User:Flirora/31edo chords: Difference between revisions

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{| class="wikitable sortable"
{| class="wikitable sortable"
|+A list of chords in [[31edo]]
|+ An incomplete list of chords in [[31edo]]
!Name
! Name
!Symbol
! Symbol
!Notation (from C)
! Symbol (Kite)
!Steps
! Notation (from C)
!Approximate JI
! Steps
!Notes
! Approximate JI
! Notes
|-
|-
|major
| major
|(M)
| (M)
|C E G
| (M)
|0 10 18
| C E G
|4:5:6
| 0 10 18
| 4:5:6
|
|
|-
|-
|minor
| minor
|m
| m
|C Eb G
| m
|0 8 18
| C Eb G
|10:12:15
| 0 8 18
| 10:12:15
|
|
|-
|-
|neutral
| neutral
|n
| n
|C Ed G
| ~
|0 9 18
| C Ed G
|18:22:27
| 0 9 18
| 18:22:27
|
|
|-
|-
|subminor
| subminor
|sm
| sm
|C Edb G
| vm
|0 7 18
| C Edb G
|6:7:9
| 0 7 18
| 6:7:9
|
|
|-
|-
|supermajor
| supermajor
|SM
| SM
|C Et G
| ^
|0 11 18
| C Et G
|14:18:21
| 0 11 18
| 14:18:21
|
|
|-
|-
|suspended 4
| suspended 4
|sus4
| sus4
|C F G
| 4
|0 13 18
| C F G
|6:8:9
| 0 13 18
| 6:8:9
|
|
|-
|-
|suspended 2
| suspended 2
|sus2
| sus2
|C D G
| 2
|0 5 18
| C D G
|8:9:12
| 0 5 18
| 8:9:12
|
|
|-
|-
|suspended d4
| suspended d4
|susd4
| susd4
|C Fd G
| (v4)
|0 12 18
| C Fd G
|16:21:24
| 0 12 18
| 16:21:24
|
|
|-
|-
|suspended t4
| suspended t4
|sust4
| sust4
|C Ft G
| (^4)
|0 14 18
| C Ft G
|8:11:12
| 0 14 18
| 8:11:12
|
|
|-
|-
|suspended #4
| suspended #4
|sus#4
| sus#4
|C F# G
| (#4)
|0 15 18
| C F# G
|10:14:15
| 0 15 18
| 10:14:15
|
|
|-
|-
|suspended t2
| suspended t2
|sust2
| sust2
|C Dt G
| (^2)
|0 6 18
| C Dt G
|14:16:21
| 0 6 18
| 14:16:21
|
|
|-
|-
|suspended d2
| suspended d2
|susd2
| susd2
|C Dd G
| (v2)
|0 4 18
| C Dd G
|10:11:15
| 0 4 18
| 10:11:15
|
|
|-
|-
|suspended b2
| suspended b2
|susb2
| susb2
|C Db G
| (b2)
|0 3 18
| C Db G
|14:15:21
| 0 3 18
| 14:15:21
|
|
|-
|-
|major 7th
| major 7th
|M7
| M7
|C E G B
| M7
|0 10 18 28
| C E G B
|8:10:12:15
| 0 10 18 28
| 8:10:12:15
|
|
|-
|-
|minor 7th
| minor 7th
|m7
| m7
|C Eb G Bb
| m7
|0 8 18 26
| C Eb G Bb
|10:12:15:18
| 0 8 18 26
| 10:12:15:18
|
|
|-
|-
|neutral 7th
| neutral 7th
|n7
| n7
|C Ed G Bd
| ~7
|0 9 18 27
| C Ed G Bd
|18:22:27:33
| 0 9 18 27
| 18:22:27:33
|
|
|-
|-
|subminor 7th
| subminor 7th
|sm7
| sm7
|C Edb G Bdb
| vm7
|0 7 18 25
| C Edb G Bdb
|12:14:18:21
| 0 7 18 25
| 12:14:18:21
|
|
|-
|-
|supermajor 7th
| supermajor 7th
|SM7
| SM7
|C Et G Bt
| ^M7
|0 11 18 29
| C Et G Bt
|14:18:21:27
| 0 11 18 29
| 14:18:21:27
|
|
|-
|-
|(dominant) 7th
| (dominant) 7th
|7
| 7
|C E G Bb
| 7
|0 10 18 26
| C E G Bb
|20:25:30:36
| 0 10 18 26
| 20:25:30:36
|
|
|-
|-
|harmonic 7th
| harmonic 7th
|h7
| h7
|C E G Bdb
| ,v7
|0 10 18 25
| C E G Bdb
|4:5:6:7
| 0 10 18 25
| 4:5:6:7
|
|
|-
|-
|7th t3
| 7th t3
|7(t3)
| 7(t3)
|C Et G Bb
| ^,7
|0 11 18 26
| C Et G Bb
|70:90:105:126
| 0 11 18 26
| 70:90:105:126
|
|
|-
|-
|harmonic 7th t3
| harmonic 7th t3
|h7(t3)
| h7(t3)
|C Et G Bdb
| ^,v7
|0 11 18 25
| C Et G Bdb
|28:36:42:49
| 0 11 18 25
|"tritone" is a super 4th (~11:8)
| 28:36:42:49
| "tritone" is a super 4th (~11:8)
|-
|-
|harmonic 9th
| harmonic 9th
|h9
| h9
|C E G Bdb D
| 9(v7)
|0 10 18 25 36
| C E G Bdb D
|4:5:6:7:9
| 0 10 18 25 36
| 4:5:6:7:9
|
|
|-
|-
|harmonic 11th
| harmonic 11th
|h9(t11)
| h9(t11)
|C E G Bdb D Ft
| 9~11(v7)
|0 10 18 25 36 45
| C E G Bdb D Ft
|4:5:6:7:9:11
| 0 10 18 25 36 45
| 4:5:6:7:9:11
|
|
|-
|-
|harmonic 13th
| harmonic 13th
|h9(d13,t11)
| h9(d13,t11)
|C E G Bdb D Ft Ad
| 9~11~13(v7)
|0 10 18 25 36 45 53
| C E G Bdb D Ft Ad
|4:5:6:7:9:11:13
| 0 10 18 25 36 45 53
| 4:5:6:7:9:11:13
|
|
|-
|-
|subminor d7
| subminor d7
|sm(d7)
| sm(d7)
|C Edb G Bd
| vm,~7
|0 7 18 27
| C Edb G Bd
|6:7:9:11
| 0 7 18 27
| 6:7:9:11
|
|
|-
|-
|major add 2
| subharmonic 7th
|add2
| sh7
|C D E G
| vm7(vb5)
|0 5 10 18
| C Edb Gdb Bdb
|8:9:10:12
| 0 7 15 25
| 60:70:84:105
| = sm7(db5)
|-
| major add 2
| add2
| ,2
| C D E G
| 0 5 10 18
| 8:9:10:12
|
|
|-
|-
|major add t4
| major add t4
|addt4
| addt4
|C E Ft G
| ,^4
|0 10 14 18
| C E Ft G
|8:10:11:12
| 0 10 14 18
| 8:10:11:12
|
|
|-
|-
|major add 2,t4
| major add 2,t4
|add2,t4
| add2,t4
|C D E Ft G
| ,2,^4
|0 5 10 14 18
| C D E Ft G
|8:9:10:11:12
| 0 5 10 14 18
| 8:9:10:11:12
|
|
|-
|-
|minor add d2
| minor add d2
|m(addd2)
| m(addd2)
|C Dd Eb G
| m,v2
|0 4 8 18
| C Dd Eb G
|10:11:12:15
| 0 4 8 18
| 10:11:12:15
|
|
|-
|-
|minor add #4
| minor add #4
|m(add#4)
| m(add#4)
|C Eb F# G
| m,#4
|0 8 15 18
| C Eb F# G
|10:12:14:15
| 0 8 15 18
| 10:12:14:15
|
|
|-
|-
|minor add d2,#4
| minor add d2,#4
|m(addd2,#4)
| m(addd2,#4)
|C Dd Eb F# G
| m,v2,#4
|0 4 8 15 18
| C Dd Eb F# G
|10:11:12:14:15
| 0 4 8 15 18
| 10:11:12:14:15
|
|
|-
|-
|subminor add 4
| subminor add 4
|sm(add4)
| sm(add4)
|C Edb F G
| vm,4
|0 7 13 18
| C Edb F G
|6:7:8:9
| 0 7 13 18
| 6:7:8:9
|
|
|-
|-
|supermajor add t2
| supermajor add t2
|SM(addt2)
| SM(addt2)
|C Dt Et G
| ^,^2
|0 6 11 18
| C Dt Et G
|14:16:18:21
| 0 6 11 18
| 14:16:18:21
|
|
|-
|-
|suspended t2,d4
| suspended t2,d4
|sust2,d4
| sust2,d4
|C Dt Fd G
| ^2,v4
|0 6 12 18
| C Dt Fd G
|686:784:896:(1024 ≈ 1029)
| 0 6 12 18
|essentially tempered slendric
| 686:784:896:(1024 ≈ 1029)
| essentially tempered slendric
|-
| 6/9
| 6/9
| 6,9
| C D E G A
| 0 5 10 18 23
| 64:72:(80 ≈ 81):96:108
| essentially tempered meantone
|-
| major 6th
| 6
| 6
| C E G A
| 0 10 18 23
| 12:15:18:20
| inversion of Am7
|-
|-
|6/9
| minor 6th
|6/9
| m6
|C D E G A
| m6
|0 5 10 18 23
| C Eb G A
|64:72:(80 ≈ 81):96:108
| 0 8 18 23
|essentially tempered meantone
| 30:36:45:50
| inversion of Am7(b5)
|-
|-
|major 6th
| subminor add 6
|6
| sm(add6)
|C E G A
| vm,6
|0 10 18 23
| C Edb G A
|12:15:18:20
| 0 7 18 23
| 6:7:9:10
|
|
|-
|-
|subminor add 6
| subharmonic 6th
|sm(add6)
| sh6
|C Edb G A
| m,^6
|0 7 18 23
| C Eb G At
|6:7:9:10
| 0 8 18 24
|
| 70:84:105:120
| inversion of Atsh7
|-
|-
|diminished
| diminished
|°
| °
|C Eb Gb
| d
|0 8 16
| C Eb Gb
|25:30:36
| 0 8 16
| 25:30:36
|
|
|-
|-
|diminished 7th
| diminished 7th
|°7
| °7
|C Eb Gb Bbb
| d7
|0 8 16 24
| C Eb Gb Bbb
|
| 0 8 16 24
|
|
| not symmetrical unlike in [[12edo]]
|-
|-
|minor 7th b5
| minor 7th b5
|m7(b5)
| m7(b5)
|C Eb Gb Bb
| d,7
|0 8 16 26
| C Eb Gb Bb
| 0 8 16 26
|
|
|
|
|-
|-
|supermajor b5
| supermajor b5
|SM(b5)
| SM(b5)
|C Et Gb
| ^(b5)
|0 11 16
| C Et Gb
|7:9:10
| 0 11 16
| 7:9:10
|
|
|-
|-
|supermajor b5 add t2
| supermajor b5 add 2
|SM(b5)(addt2)
| SM(b5)(add2)
|C D Et Gb
| ^,2(b5)
|0 6 11 16
| C D Et Gb
|7:8:9:10
| 0 6 11 16
| 7:8:9:10
|
|
|-
|-
|augmented
| augmented
| +
| +
|C E G#
| a
|0 10 20
| C E G#
|16:20:25
| 0 10 20
| 16:20:25
| not symmetrical unlike in [[12edo]]
|-
| major d5
| (d5)
| (v5)
| C E Gd
| 0 10 17
| 36:45:52
| oneirotonic R-M3-M5 ("falling major")
|-
| minor d5
| m(d5)
| m(v5)
| C Eb Gd
| 0 8 17
| 45:54:65
|
|
|-
|-
|major d5
| subminor d5
|d5
| sm(d5)
|C E Gd
| vm(v5)
|0 10 17
| C Edb Gd
| 0 7 17
| 18:21:26
| oneirotonic R-m3-M5 ("falling minor")
|-
| major t5
| (t5)
| (^5)
| C E Gt
| 0 10 19
| 84:105:128
| oneirotonic R-M3-P6 ("rising major")
|-
| minor t5
| m(t5)
| m(^5)
| C Eb Gt
| 0 8 19
| 105:126:160
|
|
|oneirotonic R-M3-M5 ("falling major")
|-
|-
|minor d5
| subminor t5
|m(d5)
| sm(t5)
|C Eb Gd
| vm(^5)
|0 8 17
| C Edb Gt
|
| 0 7 19
|oneirotonic R-m3-M5 ("falling minor")
| 42:49:64
| oneirotonic R-m3-P6 ("rising minor")
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Harmonic series approximations in 31edo
|+ Harmonic series approximations in 31edo (with prime limit 11)
!Approximate JI
! Approximate JI
!Notation (from C)
! Notation (from C)
!Steps
! Steps
|-
| 8:9:10:11:12:14:15:16
| C D E Ft G Bdb B C
| 0 5 10 14 18 25 28 31
|-
| 9:10:11:12:14:15:16:18
| C D Ed F G# A Bb C
| 0 5 9 13 20 23 26 31
|-
| 10:11:12:14:15:16:18:20
| C Dd Eb F# G Ab Bb C
| 0 4 8 15 18 21 26 31
|-
| 11:12:14:15:16:18:20:21:22
| C Dd Et Ft Gd Ad Bd Bt C
| 0 4 11 14 17 22 27 29 31
|-
|-
|8:9:10:11:12:14:15:16
| 12:14:15:16:18:20:21:22:24
|C D E Ft G Bdb B C
| C Edb E F G A Bdb Bd C
|0 5 10 14 18 25 28 31
| 0 7 10 13 18 23 25 27 31
|-
|-
|9:10:11:12:14:15:16:18
| 14:15:16:18:20:21:22:24:25:27:28
|C D Ed F G# A Bb C
| C Db Dt Et F# G G# At Bb Bt C
|0 5 9 13 20 23 26 31
| 0 3 6 11 15 18 20 24 26 29 31
|-
|-
|10:11:12:14:15:16:18:20
| 15:16:18:20:21:22:24:25:27:28:30
|C Dd Eb F# G A Bb C
| C Db Eb F F# Gd Ab A Bb B C
|0 4 8 15 18 23 26 31
| 0 3 8 13 15 17 21 23 26 28 31
|-
|-
|11:12:14:15:16:18:20:21:22
| 16:18:20:21:22:24:25:27:28:30:32
|C Dd Et Ft Gd Ad Bd Bt C
| C D E Fb Ft G G# A Bdb B C  
|0 4 11 14 17 22 27 29 31
| 0 5 10 12 14 18 20 23 25 28 31
|-
|-
|12:14:15:16:18:20:21:22:24
| 18:20:21:22:24:25:27:28:30:32:33:35:36
|C Edb E F G A Bdb Bd C
| C D Edb Ed F F# G G# A Bb Bd Cd C
|0 7 10 13 18 23 25 27 31
| 0 5 7 9 13 15 18 20 23 26 27 29 31
|-
|-
|14:15:16:18:20:21:22:24:25:27:28
| 20:21:22:24:25:27:28:30:32:33:35:36:40
|C Db Dt Et F# G G# At Bb Bt C
| C C# Dd Eb E F F# G Ab Ad Bdb Bb C
|0 3 6 11 15 18 20 24 26 29 31
| 0 2 4 8 10 13 15 18 21 22 25 26 31
|-
|-
|15:16:18:20:21:22:24:25:27:28:30
| 21:22:24:25:27:28:30:32:33:35:36:40:42
|C Db Eb F F# Gd Ab A Bb B C
| C C# Dt Eb Et F F# Gt G# A At Bt C
|0 3 8 13 15 17 21 23 26 28 31
| 0 2 6 8 11 13 15 19 20 23 24 29 31
|}
|}

Latest revision as of 16:56, 29 May 2021

An incomplete list of chords in 31edo
Name Symbol Symbol (Kite) Notation (from C) Steps Approximate JI Notes
major (M) (M) C E G 0 10 18 4:5:6
minor m m C Eb G 0 8 18 10:12:15
neutral n ~ C Ed G 0 9 18 18:22:27
subminor sm vm C Edb G 0 7 18 6:7:9
supermajor SM ^ C Et G 0 11 18 14:18:21
suspended 4 sus4 4 C F G 0 13 18 6:8:9
suspended 2 sus2 2 C D G 0 5 18 8:9:12
suspended d4 susd4 (v4) C Fd G 0 12 18 16:21:24
suspended t4 sust4 (^4) C Ft G 0 14 18 8:11:12
suspended #4 sus#4 (#4) C F# G 0 15 18 10:14:15
suspended t2 sust2 (^2) C Dt G 0 6 18 14:16:21
suspended d2 susd2 (v2) C Dd G 0 4 18 10:11:15
suspended b2 susb2 (b2) C Db G 0 3 18 14:15:21
major 7th M7 M7 C E G B 0 10 18 28 8:10:12:15
minor 7th m7 m7 C Eb G Bb 0 8 18 26 10:12:15:18
neutral 7th n7 ~7 C Ed G Bd 0 9 18 27 18:22:27:33
subminor 7th sm7 vm7 C Edb G Bdb 0 7 18 25 12:14:18:21
supermajor 7th SM7 ^M7 C Et G Bt 0 11 18 29 14:18:21:27
(dominant) 7th 7 7 C E G Bb 0 10 18 26 20:25:30:36
harmonic 7th h7 ,v7 C E G Bdb 0 10 18 25 4:5:6:7
7th t3 7(t3) ^,7 C Et G Bb 0 11 18 26 70:90:105:126
harmonic 7th t3 h7(t3) ^,v7 C Et G Bdb 0 11 18 25 28:36:42:49 "tritone" is a super 4th (~11:8)
harmonic 9th h9 9(v7) C E G Bdb D 0 10 18 25 36 4:5:6:7:9
harmonic 11th h9(t11) 9~11(v7) C E G Bdb D Ft 0 10 18 25 36 45 4:5:6:7:9:11
harmonic 13th h9(d13,t11) 9~11~13(v7) C E G Bdb D Ft Ad 0 10 18 25 36 45 53 4:5:6:7:9:11:13
subminor d7 sm(d7) vm,~7 C Edb G Bd 0 7 18 27 6:7:9:11
subharmonic 7th sh7 vm7(vb5) C Edb Gdb Bdb 0 7 15 25 60:70:84:105 = sm7(db5)
major add 2 add2 ,2 C D E G 0 5 10 18 8:9:10:12
major add t4 addt4 ,^4 C E Ft G 0 10 14 18 8:10:11:12
major add 2,t4 add2,t4 ,2,^4 C D E Ft G 0 5 10 14 18 8:9:10:11:12
minor add d2 m(addd2) m,v2 C Dd Eb G 0 4 8 18 10:11:12:15
minor add #4 m(add#4) m,#4 C Eb F# G 0 8 15 18 10:12:14:15
minor add d2,#4 m(addd2,#4) m,v2,#4 C Dd Eb F# G 0 4 8 15 18 10:11:12:14:15
subminor add 4 sm(add4) vm,4 C Edb F G 0 7 13 18 6:7:8:9
supermajor add t2 SM(addt2) ^,^2 C Dt Et G 0 6 11 18 14:16:18:21
suspended t2,d4 sust2,d4 ^2,v4 C Dt Fd G 0 6 12 18 686:784:896:(1024 ≈ 1029) essentially tempered slendric
6/9 6/9 6,9 C D E G A 0 5 10 18 23 64:72:(80 ≈ 81):96:108 essentially tempered meantone
major 6th 6 6 C E G A 0 10 18 23 12:15:18:20 inversion of Am7
minor 6th m6 m6 C Eb G A 0 8 18 23 30:36:45:50 inversion of Am7(b5)
subminor add 6 sm(add6) vm,6 C Edb G A 0 7 18 23 6:7:9:10
subharmonic 6th sh6 m,^6 C Eb G At 0 8 18 24 70:84:105:120 inversion of Atsh7
diminished ° d C Eb Gb 0 8 16 25:30:36
diminished 7th °7 d7 C Eb Gb Bbb 0 8 16 24 not symmetrical unlike in 12edo
minor 7th b5 m7(b5) d,7 C Eb Gb Bb 0 8 16 26
supermajor b5 SM(b5) ^(b5) C Et Gb 0 11 16 7:9:10
supermajor b5 add 2 SM(b5)(add2) ^,2(b5) C D Et Gb 0 6 11 16 7:8:9:10
augmented + a C E G# 0 10 20 16:20:25 not symmetrical unlike in 12edo
major d5 (d5) (v5) C E Gd 0 10 17 36:45:52 oneirotonic R-M3-M5 ("falling major")
minor d5 m(d5) m(v5) C Eb Gd 0 8 17 45:54:65
subminor d5 sm(d5) vm(v5) C Edb Gd 0 7 17 18:21:26 oneirotonic R-m3-M5 ("falling minor")
major t5 (t5) (^5) C E Gt 0 10 19 84:105:128 oneirotonic R-M3-P6 ("rising major")
minor t5 m(t5) m(^5) C Eb Gt 0 8 19 105:126:160
subminor t5 sm(t5) vm(^5) C Edb Gt 0 7 19 42:49:64 oneirotonic R-m3-P6 ("rising minor")
Harmonic series approximations in 31edo (with prime limit 11)
Approximate JI Notation (from C) Steps
8:9:10:11:12:14:15:16 C D E Ft G Bdb B C 0 5 10 14 18 25 28 31
9:10:11:12:14:15:16:18 C D Ed F G# A Bb C 0 5 9 13 20 23 26 31
10:11:12:14:15:16:18:20 C Dd Eb F# G Ab Bb C 0 4 8 15 18 21 26 31
11:12:14:15:16:18:20:21:22 C Dd Et Ft Gd Ad Bd Bt C 0 4 11 14 17 22 27 29 31
12:14:15:16:18:20:21:22:24 C Edb E F G A Bdb Bd C 0 7 10 13 18 23 25 27 31
14:15:16:18:20:21:22:24:25:27:28 C Db Dt Et F# G G# At Bb Bt C 0 3 6 11 15 18 20 24 26 29 31
15:16:18:20:21:22:24:25:27:28:30 C Db Eb F F# Gd Ab A Bb B C 0 3 8 13 15 17 21 23 26 28 31
16:18:20:21:22:24:25:27:28:30:32 C D E Fb Ft G G# A Bdb B C 0 5 10 12 14 18 20 23 25 28 31
18:20:21:22:24:25:27:28:30:32:33:35:36 C D Edb Ed F F# G G# A Bb Bd Cd C 0 5 7 9 13 15 18 20 23 26 27 29 31
20:21:22:24:25:27:28:30:32:33:35:36:40 C C# Dd Eb E F F# G Ab Ad Bdb Bb C 0 2 4 8 10 13 15 18 21 22 25 26 31
21:22:24:25:27:28:30:32:33:35:36:40:42 C C# Dt Eb Et F F# Gt G# A At Bt C 0 2 6 8 11 13 15 19 20 23 24 29 31
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