| | Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
|}
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.
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.)
=== 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
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:
In [[13edo]], archeodim is a subset of the 9-note [[4L 5s]] MOS generated by the subminor third 3\13.
==== Other MODMOSes ====
Other potentially interesting oneirotonic MODMOSes (that do not use half-sharps or half-flats) are:
* the distorted harmonic minor LSLLSALS (A = aug oneiro2nd = 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 ===
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. R-Lo2-Po4-Lo5-Lo7, 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'' R-Lo2-Po4-Po6-Lo7 (J-K-M-O-P) can be used for similar effect.
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. This would allow, for example, using the perfect oneirofourth and small oneirofifth (instead of the large oneirothird and the perfect oneirofourth) as stand-ins for major thirds and fourths in neobaroque contexts (this adds some dissonance which might be what you want sometimes, e.g. in a chord that is supposed to resolve to a more consonant chord).
===== 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 ===
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-Lo3-Lo5: Falling Major Triad; Squashed Major Triad
* R-so3-Lo5: Falling Minor Triad; Squashed Minor Triad
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 meantone-like 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 5:9:11:13 (R-so8-Lo2-Po4) and 16:23:30 (R-Lo5-Lo8). Importantly, the sharp fifth is now harmonically much more fifth-like than the flat fifth, unlike in [[13edo]] and harder tunings. Rather than squashed tertian triads, it may be preferable to use triads with sharp fifths, quartal harmony, stacks of seconds and thirds, third+sixth and third+seventh chords, and using the JI approximations (subsets of 5:9:11:13 (R-so8-Lo2-Po4), 9:10:11:13 (R-Lo2-Lo3-Lo5), and 8:15:23 (R-Lo7-Lo5)).
34edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like, and it is a bit more optimized for the 5:9:11:13 approximation.
Approximate low-complexity JI chords in the JKLMNOPQ = Ultharian mode:
5L 3s 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).
5L 3s 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 mode LLsLLsLs.
Any edo with an interval between 450¢ and 480¢ has a 5L 3s scale. 13edo is the smallest edo with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.
5L 3s has a pentatonic MOS subset 3L 2s (SLSLL). (Note: 3L 5s scales also have 3L 2s subsets.)
The TAMNAMS system, used by this article, uses 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, not a generator range. A more correct way to say it would be 'father[8]' or 'father octatonic'. "Father" is also vague because optimal generators for it also generate 3L 2s.
Notation
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.
The chain of oneirofourths becomes: ... P@ K@ N@ Q L O J M P K N Q& L& O& ...
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
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 of generators it takes to reach the interval and reducing mod 1200 if necessary (The % sign can be used for the modulo operation on many search engines). For example, since the large oneirothird is reached by six subfourth generators, 18edo's large oneirothird is 6*466.67 mod 1200 = 2800 mod 1200 = 400¢, same as the 12edo major third.
# generators up
Notation (1/1 = J)
Octatonic interval category name
Abbrev.
# generators up
Notation of 2/1 inverse
Octatonic interval category name
Abbrev.
The 8-note MOS has the following intervals (from some root):
0
J
perfect unison
P1
0
J
octave
Po9
1
M
perfect oneirofourth (aka minor fourth, falling fourth)
Po4
-1
O
perfect oneirosixth (aka major fifth, rising fifth)
Po6
2
P
large oneiroseventh
Lo7
-2
L
small oneirothird
so3
3
K
large oneirosecond
Lo2
-3
Q
small oneiroeighth
so8
4
N
large oneirofifth (aka minor fifth, falling fifth)
Lo5
-4
N@
small oneirofifth (aka major fourth, rising fourth)
so4
5
Q&
large oneiroeighth
Lo8
-5
K@
small oneirosecond
so2
6
L&
large oneirothird
Lo3
-6
P@
small oneiroseventh
so7
7
O&
augmented oneirosixth
Ao6
-7
M@
diminished oneirofourth
d-o4
The chromatic 13-note MOS (either 5L 8s, 8L 5s, or 13edo) also has the following intervals (from some root):
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:
The large step is a "meantone", somewhere between near-10/9 (as in 13edo) and near-9/8 (as in 18edo).
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.
EDOs that are in the hypohard range include 13edo, 18edo, and 31edo.
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.
↑The ratio interpretations that are not valid for 18edo are italicized.
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-Lo2-Lo3-Lo5 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¢).
Sortable table of major and minor intervals in hyposoft tunings (13edo not shown):
Degree
Size in 21edo (soft)
Size in 34edo (semisoft)
Note name on J
Approximate ratios
#Gens up
unison
0\21, 0.00
0\34, 0.00
J
1/1
0
small o2nd
2\21, 114.29
3\34, 105.88
K@
16/15
-5
large o2nd
3\21, 171.43
5\34, 176.47
K
10/9, 11/10
+3
small o3rd
5\21, 285.71
8\34, 282.35
L
13/11, 20/17
-2
large o3rd
6\21, 342.86
10\34, 352.94
L&
11/9
+6
dim. o4th
7\21, 400.00
11\34, 388.24
M@
5/4
-7
perf. o4th
7\18, 457.14
12\31, 458.82
M
13/10
+1
small o5th
10\21, 571.43
16\34, 564.72
N@
18/13, 32/23
-4
large o5th
11\21, 628.57
18\34, 635.29
N
13/9, 23/16
+4
perf. o6th
13\21, 742.86
21\34, 741.18
O
20/13
-1
aug. o6th
14\21, 800.00
23\34, 811.77
O&
8/5
+7
small o7th
15\21, 857.14
24\34, 847.06
P@
18/11
-6
large o7th
16\21, 914.29
26\34, 917.65
P
22/13, 17/10
+2
small o8th
18\21, 1028.57
29\34, 1023.53
Q
9/5
-3
large o8th
19\21, 1085.71
31\34, 1094.12
Q&
15/8
+5
Parasoft to ultrasoft tunings
The range of oneirotonic tunings of step ratio between 6/5 and 3/2 (thus in the parasoft to ultrasoft range) may be of interest because it 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. [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.
