List of 31edo chords: Difference between revisions

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remove "complexity" columns
Line 10: Line 10:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Major
!Major
Line 16: Line 15:
|P1 M3 P5
|P1 M3 P5
|I
|I
|Meantone:4, Würschmidt:8, Mohajira:8, Myna:10
|-
|-
!Minor
!Minor
Line 22: Line 20:
|P1 m3 P5
|P1 m3 P5
|Im
|Im
|Meantone:4, Würschmidt:8, Mohajira:8, Myna:10
|-
|-
!Subminor
!Subminor
Line 28: Line 25:
|P1 s3 P5
|P1 s3 P5
|Is
|Is
|Squares:5, Mothra:7, Orwell:7, Meantone:9
|-
|-
!Supermajor
!Supermajor
Line 34: Line 30:
|P1 S3 P5
|P1 S3 P5
|IS
|IS
|Squares:5, Mothra:7, Orwell:7, Meantone:9
|-
|-
!Neutral
!Neutral
Line 40: Line 35:
|P1 n3 P5
|P1 n3 P5
|In
|In
|Mohajira:2, Squares:4, Miracle:6, Würschmidt:8, Myna:10
|-
|-
!Augmented
!Augmented
Line 46: Line 40:
|P1 M3 A5
|P1 M3 A5
|I+
|I+
|Würschmidt:2, Tutone:4, Orwell:6, Meantone:8, Valentine:10
|-
|-
!Diminished
!Diminished
Line 52: Line 45:
|P1 m3 d5
|P1 m3 d5
|I<sup>o</sup>
|I<sup>o</sup>
|Myna:2, Nusecond:4, Meantone:6, Valentine:8, Joan:10
|-
|-
!Harmonic Diminished
!Harmonic Diminished
Line 58: Line 50:
|P1 m3 vd5
|P1 m3 vd5
|Im(db5)
|Im(db5)
|Myna:3, Nusecond:6, Meantone:9
|-
|-
!Subminor Diminished
!Subminor Diminished
Line 64: Line 55:
|P1 s3 vd5
|P1 s3 vd5
|Is(db5)
|Is(db5)
|Myna:3, Nusecond:6, Meantone:9
|-
|-
!Septimal Wolf Major
!Septimal Wolf Major
Line 70: Line 60:
|P1 S3 ^5
|P1 S3 ^5
|IS(t5)
|IS(t5)
|Nusecond:5, Würschmidt:7, Joan:8, Valentine:10
|-
|-
!Septimal Wolf Minor
!Septimal Wolf Minor
Line 76: Line 65:
|P1 m3 ^5
|P1 m3 ^5
|Im(t5)
|Im(t5)
|Nusecond:5, Würschmidt:7, Joan:8, Valentine:10
|-
|-
!Subfifth Minor
!Subfifth Minor
Line 82: Line 70:
|P1 m3 v5
|P1 m3 v5
|Im(d5)
|Im(d5)
|Mohajira:6, Joan:6, Myna:6
|-
|-
!Subfifth Neutral
!Subfifth Neutral
Line 88: Line 75:
|P1 n3 v5
|P1 n3 v5
|In(d5)
|In(d5)
|Mohajira:6, Joan:6, Myna:6
|-
|-
!DRmaj
!DRmaj
Line 94: Line 80:
|P1 M3 v5
|P1 M3 v5
|I(d5)
|I(d5)
|Orwell:3, A-Team:6, Myna:9
|-
|-
!DRmindim
!DRmindim
Line 100: Line 85:
|P1 s3 v5
|P1 s3 v5
|Is(d5)
|Is(d5)
|Orwell:3, A-Team:6, Myna:9
|-
|-
!Orwell
!Orwell
Line 106: Line 90:
|P1 s3 dd5
|P1 s3 dd5
|Is(bb5)
|Is(bb5)
|Orwell:2, A-Team:4, Myna:6, Mothra:8, Squares:10
|-
|-
!Squares
!Squares
Line 112: Line 95:
|P1 S3 AA5
|P1 S3 AA5
|IS(x5)
|IS(x5)
|Squares:2, Würschmidt:4, Joan:6, Tutone:8, Nusecond:10
|}
|}


Line 122: Line 104:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Double Diminished
!Double Diminished
Line 128: Line 109:
|P1 d3 d5
|P1 d3 d5
|I<sup>o</sup>(bb3)
|I<sup>o</sup>(bb3)
|Tutone:5, Miracle:7, Myna:9, Meantone:10
|-
|-
!Major b5
!Major b5
Line 134: Line 114:
|P1 M3 d5
|P1 M3 d5
|I(b5)
|I(b5)
|Tutone:5, Miracle:7, Myna:9, Meantone:10
|-
|-
!Minor Augmented
!Minor Augmented
Line 140: Line 119:
|P1 m3 A5
|P1 m3 A5
|Im+
|Im+
|Nusecond:5, Würschmidt:7, Joan:8
|-
|-
!Double Augmented
!Double Augmented
Line 146: Line 124:
|P1 A3 A5
|P1 A3 A5
|I+(#3)
|I+(#3)
|Nusecond:5, Würschmidt:7, Joan:8
|-
|-
!Doubly Augmented
!Doubly Augmented
Line 152: Line 129:
|P1 M3 AA5
|P1 M3 AA5
|I(x5)
|I(x5)
|Würschmidt:5, A-Team:7, Miracle:7, Mohajira:9
|-
|-
!Sus4
!Sus4
Line 158: Line 134:
|P1 P4 P5
|P1 P4 P5
|Isus4
|Isus4
|Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
|-
|-
!Sus2
!Sus2
Line 164: Line 139:
|P1 M2 P5
|P1 M2 P5
|Isus2
|Isus2
|Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
|-
|-
!Sus(t4)
!Sus(t4)
Line 170: Line 144:
|P1 ^4 P5
|P1 ^4 P5
|Isus(t4)
|Isus(t4)
|Mohajira:5, Orwell:7, Tritonic:8, Squares:10
|-
|-
!Sus(d4)
!Sus(d4)
Line 176: Line 149:
|P1 v4 P5
|P1 v4 P5
|Isus(d4)
|Isus(d4)
|Mothra:3, Miracle:6, Valentine:9, Tritonic:12
|-
|-
!Sus(t2)
!Sus(t2)
Line 182: Line 154:
|P1 ^2 P5
|P1 ^2 P5
|Isus(t2)
|Isus(t2)
|Mothra:3, Miracle:6, Valentine:9, Tritonic:12
|-
|-
!DRsus4
!DRsus4
Line 188: Line 159:
|P1 v4 v5
|P1 v4 v5
|Isus(d4)(d5)
|Isus(d4)(d5)
|A-Team:4, Mothra:8, Joan:8, Mohajira:9, Tritonic:10
|-
|-
!DRsus2
!DRsus2
Line 194: Line 164:
|P1 M2 v5
|P1 M2 v5
|Isus2(d5)
|Isus2(d5)
|A-Team:4, Mothra:8, Joan:8, Mohajira:9, Tritonic:10
|-
|-
!Terrain Triad
!Terrain Triad
Line 200: Line 169:
|P1 A4 m7
|P1 A4 m7
|I(db5)m7
|I(db5)m7
|Tutone:4, Meantone:8, Squares:8, Joan:10, Tritonic:10
|-
|-
!Harmonic Shell
!Harmonic Shell
Line 206: Line 174:
|P1 M3 s7
|P1 M3 s7
|Ih7$
|Ih7$
|Tutone:5, Miracle:7, Myna:9, Meantone:10, Tritonic:12
|-
|-
!Mothwellsmic Shell
!Mothwellsmic Shell
Line 212: Line 179:
|P1 S3 s7
|P1 S3 s7
|ISs7$
|ISs7$
|Joan:4, Orwell:8, Mothra:8, Tutone:9, Squares:10
|-
|-
!Orgone Triad
!Orgone Triad
Line 218: Line 184:
|P1 ^4 s7
|P1 ^4 s7
|Is7sus(t4)$
|Is7sus(t4)$
|Joan:4, Orwell:8, Mothra:8, Tutone:9, Squares:10
|-
|-
!Quartal
!Quartal
Line 224: Line 189:
|P1 P4 m7
|P1 P4 m7
|Iq
|Iq
|Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
|-
|-
!Joan
!Joan
Line 230: Line 194:
|P1 ^4 M7
|P1 ^4 M7
|IJ
|IJ
|Joan:2, Orwell:4, Tritonic:6, A-Team:8, Mohajira:10
|}
|}
Notes: $ used to represent shell voicing, DR means [[Delta-rational]].
Notes: $ used to represent shell voicing, DR means [[Delta-rational]].
Line 244: Line 207:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Major Seven
!Major Seven
Line 250: Line 212:
|P1 M3 P5 M7
|P1 M3 P5 M7
|IM7
|IM7
|Meantone:5, Würschmidt:9, Mohajira:10
|-
|-
!Harmonic Seven
!Harmonic Seven
Line 256: Line 217:
|P1 M3 P5 s7
|P1 M3 P5 s7
|Ih7
|Ih7
|Myna:10, Meantone:10, Orwell:11
|-
|-
!Minor Seven
!Minor Seven
Line 262: Line 222:
|P1 m3 P5 m7
|P1 m3 P5 m7
|Im7
|Im7
|Meantone:4, Mohajira:8
|-
|-
!Utonal Tetrad
!Utonal Tetrad
Line 268: Line 227:
|P1 m3 P5 S6
|P1 m3 P5 S6
|ImS6
|ImS6
|Myna:10, Meantone:10, Orwell:11
|-
|-
!Subminor Seven
!Subminor Seven
Line 274: Line 232:
|P1 s3 P5 s7
|P1 s3 P5 s7
|Is7
|Is7
|Mothra:7, Orwell:8, Squares:9, Meantone:10
|-
|-
!Undecimal Tetrad
!Undecimal Tetrad
Line 280: Line 237:
|P1 s3 P5 n7
|P1 s3 P5 n7
|Isn7
|Isn7
|Squares:6, Nusecond:11
|-
|-
!Supermajor Seven
!Supermajor Seven
Line 286: Line 242:
|P1 S3 P5 S7
|P1 S3 P5 S7
|IS7
|IS7
|Squares:5, Meantone:9, Mothra:10
|-
|-
!9-over Tetrad
!9-over Tetrad
Line 292: Line 247:
|P1 S3 P5 m7
|P1 S3 P5 m7
|ISm7
|ISm7
|Meantone:9, Nusecond:11
|-
|-
!Neutral Seven
!Neutral Seven
Line 298: Line 252:
|P1 n3 P5 n7
|P1 n3 P5 n7
|In7
|In7
|Mohajira:3, Squares:6, Miracle:9
|}
|}


Line 308: Line 261:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Lynch Neutral
!Lynch Neutral
Line 314: Line 266:
|P1 P5 n7 ^11
|P1 P5 n7 ^11
|I5n7t11
|I5n7t11
|Mohajira:5, Squares:10
|-
|-
!Neutral Minor Seven
!Neutral Minor Seven
Line 320: Line 271:
|P1 n3 P5 m7
|P1 n3 P5 m7
|Inm7
|Inm7
|Mohajira:6
|-
|-
!Neutral Major Tetrad
!Neutral Major Tetrad
Line 326: Line 276:
|P1 n3 P5 M6
|P1 n3 P5 M6
|InM6
|InM6
|Mohajira:6
|-
|-
!Subminor Major Tetrad
!Subminor Major Tetrad
Line 332: Line 281:
|P1 s3 P5 M6
|P1 s3 P5 M6
|IsM6
|IsM6
|Meantone:9, Nusecond:11
|-
|-
!Dominant
!Dominant
Line 338: Line 286:
|P1 M3 P5 m7
|P1 M3 P5 m7
|I7
|I7
|Meantone:6
|-
|-
!Mothwellsmic Dominant
!Mothwellsmic Dominant
Line 344: Line 291:
|P1 S3 P5 s7
|P1 S3 P5 s7
|ISs7
|ISs7
|Orwell:8, Squares:10
|-
|-
!Subminor Supermajor Seven
!Subminor Supermajor Seven
Line 350: Line 296:
|P1 s3 P5 S7
|P1 s3 P5 S7
|IsS7
|IsS7
|Squares:5, Würschmidt:10
|-
|-
!Augmented Seven
!Augmented Seven
Line 356: Line 301:
|P1 M3 A5 s7
|P1 M3 A5 s7
|Ih7(#5)
|Ih7(#5)
|Tutone:5, Meantone:10
|-
|-
!Half Augmented
!Half Augmented
Line 362: Line 306:
|P1 M3 A5 M7
|P1 M3 A5 M7
|IM7(#5)
|IM7(#5)
|Meantone:8, Würschmidt:9
|-
|-
!Fully Augmented
!Fully Augmented
Line 368: Line 311:
|P1 M3 A5 A7
|P1 M3 A5 A7
|I+7
|I+7
|Würschmidt:3, Tutone:6, Orwell:9
|-
|-
!Half Diminished
!Half Diminished
Line 374: Line 316:
|P1 m3 d5 m7
|P1 m3 d5 m7
|Im7(b5)
|Im7(b5)
|Meantone:6
|-
|-
!Fully Diminished
!Fully Diminished
Line 380: Line 321:
|P1 m3 d5 d7
|P1 m3 d5 d7
|I<sup>o</sup>7
|I<sup>o</sup>7
|Myna:3, Nusecond:6, Meantone:9
|-
|-
!Harmonic Half Diminished
!Harmonic Half Diminished
Line 386: Line 326:
|P1 m3 vd5 m7
|P1 m3 vd5 m7
|Im7(db5)
|Im7(db5)
|Meantone:9, Nusecond:11
|-
|-
!Harmonic Fully Diminished
!Harmonic Fully Diminished
Line 392: Line 331:
|P1 m3 vd5 d7
|P1 m3 vd5 d7
|I<sup>o</sup>7(db5)
|I<sup>o</sup>7(db5)
|Myna:5, Nusecond:10, A-Team:11
|-
|-
!Subminor Half Diminished
!Subminor Half Diminished
Line 398: Line 336:
|P1 s3 vd5 s7
|P1 s3 vd5 s7
|Is7(db5)
|Is7(db5)
|Myna:10, Meantone:10, Orwell:11
|-
|-
!Augmented 3&7
!Augmented 3&7
Line 404: Line 341:
|P1 A3 P5 A7
|P1 A3 P5 A7
|I(#3,#7)
|I(#3,#7)
|Mothra:5, Miracle:10
|-
|-
!Diminished 3&7
!Diminished 3&7
Line 410: Line 346:
|P1 d3 P5 d7
|P1 d3 P5 d7
|I(bb3,bb7)
|I(bb3,bb7)
|Mothra:4, Miracle:8
|-
|-
!Doubly Augmented Major Seven
!Doubly Augmented Major Seven
Line 416: Line 351:
|P1 M3 AA5 M7
|P1 M3 AA5 M7
|IM7(x5)
|IM7(x5)
|Miracle:7, Mohajira:11
|-
|-
!Supermajor Seven Augmented
!Supermajor Seven Augmented
Line 422: Line 356:
|P1 S3 A5 S7
|P1 S3 A5 S7
|IS7(#5)
|IS7(#5)
|Squares:4, Würschmidt:8
|}
|}


Line 432: Line 365:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Mu Chord
!Mu Chord
Line 438: Line 370:
|P1 M2 M3 P5
|P1 M2 M3 P5
|I(add2)
|I(add2)
|Meantone:4, Mohajira:8
|-
|-
!Nu Chord
!Nu Chord
Line 444: Line 375:
|P1 m3 P4 P5
|P1 m3 P4 P5
|Im(add4)
|Im(add4)
|Meantone:4, Mohajira:8
|-
|-
!Subminor Tetrad
!Subminor Tetrad
Line 450: Line 380:
|P1 s3 P4 P5
|P1 s3 P4 P5
|Is(add4)
|Is(add4)
|Mothra:7, Squares:9, Meantone:10
|-
|-
!Supermajor Tetrad
!Supermajor Tetrad
Line 456: Line 385:
|P1 M2 S3 P5
|P1 M2 S3 P5
|IS(add2)
|IS(add2)
|Mothra:7, Squares:9, Meantone:10
|-
|-
!Super Second Tetrad
!Super Second Tetrad
Line 462: Line 390:
|P1 S2 S3 P5
|P1 S2 S3 P5
|IS(add t2)
|IS(add t2)
|Mothra:7, Meantone:11
|-
|-
!Sub Fourth Tetrad
!Sub Fourth Tetrad
Line 468: Line 395:
|P1 s3 v4 P5
|P1 s3 v4 P5
|Is(add d4)
|Is(add d4)
|Mothra:7, Meantone:11
|-
|-
!Sus 2/4
!Sus 2/4
Line 474: Line 400:
|P1 M2 P4 P5
|P1 M2 P4 P5
|Isus(2/4)
|Isus(2/4)
|Meantone:3, Mohajira:6, Mothra:9
|-
|-
!Add^4
!Add^4
Line 480: Line 405:
|P1 M3 ^4 P5
|P1 M3 ^4 P5
|I(add t4)
|I(add t4)
|Mohajira:8, Valentine:9, Orwell:10
|-
|-
!Minor Addv2
!Minor Addv2
Line 486: Line 410:
|P1 n2 m3 P5
|P1 n2 m3 P5
|Im(add d2)
|Im(add d2)
|Mohajira:8, Valentine:9, Orwell:10
|}
|}


Line 496: Line 419:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Split Chord
!Split Chord
Line 502: Line 424:
|P1 m3 M3 P5
|P1 m3 M3 P5
|IMm3
|IMm3
|Meantone:7, Würschmidt:8, Valentine:9, Myna:10
|-
|-
!Septimal Split Chord
!Septimal Split Chord
Line 508: Line 429:
|P1 s3 S3 P5
|P1 s3 S3 P5
|ISs3
|ISs3
|Squares:6, Orwell:7, Nusecond:11
|-
|-
!Yellow/Blue Split Chord
!Yellow/Blue Split Chord
Line 514: Line 434:
|P1 s3 M3 P5
|P1 s3 M3 P5
|IMs3
|IMs3
|Meantone:9, Orwell:10
|-
|-
!Green/Red Split Chord
!Green/Red Split Chord
Line 520: Line 439:
|P1 m3 S3 P5
|P1 m3 S3 P5
|ISm3
|ISm3
|Meantone:9, Orwell:10
|-
|-
!Wolf Split Chord
!Wolf Split Chord
Line 526: Line 444:
|P1 m3 S3 ^5
|P1 m3 S3 ^5
|ISm3(t5)
|ISm3(t5)
|Nusecond:7, Joan:8, Würschmidt:9
|-
|-
!Squares Split Chord
!Squares Split Chord
Line 532: Line 449:
|P1 n3 S3 A5
|P1 n3 S3 A5
|ISn3(#5)
|ISn3(#5)
|Squares:3, Würschmidt:6, Joan:9
|-
|-
!DR Split Chord
!DR Split Chord
Line 538: Line 454:
|P1 s3 M3 v5
|P1 s3 M3 v5
|IMs3(d5)
|IMs3(d5)
|Orwell:4, A-Team:8
|}
|}


Line 548: Line 463:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!h9 Shell
!h9 Shell
Line 554: Line 468:
|P1 M3 s7 M9
|P1 M3 s7 M9
|Ih9$
|Ih9$
|Tutone:5, Meantone:10
|-
|-
!Add11 Shell
!Add11 Shell
Line 560: Line 473:
|P1 M3 s7 ^11
|P1 M3 s7 ^11
|Ih7t11$
|Ih7t11$
|Tutone:9, Valentine:11, Tritonic:12
|-
|-
!Quintal Neutral
!Quintal Neutral
Line 566: Line 478:
|P1 P5 M9 ^11
|P1 P5 M9 ^11
|I59t11
|I59t11
|Mohajira:5, Squares:10
|-
|-
!Altered-13 Shell
!Altered-13 Shell
Line 572: Line 483:
|P1 M3 s7 n13
|P1 M3 s7 n13
|Ih7d13$
|Ih7d13$
|Miracle:7
|-
|-
!Add-13
!Add-13
Line 578: Line 488:
|P1 M3 P5 n13
|P1 M3 P5 n13
|I(add d13)
|I(add d13)
|Mohajira:9, Valentine:11
|-
|-
!Altered-17 Shell
!Altered-17 Shell
Line 584: Line 493:
|P1 M3 s7 m9
|P1 M3 s7 m9
|Ih7b9$
|Ih7b9$
|Miracle:7
|-
|-
!Altered-19 Shell
!Altered-19 Shell
Line 590: Line 498:
|P1 M3 s7 m10
|P1 M3 s7 m10
|Ih7b10$
|Ih7b10$
|Valentine:8, Myna:10
|}
|}


Line 600: Line 507:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!h7#9 Shell
!h7#9 Shell
Line 606: Line 512:
|P1 M3 s7 A9
|P1 M3 s7 A9
|Ih7#9$
|Ih7#9$
|Miracle:8, Meantone:10
|-
|-
!h7db9 Shell
!h7db9 Shell
Line 612: Line 517:
|P1 M3 s7 s9
|P1 M3 s7 s9
|Ih7db9$
|Ih7db9$
|Valentine:8, Meantone:10
|-
|-
!h7d9 Shell
!h7d9 Shell
Line 618: Line 522:
|P1 M3 s7 n9
|P1 M3 s7 n9
|Ih7d9$
|Ih7d9$
|Tutone:7, Valentine:8, Miracle:9, Orwell:11
|-
|-
!DRmaj
!DRmaj
Line 624: Line 527:
|P1 M2 M3 v5
|P1 M2 M3 v5
|I(add 2, d5)
|I(add 2, d5)
|A-Team:6
|-
|-
!DRmin
!DRmin
Line 630: Line 532:
|P1 s3 ^5 S6
|P1 s3 ^5 S6
|IsS6(t5)
|IsS6(t5)
|A-Team:4, Mothra:8
|-
|-
!DRmindim
!DRmindim
Line 636: Line 537:
|P1 s3 v5 S6
|P1 s3 v5 S6
|IsS6(d5)
|IsS6(d5)
|Orwell:3, A-Team:6, Myna:9
|-
|-
!DRsus
!DRsus
Line 642: Line 542:
|P1 M2 v4 v5
|P1 M2 v4 v5
|Isus(2/d4)(d5)
|Isus(2/d4)(d5)
|A-Team:4, Mothra:8
|-
|-
!Leading DRsus2
!Leading DRsus2
Line 648: Line 547:
|P1 M2 v5 S7
|P1 M2 v5 S7
|IS7sus2(d5)
|IS7sus2(d5)
|A-Team:5, Mothra:10
|-
|-
!Mothwellsmic Dominant #9 Shell
!Mothwellsmic Dominant #9 Shell
Line 654: Line 552:
|P1 S3 s7 A9
|P1 S3 s7 A9
|ISs7#9$
|ISs7#9$
|Orwell:8, Mothra:8, Squares:10
|-
|-
!Orgone add9
!Orgone add9
Line 660: Line 557:
|P1 ^4 s7 M9
|P1 ^4 s7 M9
|Ih9sus(t4)$
|Ih9sus(t4)$
|Joan:7, Tutone:9, Squares:10
|-
|-
!Greeley Over-3
!Greeley Over-3
Line 666: Line 562:
|P1 s3 M6 n7 (n9)
|P1 s3 M6 n7 (n9)
|IsM6n7$
|IsM6n7$
|Nusecond:6(7)
|}
|}


Line 676: Line 571:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Slendric Tetrad
!Slendric Tetrad
Line 682: Line 576:
|P1 S2 v4 P5
|P1 S2 v4 P5
|Isus(t2/d4)
|Isus(t2/d4)
|Mothra:3, Miracle:6, Valentine:9
|-
|-
!Miracle Cluster
!Miracle Cluster
Line 688: Line 581:
|P1 m2 S2 n3
|P1 m2 S2 n3
|I(13:14:15:16)
|I(13:14:15:16)
|Miracle:3, Joan:6, Slender:9
|-
|-
!Orwell Tetrad
!Orwell Tetrad
Line 694: Line 586:
|P1 s3 ^4 m6
|P1 s3 ^4 m6
|IO
|IO
|Orwell:3, A-Team:6, Myna:9
|}
|}


Line 704: Line 595:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Major Nine
!Major Nine
Line 710: Line 600:
|P1 M3 P5 M7 M9
|P1 M3 P5 M7 M9
|IM9
|IM9
|Meantone:5, Mohajira:10
|-
|-
!Harmonic Nine
!Harmonic Nine
Line 716: Line 605:
|P1 M3 P5 s7 M9
|P1 M3 P5 s7 M9
|Ih9
|Ih9
|Meantone:10
|-
|-
!Minor Nine
!Minor Nine
Line 722: Line 610:
|P1 m3 P5 m7 M9
|P1 m3 P5 m7 M9
|Im9
|Im9
|Meantone:5, Mohajira:10
|-
|-
!Subminor Nine
!Subminor Nine
Line 728: Line 615:
|P1 s3 P5 s7 M9
|P1 s3 P5 s7 M9
|Is9
|Is9
|Squares:9, Meantone:10, Mothra:10
|-
|-
!Supermajor Nine
!Supermajor Nine
Line 734: Line 620:
|P1 S3 P5 S7 M9
|P1 S3 P5 S7 M9
|IS9
|IS9
|Squares:9, Meantone:10, Mothra:10
|-
|-
!9-over Pentad
!9-over Pentad
Line 740: Line 625:
|P1 S3 P5 m7 M9
|P1 S3 P5 m7 M9
|IS9b7
|IS9b7
|Meantone:10
|-
|-
!Neutral Pentad
!Neutral Pentad
Line 746: Line 630:
|P1 n3 P5 n7 M9
|P1 n3 P5 n7 M9
|In9
|In9
|Mohajira:4, Squares:8, Miracle:12
|}
|}


Line 756: Line 639:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Major 6/9
!Major 6/9
Line 762: Line 644:
|P1 M3 P5 M6 M9
|P1 M3 P5 M6 M9
|I6/9
|I6/9
|Meantone:4, Mohajira:8, Slendric:12
|-
|-
!Minor 7/11
!Minor 7/11
Line 768: Line 649:
|P1 m3 P5 m7 P11
|P1 m3 P5 m7 P11
|Im7/11
|Im7/11
|Meantone:4, Mohajira:8, Slendric:12
|-
|-
!Dominant Nine
!Dominant Nine
Line 774: Line 654:
|P1 M3 P5 m7 M9
|P1 M3 P5 m7 M9
|I9
|I9
|Meantone:6, Mohajira:12
|-
|-
!Tridecimal Pentad
!Tridecimal Pentad
Line 780: Line 659:
|P1 s3 P5 n7 n9
|P1 s3 P5 n7 n9
|Isn7d9
|Isn7d9
|Squares:12
|-
|-
!Subminor 6/9
!Subminor 6/9
Line 786: Line 664:
|P1 s3 P5 M6 M9
|P1 s3 P5 M6 M9
|IsM6/9
|IsM6/9
|Meantone:9
|-
|-
!Subminor 7/11
!Subminor 7/11
Line 792: Line 669:
|P1 s3 P5 s7 v11
|P1 s3 P5 s7 v11
|Is7d11
|Is7d11
|Mothra:7, Meantone:11
|-
|-
!Sub Neutral 11
!Sub Neutral 11
Line 798: Line 674:
|P1 s3 P5 n7 ^11
|P1 s3 P5 n7 ^11
|Isn7t11
|Isn7t11
|Squares:10, Nusecond:12
|-
|-
!Fully Augmented #9
!Fully Augmented #9
Line 804: Line 679:
|P1 M3 A5 A7 A9
|P1 M3 A5 A7 A9
|I+7#9
|I+7#9
|Orwell:10, Würschmidt:10
|}
|}


Line 814: Line 688:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Harmonic #9
!Harmonic #9
Line 820: Line 693:
|P1 M3 P5 s7 A9
|P1 M3 P5 s7 A9
|Ih7#9
|Ih7#9
|Meantone:10
|-
|-
!Harmonic db9
!Harmonic db9
Line 826: Line 698:
|P1 M3 P5 s7 s9
|P1 M3 P5 s7 s9
|Ih7db9
|Ih7db9
|Meantone:10, Myna:10
|-
|-
!Altered-13
!Altered-13
Line 832: Line 703:
|P1 M3 P5 s7 n13
|P1 M3 P5 s7 n13
|Ih7d13
|Ih7d13
|Miracle:13, Valentine:14
|-
|-
!Altered-13 #9 Shell
!Altered-13 #9 Shell
Line 838: Line 708:
|P1 M3 s7 A9 n13
|P1 M3 s7 A9 n13
|Ih7#9d13$
|Ih7#9d13$
|Miracle:8
|}
|}


Line 848: Line 717:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Sub Seventh Split
!Sub Seventh Split
Line 854: Line 722:
|P1 s3 M3 P5 s7
|P1 s3 M3 P5 s7
|IMs3s7
|IMs3s7
|Meantone:10, Orwell:11
|-
|-
!Major Seventh Split
!Major Seventh Split
Line 860: Line 727:
|P1 s3 M3 P5 M7
|P1 s3 M3 P5 M7
|IMs3M7
|IMs3M7
|Meantone:9, Orwell:10, Würschmidt:10
|-
|-
!Major Sixth Split
!Major Sixth Split
Line 866: Line 732:
|P1 s3 M3 P5 M6
|P1 s3 M3 P5 M6
|IMs3M6
|IMs3M6
|Meantone:9, Nusecond:13
|-
|-
!Minor Seventh Split
!Minor Seventh Split
Line 872: Line 737:
|P1 m3 S3 P5 m7
|P1 m3 S3 P5 m7
|ISm3m7
|ISm3m7
|Meantone:9, Nusecond:13
|-
|-
!Super Seventh Split
!Super Seventh Split
Line 878: Line 742:
|P1 m3 S3 P5 S7
|P1 m3 S3 P5 S7
|ISm3S7
|ISm3S7
|Meantone:9, Würschmidt:10
|-
|-
!Super Sixth Split
!Super Sixth Split
Line 884: Line 747:
|P1 m3 S3 P5 S6
|P1 m3 S3 P5 S6
|ISm3S6
|ISm3S6
|Meantone:10, Orwell:11
|}
|}


Line 894: Line 756:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Orwell Harmonic
!Orwell Harmonic
Line 900: Line 761:
|P1 M3 P5 s7 ^11
|P1 M3 P5 s7 ^11
|Ih7t11
|Ih7t11
|Orwell:11, Valentine:12
|-
|-
!Mohajira Harmonic
!Mohajira Harmonic
Line 906: Line 766:
|P1 M3 P5 M9 ^11
|P1 M3 P5 M9 ^11
|Ih11(no7)
|Ih11(no7)
|Mohajira:8
|-
|-
!Tutone Harmonic
!Tutone Harmonic
Line 912: Line 771:
|P1 M3 s7 M9 ^11
|P1 M3 s7 M9 ^11
|Ih11$
|Ih11$
|Tutone:9
|-
|-
!Squares Harmonic
!Squares Harmonic
Line 918: Line 776:
|P1 P5 s7 M9 ^11
|P1 P5 s7 M9 ^11
|Ih11(no3)
|Ih11(no3)
|Squares:10
|-
|-
!Over-5 Harmonic
!Over-5 Harmonic
Line 924: Line 781:
|P1 m3 vb5 m7 n9
|P1 m3 vb5 m7 n9
|Im7d9(db5)
|Im7d9(db5)
|Squares:12
|-
|-
!Miracle Harmonic
!Miracle Harmonic
Line 930: Line 786:
|P1 M3 s7 n13 m16
|P1 M3 s7 n13 m16
|Ih7d13b16$
|Ih7d13b16$
|Miracle:8
|-
|-
!A-Team Harmonic
!A-Team Harmonic
Line 936: Line 791:
|P1 M3 n13 m16 m17
|P1 M3 n13 m16 m17
|IMd13b16b17$
|IMd13b16b17$
|A-Team:11
|-
|-
!Joan Sharp Harmonic
!Joan Sharp Harmonic
Line 942: Line 796:
|P1 s7 n13 m16 m17
|P1 s7 n13 m16 m17
|I5s7d13b16b17$
|I5s7d13b16b17$
|Joan:8
|-
|-
!Joan Flat Harmonic
!Joan Flat Harmonic
Line 948: Line 801:
|P1 s7 M9 ^11 M14
|P1 s7 M9 ^11 M14
|I59s7t11M14$
|I59s7t11M14$
|Joan:7
|-
|-
!Greeley Harmonic
!Greeley Harmonic
Line 954: Line 806:
|P1 s3 M6 n7 n9
|P1 s3 M6 n7 n9
|IsM6n7d9$
|IsM6n7d9$
|Nusecond:7
|}
|}


Line 964: Line 815:
!Notes
!Notes
!Notation
!Notation
!Complexity in Temperaments
|-
|-
!Slendric Pentad
!Slendric Pentad
Line 970: Line 820:
|P1 S2 v4 P5 S6
|P1 S2 v4 P5 S6
|IS6sus(t2,d4)
|IS6sus(t2,d4)
|Mothra:4, Miracle:8, Valentine:12
|-
|-
!Miracle Cluster
!Miracle Cluster
Line 976: Line 825:
|P1 m2 S2 n3 v4
|P1 m2 S2 n3 v4
|I(13:14:15:16:17)
|I(13:14:15:16:17)
|Miracle:4, Joan:8, Slender:12
|-
|-
!Orwell Pentad
!Orwell Pentad
Line 982: Line 830:
|P1 s3 ^4 m6 M7
|P1 s3 ^4 m6 M7
|IOM7
|IOM7
|Orwell:4, A-Team:8, Myna:12
|}
|}


Revision as of 15:33, 7 October 2026

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
Major 4:5:6 P1 M3 P5 I
Minor 6/5/4 P1 m3 P5 Im
Subminor 6:7:9 P1 s3 P5 Is
Supermajor 9/7/6 P1 S3 P5 IS
Neutral 18:22:27 P1 n3 P5 In
Augmented 16:20:25 P1 M3 A5 I+
Diminished 25:30:36 P1 m3 d5 Io
Harmonic Diminished 5:6:7 P1 m3 vd5 Im(db5)
Subminor Diminished 7/6/5 P1 s3 vd5 Is(db5)
Septimal Wolf Major 21:27:32 P1 S3 ^5 IS(t5)
Septimal Wolf Minor 21:25:32 P1 m3 ^5 Im(t5)
Subfifth Minor 15:18:22 P1 m3 v5 Im(d5)
Subfifth Neutral 22/18/15 P1 n3 v5 In(d5)
DRmaj 24:30:35 P1 M3 v5 I(d5)
DRmindim 24:28:35 P1 s3 v5 Is(d5)
Orwell 24:28:33 P1 s3 dd5 Is(bb5)
Squares 11:14:18 P1 S3 AA5 IS(x5)


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

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
Major Seven 8:10:12:15 P1 M3 P5 M7 IM7
Harmonic Seven 4:5:6:7 P1 M3 P5 s7 Ih7
Minor Seven 10:12:15:18 P1 m3 P5 m7 Im7
Utonal Tetrad 12/10/8/7 P1 m3 P5 S6 ImS6
Subminor Seven 12:14:18:21 P1 s3 P5 s7 Is7
Undecimal Tetrad 6:7:9:11 P1 s3 P5 n7 Isn7
Supermajor Seven 14:18:21:27 P1 S3 P5 S7 IS7
9-over Tetrad 9/7/6/5 P1 S3 P5 m7 ISm7
Neutral Seven 18:22:27:33 P1 n3 P5 n7 In7


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


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


Split Chords Otonal/Utonal Representation Notes Notation
Split Chord 20:24:25:30 P1 m3 M3 P5 IMm3
Septimal Split Chord 28:33:36:42 P1 s3 S3 P5 ISs3
Yellow/Blue Split Chord 12:14:15:18 P1 s3 M3 P5 IMs3
Green/Red Split Chord 18/15/14/12 P1 m3 S3 P5 ISm3
Wolf Split Chord 21:25:27:32 P1 m3 S3 ^5 ISm3(t5)
Squares Split Chord 22:27:28:36 P1 n3 S3 A5 ISn3(#5)
DR Split Chord 24:28:30:35 P1 s3 M3 v5 IMs3(d5)


Harmonic Subsets Otonal/Utonal Representation Notes Notation
h9 Shell 4:5:7:9 P1 M3 s7 M9 Ih9$
Add11 Shell 4:5:7:11 P1 M3 s7 ^11 Ih7t11$
Quintal Neutral 4:6:9:11 P1 P5 M9 ^11 I59t11
Altered-13 Shell 4:5:7:13 P1 M3 s7 n13 Ih7d13$
Add-13 4:5:6:13 P1 M3 P5 n13 I(add d13)
Altered-17 Shell 8:10:14:17 P1 M3 s7 m9 Ih7b9$
Altered-19 Shell 8:10:14:19 P1 M3 s7 m10 Ih7b10$


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


Other Linear Tetrads Otonal/Utonal Representation Notes Notation
Slendric Tetrad 42:48:55:63 P1 S2 v4 P5 Isus(t2/d4)
Miracle Cluster 13:14:15:16 P1 m2 S2 n3 I(13:14:15:16)
Orwell Tetrad 48:56:66:77 P1 s3 ^4 m6 IO

Pentads

Main Ninth Chords Otonal/Utonal Representation Notes Notation
Major Nine 8:10:12:15:18 P1 M3 P5 M7 M9 IM9
Harmonic Nine 4:5:6:7:9 P1 M3 P5 s7 M9 Ih9
Minor Nine 18/15/12/10/8 P1 m3 P5 m7 M9 Im9
Subminor Nine 12:14:18:21:27 P1 s3 P5 s7 M9 Is9
Supermajor Nine 27/21/18/14/12 P1 S3 P5 S7 M9 IS9
9-over Pentad 9/7/6/5/4 P1 S3 P5 m7 M9 IS9b7
Neutral Pentad 36:44:54:66:81 P1 n3 P5 n7 M9 In9


Other Main Pentads Otonal/Utonal Representation Notes Notation
Major 6/9 12:15:18:20:27 P1 M3 P5 M6 M9 I6/9
Minor 7/11 10:12:15:18:27 P1 m3 P5 m7 P11 Im7/11
Dominant Nine 20:25:30:36:45 P1 M3 P5 m7 M9 I9
Tridecimal Pentad 6:7:9:11:13 P1 s3 P5 n7 n9 Isn7d9
Subminor 6/9 12:14:18:20:27 P1 s3 P5 M6 M9 IsM6/9
Subminor 7/11 24:28:36:42:63 P1 s3 P5 s7 v11 Is7d11
Sub Neutral 11 12:14:18:22:33 P1 s3 P5 n7 ^11 Isn7t11
Fully Augmented #9 64:80:100:125:150 P1 M3 A5 A7 A9 I+7#9


Altered Pentads Otonal/Utonal Representation Notes Notation
Harmonic #9 12:15:18:21:28 P1 M3 P5 s7 A9 Ih7#9
Harmonic db9 12:15:18:21:25 P1 M3 P5 s7 s9 Ih7db9
Altered-13 4:5:6:7:13 P1 M3 P5 s7 n13 Ih7d13
Altered-13 #9 Shell 12:15:21:28:39 P1 M3 s7 A9 n13 Ih7#9d13$


Split Pentads Otonal/Utonal Representation Notes Notation
Sub Seventh Split 12:14:15:18:21 P1 s3 M3 P5 s7 IMs3s7
Major Seventh Split 24:28:30:36:45 P1 s3 M3 P5 M7 IMs3M7
Major Sixth Split 12:14:15:18:20 P1 s3 M3 P5 M6 IMs3M6
Minor Seventh Split 18/15/14/12/10 P1 m3 S3 P5 m7 ISm3m7
Super Seventh Split 54/45/42/36/28 P1 m3 S3 P5 S7 ISm3S7
Super Sixth Split 36/30/28/24/21 P1 m3 S3 P5 S6 ISm3S6


Harmonic Pentads Otonal/Utonal Representation Notes Notation
Orwell Harmonic 4:5:6:7:11 P1 M3 P5 s7 ^11 Ih7t11
Mohajira Harmonic 4:5:6:9:11 P1 M3 P5 M9 ^11 Ih11(no7)
Tutone Harmonic 4:5:7:9:11 P1 M3 s7 M9 ^11 Ih11$
Squares Harmonic 4:6:7:9:11 P1 P5 s7 M9 ^11 Ih11(no3)
Over-5 Harmonic 5:6:7:9:11 P1 m3 vb5 m7 n9 Im7d9(db5)
Miracle Harmonic 4:5:7:13:17 P1 M3 s7 n13 m16 Ih7d13b16$
A-Team Harmonic 4:5:13:17:19 P1 M3 n13 m16 m17 IMd13b16b17$
Joan Sharp Harmonic 4:7:13:17:19 P1 s7 n13 m16 m17 I5s7d13b16b17$
Joan Flat Harmonic 4:7:9:11:15 P1 s7 M9 ^11 M14 I59s7t11M14$
Greeley Harmonic 6:7:10:11:13 P1 s3 M6 n7 n9 IsM6n7d9$


Other Linear Pentads Otonal/Utonal Representation Notes Notation
Slendric Pentad 42:48:55:63:72 P1 S2 v4 P5 S6 IS6sus(t2,d4)
Miracle Cluster 13:14:15:16:17 P1 m2 S2 n3 v4 I(13:14:15:16:17)
Orwell Pentad 48:56:66:77:90 P1 s3 ^4 m6 M7 IOM7


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.
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