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{{breadcrumb|5L 3s}}
This page describes [[User:Inthar]]'s approach to [[5L 3s]] (aka oneirotonic).
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 ==
== Standing assumptions ==
The Fox-Raven absolute pitch system is used in this article to name 5L 3s pitches.
I'll use the [[TAMNAMS]] standard to denote oneirotonic intervals and degrees (independent of their absolute pitch).
 
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 # and b.
 
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 perfect 3-steps becomes: ... Pb Kb Nb Q L O J M P K N Q# L# O# ...
 
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'''
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.


== Modes ==
== Modes ==
Line 28: Line 14:
{| class="wikitable"
{| 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
|}
|}
=== 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.
Todo: chord progs


=== Alterations ===
=== Alterations ===
Line 89: Line 76:
| | LLsLsLsL
| | LLsLsLsL
| style="text-align:center;" | 6|1 @8
| style="text-align:center;" | 6|1 @8
| | Illarmixian (Illarnekian b8)
| | Ilarmixian (Ilarnekian b8)
|-
|-
| | LsLLLsLs
| | LsLLLsLs
Line 120: Line 107:
# SLLLSLSL is Ulphrygian
# SLLLSLSL is Ulphrygian
# LLLSLSLS is Dylydian
# LLLSLSLS is Dylydian
# LLSLSLSL is Illarmixian
# LLSLSLSL is Ilarmixian
# LSLSLSLL is Mnaeolian
# LSLSLSLL is Mnaeolian
# SLSLSLLL is Sarlocrian
# SLSLSLLL is Sarlocrian
Line 132: Line 119:
* LSLSLSAS Harmonic Mnarian
* LSLSLSAS Harmonic Mnarian


== 13edo oneiro theory ==
== 13edo oneiro chordal theory ==
Favorite modes: Dylathian (22122121), Illarnekian (22121221), Celephaisian (21221221), Ultharian (21221212), Celdorian (21222121)
{{main|13edo/Inthar's approach}}
 
(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: major 0-185-369-646 and minor 0-277-738-923. 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.
 
Todo: Inversions of functional chords and counterpoint
 
On O Celephaisian:
* O: 0 277 738 923 (O Q L M)
* P: 0 277 738 923 (P J M N)
* Q: 0 185 369 646 (Q J K M)
* J: 0 277 738 923 (J L O P)
* K: 0 277 738 1015 (K M P J)
* L: 0 185 369 646 (L M N P)
* M: 0 277 738 923 (M O J K)
* N: 0 277 738 1015 (N P K M)
* O: 0 277 738 923 (O Q L M)
 
[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_''0%5D- A progression on the ascending Celephaïsian scale]
 
On M Mnionian (Melodic Mnarian):
* M: 0 277 738 923 (M O J K)
* N: 0 277 738 923 (N P K L#)
* O: 0 277 831 (O Q L#)?
* P: 0 277 738 923 (P J M N); 0 277 646 923 (P J L# N)
* Q: 0 185 369 646 (Q J K M)
* J: 0 185 369 646 (J K L# N)
* K: 0 277 738 1015 (K N P J)
* L#: 0 369 646 (L# O Q) ("misspelled"); 0 277 553 (L# N P); 0 277 831 (L# N J)
 
[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 to chords works well, and for jazzy extensions one can add 185, 461, and 646 to the upper octave.
 
Some more dissonant sonorities are
0 277 646 923.
 
== 18edo oneiro theory ==
== 18edo oneiro theory ==
Favorite modes: Mnionian (31313331), Mnaeolian (31313133), Ulphrygian (13331313), Celdorian (31333131), Sardorian (13133313)
Favorite modes: Mnionian (31313331), Mnaeolian (31313133), Ulphrygian (13331313), Celdorian (31333131), Sardorian (13133313)


The biggest difference from 13edo oneiro is that the P0ms-M2ms-m4ms chord (0 400 667) is now dissonant.
The biggest difference from 13edo oneiro is that the P0ms-M2ms-m4ms chord (0 400 667) is now dissonant.
[https://xenpaper.com/#(bpm%3A110)(osc%3Asawtooth2)%7B18edo%7D%0A%7Br178hz%7D%0A(env%3A1811)%0A%23_0_3_4_7_8_11_12_15_18%0A%5B0_4_7_11_'0_'22%5D-'18-%0A%5B3_7_15_18_'3_'21%5D-'15_'11%0A%5B4_8_12_18_'4_'8%5D-_'15-%0A%5B7_11_15_'0_'7_'11%5D-_'7'12%0A%5B8_12_15_'0_'4_'8%5D'0_'4_'11%0A%5B11_15_18_'3_'11_'15%5D-_'18_'21%0A%5B12_15_18_'7_'12_'22%5D-_'21_'29%0A%5B15_'0_'3_'8_'12_'15_'26%5D_'25_'22_'21%0A%5B0_11_'4_'7_'18%5D- A progression on ascending 18edo Mnaeolian]


== 21edo oneiro theory ==
== 21edo oneiro theory ==
Favorite modes: Dylathian (33233232), Sarn (23233233)
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
* 0-342-629: buzzy with sine-like timbres
* 0-343-457
* 0-343-457
Line 191: 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]
* [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 ==
== Nejis ==
Line 212: Line 149:
* 26:29:32:34:38:42:44:49:52 Tridecimal Dylathian
* 26:29:32:34:38:42:44:49:52 Tridecimal Dylathian
* 26:29:30:34:38:42:44:49:52 Tridecimal Celdorian
* 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]]
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