User:Inthar/5L 3s: Difference between revisions

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This page describes [[User:Inthar]]'s approach to [[5L 3s]] (aka oneirotonic).

Now with new theory (thanks to tprice and Jaimbee)

Now with new theory (thanks in part to tprice and Jaimbee)

== Standing assumptions ==

The Fox-Raven absolute pitch system is used in this article to name 5L 3s pitches: The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz. I denote raising and lowering by a chroma (L − s) by # and b.

I'll use the [[TAMNAMS]] standard to denote oneirotonic intervals and degrees (independent of their absolute pitch).

~~The chain of perfect 3-steps becomes~~: ~~... Pb Kb Nb Q L O J M P K N Q# L# O# ...~~

Todo: In the following, I will use the [[diamond-mos notation]] standard to discuss oneirotonic harmony. JKLMNOPQ will refer to the mode being discussed, if the mode is unaltered.

~~Thus~~ the [[~~13edo~~]] ~~gamut~~ is ~~as follows:~~

~~'''J/Q#''' J#/Kb '''K/Lb''' '''L/K#''' L#/Mb '''M''' M#/Nb '''N/Ob''' '''O/N#''' O#/Pb '''P''' '''Q''' Q#/Jb '''J'''~~

~~The [[18edo]] gamut is notated as follows:~~

~~'''J''' Q#/Kb J#/Lb '''K''' '''L''' K#/Mb L# '''M''' Nb M#/Ob '''N''' '''O''' Pb O# '''P''' '''Q''' P#/Jb Qb '''J'''~~

~~The [[21edo]] gamut:~~

~~'''J''' J# Kb '''K''' K#/Lb '''L''' L# Mb '''M''' M# Nb '''N''' N#/Ob '''O''' O# Pb '''P''' P#/Qb '''Q''' Q# Jb '''J'''~~

== Modes ==

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{| class="wikitable"

|-

| style="text-align:center;" | '''Mode'''

| style="text-align:center;" |'''Mode'''

| style="text-align:center;" | [[Modal UDP Notation|'''UDP''']]

| style="text-align:center;" |[[Modal UDP Notation|'''UDP''']]

| style="text-align:center;" | '''Name'''

| style="text-align:center;" |'''Name'''

|'''Former names'''

|-

| | LLsLLsLs

| |LLsLLsLs

| style="text-align:center;" | 7|0

| style="text-align:center;" |<nowiki>7|0</nowiki>

| | Dylathian ~~(də-LA(H)TH-iən)~~

| |Dylian

| |Dylathian

|-

| | LLsLsLLs

| |LLsLsLLs

| style="text-align:center;" | 6|1

| style="text-align:center;" |<nowiki>6|1</nowiki>

| | ~~Illarnekian (ill-ar-NEK-iən)~~

| |Ilarnekian

| |

|-

| | LsLLsLLs

| |LsLLsLLs

| style="text-align:center;" | 5|2

| style="text-align:center;" |<nowiki>5|2</nowiki>

| | Celephaïsian ~~(kel-ə-FAY-zhən)~~

| |Celephaïsian

| |

|-

| | LsLLsLsL

| |LsLLsLsL

| style="text-align:center;" | 4|3

| style="text-align:center;" |<nowiki>4|3</nowiki>

| | Ultharian ~~(ul-THA(I)R-iən)~~

| |Ultharian

| |

|-

| | LsLsLLsL

| |LsLsLLsL

| style="text-align:center;" | 3|4

| style="text-align:center;" |<nowiki>3|4</nowiki>

| | Mnarian ~~(mə-NA(I)R-iən)~~

| |Mnarian

| |

|-

| | sLLsLLsL

| |sLLsLLsL

| style="text-align:center;" | 2|5

| style="text-align:center;" |<nowiki>2|5</nowiki>

| | Kadathian ~~(kə-DA(H)TH-iən)~~

| |Kadian

| |Kadathian

|-

| | sLLsLsLL

| |sLLsLsLL

| style="text-align:center;" | 1|6

| style="text-align:center;" |<nowiki>1|6</nowiki>

| | Hlanithian ~~(lə-NITH-iən)~~

| |Hlanian

| |Hlanithian

|-

| | sLsLLsLL

| |sLsLLsLL

| style="text-align:center;" | 0|7

| style="text-align:center;" |<nowiki>0|7</nowiki>

| | Sarnathian ~~(sar-NA(H)TH-iən), can be shortened to "Sarn"~~

| |Sarnian

| |Sarnathian

|}

=== Alterations ===

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| | LLsLsLsL

| style="text-align:center;" | 6|1 @8

| | ~~Illarmixian~~ (~~Illarnekian~~ b8)

| | Ilarmixian (Ilarnekian b8)

|-

| | LsLLLsLs

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# SLLLSLSL is Ulphrygian

# LLLSLSLS is Dylydian

# LLSLSLSL is ~~Illarmixian~~

# LLSLSLSL is Ilarmixian

# LSLSLSLL is Mnaeolian

# SLSLSLLL is Sarlocrian

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== 13edo oneiro chordal theory ==

~~Favorite modes: Dylathian (22122121), Illarnekian (22121221), Celephaisian (21221221), Mnionian (21212221)~~

We will primarily discuss functional harmony using pseudo-JI chords, treating these separately from counterpoint. h/t to tprice and Jaimbee for the pseudo-JI chords presented here and for other discussions.

13edo oneiro enjoys two main (rooted) pseudo-JI sonorities analogous to major and minor triads: 0-(185)-369-646 ("pseudo-JI major triad" or just "major"/"Maj") and 0-277-738-923 ("pseudo-JI minor tetrad" or just "minor"/"min"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "minor triad" or "mintri".

[https://xenpaper.com/#(bpm%3A60)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br179hz%7D%0A(env%3A1811)%0A%23_0_2_3_5_7_8_10_12_13%0A%5B%600_%608_3_8_10_'0%5D-%0A%5B%602_5_10_12_'2%5D-%0A%5B%603_5_7_10_'0_'3%5D-%0A%5B%605_8_13_'2_'5%5D-%0A%5B%607_10_13_'3_'7%5D-%0A%5B%608_10_12_'2_'8%5D-%0A%5B%6010_'0_'5_'7_'10%5D-%0A%5B%6012_'2_'5_'8_'12%5D-%0A%5B0_'3_8_10_'13%5D- A progression on the ascending Celephaïsian scale]

[https://xenpaper.com/#(bpm%3A60)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br274.988hz%7D%0A(env%3A1811)%0A%23_0_2_3_5_6_8_10_12_13%0A%5B%600_%608_0_3_10_%270%5D-%0A%5B%602_%6010_2_5_10%5D12%0A%5B%603_0_3_6_13_%273%5D-%0A%5B%605_2_8_13_15_%278%5D%275%0A%5B%606_0_3_8_10_%276%5D-%0A%5B%608_2_5_10_%275%5D-%0A%5B%6010_0_6_8_%273%5D-%0A%5B%6012_5_8_12_%272%5D-%0A%5B0_3_8_10_12_13%5D- A progression on the ascending Melodic Mnarian scale]

~~Adding 923 and 1108 to chords works well, and for jazzy extensions one can add 185, 461, and 646 to the upper octave.~~

~~[https://xenpaper.com~~/#(bpm%3A240)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br360hz%7D%0A(env%3A1847)%0A%23_0_2_3_5_6_8_10_11~12_13%0A%5B%600_%608_0%5D_3_6_8-----........%0A%5B%600_%608_0%5D_3_8_10-----.......13%0A%5B%60%608_%608_11%5D_%6011_2_3---6_3-2-3-5-%0A%5B%605_5_8_11_13_8%5D-_11_13----_13_'2------%0A%5B%600_%608_0%5D_3_6_8-----........%0A%5B%600_%608_0%5D_3_8_10-----.....'3'2'0%0A%5B%603_3_6_8_0_11%5D-13_%5B%602_5_8%5D-_11-_8_%5B0_10%5D-_%5B%6011_8%5D_%5B%6010_6%5D-%5B%6011_8%5D_%5B%6010_6%5D_%5B%608_5%5D%0A%5B%603_%606_%6011_3%5D-_%5B%602_5%5D-_%5B%600_3%5D-.._%0A%5B%608_%608_%6010_%6012_2%5D_%608_%6010_%6012---- A Mnarian loop with an &8 leading tone at the end]

~~=== Functional chords on each degree ===~~

~~Celephaisian~~

* 0md: minor

* 1md: minor

* 2md: major

* 3md: minor

* 4md: minor triad, minor 4ms, minor 6ms, minor 7ms

* 5md: major

* 6md: minor

* 7md: minor triad, minor 4ms, minor 6ms, minor 7ms

~~Mnionian (Melodic Mnarian)~~

* 0md: minor

* 1md: minor

* 2md: minor @5

* 3md: minor

* 4md: major, augmented 3ms

* 5md: major, minor 7ms

* 6md: minor triad, minor 6ms, minor 7ms

* 7md: "diminished triad", diminished 5ms, minor 6ms, minor 7ms

~~=== Progressions ===~~

~~kmd(maj) means the triad 0 369 646 on kmd, kmd(min) means the tetrad 0 277 738 923 on kmd~~

~~Common motions:~~

* 0md(maj or min) → M1md(min)

* 0md(maj or min) → 4md(min) (when ending on 0md this sounds like diatonic V to I)

* 0md(maj or min) → m6md(min)

* 0md(maj) → 5md(maj), 0md(min) → 5md(maj or min) (when ending on 0md this is a "dominant to tonic" motion)

* 0md(maj) → M3md(maj)

* 2md(min) → m1md(maj) → 0md(maj) (pseudo tritone sub)

~~=== Modulations ===~~

~~=== Modal harmony ===~~

~~Modes can be grouped by their functional properties.~~

* Major pJI chord on root: Dylathian, Illarnekian; Dylydian, Illarmixian

* Leading tone: Dylathian, Illarnekian, Celephaïsian; Dylydian, Mnionian

* "Classical functional modes" (loose grouping): Dylathian, Illarnekian, Celephaïsian, Ultharian; Mnionian, Mnaeolian(?)

* Minor pJI triad on root: Celephaïsian, Ultharian, Mnarian, Kadathian; Mnionian, Sardorian, Ulphrygian

* Upper leading tone: Kadathian, Hlanithian, Sarnathian, Sardorian, Sarlocrian

* Minor 6-mosstep: Hlanithian, Sarnathian, Mnaeolian, Sarlocrian

* 0 462 831 pseudo-JI chord on root: Dylathian, Dylydian, Hlanithian, Mnaeolian

We'll call degrees that don't have the major pseudo-JI or the minor pseudo-JI chord ''dissonant degrees'' (keeping in mind that dissonance is a feature a chord has in a musical language rather than a purely psychoacoustic property).

~~==== Celephaïsian ====~~

* 0d: min

* 1d: min

* 2d: Maj

* 3d: min

* 4d: minor triad, minor 4ms, minor 6ms, minor 7ms

* 5d: Maj

* 6d: min

* 7d: minor triad, minor 4ms, minor 6ms, minor 7ms

~~The main resolving degrees (analogues to dominant in diatonic) are 3md and 5md because of their leading tones.~~

~~Progressions:~~

* 0d(min) 1d(min) 3d(min, or 0-3-7-10\13) 0d(min)

* 0d(min) 1d(min) 6d(min) 3(min) 0d(min)

* 0d(min) 6d(min) 3d(min) 0d(min)

* 0d(min) 2d(Maj) 3d(min) 0d(min)

* 0d(min) 4d(min7) 5d(Maj)/3d(min) 0d(min)

* 0d(min) 6d(min) 5d(Maj) 0d(min)

~~==== Ultharian ====~~

* 0md: min

* 1md: minor triad, minor 4ms, minor 6ms, minor 7ms

* 2md: Maj

* 3md: min

* 4md: minor triad, minor 4ms, minor 6ms, minor 7ms

* 5md: min

* 6md: min

* 7md: Maj

~~==== Mnarian ====~~

* 0md: min

* 1md: minor triad, minor 4ms, minor 6ms, minor 7ms

* 2md: min

* 3md: min

* 4md: Maj

* 5md: min

* 6md: minor triad, minor 4ms, minor 6ms, minor 7ms

* 7md: Maj

~~==== Kadathian ====~~

* 0md: min

* 1md: Maj

* 2md: min

* 3md: minor triad, minor 4ms, minor 6ms, minor 7ms

* 4md: Maj

* 5md: min

* 6md: minor triad, minor 4ms, minor 6ms, minor 7ms

* 7md: min

== 18edo oneiro theory ==

Favorite modes: Mnionian (31313331), Mnaeolian (31313133), Ulphrygian (13331313), Celdorian (31333131), Sardorian (13133313)

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Favorite modes: Dylathian (33233232), Sarn (23233233)

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 4-steps (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 16:23:30 (R~~-~~Lmos5~~-~~L7ms). Importantly, the sharp fifth~~ is ~~now harmonically much more fifth~~-~~like than the flat fifth, unlike in [[13edo]]~~ and ~~harder tunings. The main consonances are now chords using seconds and sevenths (~~in ~~addition~~ to thirds and sixths). The relatively consonant 114¢ and 1086¢ intervals may help to mask some of the more dissonant sonorities such as the naiadic and the sharp fifth, and work for chill and lo-fi styles.

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 4-steps (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. The chord 0-342-629-1085 is delta-rational and is in fact very close to 32:39:46:60.

* 0-342-629: buzzy with sine-like timbres

* 0-343-457

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* [https://xenpaper.com/#(bpm%3A115)%7Br236.960465669hz%7D(osc%3Atriangle)%7B21edo%7D%0A%0A%5B0%2C6%2C8%5D-------%0A%7Br3%7D%5B0%2C3%2C8%5D-------%0A%7Br3%7D%5B0%2C5%2C7%5D-------%0A%7Br5%7D%5B0%2C5%5D---%0A%7Br%6018%7D%5B0%2C5%5D---%0A%7Br%6018%7D%5B0%2C3%2C8%2C13%5D-------%0A%7Br6%7D%5B0%2C2%2C10%5D---%0A%7Br%6018%7D%5B0%2C5%2C10%5D---%0A%7Br%6019%7D%5B0%2C5%2C12%5D-------%0A%7Br%6018%7D%5B0%2C8%2C10%5D--..%7Br%6015%7D0_3_6 Example progression using the above chords]

~~<!--~~

~~34edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like.~~

* sus24 non5: J-K-M, L-M-O, M-N-P, O-P-J, Q-J-L

* sus24 non5 addmin7: J-Q-K-M, M-L-N-P

* falling fifth addmaj7 ≈ 16:23:30: O-K-N, L-P-K, Q-M-P

* Falling Major Triad: Q-K-M, L-N-P

* 16:23:29 (in 21edo): J-N-Q

~~Other chords:~~

* Quartal Tetrad: Q-J-L-O, L-M-O-J, O-P-J-M, J-K-M-P, M-N-P-K

* Quartal Pentad: L-M-O-P-J, O-P-J-K-M, J-K-M-N-P, M-N-P-Q-K

* Falling Minor Triad: J-L-N, O-Q-K

* squashed diminished: M-O-Q, P-J-L, K-M-O, N-P-J

~~-->~~

Seconds, tritones and sevenths are consonances in addition to thirds and sixths. The naiadic is a semiconsonance. The sharp fifth is fifth-like but is still dissonant. The triad root-third-629 can resolve to a more consonant chord such as 0-343-457.

It is suggested to use R-2ms-mos5-6ms carefully in 21edo oneiro - it sounds more like a dissonant, unstable 12edo diminished 7th, unlike in 13edo and harder oneiro tunings where they have a more discernible (though complex) identity.

== Nejis ==

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* 26:29:32:34:38:42:44:49:52 Tridecimal Dylathian

* 26:29:30:34:38:42:44:49:52 Tridecimal Celdorian

== Samples ==

=== Modal studies ===

[[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3|thumb|center|Dylathian study]]

[[Category:Oneirotonic]]

[[Category:13edo]]

[[Category:18edo]]

[[Category:21edo]]

[[Category:Method]]

[[Category:Approaches to tuning systems]]

@@ Line 1: / Line 1: @@
+{{breadcrumb|5L 3s}}
 This page describes [[User:Inthar]]'s approach to [[5L 3s]] (aka oneirotonic).
-Now with new theory (thanks to tprice and Jaimbee)
+Now with new theory (thanks in part to tprice and Jaimbee)
 == Standing assumptions ==
-The Fox-Raven absolute pitch system is used in this article to name 5L 3s pitches: The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz. I denote raising and lowering by a chroma (L &minus; s) by # and b.
 I'll use the [[TAMNAMS]] standard to denote oneirotonic intervals and degrees (independent of their absolute pitch).
-The chain of perfect 3-steps becomes: ... Pb Kb Nb Q L O J M P K N Q# L# O# ...
+Todo: In the following, I will use the [[diamond-mos notation]] standard to discuss oneirotonic harmony. JKLMNOPQ will refer to the mode being discussed, if the mode is unaltered.
-Thus the [[13edo]] gamut is as follows:
-'''J/Q#''' J#/Kb '''K/Lb''' '''L/K#''' L#/Mb '''M''' M#/Nb '''N/Ob''' '''O/N#''' O#/Pb '''P''' '''Q''' Q#/Jb '''J'''
-The [[18edo]] gamut is notated as follows:
-'''J''' Q#/Kb J#/Lb '''K''' '''L''' K#/Mb L# '''M''' Nb M#/Ob '''N''' '''O''' Pb O# '''P''' '''Q''' P#/Jb Qb '''J'''
-The [[21edo]] gamut:
-'''J''' J# Kb '''K''' K#/Lb '''L''' L# Mb '''M''' M# Nb '''N''' N#/Ob '''O''' O# Pb '''P''' P#/Qb '''Q''' Q# Jb '''J'''
 == Modes ==
@@ Line 26: / Line 14: @@
 {| class="wikitable"
 |-
-| style="text-align:center;" | '''Mode'''
+| style="text-align:center;" |'''Mode'''
-| style="text-align:center;" | [[Modal UDP Notation|'''UDP''']]
+| style="text-align:center;" |[[Modal UDP Notation|'''UDP''']]
-| style="text-align:center;" | '''Name'''
+| style="text-align:center;" |'''Name'''
+|'''Former names'''
 |-
-| | LLsLLsLs
+| |LLsLLsLs
-| style="text-align:center;" | 7|0
+| style="text-align:center;" |<nowiki>7|0</nowiki>
-| | Dylathian (də-LA(H)TH-iən)
+| |Dylian
+| |Dylathian
 |-
-| | LLsLsLLs
+| |LLsLsLLs
-| style="text-align:center;" | 6|1
+| style="text-align:center;" |<nowiki>6|1</nowiki>
-| | Illarnekian (ill-ar-NEK-iən)
+| |Ilarnekian
+| |
 |-
-| | LsLLsLLs
+| |LsLLsLLs
-| style="text-align:center;" | 5|2
+| style="text-align:center;" |<nowiki>5|2</nowiki>
-| | Celephaïsian (kel-ə-FAY-zhən)
+| |Celephaïsian
+| |
 |-
-| | LsLLsLsL
+| |LsLLsLsL
-| style="text-align:center;" | 4|3
+| style="text-align:center;" |<nowiki>4|3</nowiki>
-| | Ultharian (ul-THA(I)R-iən)
+| |Ultharian
+| |
 |-
-| | LsLsLLsL
+| |LsLsLLsL
-| style="text-align:center;" | 3|4
+| style="text-align:center;" |<nowiki>3|4</nowiki>
-| | Mnarian (mə-NA(I)R-iən)
+| |Mnarian
+| |
 |-
-| | sLLsLLsL
+| |sLLsLLsL
-| style="text-align:center;" | 2|5
+| style="text-align:center;" |<nowiki>2|5</nowiki>
-| | Kadathian (kə-DA(H)TH-iən)
+| |Kadian
+| |Kadathian
 |-
-| | sLLsLsLL
+| |sLLsLsLL
-| style="text-align:center;" | 1|6
+| style="text-align:center;" |<nowiki>1|6</nowiki>
-| | Hlanithian (lə-NITH-iən)
+| |Hlanian
+| |Hlanithian
 |-
-| | sLsLLsLL
+| |sLsLLsLL
-| style="text-align:center;" | 0|7
+| style="text-align:center;" |<nowiki>0|7</nowiki>
-| | Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
+| |Sarnian
+| |Sarnathian
 |}
 === Alterations ===
@@ Line 80: / Line 76: @@
 | | LLsLsLsL
 | style="text-align:center;" | 6|1 @8
-| | Illarmixian (Illarnekian b8)
+| | Ilarmixian (Ilarnekian b8)
 |-
 | | LsLLLsLs
@@ Line 111: / Line 107: @@
 # SLLLSLSL is Ulphrygian
 # LLLSLSLS is Dylydian
-# LLSLSLSL is Illarmixian
+# LLSLSLSL is Ilarmixian
 # LSLSLSLL is Mnaeolian
 # SLSLSLLL is Sarlocrian
@@ Line 124: / Line 120: @@
 == 13edo oneiro chordal theory ==
-Favorite modes: Dylathian (22122121), Illarnekian (22121221), Celephaisian (21221221), Mnionian (21212221)
+{{main|13edo/Inthar's approach}}
-We will primarily discuss functional harmony using pseudo-JI chords, treating these separately from counterpoint. h/t to tprice and Jaimbee for the pseudo-JI chords presented here and for other discussions.
-edo oneiro enjoys two main (rooted) pseudo-JI sonorities analogous to major and minor triads: 0-(185)-369-646 ("pseudo-JI major triad" or just "major"/"Maj") and 0-277-738-923 ("pseudo-JI minor tetrad" or just "minor"/"min"). One of these chords are on the root in the 6 brightest modes of oneirotonic. In the two darkest modes, I think 0-277-738-1015 or 0-738-1015-277 works well. The chord 0-277-738 will be called "minor triad" or "mintri".
-[https://xenpaper.com/#(bpm%3A60)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br179hz%7D%0A(env%3A1811)%0A%23_0_2_3_5_7_8_10_12_13%0A%5B%600_%608_3_8_10_'0%5D-%0A%5B%602_5_10_12_'2%5D-%0A%5B%603_5_7_10_'0_'3%5D-%0A%5B%605_8_13_'2_'5%5D-%0A%5B%607_10_13_'3_'7%5D-%0A%5B%608_10_12_'2_'8%5D-%0A%5B%6010_'0_'5_'7_'10%5D-%0A%5B%6012_'2_'5_'8_'12%5D-%0A%5B0_'3_8_10_'13%5D- A progression on the ascending Celephaïsian scale]
-[https://xenpaper.com/#(bpm%3A60)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br274.988hz%7D%0A(env%3A1811)%0A%23_0_2_3_5_6_8_10_12_13%0A%5B%600_%608_0_3_10_%270%5D-%0A%5B%602_%6010_2_5_10%5D12%0A%5B%603_0_3_6_13_%273%5D-%0A%5B%605_2_8_13_15_%278%5D%275%0A%5B%606_0_3_8_10_%276%5D-%0A%5B%608_2_5_10_%275%5D-%0A%5B%6010_0_6_8_%273%5D-%0A%5B%6012_5_8_12_%272%5D-%0A%5B0_3_8_10_12_13%5D- A progression on the ascending Melodic Mnarian scale]
-Adding 923 and 1108 to chords works well, and for jazzy extensions one can add 185, 461, and 646 to the upper octave.
-[https://xenpaper.com/#(bpm%3A240)(osc%3Asawtooth2)%7B13edo%7D%0A%7Br360hz%7D%0A(env%3A1847)%0A%23_0_2_3_5_6_8_10_11~12_13%0A%5B%600_%608_0%5D_3_6_8-----........%0A%5B%600_%608_0%5D_3_8_10-----.......13%0A%5B%60%608_%608_11%5D_%6011_2_3---6_3-2-3-5-%0A%5B%605_5_8_11_13_8%5D-_11_13----_13_'2------%0A%5B%600_%608_0%5D_3_6_8-----........%0A%5B%600_%608_0%5D_3_8_10-----.....'3'2'0%0A%5B%603_3_6_8_0_11%5D-13_%5B%602_5_8%5D-_11-_8_%5B0_10%5D-_%5B%6011_8%5D_%5B%6010_6%5D-%5B%6011_8%5D_%5B%6010_6%5D_%5B%608_5%5D%0A%5B%603_%606_%6011_3%5D-_%5B%602_5%5D-_%5B%600_3%5D-.._%0A%5B%608_%608_%6010_%6012_2%5D_%608_%6010_%6012---- A Mnarian loop with an &8 leading tone at the end]
-=== Functional chords on each degree ===
-Celephaisian
-* 0md: minor
-* 1md: minor
-* 2md: major
-* 3md: minor
-* 4md: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 5md: major
-* 6md: minor
-* 7md: minor triad, minor 4ms, minor 6ms, minor 7ms
-Mnionian (Melodic Mnarian)
-* 0md: minor
-* 1md: minor
-* 2md: minor @5
-* 3md: minor
-* 4md: major, augmented 3ms
-* 5md: major, minor 7ms
-* 6md: minor triad, minor 6ms, minor 7ms
-* 7md: "diminished triad", diminished 5ms, minor 6ms, minor 7ms
-=== Progressions ===
-kmd(maj) means the triad 0 369 646 on kmd, kmd(min) means the tetrad 0 277 738 923 on kmd
-Common motions:
-* 0md(maj or min) → M1md(min)
-* 0md(maj or min) → 4md(min) (when ending on 0md this sounds like diatonic V to I)
-* 0md(maj or min) → m6md(min)
-* 0md(maj) → 5md(maj), 0md(min) → 5md(maj or min) (when ending on 0md this is a "dominant to tonic" motion)
-* 0md(maj) → M3md(maj)
-* 2md(min) → m1md(maj) → 0md(maj) (pseudo tritone sub)
-=== Modulations ===
-=== Modal harmony ===
-Modes can be grouped by their functional properties.
-* Major pJI chord on root: Dylathian, Illarnekian; Dylydian, Illarmixian
-* Leading tone: Dylathian, Illarnekian, Celephaïsian; Dylydian, Mnionian
-* "Classical functional modes" (loose grouping): Dylathian, Illarnekian, Celephaïsian, Ultharian; Mnionian, Mnaeolian(?)
-* Minor pJI triad on root: Celephaïsian, Ultharian, Mnarian, Kadathian; Mnionian, Sardorian, Ulphrygian
-* Upper leading tone: Kadathian, Hlanithian, Sarnathian, Sardorian, Sarlocrian
-* Minor 6-mosstep: Hlanithian, Sarnathian, Mnaeolian, Sarlocrian
-* 0 462 831 pseudo-JI chord on root: Dylathian, Dylydian, Hlanithian, Mnaeolian
-We'll call degrees that don't have the major pseudo-JI or the minor pseudo-JI chord ''dissonant degrees'' (keeping in mind that dissonance is a feature a chord has in a musical language rather than a purely psychoacoustic property).
-==== Celephaïsian ====
-* 0d: min
-* 1d: min
-* 2d: Maj
-* 3d: min
-* 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 5d: Maj
-* 6d: min
-* 7d: minor triad, minor 4ms, minor 6ms, minor 7ms
-The main resolving degrees (analogues to dominant in diatonic) are 3md and 5md because of their leading tones.
-Progressions:
-* 0d(min) 1d(min) 3d(min, or 0-3-7-10\13) 0d(min)
-* 0d(min) 1d(min) 6d(min) 3(min) 0d(min)
-* 0d(min) 6d(min) 3d(min) 0d(min)
-* 0d(min) 2d(Maj) 3d(min) 0d(min)
-* 0d(min) 4d(min7) 5d(Maj)/3d(min) 0d(min)
-* 0d(min) 6d(min) 5d(Maj) 0d(min)
-==== Ultharian ====
-* 0md: min
-* 1md: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 2md: Maj
-* 3md: min
-* 4md: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 5md: min
-* 6md: min
-* 7md: Maj
-==== Mnarian ====
-* 0md: min
-* 1md: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 2md: min
-* 3md: min
-* 4md: Maj
-* 5md: min
-* 6md: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 7md: Maj
-==== Kadathian ====
-* 0md: min
-* 1md: Maj
-* 2md: min
-* 3md: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 4md: Maj
-* 5md: min
-* 6md: minor triad, minor 4ms, minor 6ms, minor 7ms
-* 7md: min
 == 18edo oneiro theory ==
 Favorite modes: Mnionian (31313331), Mnaeolian (31313133), Ulphrygian (13331313), Celdorian (31333131), Sardorian (13133313)
@@ Line 236: / Line 131: @@
 Favorite modes: Dylathian (33233232), Sarn (23233233)
-edo 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 4-steps (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 16:23:30 (R-Lmos5-L7ms). Importantly, the sharp fifth is now harmonically much more fifth-like than the flat fifth, unlike in [[13edo]] and harder tunings. The main consonances are now chords using seconds and sevenths (in addition to thirds and sixths). The relatively consonant 114¢ and 1086¢ intervals may help to mask some of the more dissonant sonorities such as the naiadic and the sharp fifth, and work for chill and lo-fi styles.
+edo 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 4-steps (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. The chord 0-342-629-1085 is delta-rational and is in fact very close to 32:39:46:60.
 * 0-342-629: buzzy with sine-like timbres
 * 0-343-457
@@ Line 248: / Line 144: @@
 * [https://xenpaper.com/#(bpm%3A115)%7Br236.960465669hz%7D(osc%3Atriangle)%7B21edo%7D%0A%0A%5B0%2C6%2C8%5D-------%0A%7Br3%7D%5B0%2C3%2C8%5D-------%0A%7Br3%7D%5B0%2C5%2C7%5D-------%0A%7Br5%7D%5B0%2C5%5D---%0A%7Br%6018%7D%5B0%2C5%5D---%0A%7Br%6018%7D%5B0%2C3%2C8%2C13%5D-------%0A%7Br6%7D%5B0%2C2%2C10%5D---%0A%7Br%6018%7D%5B0%2C5%2C10%5D---%0A%7Br%6019%7D%5B0%2C5%2C12%5D-------%0A%7Br%6018%7D%5B0%2C8%2C10%5D--..%7Br%6015%7D0_3_6 Example progression using the above chords]
-<!--
-edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like.
-* sus24 non5: J-K-M, L-M-O, M-N-P, O-P-J, Q-J-L
-* sus24 non5 addmin7: J-Q-K-M, M-L-N-P
-* falling fifth addmaj7 ≈ 16:23:30: O-K-N, L-P-K, Q-M-P
-* Falling Major Triad: Q-K-M, L-N-P
-* 16:23:29 (in 21edo): J-N-Q
-Other chords:
-* Quartal Tetrad: Q-J-L-O, L-M-O-J, O-P-J-M, J-K-M-P, M-N-P-K
-* Quartal Pentad: L-M-O-P-J, O-P-J-K-M, J-K-M-N-P, M-N-P-Q-K
-* Falling Minor Triad: J-L-N, O-Q-K
-* squashed diminished: M-O-Q, P-J-L, K-M-O, N-P-J
--->
-Seconds, tritones and sevenths are consonances in addition to thirds and sixths. The naiadic is a semiconsonance. The sharp fifth is fifth-like but is still dissonant. The triad root-third-629 can resolve to a more consonant chord such as 0-343-457.
-It is suggested to use R-2ms-mos5-6ms carefully in 21edo oneiro - it sounds more like a dissonant, unstable 12edo diminished 7th, unlike in 13edo and harder oneiro tunings where they have a more discernible (though complex) identity.
 == Nejis ==
@@ Line 269: / Line 149: @@
 * 26:29:32:34:38:42:44:49:52 Tridecimal Dylathian
 * 26:29:30:34:38:42:44:49:52 Tridecimal Celdorian
+== Samples ==
+=== Modal studies ===
+[[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3|thumb|center|Dylathian study]]
+[[Category:Oneirotonic]]
+[[Category:13edo]]
+[[Category:18edo]]
+[[Category:21edo]]
+[[Category:Method]]
+[[Category:Approaches to tuning systems]]