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In terms of [[Tour of Regular Temperaments|regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic (see also [[5L 3s#Tuning_ranges|Tuning ranges]]):
In terms of [[Tour of Regular Temperaments|regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic (see also [[5L 3s#Tuning_ranges|Tuning ranges]]):
# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[Petrtri]] (13&21, a 2.5.9.11.13.17 temperament that mainly approximates the harmonic series chord 5:9:11:13)
# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[5L_3s#Petrtri_.2813.2621.2C_2.5.9.11.13.17.29|Petrtri]] (13&21, a 2.5.9.11.13.17 temperament that mainly approximates the harmonic series chord 5:9:11:13)
# When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 2.9.5.21 temperament where two major mosseconds or "whole tones" approximate a [[5/4]] classical major third)
# When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 2.9.5.21 temperament where two major mosseconds or "whole tones" approximate a [[5/4]] classical major third)
In a sense, these two temperaments represent the middle of the oneirotonic spectrum (with the [[step ratio]] (L/s) ranging from 3/2 to 3/1); [[13edo]] represents both temperaments, with a step ratio of 2/1. This is analogous to how in the diatonic spectrum, the [[19edo]]-to-[[17edo]]-range has the least extreme ratio of large to small step sizes, with [[12edo]] representing both [[meantone]] (19edo to 12edo) and [[pythagorean]]/[[neogothic]] (12edo to 17edo).
In a sense, these two temperaments represent the middle of the oneirotonic spectrum (with the [[step ratio]] (L/s) ranging from 3/2 to 3/1); [[13edo]] represents both temperaments, with a step ratio of 2/1. This is analogous to how in the diatonic spectrum, the [[19edo]]-to-[[17edo]]-range has the least extreme ratio of large to small step sizes, with [[12edo]] representing both [[meantone]] (19edo to 12edo) and [[pythagorean]]/[[neogothic]] (12edo to 17edo).
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|  | 184.615
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|  | 646.154
|  | 646.154
|  | ...and ends here<br/>Boundary of propriety (generators smaller than this are proper)<br/>[[Petrtri]] starts here...
|  | ...and ends here<br/>Boundary of propriety (generators smaller than this are proper)<br/>[[5L_3s#Petrtri_.2813.2621.2C_2.5.9.11.13.17.29|Petrtri]] starts here...
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==  Tuning ranges ==
==  Tuning ranges ==
=== A-Team (13&18) ===
=== A-Team (13&18) ===
:''Main article: [[A-Team]]''
A-Team tunings (with generator between 5\13 and 7\18) have step ratios between 2/1 and 3/1.  
 
A-Team tunings (with generator between 5\13 and 7\18) have step ratios between 2/1 and 3/1. Hence A-Team tunings have [[5L 8s]] chromatic MOSes and [[13L 5s]] superchromatic MOSes.


A short definition of A-Team is "meantone oneirotonic". This is because A-Team tunings share the following features with [[meantone]] diatonic tunings:  
A short definition of A-Team is "meantone oneirotonic". This is because A-Team tunings share the following features with [[meantone]] diatonic tunings:  
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=== Petrtri (13&21) ===
=== Petrtri (13&21) ===
:''Main article: [[Petrtri]]''
Petrtri tunings (with generator between 8\21 and 5\13) have less extreme step ratios than A-Team tunings, between 3/2 and 2/1. The 8\21-to-5\13 range of oneirotonic tunings remains relatively unexplored. In these tunings,  
Petrtri tunings (with generator between 8\21 and 5\13) have less extreme step ratios than A-Team tunings, 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 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¢.
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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


=== Ana modes ===
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.
We call modes (see [[5L 3s#Modes|oneirotonic 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.
 
=== 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.
 
=== Alterations ===
=== Alterations ===
==== Archeodim ====
==== Archeodim ====
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* the distorted Freygish SASLSLLS
* the distorted Freygish SASLSLLS
* Celephaïsian &4 &6 LsAsLsLs
* Celephaïsian &4 &6 LsAsLsLs
=== Pentatonic subsets ===
 
Modes of the oneiro-pentatonic [[3L 2s]] MOS:
== A-Team 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 an [[A-Team]] 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-M5-M7 Oneiro Falling Suspended Pentatonic
# P1-M2-P4-P6-M7 Oneiro Rising Suspended Pentatonic
# P1-M2-P4-P6-M7 Oneiro Rising Suspended Pentatonic
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# P1-m3-P4-P6-m8 Oneiro Expanding Quartal Pentatonic
# P1-m3-P4-P6-m8 Oneiro Expanding Quartal Pentatonic
# P1-m3-m5-P6-m8 Oneiro Diminished 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]] for comparison)
[[File:Oneiro Baroque Exercises 31edo.mp3]]
([[31edo]] 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 (though 34edo is not an A-Team tuning) 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
==== Over small prime multiples ====
=== Some oneirotonic 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
==== 21nejis ====
# 128:132:137:141:146:151:156:161:166:172:178:184:190:197:204:210:217:224:232:240:248:256
==== 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
==== 34nejis ====


== Rank-2 temperaments ==
== Rank-2 temperaments ==
Line 1,171: Line 1,449:


</div></div>
</div></div>
==== Intervals ====
Sortable table of intervals in the Dylathian mode and their Petrtri interpretations:
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
|-
! Degree
! Size in 13edo
! Size in 21edo
! Size in 34edo
! Size in POTE tuning
! Note name on Q
! class="unsortable"| Approximate ratios
! #Gens up
|-
| 1
| 0\13, 0.00
| 0\21, 0.00
| 0\34, 0.00
| 0.00
| Q
| 1/1
| 0
|-
| 2
| 2\13, 184.62
| 3\21, 171.43
| 5\34, 176.47
| 177.45
| J
| 10/9, 11/10
| +3
|-
| 3
| 4\13, 369.23
| 6\21, 342.86
| 10\34, 352.94
| 354.90
| K
| 11/9, 16/13
| +6
|-
| 4
| 5\13, 461.54
| 8\21, 457.14
| 13\34, 458.82
| 459.15
| L
| 13/10, 17/13, 22/17
| +1
|-
| 5
| 7\13, 646.15
| 11\21, 628.57
| 18\34, 635.294
| 636.60
| M
| 13/9, 16/11, 23/16 (esp. 21edo)
| +4
|-
| 6
| 9\13, 830.77
| 14\21, 800.00
| 23\34, 811.77
| 814.05
| N
| 8/5
| +7
|-
| 7
| 10\13, 923.08
| 16\21, 914.29
| 26\34, 917.65
| 918.30
| O
| 17/10
| +2
|-
| 8
| 12\13, 1107.69
| 19\21, 1085.71
| 31\34, 1094.12
| 1095.75
| P
| 17/9, 32/17, 15/8
| +5
|}
=== A-Team ===
=== A-Team ===
Subgroup: 2.5.9.21
Subgroup: 2.5.9.21
Line 1,193: Line 1,557:


</div></div>
</div></div>
==== Intervals ====
Sortable table of intervals in the Dylathian mode and their A-Team interpretations:
{| 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/>
=== Buzzard ===
=== Buzzard ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 1,305: Line 1,748:
| +5
| +5
|}
|}
== Samples ==
[[File:13edo Prelude in J Oneirominor.mp3]]
[[WT13C]] [[:File:13edo Prelude in J Oneirominor.mp3|Prelude II (J Oneirominor)]] ([[:File:13edo Prelude in J Oneirominor Score.pdf|score]]) – Simple two-part Baroque piece. It stays in oneirotonic even though it modulates to other keys a little.
[[File:13edo_1MC.mp3]]
(13edo, first 30 seconds is in J Celephaïsian)
[[File:A Moment of Respite.mp3]]
(13edo, L Illarnekian)
[[File:Lunar Approach.mp3]]
(by [[Igliashon Jones]], 13edo, J Celephaïsian)


== See also ==
== See also ==
Line 1,314: Line 1,774:
[[Category:MOS scales]]
[[Category:MOS scales]]


[[Category:Abstract MOS patterns]][[Category:Oneirotonic|*]]
[[Category:Abstract MOS patterns]][[Category:Oneirotonic]]
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