M3-(M2): Oneiro Major Add9
* R-m3-(M2): Oneiro Minor Add9
* R-M3-M5-(M2): Falling Major Triad Add9
* R-m3-M5-(M2): Falling Minor Triad Add9
* R-M3-(M2)-(P4): no5 Major Add9 Sub11
* R-m3-(M2)-(P4): no5 Minor Add9 Sub11
* R-m3-P6-M7-(M2)-(P4)-(A6)-(M8)
* R-M2-P4: Sus24 No5
* R-M2-M5: Falling Sus2 Triad
* R-P4-M5: Falling Sus4 Triad
* R-M2-P4-M5: Falling Sus24
* R-P4-M7: Oneiro Quartal Triad
* R-P4-M7-(M2): Oneiro Quartal Tetrad, Core Tetrad
* R-P4-M7-(M2)-(M5): Oneiro Quartal Pentad, Core Pentad
* R-P4-M7-(M2)-(M5)-(M8): Oneiro Quartal Hexad
* R-P4-M7-M8: Oneiro Quartal Seventh Tetrad
* R-P4-m8: Expanding Quartal Triad
* R-M2-P4-m8: Expanding Quartal Triad add2
* R-m3-P4-m8: Expanding Quartal Triad Addm3
* R-m5-m8: Contracting Quartal Triad
* R-m5-m7-m8: Contracting Quartal Triad Addm7
* R-M3-M5-m8: Falling Major Triad addm7
=== Primodal theory ===
{{todo|Needs attention from primodalists}}
 
18edo may be a better basis for a style of oneirotonic primodality using comma sharp and comma flat fifths than 13edo (in particular diesis sharp and diesis flat fifths; diesis is a category with a central region of 32 to 40¢). In 18edo both the major fifth (+31.4¢) and the minor fifth (-35.3¢) are about a diesis off from a just perfect fifth. In 13edo only the major fifth is a diesis sharp, and it is +36.5¢ off from just; so there's less wiggle room for a [[neji]] if you want every major fifth to be at most a diesis sharp).
 
31nejis and 34nejis also provide opportunities to use dieses directly, since 1\31 (38.71¢) and 1\34 (35.29¢) are both dieses.
==== Primodal chords ====
Some relatively low-complexity oneirotonic-inspired primodal chords. They are grouped by [[prime family]].
===== /11 =====
* 22:25:26:29:32:34:38:42:44 Undecimal Celephaïsian
* 22:25:26:29:32:34:38:40:44 Undecimal Ultharian
===== /13 =====
* 13:15:19 Tridecimal Falling Ultraminor Triad
* 13:16:19 Tridecimal Falling Submajor Triad
* 13:16:21 Tridecimal Squashed 1st Inversion Minor Triad
* 13:17:19 Tridecimal Naiadic Maj2; Tridecimal Falling Sus4
* 13:17:20 Tridecimal Rising Sus4
* 13:17:21 Tridecimal Squashed 2nd Inversion Major Triad
* 13:16:19:22 Tridecimal Falling Major Tetrad
* 26:29:38 Tridecimal Falling Sus2 Triad
* 26:31:38 Tridecimal Falling Bright Minor Triad
* 26:33:38 Tridecimal Falling Bright Major Triad
* 26:29:34:38 Tridecimal Falling Sus24
 
===== /17 =====
* 17:20:25 Septendecimal Falling Minor Triad
* 17:21:25 Septen Falling Major Triad
* 17:20:26 Septen Rising Minor Triad
* 17:20:25:29 Septen Falling Minor Tetrad
* 17:21:25:29 Septen Falling Major Tetrad
* 17:20:26:29 Septen Rising Minor Triad addM6
* 34:41:50 Septen Falling Bright Minor Triad
* 34:43:50 Septen Falling Octodecous Major Triad (''octodecous'' means '18edo-like')
* 34:40:47:55 Septen Orwell Tetrad
* 34:40:52:58:76:89:102:129 (Celephaïsian + P5; R-min3-r5-M6-M9-sub11-P12(fc)-M14)
* 34:40:52:58:76:89:102:110:129 (Celephaïsian + P5; R-min3-r5-M6-M9-sub11-P12(fc)-supmin13-M14)
* 34:40:50:58:89:102:129 (R-min3-f5-M6-M9-sub11-P12(rc)-M14)
* 34:40:50:58:89:102:110:129 (R-min3-f5-M6-M9-sub11-P12(rc)-supmin13-M14)
* 34:40:50:58:76:89:110:129 (R-m3-f5-M6-M9-sub11-supm13-M7)
* 34:40:50:58:76:89:102:110:129:208 (R-m3-f5-M6-M9-sub11-P12(rc)-supm13-M14-r19(rc^2))
* 34:38:40:44:49:52:58:64:68 Septen Celephaïsian
===== /19 =====
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.
* 19:24:28 Novemdecimal Falling Bright Major Triad
* 19:23:28 Novem Falling Supraminor Triad
* 19:22:28 Novem Falling Ultraminor Triad
* 19:24:29 Novem Rising Major Triad
* 19:24:30 Novem Augmented Triad
* 19:24:43 Novem Major no5 add9
* 19:24:43:50 Novem Major no5 add9sub11
* 19:24:28:43:50 Novem Falling Major Triad add9 sub11
* 19:24:29:43:50 Novem Rising Major Triad add9 sub11
* 19:25:34 Novem Expanding Quartal
* 19:26:34 Novem Contracting Quartal
* 38:43:56 Novem Falling Minor Triad
* 38:45:56 Novemdecimal Falling Dark Major Triad
* 38:48:56:65 Novem Falling Major Tetrad
* 38:48:73 Novem Major Seventh no5
* 38:48:63 Novem Falling Major Triad
* 38:50:65 Novem Oneiro Quartal Triad
* 38:50:65:73 Novem Oneiro Quartal Seventh Tetrad
* 38:50:65:86 Novem Oneiro Core Tetrad
* 38:50:65:86:112 Novem Oneiro Core Pentad
* 38:50:65:86:112:146 Novem Oneiro Core Hexad
* 38:50:63 Novem Squashed First Inversion Neutral Triad
* 38:43:45:50:56:58:65:72:76 Novem Bright Celephaïsian
* 38:42:44:49:55:58:65:72:76 Novem Dark Celephaïsian
===== /23 =====
23(2:4) has many oneiro pitches, some close to 13edo, and some close to 18edo:
46:48:50:51:52:54:56:57:58:60:63:65:67:68:70:73:74:76:79:82:83:85:87:88:92
 
* 23:27:30 Vicesimotertial Falling Min4 no5
* 23:27:30:35:44 Vice Falling Min4 addM5,M7
* 23:27:37 Vice Orwell Tetrad no4
* 23:29:34 Vice Octodecous Falling Major Triad
* 46:54:68 Vice Octodecous Falling Minor Triad
* 46:54:60:67 Vice Falling Min4
* 46:54:63 Vice Squashed Dim
* 46:54:63:68 Vice Oneiro Half-diminished Tetrad
* 46:54:63:74 Vice Orwell Tetrad
* 46:54:67 Vice Tridecous Falling Minor Triad (''tridecous'' means '13edo-like')
* 46:57:67 Vice Tridecous Falling Major Triad
* 46:54:67:78 Vice Tridecous Falling Minor Tetrad
* 46:57:67:78 Vice Tridecous Falling Major Tetrad
* 46:54:60:67:78 Vice Falling Minor Tetrad Add Min4
* 46:60:67 Vice Falling Sus4
* 46:54:60:67 Vice Falling Min3 Sus4
* 46:52:58:60:68:76:79:89:92 Vice Bright Dylathian
* 46:51:57:60:67:75:78:88:92 Vice Dark Dylathian
* 46:52:58:60:68:71:79:89:92 Vice Bright Illarnekian
* 46:51:57:60:67:70:78:88:92 Vice Dark Illarnekian
* 46:52:54:60:68:71:79:89:92 Vice Bright Celephaïsian
* 46:51:54:60:67:70:78:88:92 Vice Dark Celephaïsian
* 46:52:54:60:68:71:79:83:92 Vice Bright Ultharian
* 46:51:54:60:67:70:78:82:92 Vice Dark Ultharian
* 46:52:54:60:64:71:79:83:92 Vice Bright Mnarian
* 46:51:54:60:63:70:78:82:92 Vice Dark Mnarian
* 46:49:54:60:64:71:79:83:92 Vice Bright Kadathian
* 46:48:54:60:63:70:78:82:92 Vice Dark Kadathian
* 46:49:54:60:64:71:75:83:92 Vice Bright Hlanithian
* 46:48:54:60:63:70:74:82:92 Vice Dark Hlanithian
* 46:49:54:58:64:71:75:83:92 Vice Bright Sarn
* 46:48:54:57:63:70:74:82:92 Vice Dark Sarn
 
===== /29 =====
* 29:34:38 Vicesimononal Falling Sus4
* 29:34:42 Vicenon Falling Minor Triad
* 29:36:42 Vicenon Falling Major Triad
* 29:34:40:47 Vicenon Orwell Tetrad
* 29:38:52 Vicenon Expanding Quartal Triad
* 29:40:52 Vicenon Contracting Quartal Triad
* 29:38:65:84:99 Vicenon Oneiro Core Pentad
* 29:38:65:84:99:110 Vicenon Oneiro Core Hexad
* 58:65:76:84:99:116 Vicenon Oneiro Falling Suspended Pentatonic
* 58:65:76:89:99:116 Vicenon Oneiro Rising Suspended Pentatonic
* 58:72:76:89:99:116 Vicenon Oneiro Symmetrical Pentatonic
* 58:72:76:89:104:116 Vicenon Oneiro Expanding Quartal Pentatonic
* 58:72:80:89:104:116 Vicenon Oneiro Diminished Pentatonic
* 58:65:72:80:84:94:99:110:116 Vicenon Dylydian
* 58:65:72:76:84:94:99:110:116 Vicenon Dylathian
* 58:65:72:76:84:89:99:110:116 Vicenon Illarnekian
* 58:65:72:76:84:89:99:104:116 Vicenon Illarmixian
* 58:65:68:76:84:94:99:110:116 Vicenon Celdorian
* 58:65:68:76:84:89:99:110:116 Vicenon Celephaïsian
* 58:65:68:76:84:89:99:104:116 Vicenon Ultharian
* 58:65:68:76:80:89:99:104:116 Vicenon Mnarian
* 58:65:68:76:80:89:99:110:116 Vicenon Mnionian
* 58:65:68:76:80:89:94:104:116 Vicenon Mnaeolian
* 58:61:68:76:80:89:99:104:116 Vicenon Kadathian
* 58:61:68:76:84:89:99:104:116 Vicenon Ulphrygian
* 58:61:68:76:80:89:94:104:116 Vicenon Hlanithian
* 58:61:68:72:80:89:99:104:116 Vicenon Sardorian
* 58:61:68:72:80:89:94:104:116 Vicenon Sarnathian
* 58:61:68:72:80:84:94:104:116 Vicenon Sarlocrian
===== /47 =====
* 47:52:55:61:68:72:80:89:94 Quadseptimal Celephaïsian
===== /61 =====
* 61:68:72:80:89:93:104:116:122 Sessantunesimal Celephaïsian
 
==== Nejis ====
The reader is encouraged to tweak these nejis and add more nejis that they like.
===== 13nejis =====
# '''58''':61:65:'''68''':72:'''76''':80:84:89:94:99:'''104''':110:116 - A low-complexity 13neji; has /13, /17, /19, and /29 prime modes
#* For lower complexity, can use 64 instead of 65 or 100 instead of 99
# 92:97:102:108:114:120:127:134:141:149:157:165:174:184 - Vice 13neji
===== 18nejis =====
# '''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
===== 31nejis =====
# 92:94:96:98:101:103:105:108:110:113:115:118:120:123:126:129:132:135:138:141:144:147:150:154:157:161:165:168:172:176:180:184
 
== Hyposoft oneiro theory ==
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 Baroque 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 9:10:11:13 and 16:23:30.
 
=== Primodal theory ===
==== Nejis ====
===== 21nejis =====
# 128:132:137:141:146:151:156:161:167:172:178:184:190:197:203:210:217:224:232:240:248:256
 
===== 34nejis =====


== Temperaments ==
:''Main article: [[5L 3s/Temperaments]]''
== Samples ==
[[File:13edo Prelude in J Oneirominor.mp3]]
[[File:13edo Prelude in J Oneirominor.mp3]]


Line 1,173: Line 188:
[[File:A Moment of Respite.mp3]]
[[File:A Moment of Respite.mp3]]


(13edo, L Illarnekian)
(13edo, L Ilarnekian)


[[File:Lunar Approach.mp3]]
[[File:Lunar Approach.mp3]]
Line 1,179: Line 194:
(by [[Igliashon Jones]], 13edo, J Celephaïsian)
(by [[Igliashon Jones]], 13edo, J Celephaïsian)


== See also ==
=== 13edo Oneirotonic Modal Studies ===
* [[Well-Tempered 13-Tone Clavier]] (collab project to create 13edo oneirotonic keyboard pieces in a variety of keys and modes)
* [[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3]]: Tonal Study in Dylathian
* [[File:Inthar-13edo Oneirotonic Studies 2 Ultharian.mp3]]: Tonal Study in Ultharian
* [[File:Inthar-13edo Oneirotonic Studies 3 Hlanithian.mp3]]: Tonal Study in Hlanithian
* [[File:Inthar-13edo Oneirotonic Studies 4 Illarnekian.mp3]]: Tonal Study in Ilarnekian
* [[File:Inthar-13edo Oneirotonic Studies 5 Mnarian.mp3]]: Tonal Study in Mnarian
* [[File:Inthar-13edo Oneirotonic Studies 6 Sarnathian.mp3]]: Tonal Study in Sarnathian
* [[File:Inthar-13edo Oneirotonic Studies 7 Celephaisian.mp3]]: Tonal Study in Celephaïsian
* [[File:Inthar-13edo Oneirotonic Studies 8 Kadathian.mp3]]: Tonal Study in Kadathian
 
== Scale tree ==
== Scale tree ==
{| class="wikitable" style="text-align:center;"
{{MOS tuning spectrum
|-
| 13/8 = Golden oneirotonic (458.3592{{c}})
! colspan="5" | generator
| 13/5 = Golden A-Team (465.0841{{c}})
! | tetrachord
}}
! | g in cents
! | 2g
! | 3g
! | 4g
! | Comments
|-
| | 2\5
| |
| |
| |
| |
| | 1 0 1
|  | 480.000
|  | 960.000
|  | 240.00
|  | 720.000
|  |
|-
| | 21\53
| |
| |
| |
| |
|  | 10 1 10
|  | 475.472
|  | 950.943
|  | 226.415
|  | 701.887
|  |
|-
| | 19\48
| |
| |
| |
| |
|  | 9 1 9
|  | 475
|  | 950
|  | 225
|  | 700
|  |
|-
| | 17\43
| |
| |
| |
| |
|  | 8 1 8
|  | 474.419
|  | 948.837
|  | 223.256
|  | 697.674
|  |
|-
| | 15\38
| |
| |
| |
| |
|  | 7 1 7
|  | 473.684
|  | 947.368
|  | 221.053
|  | 694.737
|  |
|-
| | 13\33
| |
| |
| |
| |
|  | 6 1 6
|  | 472.727
|  | 945.455
|  | 218.181
|  | 690.909
|  |
|-
| | 11\28
| |
| |
| |
| |
|  | 5 1 5
|  | 471.429
|  | 942.857
|  | 214.286
|  | 685.714
|  |
|-
| | 9\23
| |
| |
| |
| |
|  | 4 1 4
|  | 469.565
|  | 939.130
|  | 208.696
|  | 678.261
|  | L/s = 4
|-
|
|16\41
|
|
|
|7 2 7
|468.293
|936.585
|204.878
|673.171
|
|-
| | 7\18
| |
| |
| |
| |
|  | 3 1 3
|  | 466.667
|  | 933.333
|  | 200.000
|  | 666.667
|  | L/s = 3
|-
| |
| | 19\49
| |
| |
| |
|  | 8 3 8
|  | 465.306
|  | 930.612
|  | 195.918
|  | 661.2245
| |
|-
| |
| |
| | 50\129
| |
| |
|  | 21 8 21
|  | 465.116
|  | 930.233
|  | 195.349
|  | 660.465
| |
|-
| |
| |
| |
| | 131\338
| |
|  | 55 21 55
|  | 465.089
|  | 930.1775
|  | 195.266
|  | 660.335
| |
|-
| |
| |
| |
| |
| | 212\547
|  | 89 34 89
|  | 465.082
|  | 930.1645
|  | 195.247
|  | 660.329
| |
|-
| |
| |
| |
| | 81\209
| |
|  | 34 13 34
|  | 465.072
|  | 930.1435
|  | 195.215
|  | 660.287
| |
|-
| |
| |
| | 31\80
| |
| |
|  | 13 5 13
|  | 465
|  | 930
|  | 195
|  | 660
| |
|-
| |
| | 12\31
| |
| |
| |
|  | 5 2 5
|  | 464.516
|  | 929.032
|  | 193.549
|  | 658.065
|  |
|-
| | 5\13
| |
| |
| |
| |
|  | 2 1 2
|  | 461.538
|  | 923.077
|  | 184.615
|  | 646.154
|  | Boundary of propriety (generators smaller than this are proper)
|-
| |
| | 13\34
| |
| |
| |
|  | 5 3 5
|  | 458.824
|  | 917.647
|  | 176.471
|  | 635.294
|  |
|-
| |
| |
| | 34\89
| |
| |
|  | 13 8 13
|  | 458.427
|  | 916.854
|  | 175.281
|  | 633.708
|  |
|-
| |
| |
| |
| | 89\233
| |
|  | 34 21 34
|  | 458.369
|  | 916.738
|  | 175.107
|  | 633.473
|  |
|-
| |
| |
| |
| |
| | 233\610
|  | 89 55 89
|  | 458.361
|  | 916.721
|  | 175.082
|  | 633.443
|  | Golden oneirotonic; generator is 2 octaves minus logarithmic [[phi]]
|-
| |
| |
| |
| | 144\377
| |
|  | 55 34 55
|  | 458.355
|  | 916.711
|  | 175.066
|  | 633.422
|  |
|-
| |
| |
| | 55\144
| |
| |
|  | 21 13 21
|  | 458.333
|  | 916.666
|  | 175
|  | 633.333
|  |
|-
| |
| | 21\55
| |
| |
| |
|  | 8 5 8
|  | 458.182
|  | 916.364
|  | 174.545
|  | 632.727
|  |
|-
| | 8\21
| |
| |
| |
| |
|  | 3 2 3
|  | 457.143
|  | 914.286
|  | 171.429
|  | 628.571
|  | Optimum rank range (L/s=3/2) oneirotonic
|-
| | 11\29
| |
| |
| |
| |
|  | 4 3 4
|  | 455.172
|  | 910.345
|  | 165.517
|  | 620.690
|  |
|-
| | 14\37
| |
| |
| |
| |
|  | 5 4 5
|  | 454.054
|  | 908.108
|  | 162.162
|  | 616.216
| |
|-
| | 17\45
| |
| |
| |
| |
|  | 6 5 6
|  | 453.333
|  | 906.667
|  | 160
|  | 613.333
| |
|-
| | 20\53
| |
| |
| |
| |
|  | 7 6 7
|  | 452.83
|  | 905.66
|  | 158.491
|  | 611.321
| |
|-
| | 23\61
| |
| |
| |
| |
|  | 8 7 8
|  | 452.459
|  | 904.918
|  | 157.377
|  | 609.836
| |
|-
| | 26\69
| |
| |
| |
| |
|  | 9 8 9
|  | 452.174
|  | 904.348
|  | 156.522
|  | 608.696
| |
|-
| | 29\77
| |
| |
| |
| |
|  | 10 9 10
|  | 451.948
|  | 903.896
|  | 155.844
|  | 607.792
| |
|-
| | 3\8
| |
| |
| |
| |
|  | 1 1 1
|  | 450.000
|  | 900.000
|  | 150.000
|  | 600.000
|  |
|}


[[Category:Scales]]
[[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A -->
[[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A -->
[[Category:Mos]]
[[Category:Pages with internal sound examples]]
[[Category:MOS scales]]
 
[[Category:Abstract MOS patterns]][[Category:Oneirotonic]]
Retrieved from "https://en.xen.wiki/w/5L_3s"