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List of 31edo chords: Difference between revisions

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Added pentads and extended chords
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!Altered-13 Shell
!Altered-13 Shell
|4:5:7:13
|4:5:7:13
|P1 M3 s7 v13
|P1 M3 s7 n13
|Ih7d13$
|Ih7d13$
|Miracle:7
|Miracle:7
Line 576: Line 576:
!Add-13
!Add-13
|4:5:6:13
|4:5:6:13
|P1 M3 P5 v13
|P1 M3 P5 n13
|I(add d13)
|I(add d13)
|Mohajira:9, Valentine:11
|Mohajira:9, Valentine:11
Line 695: Line 695:
|IO
|IO
|Orwell:3, A-Team:6, Myna:9
|Orwell:3, A-Team:6, Myna:9
|}
== Pentads ==
{| class="wikitable"
!Main Ninth Chords
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
!Major Nine
|8:10:12:15:18
|P1 M3 P5 M7 M9
|IM9
|Meantone:5, Mohajira:10
|-
!Harmonic Nine
|4:5:6:7:9
|P1 M3 P5 s7 M9
|Ih9
|Meantone:10
|-
!Minor Nine
|18/15/12/10/8
|P1 m3 P5 m7 M9
|Im9
|Meantone:5, Mohajira:10
|-
!Subminor Nine
|12:14:18:21:27
|P1 s3 P5 s7 M9
|Is9
|Squares:9, Meantone:10, Mothra:10
|-
!Supermajor Nine
|27/21/18/14/12
|P1 S3 P5 S7 M9
|IS9
|Squares:9, Meantone:10, Mothra:10
|-
!9-over Pentad
|9/7/6/5/4
|P1 S3 P5 m7 M9
|IS9b7
|Meantone:10
|-
!Neutral Pentad
|36:44:54:66:81
|P1 n3 P5 n7 M9
|In9
|Mohajira:4, Squares:8, Miracle:12
|}
{| class="wikitable"
!Other Main Pentads
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
!Major 6/9
|12:15:18:20:27
|P1 M3 P5 M6 M9
|I6/9
|Meantone:4, Mohajira:8, Slendric:12
|-
!Minor 7/11
|10:12:15:18:27
|P1 m3 P5 m7 P11
|Im7/11
|Meantone:4, Mohajira:8, Slendric:12
|-
!Dominant Nine
|20:25:30:36:45
|P1 M3 P5 m7 M9
|I9
|Meantone:6, Mohajira:12
|-
!Tridecimal Pentad
|6:7:9:11:13
|P1 s3 P5 n7 n9
|Isn7d9
|Squares:12
|-
!Subminor 6/9
|12:14:18:20:27
|P1 s3 P5 M6 M9
|IsM6/9
|Meantone:9
|-
!Subminor 7/11
|24:28:36:42:63
|P1 s3 P5 s7 v11
|Is7d11
|Mothra:7, Meantone:11
|-
!Sub Neutral 11
|12:14:18:22:33
|P1 s3 P5 n7 ^11
|Isn7t11
|Squares:10, Nusecond:12
|-
!Fully Augmented #9
|64:80:100:125:150
|P1 M3 A5 A7 A9
|I+7#9
|Orwell:10, Würschmidt:10
|}
{| class="wikitable"
!Altered Pentads
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
!Harmonic #9
|12:15:18:21:28
|P1 M3 P5 s7 A9
|Ih7#9
|Meantone:10
|-
!Harmonic db9
|12:15:18:21:25
|P1 M3 P5 s7 s9
|Ih7db9
|Meantone:10, Myna:10
|-
!Altered-13
|4:5:6:7:13
|P1 M3 P5 s7 n13
|Ih7d13
|Miracle:13, Valentine:14
|-
!Altered-13 #9 Shell
|12:15:21:28:39
|P1 M3 s7 A9 n13
|Ih7#9d13$
|Miracle:8
|}
{| class="wikitable"
!Split Pentads
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
!Sub Seventh Split
|12:14:15:18:21
|P1 s3 M3 P5 s7
|IMs3s7
|Meantone:10, Orwell:11
|-
!Major Seventh Split
|24:28:30:36:45
|P1 s3 M3 P5 M7
|IMs3M7
|Meantone:9, Orwell:10, Würschmidt:10
|-
!Major Sixth Split
|12:14:15:18:20
|P1 s3 M3 P5 M6
|IMs3M6
|Meantone:9, Nusecond:13
|-
!Minor Seventh Split
|18/15/14/12/10
|P1 m3 S3 P5 m7
|ISm3m7
|Meantone:9, Nusecond:13
|-
!Super Seventh Split
|54/45/42/36/28
|P1 m3 S3 P5 S7
|ISm3S7
|Meantone:9, Würschmidt:10
|-
!Super Sixth Split
|36/30/28/24/21
|P1 m3 S3 P5 S6
|ISm3S6
|Meantone:10, Orwell:11
|}
{| class="wikitable"
!Harmonic Pentads
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
!Orwell Harmonic
|4:5:6:7:11
|P1 M3 P5 s7 ^11
|Ih7t11
|Orwell:11, Valentine:12
|-
!Mohajira Harmonic
|4:5:6:9:11
|P1 M3 P5 M9 ^11
|Ih11(no7)
|Mohajira:8
|-
!Tutone Harmonic
|4:5:7:9:11
|P1 M3 s7 M9 ^11
|Ih11$
|Tutone:9
|-
!Squares Harmonic
|4:6:7:9:11
|P1 P5 s7 M9 ^11
|Ih11(no3)
|Squares:10
|-
!Over-5 Harmonic
|5:6:7:9:11
|P1 m3 vb5 m7 n9
|Im7d9(db5)
|Squares:12
|-
!Miracle Harmonic
|4:5:7:13:17
|P1 M3 s7 n13 m16
|Ih7d13b16$
|Miracle:8
|-
!A-Team Harmonic
|4:5:13:17:19
|P1 M3 n13 m16 m17
|IMd13b16b17$
|A-Team:11
|-
!Joan Sharp Harmonic
|4:7:13:17:19
|P1 s7 n13 m16 m17
|I5s7d13b16b17$
|Joan:8
|-
!Joan Flat Harmonic
|4:7:9:11:15
|P1 s7 M9 ^11 M14
|I59s7t11M14$
|Joan:7
|-
!Greeley Harmonic
|6:7:10:11:13
|P1 s3 M6 n7 n9
|IsM6n7d9$
|Nusecond:7
|}
{| class="wikitable"
!Other Linear Pentads
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
!Slendric Pentad
|42:48:55:63:72
|P1 S2 v4 P5 S6
|IS6sus(t2,d4)
|Mothra:4, Miracle:8, Valentine:12
|-
!Miracle Cluster
|13:14:15:16:17
|P1 m2 S2 n3 v4
|I(13:14:15:16:17)
|Miracle:4, Joan:8, Slender:12
|-
!Orwell Pentad
|48:56:66:77:90
|P1 s3 ^4 m6 M7
|IOM7
|Orwell:4, A-Team:8, Myna:12
|}
== Other Extended Chords ==
{| class="wikitable"
!
!Otonal/Utonal Representation
!Notes
!Notation
!Explanation
|-
!Undecimal Hexad
|4:5:6:7:9:11
|P1 M3 P5 s7 M9 ^11
|Ih11
|The holy grail chord, a rich complex sound made up of the main harmonics in 31, nothing much to it.
|-
!Novemdecimal Hexad
|4:5:7:13:17:19
|P1 M3 s7 n13 m16 m17
|Ih7d13b16b17$
|All the sharp harmonics on a basic harmonic shell, works decently due to the extreme accuracy of the 13:17:19.
|-
!?
|6:7:9:11:15:20
|P1 s3 P5 n7 M10 M13
|Isn7(10,13)
|Standard undecimal triad but with some quartal flavor in the tensions, adds a good unique sound that can be sort of hard to add with this tetrad.
|-
!?
|8:10:12:15:22:33
|P1 M3 P5 M7 ^11 ^15
|Imaj7t11t15
|Zhea Erose Chord, can also be used with a harmonic seventh to avoid the subfifth dissonance.
|-
!Rast Minor Parent Chord
|10:12:15:18:22:27:33
|P1 m3 P5 m7 n9 P11 n13
|Im7/11n9n13
|Subset chords excluding one of the tensions may be preferable to avoid chains of neutral thirds.
|-
!Graham Hexad
|12:15:18:21:28:33
|P1 M3 P5 s7 A9 ^11
|Ih11#9
|The whole thing works as a chord but just using subsets works well too, the shell voicing is often a better choice.
|-
!?
|48/40/32/28/21/18
|P1 m3 P5 S6 S9 P11
|ImS69add11
|Analog of a minor 69 type chord. Shows why utonal chords don’t always work well with tensions , with high complexity for a simple base tetrad.
|-
!?
|16:20:24:28:42:63
|P1 M3 P5 s7 v11 v15
|Ih7d11d13
|Subminor ninth and suboctave add dissonance, but strong fifths between 7, 11, and 15 add structure that allows the chord to function.
|-
!?
|32:40:56:75:100:125
|P1 M3 s7 A9 s13 v15
|Ih7#9db13d15$
|Extension of a standard jazz chord, with the 3:4:5 on top providing stability to balance the suboctave dissonance.
|-
!?
|48:60:75:90:112:140
|P1 M3 A5 M7 A9 x11
|Imaj7+(#9,x11)
|An interesting chord, pretty much as many major thirds as you can have without any augmented sevenths.
|-
!Mothra[6] 5 Parent Chord
|84:98:128:147:192:224
|P1 s3 ^5 s7 S9 P11
|Is7/11t9(t5)
|Subsets work well too, emphasizes the mothra sound through the superfifths and subfourths present.
|}
|}


[[Category:31edo]]
[[Category:31edo]]
[[Category:Lists of chords]]
[[Category:Lists of chords]]
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