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== Defining Terms ==
== Defining Terms ==
For the purposes of this page, I will be describing the degrees of the Oneiro scale using a system based on a system of seven nominals and one interordinal; this allows for the octave to land on the interval of equivalence, maintaining the octave complement relationships (e.g. m7 ~ M2, M3 ~ m6, etc.)
For the purposes of this page, I will be describing the degrees of the Oneiro scale using a system based on a system of seven nominals and one interordinal; this allows for the octave to land on the interval of equivalence, maintaining the octave complement relationships (e.g. m7 ~ M2, M3 ~ m6, etc.).  Each scale degree has a distinct formula, allowing a composer to find the exact size of any degree by only knowing the size of L and s.
{| class="wikitable"
{| class="wikitable"
|+Degrees of Oneiro
|+Degrees of Oneiro
!Degree
!Degree
!Formula
!Soft Range
!Soft Range
!Hard Range
!Hard Range
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|-
|-
|1
|1
|N/A
|1/1
|1/1
|1/1
|1/1
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|-
|-
|chroma
|chroma
|L - s
|1/13 - 1\5
|1/13 - 1\5
|1/1 - 1\13
|1/1 - 1\13
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|-
|-
|m2
|m2
|s
|1/1 - 1\13
|1/1 - 1\13
|1\13 - 1\8
|1\13 - 1\8
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|-
|-
|M2
|M2
|L
|2\13 - 1\5
|2\13 - 1\5
|1\8 - 2\13
|1\8 - 2\13
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|-
|-
|m3
|m3
|L + s
|1\5 - 2\8
|1\5 - 2\8
|3\13 - 1\4
|3\13 - 1\4
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|-
|-
|M3
|M3
|L + L
|4\13 - 2\5
|4\13 - 2\5
|1\4 - 4\13
|1\4 - 4\13
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|-
|-
|d4
|d4
|L + 2s
|1\5 - 4\13
|1\5 - 4\13
|4\13 - 3\8
|4\13 - 3\8
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|-
|-
|P4
|P4
|2L + s
|5\13 - 2\5
|5\13 - 2\5
|3\8 - 5\13
|3\8 - 5\13
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|
|
|-
|-
|t
|mT
|2L + 2s
|2\5 - 6\13
|2\5 - 6\13
|6\13 - 1\2
|6\13 - 1\2
|G♭
|G♭
|Minor Tritone
|Minor Tritone/Antitonic
|-
|-
|T
|MT
|3L + s
|7\13 - 3\5
|7\13 - 3\5
|1\2 - 7\13
|1\2 - 7\13
|G
|G
|Major Tritone
|Major Tritone/Antitonic
|-
|-
|P5
|P5
|3L + 2s
|3\5 - 8\13
|3\5 - 8\13
|8\13 - 5\8
|8\13 - 5\8
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|-
|-
|A5
|A5
|4L + s
|9\13 - 4\5
|9\13 - 4\5
|5\8 - 9\13
|5\8 - 9\13
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|-
|-
|m6
|m6
|3L + 3s
|3\5 - 9\13
|3\5 - 9\13
|9\13 - 3\4
|9\13 - 3\4
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|-
|-
|M6
|M6
|4L + 2s
|10\13 - 4\5
|10\13 - 4\5
|3\4 - 10\13
|3\4 - 10\13
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|-
|-
|m7
|m7
|4L + 3s
|4\5 - 11\13
|4\5 - 11\13
|11\13 - 7\8
|11\13 - 7\8
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|-
|-
|M7
|M7
|5L + 2s
|12\13 - 2/1
|12\13 - 2/1
|7\8 - 12\13
|7\8 - 12\13
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|-
|-
|8
|8
|5L + 3s
|2/1
|2/1
|2/1
|2/1
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|-
|-
|Major
|Major
|
|CM
|M3 + m3
|M3 + m3
|C - E - G
|C - E - G
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|-
|-
|Minor
|Minor
|
|Cm
|m3 + M3
|m3 + M3
|C - E♭ - G
|C - E♭ - G
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|-
|-
|Diminished
|Diminished
|
|C<sup>o</sup>
|m3 + m3
|m3 + m3
|C - E♭ - G♭
|C - E♭ - G♭
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|-
|-
|Augmented
|Augmented
|
|C+
|M3 + M3
|M3 + M3
|C - E - G♯
|C - E - G♯
|N/A
|N/A
|}
|}
As can be seen here, the distribution between major, minor, and diminished triads in Oneirotonic is rather even.  In hard tunings, these chords may provide a useful place of rest, since the major triad resembles [[13/10|10:13:15]] and the diminished triad resembles [[6:7:8:9|6:7:8]].  In soft tunings, however, these chords are much less stable, as the tritones approach the semioctave.
As can be seen here, the distribution between major, minor, and diminished triads in Oneirotonic is rather even.  In hard tunings, these chords may provide a useful place of rest, since the major triad resembles the harmonic shape [[13/10|10:13:15]] and the diminished triad resembles [[6:7:8:9|6:7:8]].  In soft tunings, however, these chords are much less stable, as the tritones approach the semioctave.


MODMOS scales of Oneirotonic can be designed to target specific combinations of triads, including the usage of augmented triads.
MODMOS scales of Oneirotonic can be designed to target specific combinations of triads, including the usage of augmented triads.
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|Celephaïsian, Sarnathian
|Celephaïsian, Sarnathian
|}
|}
In soft tunings, these chords are useful resolutions, since C<sup>4</sup> resembles [[6:8:9]], and C<sup>3</sup> resembles [[4:5:6]].  In hard tunings, however, these chords are much less stable, as C<sup>4</sup> better resembles 13:17:20 and C<sup>3</sup> better resembles 13:16:20.
In soft tunings, these chords are useful resolutions, since C<sup>4</sup> resembles the harmonic shape of [[6:8:9]], and C<sup>3</sup> resembles [[4:5:6]].  In hard tunings, however, these chords are much less stable, as C<sup>4</sup> better resembles 13:17:20 and C<sup>3</sup> better resembles 13:16:20.
 
The altered chords C<sup>4+5</sup> (C - F - H♯) and C<sup>3+5</sup> (C - E - H♯) replace the standard genspan triads in the outlier Dylathian mode, which makes it a standout mode in this analysis.  Unlike the tertiary triads, it is difficult to reconcile the altered nature of these "Augmented Genspan" chords, as genspan triads are formed via splitting a constant interval rather than stacking a constant group.


== Chord Functions ==
== Chord Functions ==
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In soft tunings of the Oneirotonic scale, the Fourth genspan chord will be used as the primary tonic function, since that chord is the most consonant, and is included in six of the eight modes, making it an efficient choice for a general resolution.
In soft tunings of the Oneirotonic scale, the Fourth genspan chord will be used as the primary tonic function, since that chord is the most consonant, and is included in six of the eight modes, making it an efficient choice for a general resolution.


==== Dominant ====
==== Defining a Dominant ====
In order to define a dominant chord, we need three primary features:
In order to define a dominant chord, we need three primary features:


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# Is regularly contained within the same mode as the tonic
# Is regularly contained within the same mode as the tonic


While there are a number of chords that satisfy one or two of these properties, there are very few that satisfy them all; however, the Third genspan chord built on the fifth degree of the scale manages to rise above those other options.  It creates motion around the generator, which makes it relevant to many scales and allows secondary dominants to be generalized; it creates tension due to the third above the fifth degree being a leading tone into the tonic; and allowing it to be altered to a Flat-Third chord makes it recognizably appear in four of the six modes that contain the tonic Fourth chord.
While there are a number of chords that satisfy one or two of these properties, there are very few that satisfy them all; however, the Third genspan chord built on the fifth degree of the scale manages to rise above those other options.  It creates motion around the generator, which makes it relevant to many scales and allows secondary dominants to be generalized, and it creates tension due to the third above the fifth degree being a leading tone into the tonic.
 
The Celephaïsian mode is the only mode to contain the Third genspan chord over the fifth degree, but the Flat-Third chord is contained in all five of the modes darker than it.  These modes are prime candidates for MODMOS scales, as the seventh degree can be raised to form "harmonic" forms of each scale.  Celephaïsian already serves as the harmonic form of Ultharian, which means that there are four MODMOS scales that can be constructed this way.
 
The Ilarnekian mode contrastively contains a major third degree over the root rather than a minor third, which creates an awkward "Augmented Genspan" chord on the fifth degree.  The Dylathian mode doesn't have a perfect fifth degree at all, instead containing an augmented fifth.
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