List of 31edo chords

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This is an extensive list of chords that exist and can be utilized in 31edo. Some only exist in 31 due to tempering, and some exist due to 31's excellence in and


Triads can be standard, meaning they're a stack of thirds selection of s3, m3, n3, M3, or S3, or nonstandard, meaning that they aren't.

Standard Triads Otonal/Utonal Representation Notes Notation Complexity in Temperaments
Major 4:5:6 P1 M3 P5 I Meantone:4, Würschmidt:8, Mohajira:8, Myna:10
Minor 6/5/4 P1 m3 P5 Im Meantone:4, Würschmidt:8, Mohajira:8, Myna:10
Subminor 6:7:9 P1 s3 P5 Is Squares:5, Mothra:7, Orwell:7, Meantone:9
Supermajor 9/7/6 P1 S3 P5 IS Squares:5, Mothra:7, Orwell:7, Meantone:9
Neutral 18:22:27 P1 n3 P5 In Mohajira:2, Squares:4, Miracle:6, Würschmidt:8, Myna:10
Augmented 16:20:25 P1 M3 A5 I+ Würschmidt:2, Tutone:4, Orwell:6, Meantone:8, Valentine:10
Diminished 25:30:36 P1 m3 d5 Io Myna:2, Nusecond:4, Meantone:6, Valentine:8, Joan:10
Harmonic Diminished 5:6:7 P1 m3 vd5 Im(db5) Myna:3, Nusecond:6, Meantone:9
Subminor Diminished 7/6/5 P1 s3 vd5 Is(db5) Myna:3, Nusecond:6, Meantone:9
Septimal Wolf Major 21:27:32 P1 S3 ^5 IS(t5) Nusecond:5, Würschmidt:7, Joan:8, Valentine:10
Septimal Wolf Minor 21:25:32 P1 m3 ^5 Im(t5) Nusecond:5, Würschmidt:7, Joan:8, Valentine:10
Subfifth Minor 15:18:22 P1 m3 v5 Im(d5) Mohajira:6, Joan:6, Myna:6
Subfifth Neutral 22/18/15 P1 n3 v5 In(d5) Mohajira:6, Joan:6, Myna:6
DRmaj 24:30:35 P1 M3 v5 I(d5) Orwell:3, A-Team:6, Myna:9
DRmindim 24:28:35 P1 s3 v5 Is(d5) Orwell:3, A-Team:6, Myna:9
Orwell 24:28:33 P1 s3 dd5 Is(bb5) Orwell:2, A-Team:4, Myna:6, Mothra:8, Squares:10
Squares 11:14:18 P1 S3 AA5 IS(x5) Squares:2, Würschmidt:4, Joan:6, Tutone:8, Nusecond:10

Other Triads Otonal/Utonal Representation Notes Notation Complexity in Temperaments
Double Diminished 7:8:10 P1 d3 d5 Io(bb3) Tutone:5, Miracle:7, Myna:9, Meantone:10
Major b5 10/8/7 P1 M3 d5 I(b5) Tutone:5, Miracle:7, Myna:9, Meantone:10
Minor Augmented 27:32:42 P1 m3 A5 Im+ Nusecond:5, Würschmidt:7, Joan:8
Double Augmented 27:35:42 P1 A3 A5 I+(#3) Nusecond:5, Würschmidt:7, Joan:8
Doubly Augmented 8:10:13 P1 M3 AA5 I(x5) Würschmidt:5, A-Team:7, Miracle:7, Mohajira:9
Sus4 6:8:9 P1 P4 P5 Isus4 Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
Sus2 8:9:12 P1 M2 P5 Isus2 Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
Sus(t4) 8:11:12 P1 ^4 P5 Isus(t4) Mohajira:5, Orwell:7, Tritonic:8, Squares:10
Sus(d4) 10:13:15 P1 v4 P5 Isus(d4) Mothra:3, Miracle:6, Valentine:9, Tritonic:12
Sus(t2) 14:16:21 P1 ^2 P5 Isus(t2) Mothra:3, Miracle:6, Valentine:9, Tritonic:12
DRsus4 13:17:19 P1 v4 v5 Isus(d4)(d5) A-Team:4, Mothra:8, Joan:8, Mohajira:9, Tritonic:10
DRsus2 19/17/13 P1 M2 v5 Isus2(d5) A-Team:4, Mothra:8, Joan:8, Mohajira:9, Tritonic:10
Terrain Triad 5:7:9 P1 A4 m7 I(db5)m7 Tutone:4, Meantone:8, Squares:8, Joan:10, Tritonic:10
Harmonic Shell 4:5:7 P1 M3 s7 Ih7$ Tutone:5, Miracle:7, Myna:9, Meantone:10, Tritonic:12
Mothwellsmic Shell 14/11/8 P1 S3 s7 ISs7$ Joan:4, Orwell:8, Mothra:8, Tutone:9, Squares:10
Orgone Triad 8:11:14 P1 ^4 s7 Is7sus(t4)$ Joan:4, Orwell:8, Mothra:8, Tutone:9, Squares:10
Quartal 9:12:16 P1 P4 m7 Iq Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
Joan 8:11:15 P1 ^4 M7 IJ Joan:2, Orwell:4, Tritonic:6, A-Team:8, Mohajira:10

Notes: $ used to represent shell voicing, DR means Delta-rational.


These tetrads are split into a few general categories.

Basic Tetrads Otonal/Utonal Representation Notes Notation Complexity in Temperaments
Major Seven 8:10:12:15 P1 M3 P5 M7 IM7 Meantone:5, Würschmidt:9, Mohajira:10
Harmonic Seven 4:5:6:7 P1 M3 P5 s7 Ih7 Myna:10, Meantone:10, Orwell:11
Minor Seven 10:12:15:18 P1 m3 P5 m7 Im7 Meantone:4, Mohajira:8
Utonal Tetrad 12/10/8/7 P1 m3 P5 S6 ImS6 Myna:10, Meantone:10, Orwell:11
Subminor Seven 12:14:18:21 P1 s3 P5 s7 Is7 Mothra:7, Orwell:8, Squares:9, Meantone:10
Undecimal Tetrad 6:7:9:11 P1 s3 P5 n7 Isn7 Squares:6, Nusecond:11
Supermajor Seven 14:18:21:27 P1 S3 P5 S7 IS7 Squares:5, Meantone:9, Mothra:10
9-over Tetrad 9/7/6/5 P1 S3 P5 m7 ISm7 Meantone:9, Nusecond:11
Neutral Seven 18:22:27:33 P1 n3 P5 n7 In7 Mohajira:3, Squares:6, Miracle:9

Other Basic Tetrads Otonal/Utonal Representation Notes Notation Complexity in Temperaments
Lynch Neutral 12:18:22:33 P1 P5 n7 ^11 I5n7t11 Mohajira:5, Squares:10
Neutral Minor Seven 27/22/18/15 P1 n3 P5 m7 Inm7 Mohajira:6
Neutral Major Tetrad 27/22/18/16 P1 n3 P5 M6 InM6 Mohajira:6
Subminor Major Tetrad 6:7:9:10 P1 s3 P5 M6 IsM6 Meantone:9, Nusecond:11
Dominant 20:25:30:36 P1 M3 P5 m7 I7 Meantone:6
Mothwellsmic Dominant 42/33/28/24 P1 S3 P5 s7 ISs7 Orwell:8, Squares:10
Subminor Supermajor Seven 21/18/14/11 P1 s3 P5 S7 IsS7 Squares:5, Würschmidt:10
Augmented Seven 16:20:25:28 P1 M3 A5 s7 Ih7(#5) Tutone:5, Meantone:10
Half Augmented 16:20:25:30 P1 M3 A5 M7 IM7(#5) Meantone:8, Würschmidt:9
Fully Augmented 64:80:100:125 P1 M3 A5 A7 I+7 Würschmidt:3, Tutone:6, Orwell:9
Half Diminished 36/30/25/20 P1 m3 d5 m7 Im7(b5) Meantone:6
Fully Diminished 21:25:30:36 P1 m3 d5 d7 Io7 Myna:3, Nusecond:6, Meantone:9
Harmonic Half Diminished 5:6:7:9 P1 m3 vd5 m7 Im7(db5) Meantone:9, Nusecond:11
Harmonic Fully Diminished 10:12:14:17 P1 m3 vd5 d7 Io7(db5) Myna:5, Nusecond:10, A-Team:11
Subminor Half Diminished 7/6/5/4 P1 s3 vd5 s7 Is7(db5) Myna:10, Meantone:10, Orwell:11
Augmented 3&7 20:26:30:39 P1 A3 P5 A7 I(#3,#7) Mothra:5, Miracle:10
Diminished 3&7 26:30:39:45 P1 d3 P5 d7 I(bb3,bb7) Mothra:4, Miracle:8
Doubly Augmented Major Seven 8:10:13:15 P1 M3 AA5 M7 IM7(x5) Miracle:7, Mohajira:11
Supermajor Seven Augmented 14:18:22:27 P1 S3 A5 S7 IS7(#5) Squares:4, Würschmidt:8

Fifth-Contained Tetrads Otonal/Utonal Representation Notes Notation Complexity in Temperaments
Mu Chord 8:9:10:12 P1 M2 M3 P5 I(add2) Meantone:4, Mohajira:8
Nu Chord 12/10/9/8 P1 m3 P4 P5 Im(add4) Meantone:4, Mohajira:8
Subminor Tetrad 6:7:8:9 P1 s3 P4 P5 Is(add4) Mothra:7, Squares:9, Meantone:10
Supermajor Tetrad 9/8/7/6 P1 M2 S3 P5 IS(add2) Mothra:7, Squares:9, Meantone:10
Super Second Tetrad 14:16:18:21 P1 S2 S3 P5 IS(add t2) Mothra:7, Meantone:11
Sub Fourth Tetrad 21/18/16/14 P1 s3 v4 P5 Is(add d4) Mothra:7, Meantone:11
Sus 2/4 18:20:24:27 P1 M2 P4 P5 Isus(2/4) Meantone:3, Mohajira:6, Mothra:9
Add^4 8:10:11:12 P1 M3 ^4 P5 I(add t4) Mohajira:8, Valentine:9, Orwell:10
Minor Addv2 12/11/10/8 P1 n2 m3 P5 Im(add d2) Mohajira:8, Valentine:9, Orwell:10

Split Chords Otonal/Utonal Representation Notes Notation Complexity in Temperaments
Split Chord 20:24:25:30 P1 m3 M3 P5 IMm3 Meantone:7, Würschmidt:8, Valentine:9, Myna:10
Septimal Split Chord 28:33:36:42 P1 s3 S3 P5 ISs3 Squares:6, Orwell:7, Nusecond:11
Yellow/Blue Split Chord 12:14:15:18 P1 s3 M3 P5 IMs3 Meantone:9, Orwell:10
Green/Red Split Chord 18/15/14/12 P1 m3 S3 P5 ISm3 Meantone:9, Orwell:10
Wolf Split Chord 21:25:27:32 P1 m3 S3 ^5 ISm3(t5) Nusecond:7, Joan:8, Würschmidt:9
Squares Split Chord 22:27:28:36 P1 n3 S3 A5 ISn3(#5) Squares:3, Würschmidt:6, Joan:9
DR Split Chord 24:28:30:35 P1 s3 M3 v5 IMs3(d5) Orwell:4, A-Team:8

Harmonic Subsets Otonal/Utonal Representation Notes Notation Complexity in Temperaments
h9 Shell 4:5:7:9 P1 M3 s7 M9 Ih9$ Tutone:5, Meantone:10
Add11 Shell 4:5:7:11 P1 M3 s7 ^11 Ih7t11$ Tutone:9, Valentine:11, Tritonic:12
Quintal Neutral 4:6:9:11 P1 P5 M9 ^11 I59t11 Mohajira:5, Squares:10
Altered-13 Shell 4:5:7:13 P1 M3 s7 n13 Ih7d13$ Miracle:7
Add-13 4:5:6:13 P1 M3 P5 n13 I(add d13) Mohajira:9, Valentine:11
Altered-17 Shell 8:10:14:17 P1 M3 s7 m9 Ih7b9$ Miracle:7
Altered-19 Shell 8:10:14:19 P1 M3 s7 m10 Ih7b10$ Valentine:8, Myna:10

Misc Tetrads Otonal/Utonal Representation Notes Notation Complexity in Temperaments
h7#9 Shell 12:15:21:28 P1 M3 s7 A9 Ih7#9$ Miracle:8, Meantone:10
h7db9 Shell 12:15:21:25 P1 M3 s7 s9 Ih7db9$ Valentine:8, Meantone:10
h7d9 Shell 16:20:28:35 P1 M3 s7 n9 Ih7d9$ Tutone:7, Valentine:8, Miracle:9, Orwell:11
DRmaj 24:27:30:35 P1 M2 M3 v5 I(add 2, d5) A-Team:6
DRmin 42:49:64:72 P1 s3 ^5 S6 IsS6(t5) A-Team:4, Mothra:8
DRmindim 66:77:96:112 P1 s3 v5 S6 IsS6(d5) Orwell:3, A-Team:6, Myna:9
DRsus 48:54:63:70 P1 M2 v4 v5 Isus(2/d4)(d5) A-Team:4, Mothra:8
Leading DRsus2 19/17/13/10 P1 M2 v5 S7 IS7sus2(d5) A-Team:5, Mothra:10
Mothwellsmic Dominant #9 Shell 14/11/8/6 P1 S3 s7 A9 ISs7#9$ Orwell:8, Mothra:8, Squares:10
Orgone add9 8:11:14:18 P1 ^4 s7 M9 Ih9sus(t4)$ Joan:7, Tutone:9, Squares:10
Greeley Over-3 6:7:10:11:(13) P1 s3 M6 n7 (n9) IsM6n7$ Nusecond:6(7)

Other Linear Tetrads Otonal/Utonal Representation Notes Notation Complexity in Temperaments
Slendric Tetrad 42:48:55:63 P1 S2 v4 P5 Isus(t2/d4) Mothra:3, Miracle:6, Valentine:9
Miracle Cluster 13:14:15:16 P1 m2 S2 n3 I(13:14:15:16) Miracle:3, Joan:6, Slender:9
Orwell Tetrad 48:56:66:77 P1 s3 ^4 m6 IO Orwell:3, A-Team:6, Myna:9


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

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

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

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

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

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

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 more to say.
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 Ih7d11d15 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.