List of 31edo chords
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 2.3.5.7.11.23 and 2.5.7.13.17.19.
Triads
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.
Tetrads
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 | 25:30:36:42 | 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 v13 | Ih7d13$ | Miracle:7 |
| Add-13 | 4:5:6:13 | P1 M3 P5 v13 | 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 |