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List of 31edo chords: Difference between revisions

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Added tetrads
Line 232: Line 232:
|Joan:2, Orwell:4, Tritonic:6, A-Team:8, Mohajira:10
|Joan:2, Orwell:4, Tritonic:6, A-Team:8, Mohajira:10
|}
|}
Note: $ used to represent shell voicing
Notes: $ used to represent shell voicing, DR means [[Delta-rational]].
 
 
== Tetrads ==
 
These tetrads are split into a few general categories.
 
{| class="wikitable"
!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
|}
 
 
 
{| class="wikitable"
!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
|I<sup>o</sup>7
|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
|I<sup>o</sup>7(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
|}
 
 
 
{| class="wikitable"
!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
|}
 
 
 
{| class="wikitable"
!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
|}
 
 
 
{| class="wikitable"
!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
|}
 
 
 
{| class="wikitable"
!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)
|}
 
 
 
{| class="wikitable"
!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
|}
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