User:Unque/5L 3s Tonal Theory - Revision history

Unque at 14:51, 5 December 2025

2025-12-05T14:51:25Z

← Older revision		Revision as of 14:51, 5 December 2025
Line 72:		Line 72:
	\|		\|
	\|-		\|-
	\|t		\|mT
	\|2L + 2s		\|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		\|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
Line 232:		Line 232:
	\|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.
Line 270:		Line 270:
	\|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 ==
Line 280:		Line 282:
	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:

Line 287:		Line 289:
	# 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.

Unque: Added formulas for scale degrees

2025-09-22T15:13:52Z

Added formulas for scale degrees

← Older revision		Revision as of 15:13, 22 September 2025
Line 6:		Line 6:

	== 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		\|t
			\|2L + 2s
	\|2\5 - 6\13		\|2\5 - 6\13
	\|6\13 - 1\2		\|6\13 - 1\2
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	\|-		\|-
	\|T		\|T
			\|3L + s
	\|7\13 - 3\5		\|7\13 - 3\5
	\|1\2 - 7\13		\|1\2 - 7\13
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	\|-		\|-
	\|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
Line 88:		Line 101:
	\|-		\|-
	\|m6		\|m6
			\|3L + 3s
	\|3\5 - 9\13		\|3\5 - 9\13
	\|9\13 - 3\4		\|9\13 - 3\4
Line 94:		Line 108:
	\|-		\|-
	\|M6		\|M6
			\|4L + 2s
	\|10\13 - 4\5		\|10\13 - 4\5
	\|3\4 - 10\13		\|3\4 - 10\13
Line 100:		Line 115:
	\|-		\|-
	\|m7		\|m7
			\|4L + 3s
	\|4\5 - 11\13		\|4\5 - 11\13
	\|11\13 - 7\8		\|11\13 - 7\8
Line 106:		Line 122:
	\|-		\|-
	\|M7		\|M7
			\|5L + 2s
	\|12\13 - 2/1		\|12\13 - 2/1
	\|7\8 - 12\13		\|7\8 - 12\13
Line 112:		Line 129:
	\|-		\|-
	\|8		\|8
			\|5L + 3s
	\|2/1		\|2/1
	\|2/1		\|2/1

Unque at 15:01, 22 September 2025

2025-09-22T15:01:32Z

← Older revision		Revision as of 15:01, 22 September 2025
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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
Line 203:		Line 203:
	\|-		\|-
	\|Diminished		\|Diminished
	\|		\|C<sup>o</sup>
	\|m3 + m3		\|m3 + m3
	\|C - E♭ - G♭		\|C - E♭ - G♭
Line 209:		Line 209:
	\|-		\|-
	\|Augmented		\|Augmented
	\|		\|C+
	\|M3 + M3		\|M3 + M3
	\|C - E - G♯		\|C - E - G♯

Unque at 19:40, 18 June 2025

2025-06-18T19:40:31Z

← Older revision		Revision as of 19:40, 18 June 2025
Line 85:		Line 85:
	\|5\8 - 9\13		\|5\8 - 9\13
	\|H♯		\|H♯
	\|Enharmonically equivalent to m7 in basic tuning ([[13edo]])		\|Enharmonically equivalent to m6 in basic tuning ([[13edo]])
	\|-		\|-
	\|m6		\|m6

Unque: Began work on specific functions of soft oneiro

2025-05-08T18:11:11Z

Began work on specific functions of soft oneiro

← Older revision		Revision as of 18:11, 8 May 2025
Line 258:		Line 258:

	Because of this dichotomy, I will be outlining two primary sets of chord functions: those that describe soft Oneirotonic, and those that describe hard.		Because of this dichotomy, I will be outlining two primary sets of chord functions: those that describe soft Oneirotonic, and those that describe hard.

			=== Soft Oneiro Functions ===
			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 ====
			In order to define a dominant chord, we need three primary features:

			# Creates satisfying motion around a relevant circle, especially a generator
			# Contains a tension that resolves cleanly to the tonic chord
			# 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.

Unque at 12:38, 7 May 2025

2025-05-07T12:38:39Z

← Older revision		Revision as of 12:38, 7 May 2025
Line 232:		Line 232:
	\|P4 + m3		\|P4 + m3
	\|C - F - H		\|C - F - H
	\|~~Ikarnekian~~, Hlanithian		\|Ilarnekian, Hlanithian
	\|-		\|-
	\|Third		\|Third

Unque: Created page with "{{breadcrumb|5L_3s}}'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!''' The 5L 3s scale, or Oneirotonic, is particularly interesting as far as scales go. Its doesn't arise very intuitively from low-complexity harmonic relationships in the same way as the diatonic scale or the third-generated smitonic and mosh scales; however, once its structure is asserted, it can be a very fruitful system to..."

2025-05-07T00:45:06Z

Created page with "{{breadcrumb|5L_3s}}'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!''' The 5L 3s scale, or Oneirotonic, is particularly interesting as far as scales go. Its doesn't arise very intuitively from low-complexity harmonic relationships in the same way as the diatonic scale or the third-generated smitonic and mosh scales; however, once its structure is asserted, it can be a very fruitful system to..."

New page

{{breadcrumb|5L_3s}}'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!'''

The 5L 3s scale, or Oneirotonic, is particularly interesting as far as scales go. Its doesn't arise very intuitively from low-complexity harmonic relationships in the same way as the diatonic scale or the third-generated smitonic and mosh scales; however, once its structure is asserted, it can be a very fruitful system to use as a basis for many useful harmonic ideas. On this page, I aim to document a coherent theory of tonal harmony based on Oneirotonic and related [[MODMOS scale]]<nowiki/>s.

It should be noted that the notation and interval categories used here are based on my own derivations from Oneirotonic structure, mostly because I found that other existing systems were unsatisfactory in describing it.

== 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.)
{| class="wikitable"
|+Degrees of Oneiro
!Degree
!Soft Range
!Hard Range
!General Notation
!Notes
|-
|1
|1/1
|1/1
|C
|
|-
|chroma
|1/13 - 1\5
|1/1 - 1\13
|C♯
|Doesn't occur directly in the scale, but very useful to note anyways
|-
|m2
|1/1 - 1\13
|1\13 - 1\8
|D♭
|
|-
|M2
|2\13 - 1\5
|1\8 - 2\13
|D
|
|-
|m3
|1\5 - 2\8
|3\13 - 1\4
|E♭
|
|-
|M3
|4\13 - 2\5
|1\4 - 4\13
|E
|
|-
|d4
|1\5 - 4\13
|4\13 - 3\8
|F♭
|Enharmonically equivalent to M3 in basic tuning ([[13edo]])
|-
|P4
|5\13 - 2\5
|3\8 - 5\13
|F
|
|-
|t
|2\5 - 6\13
|6\13 - 1\2
|G♭
|Minor Tritone
|-
|T
|7\13 - 3\5
|1\2 - 7\13
|G
|Major Tritone
|-
|P5
|3\5 - 8\13
|8\13 - 5\8
|H
|
|-
|A5
|9\13 - 4\5
|5\8 - 9\13
|H♯
|Enharmonically equivalent to m7 in basic tuning ([[13edo]])
|-
|m6
|3\5 - 9\13
|9\13 - 3\4
|A♭
|
|-
|M6
|10\13 - 4\5
|3\4 - 10\13
|A
|
|-
|m7
|4\5 - 11\13
|11\13 - 7\8
|B♭
|
|-
|M7
|12\13 - 2/1
|7\8 - 12\13
|B
|
|-
|8
|2/1
|2/1
|C
|Assuming justly-tuned octave
|}
Additionally, the eight modes of the Oneirotonic scale have been given names based on the Dreamlands from the works of H.P. Lovecraft:
{| class="wikitable"
|+Oneiro Modes
!Brightness
!Pattern
!Name
!Notation
!Notes
|-
|7
|LLsLLsLs
|Dylathian
|C - D - E - F - G - H♯ - A - B - C
|
|-
|6
|LLsLsLLs
|Ilarnekian
|C - D - E - F - G - H - A - B - C
|Natural major mode
|-
|5
|LsLLsLLs
|Celephaïsian
|C - D - E♭ - F - G - H - A - B - C
|Harmonic minor mode
|-
|4
|LsLLsLsL
|Ultharian
|C - D - E♭ - F - G - H - A - B♭ - C
|Natural minor mode
|-
|3
|LsLsLLsL
|Mnarian
|C - D - E♭ - F - G♭ - H - A - B♭ - C
|
|-
|2
|sLLsLLsL
|Kadathian
|C - D♭ - E♭ - F - G♭ - H - A - B♭ - C
|
|-
|1
|sLLsLsLL
|Hlanithian
|C - D♭ - E♭ - F - G♭ - H - A♭ - B♭ - C
|Natural diminished mode
|-
|0
|sLsLLsLL
|Sarnathian
|C - D♭ - E♭ - F♭ - G♭ - H - A♭ - B♭ - C
|
|}

== Chords of Oneirotonic ==
Unlike in the diatonic scale, the Oneirotonic scale has its generator an odd number of steps above the root, which means that it cannot be split into two intervals of the same category; because of this, the Oneirotonic scale does not have a dichotomy of tonalities.

Rather than the dichotomy, there are two primary ways to categorize useful chords in Oneirotonic: tertiary chords (which generally display a three-way distinction), and genspan chords (which have up to a five-way distinction).

=== Tertiary Triads ===
The first class of chords is built by stacking major and minor thirds; as such, I will call this class of chords "tertiary." There are three types of tertiary triads which occur in the Oneirotonic scale, and one type which can be extrapolated:
{| class="wikitable"
|+Tertiary Triads
!Quality
!Symbol
!Formula
!Notation
!Modes
|-
|Major
|
|M3 + m3
|C - E - G
|Dylathian, Ilarnekian
|-
|Minor
|
|m3 + M3
|C - E♭ - G
|Celaphaïsian, Ultharian, Mnarian
|-
|Diminished
|
|m3 + m3
|C - E♭ - G♭
|Kadathian, Hlanithian, Sarnathian
|-
|Augmented
|
|M3 + M3
|C - E - G♯
|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.

MODMOS scales of Oneirotonic can be designed to target specific combinations of triads, including the usage of augmented triads.

=== Genspan Triads ===
The other primary approach to chords in Oneirotonic is to use chords that split the perfect fifth into two unequal parts; I will hereby refer to these as "genspan" chords, as they have a span of one generator. The fifth can be broken up into the sum of a third and fourth; because the two constituent intervals do not fall on the same degree, each mode of the scale has two genspan triads over the root, rather than just one.
{| class="wikitable"
|+
!Quality
!Symbol
!Formula
!Notation
!Modes
|-
|Fourth
|C4
|P4 + m3
|C - F - H
|Ikarnekian, Hlanithian
|-
|Third
|C3
|M3 + d4
|C - E - H
|Ilarnekian
|-
|Flat-Fourth
|C♭4
|d4 + M3
|C - F♭ - H
|Sarnathian
|-
|Flat-Third
|C♭3
|m3 + P4
|C - E♭ - H
|Celephaïsian, Sarnathian
|}
In soft tunings, these chords are useful resolutions, since C4 resembles [[6:8:9]], and C3 resembles [[4:5:6]]. In hard tunings, however, these chords are much less stable, as C4 better resembles 13:17:20 and C3 better resembles 13:16:20.

== Chord Functions ==
The tertiary chords and genspan chords occupy two distinct sects of Oneirotonic harmony, and effectively "switch places" between soft and hard tunings of the scale; in this respect, I find them comparable to the tertiary and suspended chords in Diatonic, which similarly seem to "switch places" between soft and hard tunings.

Because of this dichotomy, I will be outlining two primary sets of chord functions: those that describe soft Oneirotonic, and those that describe hard.