List of 31edo chords

This is an extensive list of chords that exist and can be utilized in 31edo.

Intervals are written in ups and downs notation. Harmonics are omitted if any of the harmonics are larger than 100.

The names, as well as the shorthand chord symbols are given only as a suggestion, as there is no single standardized system.

Triads

Standard triads are stacks of thirds, selected from vm3, m3, ~3, M3, or ^M3.

Standard triads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Major	1/1 – 5/4 – 3/2	4:5:6	0, 10, 18	P1 M3 P5	I
Minor	1/1 – 6/5 – 3/2	10:12:15	0, 8, 18	P1 m3 P5	Im
Subminor	1/1 – 7/6 – 3/2	6:7:9	0, 7, 18	P1 vm3 P5	Is
Supermajor	1/1 – 9/7 – 3/2	14:18:21	0, 11, 18	P1 ^M3 P5	IS
Neutral	1/1 – 11/9 – 3/2	18:22:27	0, 9, 18	P1 ~3 P5	In
Augmented	1/1 – 5/4 – 25/16	16:20:25	0, 10, 20	P1 M3 A5	I+
Diminished	1/1 – 6/5 – 36/25	25:30:36	0, 8, 16	P1 m3 d5	Io
Harmonic diminished	1/1 – 6/5 – 7/5	5:6:7	0, 8, 15	P1 m3 vd5	Im(db5)
Subminor diminished	1/1 – 7/6 – 7/5	30:35:42	0, 7, 15	P1 vm3 vd5	Is(db5)
Septimal wolf major	1/1 – 9/7 – 32/21	21:27:32	0, 11, 19	P1 ^M3 ^5	IS(t5)
Septimal wolf minor	1/1 – 25/21 – 32/21	21:25:32	0, 8, 19	P1 m3 ^5	Im(t5)
Subfifth minor	1/1 – 6/5 – 22/15	15:18:22	0, 8, 17	P1 m3 v5	Im(d5)
Subfifth neutral	1/1 – 11/9 – 22/15	45:55:66	0, 9, 17	P1 ~3 v5	In(d5)
DRmaj	1/1 – 5/4 – 35/24	24:30:35	0, 10, 17	P1 M3 v5	I(d5)
DRmindim	1/1 – 7/6 – 35/24	24:28:35	0, 7, 17	P1 vm3 v5	Is(d5)
Orwell	1/1 – 7/6 – 11/8	24:28:33	0, 7, 14	P1 vm3 dd5	Is(bb5)
Squares	1/1 – 14/11 – 18/11	11:14:18	0, 11, 22	P1 ^M3 AA5	IS(x5)

Other triads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Double diminished	1/1 – 8/7 – 10/7	7:8:10	0, 6, 16	P1 d3 d5	Io(bb3)
Major b5	1/1 – 5/4 – 10/7	28:35:40	0, 10, 16	P1 M3 d5	I(b5)
Minor augmented	1/1 – 32/27 – 14/9	27:32:42	0, 8, 20	P1 m3 A5	Im+
Double augmented	1/1 – 35/27 – 14/9	27:35:42	0, 12, 20	P1 A3 A5	I+(#3)
Doubly augmented	1/1 – 5/4 – 13/8	8:10:13	0, 10, 22	P1 M3 AA5	I(x5)
Sus4	1/1 – 4/3 – 3/2	6:8:9	0, 13, 18	P1 P4 P5	Isus4
Sus2	1/1 – 9/8 – 3/2	8:9:12	0, 5, 18	P1 M2 P5	Isus2
Sus(t4)	1/1 – 11/8 – 3/2	8:11:12	0, 14, 18	P1 ^4 P5	Isus(t4)
Sus(d4)	1/1 – 13/10 – 3/2	10:13:15	0, 12, 18	P1 v4 P5	Isus(d4)
Sus(t2)	1/1 – 8/7 – 3/2	14:16:21	0, 6, 18	P1 ^M2 P5	Isus(t2)
DRsus4	1/1 – 17/13 – 19/13	13:17:19	0, 12, 17	P1 v4 v5	Isus(d4)(d5)
DRsus2	1/1 – 19/17 – 19/13		0, 5, 17	P1 M2 v5	Isus2(d5)
Terrain triad	1/1 – 7/5 – 9/5	5:7:9	0, 15, 26	P1 vd5 m7	I(db5)m7
Harmonic shell	1/1 – 5/4 – 7/4	4:5:7	0, 10, 25	P1 M3 vm7	Ih7(no5)
Mothwellsmic shell	1/1 – 14/11 – 7/4	44:56:77	0, 11, 25	P1 ^M3 vm7	ISs7(no5)
Orgone triad	1/1 – 11/8 – 7/4	8:11:14	0, 14, 25	P1 ^4 vm7	Is7sus(t4)(no5)
Quartal	1/1 – 4/3 – 16/9	9:12:16	0, 13, 26	P1 P4 m7	Iq
Joan	1/1 – 11/8 – 15/8	8:11:15	0, 14, 28	P1 ^4 M7	IJ

Notes: DR means Delta-rational.

Tetrads

These tetrads are split into a few general categories.

Basic tetrads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Major seven	1/1 – 5/4 – 3/2 – 15/8	8:10:12:15	0, 10, 18, 28	P1 M3 P5 M7	IM7
Harmonic seven	1/1 – 5/4 – 3/2 – 7/4	4:5:6:7	0, 10, 18, 25	P1 M3 P5 vm7	Ih7
Minor seven	1/1 – 6/5 – 3/2 – 9/5	10:12:15:18	0, 8, 18, 26	P1 m3 P5 m7	Im7
Utonal tetrad	1/1 – 6/5 – 3/2 – 12/7		0, 8, 18, 24	P1 m3 P5 ^M6	ImS6
Subminor seven	1/1 – 7/6 – 3/2 – 7/4	12:14:18:21	0, 7, 18, 25	P1 vm3 P5 vm7	Is7
Undecimal tetrad	1/1 – 7/6 – 3/2 – 11/6	6:7:9:11	0, 7, 18, 27	P1 vm3 P5 ~7	Isn7
Supermajor seven	1/1 – 9/7 – 3/2 – 27/14	14:18:21:27	0, 11, 18, 29	P1 ^M3 P5 ^M7	IS7
9-over tetrad	1/1 – 9/7 – 3/2 – 9/5		0, 11, 18, 26	P1 ^M3 P5 m7	ISm7
Neutral seven	1/1 – 11/9 – 3/2 – 11/6	18:22:27:33	0, 9, 18, 27	P1 ~3 P5 ~7	In7

Other basic tetrads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Lynch neutral	1/1 – 3/2 – 11/6 – 11/4	12:18:22:33	0, 18, 27, 45	P1 P5 ~7 ^11	In7t11(no3)
Neutral minor Seven	1/1 – 27/22 – 3/2 – 9/5		0, 9, 18, 26	P1 ~3 P5 m7	Inm7
Neutral major tetrad	1/1 – 27/22 – 3/2 – 27/16		0, 9, 18, 23	P1 ~3 P5 M6	InM6
Subminor major tetrad	1/1 – 7/6 – 3/2 – 5/3	6:7:9:10	0, 7, 18, 23	P1 vm3 P5 M6	IsM6
Dominant	1/1 – 5/4 – 3/2 – 9/5	20:25:30:36	0, 10, 18, 26	P1 M3 P5 m7	I7
Mothwellsmic dominant	1/1 – 14/11 – 3/2 – 7/4	44:56:66:77	0, 11, 18, 25	P1 ^M3 P5 vm7	ISs7
Subminor supermajor Seven	1/1 – 7/6 – 3/2 – 21/11		0, 7, 18, 29	P1 vm3 P5 ^M7	IsS7
Augmented seven	1/1 – 5/4 – 25/16 – 7/4	16:20:25:28	0, 10, 20, 25	P1 M3 A5 vm7	Ih7(#5)
Half augmented	1/1 – 5/4 – 25/16 – 15/8	16:20:25:30	0, 10, 20, 28	P1 M3 A5 M7	IM7(#5)
Fully augmented	1/1 – 5/4 – 25/16 – 125/64		0, 10, 20, 30	P1 M3 A5 A7	I+7
Half diminished	1/1 – 6/5 – 36/25 – 9/5	25:30:36:45	0, 8, 16, 26	P1 m3 d5 m7	Im7(b5)
Fully diminished	1/1 – 25/21 – 10/7 – 12/7	21:25:30:36	0, 8, 16, 24	P1 m3 d5 d7	Io7
Harmonic half diminished	1/1 – 6/5 – 7/5 – 9/5	5:6:7:9	0, 8, 15, 26	P1 m3 vd5 m7	Im7(db5)
Harmonic fully diminished	1/1 – 6/5 – 7/5 – 17/10	10:12:14:17	0, 8, 15, 24	P1 m3 vd5 d7	Io7(db5)
Subminor half diminished	1/1 – 7/6 – 7/5 – 7/4		0, 7, 15, 25	P1 vm3 vd5 vm7	Is7(db5)
Augmented 3&7	1/1 – 13/10 – 3/2 – 39/20	20:26:30:39	0, 12, 18, 30	P1 A3 P5 A7	I(#3, #7)
Diminished 3&7	1/1 – 15/13 – 3/2 – 45/26	26:30:39:45	0, 6, 18, 24	P1 d3 P5 d7	I(bb3, bb7)
Doubly augmented major seven	1/1 – 5/4 – 13/8 – 15/8	8:10:13:15	0, 10, 22, 28	P1 M3 AA5 M7	IM7(x5)
Supermajor seven augmented	1/1 – 9/7 – 11/7 – 27/14	14:18:22:27	0, 11, 20, 29	P1 ^M3 A5 ^M7	IS7(#5)

Fifth-contained tetrads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Mu chord	1/1 – 9/8 – 5/4 – 3/2	8:9:10:12	0, 5, 10, 18	P1 M2 M3 P5	I(add2)
Nu chord	1/1 – 6/5 – 4/3 – 3/2	30:36:40:45	0, 8, 13, 18	P1 m3 P4 P5	Im(add4)
Subminor tetrad	1/1 – 7/6 – 4/3 – 3/2	6:7:8:9	0, 7, 13, 18	P1 vm3 P4 P5	Is(add4)
Supermajor tetrad	1/1 – 9/8 – 9/7 – 3/2	56:63:72:84	0, 5, 11, 18	P1 M2 ^M3 P5	IS(add2)
Super second tetrad	1/1 – 8/7 – 9/7 – 3/2	14:16:18:21	0, 6, 11, 18	P1 ^M2 ^M3 P5	IS(add t2)
Sub fourth tetrad	1/1 – 7/6 – 21/16 – 3/2	48:56:63:72	0, 7, 12, 18	P1 vm3 v4 P5	Is(add d4)
Sus 2/4	1/1 – 10/9 – 4/3 – 3/2	18:20:24:27	0, 5, 13, 18	P1 M2 P4 P5	Isus(2/4)
Add^4	1/1 – 5/4 – 11/8 – 3/2	8:10:11:12	0, 10, 14, 18	P1 M3 ^4 P5	I(add t4)
Minor addv2	1/1 – 12/11 – 6/5 – 3/2		0, 4, 8, 18	P1 ~2 m3 P5	Im(add d2)

Split chords	JI ratios	Harmonics	31edo steps	Intervals	Notation
Split chord	1/1 – 6/5 – 5/4 – 3/2	20:24:25:30	0, 8, 10, 18	P1 m3 M3 P5	IMm3
Septimal split chord	1/1 – 33/28 – 9/7 – 3/2	28:33:36:42	0, 7, 11, 18	P1 vm3 ^M3 P5	ISs3
Yellow/blue split chord	1/1 – 7/6 – 5/4 – 3/2	12:14:15:18	0, 7, 10, 18	P1 vm3 M3 P5	IMs3
Green/red split chord	1/1 – 6/5 – 9/7 – 3/2		0, 8, 11, 18	P1 m3 ^M3 P5	ISm3
Wolf split chord	1/1 – 25/21 – 9/7 – 32/21	21:25:27:32	0, 8, 11, 19	P1 m3 ^M3 ^5	ISm3(t5)
Squares split chord	1/1 – 27/22 – 14/11 – 18/11	22:27:28:36	0, 9, 11, 22	P1 ~3 ^M3 AA5	ISn3(#5)
DR split chord	1/1 – 7/6 – 5/4 – 35/24	24:28:30:35	0, 7, 10, 17	P1 vm3 M3 v5	IMs3(d5)

Harmonic subsets	JI ratios	Harmonics	31edo steps	Intervals	Notation
h9 shell	1/1 – 5/4 – 7/4 – 9/4	4:5:7:9	0, 10, 25, 36	P1 M3 vm7 M9	Ih9(no5)
Add11 shell	1/1 – 5/4 – 7/4 – 11/4	4:5:7:11	0, 10, 25, 45	P1 M3 vm7 ^11	Ih7t11(no5)
Quintal neutral	1/1 – 3/2 – 9/4 – 11/4	4:6:9:11	0, 18, 36, 45	P1 P5 M9 ^11	I59t11
Altered 13 shell	1/1 – 5/4 – 7/4 – 13/4	4:5:7:13	0, 10, 25, 53	P1 M3 vm7 ~13	Ih7d13(no5)
Add-13	1/1 – 5/4 – 3/2 – 13/4	4:5:6:13	0, 10, 18, 53	P1 M3 P5 ~13	I(add d13)
Altered 17 shell	1/1 – 5/4 – 7/4 – 17/8	8:10:14:17	0, 10, 25, 34	P1 M3 vm7 m9	Ih7b9(no5)
Altered 19 shell	1/1 – 5/4 – 7/4 – 19/8	8:10:14:19	0, 10, 25, 39	P1 M3 vm7 m10	Ih7b10(no5)

Misc tetrads	JI ratios	Harmonics	31edo steps	Intervals	Notation
h7#9 shell	1/1 – 5/4 – 7/4 – 7/3	12:15:21:28	0, 10, 25, 38	P1 M3 vm7 A9	Ih7#9(no5)
h7db9 shell	1/1 – 5/4 – 7/4 – 25/12	12:15:21:25	0, 10, 25, 33	P1 M3 vm7 vm9	Ih7db9(no5)
h7d9 shell	1/1 – 5/4 – 7/4 – 35/16	16:20:28:35	0, 10, 25, 35	P1 M3 vm7 ~9	Ih7d9(no5)
DRmaj	1/1 – 9/8 – 5/4 – 35/24	24:27:30:35	0, 5, 10, 17	P1 M2 M3 v5	I(add 2, d5)
DRmin	1/1 – 7/6 – 32/21 – 12/7	42:49:64:72	0, 7, 19, 24	P1 vm3 ^5 ^M6	IsS6(t5)
DRmindim	1/1 – 7/6 – 16/11 – 56/33		0, 7, 17, 24	P1 vm3 v5 ^M6	IsS6(d5)
DRsus	1/1 – 9/8 – 21/16 – 35/24	48:54:63:70	0, 5, 12, 17	P1 M2 v4 v5	Isus(2/d4)(d5)
Leading DRsus2	1/1 – 19/17 – 19/13 – 19/10		0, 5, 17, 29	P1 M2 v5 ^M7	IS7sus2(d5)
Mothwellsmic dominant #9 shell	1/1 – 14/11 – 7/4 – 7/3		0, 11, 25, 38	P1 ^M3 vm7 A9	ISs7#9(no5)
Orgone add9	1/1 – 11/8 – 7/4 – 9/4	8:11:14:18	0, 14, 25, 36	P1 ^4 vm7 M9	Ih9sus(t4)(no5)
Greeley over-3	1/1 – 7/6 – 5/3 – 11/6 – (13/6)	6:7:10:11:(13)	0, 7, 23, 27, (35)	P1 vm3 M6 ~7 (~9)	IsM6n7(no5)

Other linear tetrads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Slendric tetrad	1/1 – 8/7 – 55/42 – 3/2	42:48:55:63	0, 6, 12, 18	P1 ^M2 v4 P5	Isus(t2/d4)
Miracle cluster	1/1 – 14/13 – 15/13 – 16/13	13:14:15:16	0, 3, 6, 9	P1 m2 ^M2 ~3	I(13:14:15:16)
Orwell tetrad	1/1 – 7/6 – 11/8 – 77/48	48:56:66:77	0, 7, 14, 21	P1 vm3 ^4 m6	IO

Pentads

Main ninth chords	JI ratios	Harmonics	31edo steps	Intervals	Notation
Major nine	1/1 – 5/4 – 3/2 – 15/8 – 9/4	8:10:12:15:18	0, 10, 18, 28, 36	P1 M3 P5 M7 M9	IM9
Harmonic nine	1/1 – 5/4 – 3/2 – 7/4 – 9/4	4:5:6:7:9	0, 10, 18, 25, 36	P1 M3 P5 vm7 M9	Ih9
Minor nine	1/1 – 6/5 – 3/2 – 9/5 – 9/4	20:24:30:36:45	0, 8, 18, 26, 36	P1 m3 P5 m7 M9	Im9
Subminor nine	1/1 – 7/6 – 3/2 – 7/4 – 9/4	12:14:18:21:27	0, 7, 18, 25, 36	P1 vm3 P5 vm7 M9	Is9
Supermajor nine	1/1 – 9/7 – 3/2 – 27/14 – 9/4	28:36:42:54:63	0, 11, 18, 29, 36	P1 ^M3 P5 ^M7 M9	IS9
9-over pentad	1/1 – 9/7 – 3/2 – 9/5 – 9/4		0, 11, 18, 26, 36	P1 ^M3 P5 m7 M9	IS9b7
Neutral pentad	1/1 – 11/9 – 3/2 – 11/6 – 9/4	36:44:54:66:81	0, 9, 18, 27, 36	P1 ~3 P5 ~7 M9	In9

Other main pentads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Major 6/9	1/1 – 5/4 – 3/2 – 5/3 – 9/4	12:15:18:20:27	0, 10, 18, 23, 36	P1 M3 P5 M6 M9	I6/9
Minor 7/11	1/1 – 6/5 – 3/2 – 9/5 – 27/10	10:12:15:18:27	0, 8, 18, 26, 44	P1 m3 P5 m7 P11	Im7/11
Dominant nine	1/1 – 5/4 – 3/2 – 9/5 – 9/4	20:25:30:36:45	0, 10, 18, 26, 36	P1 M3 P5 m7 M9	I9
Tridecimal pentad	1/1 – 7/6 – 3/2 – 11/6 – 13/6	6:7:9:11:13	0, 7, 18, 27, 35	P1 vm3 P5 ~7 ~9	Isn7d9
Subminor 6/9	1/1 – 7/6 – 3/2 – 5/3 – 9/4	12:14:18:20:27	0, 7, 18, 23, 36	P1 vm3 P5 M6 M9	IsM6/9
Subminor 7/11	1/1 – 7/6 – 3/2 – 7/4 – 21/8	24:28:36:42:63	0, 7, 18, 25, 43	P1 vm3 P5 vm7 v11	Is7d11
Sub neutral 11	1/1 – 7/6 – 3/2 – 11/6 – 11/4	12:14:18:22:33	0, 7, 18, 27, 45	P1 vm3 P5 ~7 ^11	Isn7t11
Fully augmented #9	1/1 – 5/4 – 25/16 – 125/64 – 75/32		0, 10, 20, 30, 38	P1 M3 A5 A7 A9	I+7#9

Altered pentads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Harmonic #9	1/1 – 5/4 – 3/2 – 7/4 – 7/3	12:15:18:21:28	0, 10, 18, 25, 38	P1 M3 P5 vm7 A9	Ih7#9
Harmonic db9	1/1 – 5/4 – 3/2 – 7/4 – 25/12	12:15:18:21:25	0, 10, 18, 25, 33	P1 M3 P5 vm7 vm9	Ih7db9
Altered 13	1/1 – 5/4 – 3/2 – 7/4 – 13/4	4:5:6:7:13	0, 10, 18, 25, 53	P1 M3 P5 vm7 ~13	Ih7d13
Altered 13 #9 shell	1/1 – 5/4 – 7/4 – 7/3 – 13/4	12:15:21:28:39	0, 10, 25, 38, 53	P1 M3 vm7 A9 ~13	Ih7#9d13(no5)

Split pentads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Sub seventh split	1/1 – 7/6 – 5/4 – 3/2 – 7/4	12:14:15:18:21	0, 7, 10, 18, 25	P1 vm3 M3 P5 vm7	IMs3s7
Major seventh split	1/1 – 7/6 – 5/4 – 3/2 – 15/8	24:28:30:36:45	0, 7, 10, 18, 28	P1 vm3 M3 P5 M7	IMs3M7
Major sixth split	1/1 – 7/6 – 5/4 – 3/2 – 5/3	12:14:15:18:20	0, 7, 10, 18, 23	P1 vm3 M3 P5 M6	IMs3M6
Minor seventh split	1/1 – 6/5 – 9/7 – 3/2 – 9/5		0, 8, 11, 18, 26	P1 m3 ^M3 P5 m7	ISm3m7
Super seventh split	1/1 – 6/5 – 9/7 – 3/2 – 27/14		0, 8, 11, 18, 29	P1 m3 ^M3 P5 ^M7	ISm3S7
Super sixth split	1/1 – 6/5 – 9/7 – 3/2 – 12/7		0, 8, 11, 18, 24	P1 m3 ^M3 P5 ^M6	ISm3S6

Harmonic pentads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Orwell harmonic	1/1 – 5/4 – 3/2 – 7/4 – 11/4	4:5:6:7:11	0, 10, 18, 25, 45	P1 M3 P5 vm7 ^11	Ih7t11
Mohajira harmonic	1/1 – 5/4 – 3/2 – 9/4 – 11/4	4:5:6:9:11	0, 10, 18, 36, 45	P1 M3 P5 M9 ^11	Ih11(no7)
Tutone harmonic	1/1 – 5/4 – 7/4 – 9/4 – 11/4	4:5:7:9:11	0, 10, 25, 36, 45	P1 M3 vm7 M9 ^11	Ih11(no5)
Squares harmonic	1/1 – 3/2 – 7/4 – 9/4 – 11/4	4:6:7:9:11	0, 18, 25, 36, 45	P1 P5 vm7 M9 ^11	Ih11(no3)
Over-5 harmonic	1/1 – 6/5 – 7/5 – 9/5 – 11/5	5:6:7:9:11	0, 8, 15, 26, 35	P1 m3 vd5 m7 ~9	Im7d9(db5)
Miracle harmonic	1/1 – 5/4 – 7/4 – 13/4 – 17/4	4:5:7:13:17	0, 10, 25, 53, 65	P1 M3 vm7 ~13 m16	Ih7d13b16(no5)
A-Team harmonic	1/1 – 5/4 – 13/4 – 17/4 – 19/4	4:5:13:17:19	0, 10, 53, 65, 70	P1 M3 ~13 m16 m17	IMd13b16b17(no5)
Joan sharp harmonic	1/1 – 7/4 – 13/4 – 17/4 – 19/4	4:7:13:17:19	0, 25, 53, 65, 70	P1 vm7 ~13 m16 m17	Is7d13b16b17(no3, no5)
Joan flat harmonic	1/1 – 7/4 – 9/4 – 11/4 – 15/4	4:7:9:11:15	0, 25, 36, 45, 59	P1 vm7 M9 ^11 M14	I9s7t11M14(no3, no5)
Greeley harmonic	1/1 – 7/6 – 5/3 – 11/6 – 13/6	6:7:10:11:13	0, 7, 23, 27, 35	P1 vm3 M6 ~7 ~9	IsM6n7d9(no5)

Other linear pentads	JI ratios	Harmonics	31edo steps	Intervals	Notation
Slendric pentad	1/1 – 8/7 – 55/42 – 3/2 – 12/7	42:48:55:63:72	0, 6, 12, 18, 24	P1 ^M2 v4 P5 ^M6	IS6sus(t2, d4)
Miracle cluster	1/1 – 14/13 – 15/13 – 16/13 – 17/13	13:14:15:16:17	0, 3, 6, 9, 12	P1 m2 ^M2 ~3 v4	I(13:14:15:16:17)
Orwell pentad	1/1 – 7/6 – 11/8 – 77/48 – 15/8	48:56:66:77:90	0, 7, 14, 21, 28	P1 vm3 ^4 m6 M7	IOM7

Other extended chords

	JI ratios	Harmonics	31edo steps	Intervals	Notation	Comments
Undecimal hexad	1/1 – 5/4 – 3/2 – 7/4 – 9/4 – 11/4	4:5:6:7:9:11	0, 10, 18, 25, 36, 45	P1 M3 P5 vm7 M9 ^11	Ih11	The holy grail chord, a rich complex sound made up of the main harmonics in 31.
Novemdecimal hexad	1/1 – 5/4 – 7/4 – 13/4 – 17/4 – 19/4	4:5:7:13:17:19	0, 10, 25, 53, 65, 70	P1 M3 vm7 ~13 m16 m17	Ih7d13b16b17(no5)	All the sharp harmonics on a basic harmonic shell, works decently due to the extreme accuracy of the 13:17:19.
?	1/1 – 7/6 – 3/2 – 11/6 – 5/2 – 10/3	6:7:9:11:15:20	0, 7, 18, 27, 41, 54	P1 vm3 P5 ~7 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.
?	1/1 – 5/4 – 3/2 – 15/8 – 11/4 – 33/8	8:10:12:15:22:33	0, 10, 18, 28, 45, 63	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	1/1 – 6/5 – 3/2 – 9/5 – 11/5 – 27/10 – 33/10	10:12:15:18:22:27:33	0, 8, 18, 26, 35, 44, 53	P1 m3 P5 m7 ~9 P11 ~13	Im7/11n9n13	Subset chords excluding one of the tensions may be preferable to avoid chains of neutral thirds.
Graham hexad	1/1 – 5/4 – 3/2 – 7/4 – 7/3 – 11/4	12:15:18:21:28:33	0, 10, 18, 25, 38, 45	P1 M3 P5 vm7 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.
?	1/1 – 6/5 – 3/2 – 12/7 – 16/7 – 8/3		0, 8, 18, 24, 37, 44	P1 m3 P5 ^M6 ^M9 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.
?	1/1 – 5/4 – 3/2 – 7/4 – 21/8 – 63/16	16:20:24:28:42:63	0, 10, 18, 25, 43, 61	P1 M3 P5 vm7 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.
?	1/1 – 5/4 – 7/4 – 75/32 – 25/8 – 125/32		0, 10, 25, 38, 51, 61	P1 M3 vm7 A9 vm13 v15	Ih7#9db13d15(no5)	Extension of a standard jazz chord, with the 3:4:5 on top providing stability to balance the suboctave dissonance.
?	1/1 – 5/4 – 25/16 – 15/8 – 7/3 – 35/12		0, 10, 20, 28, 38, 48	P1 M3 A5 M7 A9 AA11	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	1/1 – 7/6 – 32/21 – 7/4 – 16/7 – 8/3		0, 7, 19, 25, 37, 44	P1 vm3 ^5 vm7 ^M9 P11	Is7/11t9(t5)	Subsets work well too, emphasizes the mothra sound through the superfifths and subfourths present.