User:Inthar/13edo - Revision history

Inthar: /* 13edo oneiro chordal theory */

2026-01-11T16:14:13Z

13edo oneiro chordal theory

← Older revision		Revision as of 16:14, 11 January 2026
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	13edo oneiro enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("delta-rational major triad" or just "major"/"Maj") and 0-277-738-923 ("delta-rational 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", and 0-277-646-923 will be called "minor diminished" or "mindim".		13edo oneiro enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("delta-rational major triad" or just "major"/"Maj") and 0-277-738-923 ("delta-rational 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", and 0-277-646-923 will be called "minor diminished" or "mindim".

	[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://luphoria.com/xenpaper/#(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]		[https://luphoria.com/xenpaper/#(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.		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]		[https://luphoria.com/xenpaper/#(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]

	[https://~~xenpaper~~.com/#(bpm%3A30)(osc%3Asawtooth2)%0A%7Br200Hz%7D%7B13edo%7D%0A(env%3A1846)%0A%5B0_4_7_10_%272_%276_%279_%2712%5D-.._%23_Dylydian%0A%5B0_5_9_%270_%272_%274_%277_%2710_%2712%5D-.._%23_Dylathian%0A%5B0_5_8_10_%270_%272_%274_%277_%2712%5D-.._%23_Illarnekian%0A%5B0_3_8_10_%272_%275_%277_%2712%5D-.._%23_Celepha%C3%AFsian%0A%5B0_5_9_%273_%277_%2710_%2712_%27%272%5D-.._%23_Celdorian%0A%5B0_3_6_8_%2711_%272_%275_10%5D-.._%23_Mnarian%0A%5B0_3_6_8_10_%272_%275_%2712%5D-.._%23_Mnionian Some motherchords of oneiro modes]		[https://luphoria.com/xenpaper/#(bpm%3A30)(osc%3Asawtooth2)%0A%7Br200Hz%7D%7B13edo%7D%0A(env%3A1846)%0A%5B0_4_7_10_%272_%276_%279_%2712%5D-.._%23_Dylydian%0A%5B0_5_9_%270_%272_%274_%277_%2710_%2712%5D-.._%23_Dylathian%0A%5B0_5_8_10_%270_%272_%274_%277_%2712%5D-.._%23_Illarnekian%0A%5B0_3_8_10_%272_%275_%277_%2712%5D-.._%23_Celepha%C3%AFsian%0A%5B0_5_9_%273_%277_%2710_%2712_%27%272%5D-.._%23_Celdorian%0A%5B0_3_6_8_%2711_%272_%275_10%5D-.._%23_Mnarian%0A%5B0_3_6_8_10_%272_%275_%2712%5D-.._%23_Mnionian Some motherchords of oneiro modes]
	=== Functional chords on each degree ===		=== Functional chords on each degree ===
	Celephaisian		Celephaisian

Lériendil: deploying new cat

2025-02-13T05:24:40Z

deploying new cat

← Older revision		Revision as of 05:24, 13 February 2025
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	=== Modulations ===		=== Modulations ===
	[[Category:13edo]]		[[Category:13edo]]
			[[Category:Method]]
			[[Category:Approaches to tuning systems]]

Inthar: Inthar moved page 13edo/Inthar's approach to User:Inthar/13edo

2023-12-29T07:54:18Z

Inthar moved page 13edo/Inthar's approach to User:Inthar/13edo

← Older revision	Revision as of 07:54, 29 December 2023
(No difference)

BudjarnLambeth: Added to category “13edo”

2023-04-14T01:46:45Z

Added to category “13edo”

← Older revision		Revision as of 01:46, 14 April 2023
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	=== Alterations ===		=== Alterations ===
	=== Modulations ===		=== Modulations ===
			[[Category:13edo]]

Inthar: /* Modes of the harmonic Mnarian scale */

2022-03-18T23:06:36Z

Modes of the harmonic Mnarian scale

← Older revision		Revision as of 23:06, 18 March 2022
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	\| \| sLsLsLsA		\| \| sLsLsLsA
	\| style="text-align:center;" \| 0\|7 b5d b7d		\| style="text-align:center;" \| 0\|7 b5d b7d
	\| \| Sarnathian b7d		\| \| Sarnathian b5d b7d
	\|}		\|}

Inthar: /* Modes of the harmonic Mnarian scale */

2022-03-18T01:46:18Z

Modes of the harmonic Mnarian scale

← Older revision		Revision as of 01:46, 18 March 2022
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	\|-		\|-
	\| \| sLsLsLsA		\| \| sLsLsLsA
	\| style="text-align:center;" \| 0\|7 b7d		\| style="text-align:center;" \| 0\|7 b5d b7d
	\| \| Sarnathian b7d		\| \| Sarnathian b7d
	\|}		\|}

Inthar: /* Modes of the Harmonic Mnarian scale */

2022-03-18T01:38:31Z

Modes of the Harmonic Mnarian scale

← Older revision		Revision as of 01:38, 18 March 2022
Line 108:		Line 108:
	In [[18edo]], the augmented 3-mosstep (LLL) is a 600¢ tritone, which can be used as a dissonance.		In [[18edo]], the augmented 3-mosstep (LLL) is a 600¢ tritone, which can be used as a dissonance.

	==== Modes of the ~~Harmonic~~ Mnarian scale ====		==== Modes of the harmonic Mnarian scale ====
	A = ~~3\13~~		We call the scale LsLsLsLAs (with A = L + chroma) the ''harmonic Mnarian'' scale. The table below shows the modes of Harmonic Mnarian.
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-

Inthar: /* Other modmosses */

2022-03-18T01:37:33Z

Other modmosses

@@ Line 108: / Line 108: @@
 In [[18edo]], the augmented 3-mosstep (LLL) is a 600¢ tritone, which can be used as a dissonance.
-==== Other modmosses ====
+==== Modes of the Harmonic Mnarian scale ====
-* LSLSLSAS Harmonic Mnarian
+A = 3\13
 == 13edo oneiro chordal theory ==

Inthar: /* Archeodim */ consistency with convention of using tamnams degree names and frn accidentals

2022-03-18T01:28:21Z

Archeodim: consistency with convention of using tamnams degree names and frn accidentals

← Older revision		Revision as of 01:28, 18 March 2022
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	\|-		\|-
	\| \| LLLsLsLs		\| \| LLLsLsLs
	\| style="text-align:center;" \| 7\|0 &4		\| style="text-align:center;" \| 7\|0 #3d
	\| \| Dylydian (Dylathian #4)		\| \| Dylydian (Dylathian #3d)
	\|-		\|-
	\| \| LLsLsLsL		\| \| LLsLsLsL
	\| style="text-align:center;" \| 6\|1 @8		\| style="text-align:center;" \| 6\|1 b7d
	\| \| Illarmixian (Illarnekian b8)		\| \| Illarmixian (Illarnekian b7d)
	\|-		\|-
	\| \| LsLLLsLs		\| \| LsLLLsLs
	\| style="text-align:center;" \| 5\|2 &6		\| style="text-align:center;" \| 5\|2 #5d
	\| \| Celdorian (Celephaïsian #6)		\| \| Celdorian (Celephaïsian #5d)
	\|-		\|-
	\| \| sLLLsLsL		\| \| sLLLsLsL
	\| style="text-align:center;" \| 4\|3 @2		\| style="text-align:center;" \| 4\|3 b1d
	\| \| Ulphrygian (Ultharian b2)		\| \| Ulphrygian (Ultharian b1d)
	\|-		\|-
	\| \| LsLsLLLs		\| \| LsLsLLLs
	\| style="text-align:center;" \| 3\|4 &8		\| style="text-align:center;" \| 3\|4 #7d
	\| \| Mnionian (Mnarian #8)		\| \| Mnionian (Mnarian #7d)
	\|-		\|-
	\| \| sLsLLLsL		\| \| sLsLLLsL
	\| style="text-align:center;" \| 0\|7 &7		\| style="text-align:center;" \| 0\|7 #6d
	\| \| Sardorian (Sarnathian #7)		\| \| Sardorian (Sarnathian #6d)
	\|-		\|-
	\| \| LsLsLsLL		\| \| LsLsLsLL
	\| style="text-align:center;" \| 3\|4 @7		\| style="text-align:center;" \| 3\|4 b6d
	\| \| Mnaeolian (Mnarian b7)		\| \| Mnaeolian (Mnarian b6d)
	\|-		\|-
	\| \| sLsLsLLL		\| \| sLsLsLLL
	\| style="text-align:center;" \| 0\|7 @6		\| style="text-align:center;" \| 0\|7 #5d
	\| \| Sarlocrian (Sarnathian b6)		\| \| Sarlocrian (Sarnathian b5d)
	\|}		\|}

Inthar: Created page with "This page describes User:Inthar's approach to 13edo, mainly based on oneirotonic (5L 3s). == Standing assumptions == The Fox-Raven absolute pitch system is used in..."

2022-03-11T06:14:39Z

Created page with "This page describes User:Inthar's approach to 13edo, mainly based on oneirotonic (5L 3s). == Standing assumptions == The Fox-Raven absolute pitch system is used in..."

New page

This page describes [[User:Inthar]]'s approach to [[13edo]], mainly based on oneirotonic ([[5L 3s]]).
== 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# ...

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'''''

== Oneirotonic modes==
{| class="wikitable"
|-
| style="text-align:center;" | '''Mode'''
| style="text-align:center;" | [[Modal UDP Notation|'''UDP''']]
| style="text-align:center;" | '''Name'''
|-
| | LLsLLsLs
| style="text-align:center;" | 7|0
| | Dylathian (də-LA(H)TH-iən)
|-
| | LLsLsLLs
| style="text-align:center;" | 6|1
| | Illarnekian (ill-ar-NEK-iən)
|-
| | LsLLsLLs
| style="text-align:center;" | 5|2
| | Celephaïsian (kel-ə-FAY-zhən)
|-
| | LsLLsLsL
| style="text-align:center;" | 4|3
| | Ultharian (ul-THA(I)R-iən)
|-
| | LsLsLLsL
| style="text-align:center;" | 3|4
| | Mnarian (mə-NA(I)R-iən)
|-
| | sLLsLLsL
| style="text-align:center;" | 2|5
| | Kadathian (kə-DA(H)TH-iən)
|-
| | sLLsLsLL
| style="text-align:center;" | 1|6
| | Hlanithian (lə-NITH-iən)
|-
| | sLsLLsLL
| style="text-align:center;" | 0|7
| | Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
|}

=== 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 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.

{| class="wikitable"
|-
| style="text-align:center;" | '''Mode'''
| style="text-align:center;" | [[Modal UDP Notation|'''UDP''']]
| style="text-align:center;" | '''Name'''
|-
| | LLLsLsLs
| style="text-align:center;" | 7|0 &4
| | Dylydian (Dylathian #4)
|-
| | LLsLsLsL
| style="text-align:center;" | 6|1 @8
| | Illarmixian (Illarnekian b8)
|-
| | LsLLLsLs
| style="text-align:center;" | 5|2 &6
| | Celdorian (Celephaïsian #6)
|-
| | sLLLsLsL
| style="text-align:center;" | 4|3 @2
| | Ulphrygian (Ultharian b2)
|-
| | LsLsLLLs
| style="text-align:center;" | 3|4 &8
| | Mnionian (Mnarian #8)
|-
| | sLsLLLsL
| style="text-align:center;" | 0|7 &7
| | Sardorian (Sarnathian #7)
|-
| | LsLsLsLL
| style="text-align:center;" | 3|4 @7
| | Mnaeolian (Mnarian b7)
|-
| | sLsLsLLL
| style="text-align:center;" | 0|7 @6
| | Sarlocrian (Sarnathian b6)
|}

The cyclic order of archeodim modes are:
# LSLLLSLS is Celdorian
# SLLLSLSL is Ulphrygian
# LLLSLSLS is Dylydian
# LLSLSLSL is Illarmixian
# LSLSLSLL is Mnaeolian
# SLSLSLLL is Sarlocrian
# LSLSLLLS is Mnionian
# SLSLLLSL is Sardorian
Notably the cyclic order is almost exactly the "circle" of diatonic modes except the "circle" breaks at Sardorian-Celdorian.

In [[18edo]], the augmented 3-mosstep (LLL) is a 600¢ tritone, which can be used as a dissonance.

==== Other modmosses ====
* LSLSLSAS Harmonic Mnarian

== 13edo oneiro chordal theory ==
Favorite modes: Dylathian (22122121), Illarnekian (22121221), Celephaisian (21221221), Mnionian (21212221), Dylydian (22212121), Harmonic Mnarian (21212131)?

We will primarily discuss functional harmony using [[delta-rational chord]]s, treating these separately from counterpoint. h/t to tprice and Jaimbee for the delta-rational chords presented here and for other discussions.

13edo oneiro enjoys two main (rooted) delta-rational sonorities analogous to major and minor triads: 0-(185)-369-646 ("delta-rational major triad" or just "major"/"Maj") and 0-277-738-923 ("delta-rational 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", and 0-277-646-923 will be called "minor diminished" or "mindim".

[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]

[https://xenpaper.com/#(bpm%3A30)(osc%3Asawtooth2)%0A%7Br200Hz%7D%7B13edo%7D%0A(env%3A1846)%0A%5B0_4_7_10_%272_%276_%279_%2712%5D-.._%23_Dylydian%0A%5B0_5_9_%270_%272_%274_%277_%2710_%2712%5D-.._%23_Dylathian%0A%5B0_5_8_10_%270_%272_%274_%277_%2712%5D-.._%23_Illarnekian%0A%5B0_3_8_10_%272_%275_%277_%2712%5D-.._%23_Celepha%C3%AFsian%0A%5B0_5_9_%273_%277_%2710_%2712_%27%272%5D-.._%23_Celdorian%0A%5B0_3_6_8_%2711_%272_%275_10%5D-.._%23_Mnarian%0A%5B0_3_6_8_10_%272_%275_%2712%5D-.._%23_Mnionian Some motherchords of oneiro modes]
=== Functional chords on each degree ===
Celephaisian
* 0d: minor
* 1d: minor
* 2d: major
* 3d: minor, mindim
* 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 5d: major
* 6d: minor
* 7d: minor triad, minor 4ms, minor 6ms, minor 7ms
Mnionian (Melodic Mnarian)
* 0d: minor
* 1d: minor
* 2d: mindim
* 3d: minor, mindim
* 4d: major, augmented 3ms
* 5d: major, minor 7ms
* 6d: minor triad, minor 6ms, minor 7ms
* 7d: "diminished triad", diminished 5ms, minor 6ms, minor 7ms

=== Progressions ===
kd(maj) means the triad 0 369 646 on kd, kd(min) means the tetrad 0 277 738 923 on kd

Common motions:
* 0d(maj or min) → M1d(min)
* 0d(maj or min) → 4d(min) (when ending on 0d this sounds like diatonic V to I)
* 0d(maj or min) → m6d(min)
* 0d(maj) → 5d(maj), 0d(min) → 5d(maj or min) (when ending on 0d this is a "dominant to tonic" motion)
* 0d(maj) → M3d(maj)
* 2d(min) → m1d(maj) → 0d(maj) (pseudo tritone sub)

=== Modal harmony ===
Modes can be grouped by their functional properties.
* Dual-fifth: Illarnekian, Celephaïsian, Ultharian; Illarmixian, Ulphrygian
* Dual-fourth: Mnarian, Kadathian, Hlanithian; Mnionian, Mnaeolian
* Major pJI chord on root: Dylathian, Illarnekian; Dylydian, Illarmixian
* Minor pJI chord on root: Celephaïsian, Ultharian, Mnarian, Kadathian; Mnionian, Sardorian, Ulphrygian
* Lower leading tone: Dylathian, Illarnekian, Celephaïsian; Dylydian, Mnionian
* "Neoclassical functional modes" (loose grouping): Dylathian, Illarnekian, Celephaïsian, Ultharian; Mnionian, Mnaeolian(?)
* Upper leading tone: Kadathian, Hlanithian, Sarnathian, Sardorian, Sarlocrian
* Minor 6-mosstep: Hlanithian, Sarnathian, Mnaeolian, Sarlocrian
* 0 462 831 delta-rational chord on root: Dylathian, Dylydian, Hlanithian, Mnaeolian
* "Dorian-like", i.e. no leading tone, 5d is minor, and m7d is major: Ultharian, Mnarian
* 7d is minor: Kadathian, Hlanithian
We'll call degrees that don't have the major delta-rational or the minor delta-rational 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 ====
Functional chords on each degree:
* 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 3d and 5d because of their leading tones.

Motherchord: 0d-m2d-P5d-M6d-(M7d)-M1d-P3d-M5d-(M7d)

Progressions:
* 0d(min) 1d(min) 3d(min or mindim) 0d(min)
* 0d(min) 1d(min) 6d(min) 3d(min or mindim) 0d(min)
* 0d(min) 6d(min) 3d(min or mindim) 0d(min)
* 0d(min) 2d(Maj) 3d(min or mindim) 0d(min)
* 0d(min) 4d(min7) 5d(Maj)/3d(min or mindim) 0d(min)
* 0d(min) 6d(min) 5d(Maj) 0d(min)

Secondary modes:
* 3d Ultharian
* 2d Dylathian
* 5d illarnekian

==== Ultharian ====
* 0d: min
* 1d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 2d: Maj
* 3d: min
* 4d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 5d: min
* 6d: min
* 7d: Maj

Ultharian and Mnarian often behave like Dorian because they lack a leading tone. Resolving degrees: 3d(min), 5d(min), 7d(Maj)

==== Mnarian ====
* 0d: min
* 1d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 2d: min
* 3d: min
* 4d: Maj
* 5d: min
* 6d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 7d: Maj
Resolving degrees: 3d(min), 5d(min), 7d(Maj)

==== Kadathian ====
* 0d: min
* 1d: Maj
* 2d: min
* 3d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 4d: Maj
* 5d: min
* 6d: minor triad, minor 4ms, minor 6ms, minor 7ms
* 7d: min
Resolving degrees: 2d(min)?, 4d(Maj), 5d(min), 7d(min)
==== Hlanithian and Sarn ====
Main tonic chord is 0-3-8-11\13 (min7), works well with m6d(maj) and m7d(min7).
=== Alterations ===
=== Modulations ===