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 |
Note: $ used to represent shell voicing