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List of 31edo chords: Difference between revisions

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


{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Standard Triads
! Standard triads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Major
| Major || {{dash|1/1, 5/4, 3/2}} || 4:5:6 || 0, 10, 18 || P1 M3 P5 || I
|4:5:6
|P1 M3 P5
|I
|Meantone:4, Würschmidt:8, Mohajira:8, Myna:10
|-
|-
!Minor
| Minor || {{dash|1/1, 6/5, 3/2}} || 10:12:15 || 0, 8, 18 || P1 m3 P5 || Im
|6/5/4
|P1 m3 P5
|Im
|Meantone:4, Würschmidt:8, Mohajira:8, Myna:10
|-
|-
!Subminor
| Subminor || {{dash|1/1, 7/6, 3/2}} || 6:7:9 || 0, 7, 18 || P1 vm3 P5 || Is
|6:7:9
|P1 s3 P5
|Is
|Squares:5, Mothra:7, Orwell:7, Meantone:9
|-
|-
!Supermajor
| Supermajor || {{dash|1/1, 9/7, 3/2}} || 14:18:21 || 0, 11, 18 || P1 ^M3 P5 || IS
|9/7/6
|P1 S3 P5
|IS
|Squares:5, Mothra:7, Orwell:7, Meantone:9
|-
|-
!Neutral
| Neutral || {{dash|1/1, 11/9, 3/2}} || 18:22:27 || 0, 9, 18 || P1 ~3 P5 || In
|18:22:27
|P1 n3 P5
|In
|Mohajira:2, Squares:4, Miracle:6, Würschmidt:8, Myna:10
|-
|-
!Augmented
| Augmented || {{dash|1/1, 5/4, 25/16}} || 16:20:25 || 0, 10, 20 || P1 M3 A5 || I+
|16:20:25
|P1 M3 A5
|I+
|Würschmidt:2, Tutone:4, Orwell:6, Meantone:8, Valentine:10
|-
|-
!Diminished
| Diminished || {{dash|1/1, 6/5, 36/25}} || 25:30:36 || 0, 8, 16 || P1 m3 d5 || I<sup>o</sup>
|25:30:36
|P1 m3 d5
|I<sup>o</sup>
|Myna:2, Nusecond:4, Meantone:6, Valentine:8, Joan:10
|-
|-
!Harmonic Diminished
| Harmonic diminished || {{dash|1/1, 6/5, 7/5}} || 5:6:7 || 0, 8, 15 || P1 m3 vd5 || Im(db5)
|5:6:7
|P1 m3 vd5
|Im(db5)
|Myna:3, Nusecond:6, Meantone:9
|-
|-
!Subminor Diminished
| Subminor diminished || {{dash|1/1, 7/6, 7/5}} || 30:35:42 || 0, 7, 15 || P1 vm3 vd5 || Is(db5)
|7/6/5
|P1 s3 vd5
|Is(db5)
|Myna:3, Nusecond:6, Meantone:9
|-
|-
!Septimal Wolf Major
| Septimal wolf major || {{dash|1/1, 9/7, 32/21}} || 21:27:32 || 0, 11, 19 || P1 ^M3 ^5 || IS(t5)
|21:27:32
|P1 S3 ^5
|IS(t5)
|Nusecond:5, Würschmidt:7, Joan:8, Valentine:10
|-
|-
!Septimal Wolf Minor
| Septimal wolf minor || {{dash|1/1, 25/21, 32/21}} || 21:25:32 || 0, 8, 19 || P1 m3 ^5 || Im(t5)
|21:25:32
|P1 m3 ^5
|Im(t5)
|Nusecond:5, Würschmidt:7, Joan:8, Valentine:10
|-
|-
!Subfifth Minor
| Subfifth minor || {{dash|1/1, 6/5, 22/15}} || 15:18:22 || 0, 8, 17 || P1 m3 v5 || Im(d5)
|15:18:22
|P1 m3 v5
|Im(d5)
|Mohajira:6, Joan:6, Myna:6
|-
|-
!Subfifth Neutral
| Subfifth neutral || {{dash|1/1, 11/9, 22/15}} || 45:55:66 || 0, 9, 17 || P1 ~3 v5 || In(d5)
|22/18/15
|P1 n3 v5
|In(d5)
|Mohajira:6, Joan:6, Myna:6
|-
|-
!DRmaj
| DRmaj || {{dash|1/1, 5/4, 35/24}} || 24:30:35 || 0, 10, 17 || P1 M3 v5 || I(d5)
|24:30:35
|P1 M3 v5
|I(d5)
|Orwell:3, A-Team:6, Myna:9
|-
|-
!DRmindim
| DRmindim || {{dash|1/1, 7/6, 35/24}} || 24:28:35 || 0, 7, 17 || P1 vm3 v5 || Is(d5)
|24:28:35
|P1 s3 v5
|Is(d5)
|Orwell:3, A-Team:6, Myna:9
|-
|-
!Orwell
| Orwell || {{dash|1/1, 7/6, 11/8}} || 24:28:33 || 0, 7, 14 || P1 vm3 dd5 || Is(bb5)
|24:28:33
|P1 s3 dd5
|Is(bb5)
|Orwell:2, A-Team:4, Myna:6, Mothra:8, Squares:10
|-
|-
!Squares
| Squares || {{dash|1/1, 14/11, 18/11}} || 11:14:18 || 0, 11, 22 || P1 ^M3 AA5 || IS(x5)
|11:14:18
|P1 S3 AA5
|IS(x5)
|Squares:2, Würschmidt:4, Joan:6, Tutone:8, Nusecond:10
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Other Triads
! Other triads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Double Diminished
| Double diminished || {{dash|1/1, 8/7, 10/7}} || 7:8:10 || 0, 6, 16 || P1 d3 d5 || I<sup>o</sup>(bb3)
|7:8:10
|P1 d3 d5
|I<sup>o</sup>(bb3)
|Tutone:5, Miracle:7, Myna:9, Meantone:10
|-
|-
!Major b5
| Major b5 || {{dash|1/1, 5/4, 10/7}} || 28:35:40 || 0, 10, 16 || P1 M3 d5 || I(b5)
|10/8/7
|P1 M3 d5
|I(b5)
|Tutone:5, Miracle:7, Myna:9, Meantone:10
|-
|-
!Minor Augmented
| Minor augmented || {{dash|1/1, 32/27, 14/9}} || 27:32:42 || 0, 8, 20 || P1 m3 A5 || Im+
|27:32:42
|P1 m3 A5
|Im+
|Nusecond:5, Würschmidt:7, Joan:8
|-
|-
!Double Augmented
| Double augmented || {{dash|1/1, 35/27, 14/9}} || 27:35:42 || 0, 12, 20 || P1 A3 A5 || I+(#3)
|27:35:42
|P1 A3 A5
|I+(#3)
|Nusecond:5, Würschmidt:7, Joan:8
|-
|-
!Doubly Augmented
| Doubly augmented || {{dash|1/1, 5/4, 13/8}} || 8:10:13 || 0, 10, 22 || P1 M3 AA5 || I(x5)
|8:10:13
|P1 M3 AA5
|I(x5)
|Würschmidt:5, A-Team:7, Miracle:7, Mohajira:9
|-
|-
!Sus4
| Sus4 || {{dash|1/1, 4/3, 3/2}} || 6:8:9 || 0, 13, 18 || P1 P4 P5 || Isus4
|6:8:9
|P1 P4 P5
|Isus4
|Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
|-
|-
!Sus2
| Sus2 || {{dash|1/1, 9/8, 3/2}} || 8:9:12 || 0, 5, 18 || P1 M2 P5 || Isus2
|8:9:12
|P1 M2 P5
|Isus2
|Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
|-
|-
!Sus(t4)
| Sus(t4) || {{dash|1/1, 11/8, 3/2}} || 8:11:12 || 0, 14, 18 || P1 ^4 P5 || Isus(t4)
|8:11:12
|P1 ^4 P5
|Isus(t4)
|Mohajira:5, Orwell:7, Tritonic:8, Squares:10
|-
|-
!Sus(d4)
| Sus(d4) || {{dash|1/1, 13/10, 3/2}} || 10:13:15 || 0, 12, 18 || P1 v4 P5 || Isus(d4)
|10:13:15
|P1 v4 P5
|Isus(d4)
|Mothra:3, Miracle:6, Valentine:9, Tritonic:12
|-
|-
!Sus(t2)
| Sus(t2) || {{dash|1/1, 8/7, 3/2}} || 14:16:21 || 0, 6, 18 || P1 ^M2 P5 || Isus(t2)
|14:16:21
|P1 ^2 P5
|Isus(t2)
|Mothra:3, Miracle:6, Valentine:9, Tritonic:12
|-
|-
!DRsus4
| DRsus4 || {{dash|1/1, 17/13, 19/13}} || 13:17:19 || 0, 12, 17 || P1 v4 v5 || Isus(d4)(d5)
|13:17:19
|P1 v4 v5
|Isus(d4)(d5)
|A-Team:4, Mothra:8, Joan:8, Mohajira:9, Tritonic:10
|-
|-
!DRsus2
| DRsus2 || {{dash|1/1, 19/17, 19/13}} ||  || 0, 5, 17 || P1 M2 v5 || Isus2(d5)
|19/17/13
|P1 M2 v5
|Isus2(d5)
|A-Team:4, Mothra:8, Joan:8, Mohajira:9, Tritonic:10
|-
|-
!Terrain Triad
| Terrain triad || {{dash|1/1, 7/5, 9/5}} || 5:7:9 || 0, 15, 26 || P1 vd5 m7 || I(db5)m7
|5:7:9
|P1 A4 m7
|I(db5)m7
|Tutone:4, Meantone:8, Squares:8, Joan:10, Tritonic:10
|-
|-
!Harmonic Shell
| Harmonic shell || {{dash|1/1, 5/4, 7/4}} || 4:5:7 || 0, 10, 25 || P1 M3 vm7 || Ih7(no5)
|4:5:7
|P1 M3 s7
|Ih7$
|Tutone:5, Miracle:7, Myna:9, Meantone:10, Tritonic:12
|-
|-
!Mothwellsmic Shell
| Mothwellsmic shell || {{dash|1/1, 14/11, 7/4}} || 44:56:77 || 0, 11, 25 || P1 ^M3 vm7 || ISs7(no5)
|14/11/8
|P1 S3 s7
|ISs7$
|Joan:4, Orwell:8, Mothra:8, Tutone:9, Squares:10
|-
|-
!Orgone Triad
| Orgone triad || {{dash|1/1, 11/8, 7/4}} || 8:11:14 || 0, 14, 25 || P1 ^4 vm7 || Is7sus(t4)(no5)
|8:11:14
|P1 ^4 s7
|Is7sus(t4)$
|Joan:4, Orwell:8, Mothra:8, Tutone:9, Squares:10
|-
|-
!Quartal
| Quartal || {{dash|1/1, 4/3, 16/9}} || 9:12:16 || 0, 13, 26 || P1 P4 m7 || Iq
|9:12:16
|P1 P4 m7
|Iq
|Meantone:2, Mohajira:4, Mothra:6, Squares:8, Tritonic:10
|-
|-
!Joan
| Joan || {{dash|1/1, 11/8, 15/8}} || 8:11:15 || 0, 14, 28 || P1 ^4 M7 || IJ
|8:11:15
|P1 ^4 M7
|IJ
|Joan:2, Orwell:4, Tritonic:6, A-Team:8, Mohajira:10
|}
|}
Notes: $ used to represent shell voicing, DR means [[Delta-rational]].
Notes: DR means [[Delta-rational]].




Line 239: Line 95:
These tetrads are split into a few general categories.
These tetrads are split into a few general categories.


{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Basic Tetrads
! Basic tetrads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Major Seven
| Major seven || {{dash|1/1, 5/4, 3/2, 15/8}} || 8:10:12:15 || 0, 10, 18, 28 || P1 M3 P5 M7 || IM7
|8:10:12:15
|P1 M3 P5 M7
|IM7
|Meantone:5, Würschmidt:9, Mohajira:10
|-
|-
!Harmonic Seven
| Harmonic seven || {{dash|1/1, 5/4, 3/2, 7/4}} || 4:5:6:7 || 0, 10, 18, 25 || P1 M3 P5 vm7 || Ih7
|4:5:6:7
|P1 M3 P5 s7
|Ih7
|Myna:10, Meantone:10, Orwell:11
|-
|-
!Minor Seven
| Minor seven || {{dash|1/1, 6/5, 3/2, 9/5}} || 10:12:15:18 || 0, 8, 18, 26 || P1 m3 P5 m7 || Im7
|10:12:15:18
|P1 m3 P5 m7
|Im7
|Meantone:4, Mohajira:8
|-
|-
!Utonal Tetrad
| Utonal tetrad || {{dash|1/1, 6/5, 3/2, 12/7}} ||  || 0, 8, 18, 24 || P1 m3 P5 ^M6 || ImS6
|12/10/8/7
|P1 m3 P5 S6
|ImS6
|Myna:10, Meantone:10, Orwell:11
|-
|-
!Subminor Seven
| Subminor seven || {{dash|1/1, 7/6, 3/2, 7/4}} || 12:14:18:21 || 0, 7, 18, 25 || P1 vm3 P5 vm7 || Is7
|12:14:18:21
|P1 s3 P5 s7
|Is7
|Mothra:7, Orwell:8, Squares:9, Meantone:10
|-
|-
!Undecimal Tetrad
| Undecimal tetrad || {{dash|1/1, 7/6, 3/2, 11/6}} || 6:7:9:11 || 0, 7, 18, 27 || P1 vm3 P5 ~7 || Isn7
|6:7:9:11
|P1 s3 P5 n7
|Isn7
|Squares:6, Nusecond:11
|-
|-
!Supermajor Seven
| Supermajor seven || {{dash|1/1, 9/7, 3/2, 27/14}} || 14:18:21:27 || 0, 11, 18, 29 || P1 ^M3 P5 ^M7 || IS7
|14:18:21:27
|P1 S3 P5 S7
|IS7
|Squares:5, Meantone:9, Mothra:10
|-
|-
!9-over Tetrad
| 9-over tetrad || {{dash|1/1, 9/7, 3/2, 9/5}} ||  || 0, 11, 18, 26 || P1 ^M3 P5 m7 || ISm7
|9/7/6/5
|P1 S3 P5 m7
|ISm7
|Meantone:9, Nusecond:11
|-
|-
!Neutral Seven
| Neutral seven || {{dash|1/1, 11/9, 3/2, 11/6}} || 18:22:27:33 || 0, 9, 18, 27 || P1 ~3 P5 ~7 || In7
|18:22:27:33
|P1 n3 P5 n7
|In7
|Mohajira:3, Squares:6, Miracle:9
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Other Basic Tetrads
! Other basic tetrads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Lynch Neutral
| Lynch neutral || {{dash|1/1, 3/2, 11/6, 11/4}} || 12:18:22:33 || 0, 18, 27, 45 || P1 P5 ~7 ^11 || In7t11(no3)
|12:18:22:33
|P1 P5 n7 ^11
|I5n7t11
|Mohajira:5, Squares:10
|-
|-
!Neutral Minor Seven
| Neutral minor Seven || {{dash|1/1, 27/22, 3/2, 9/5}} ||  || 0, 9, 18, 26 || P1 ~3 P5 m7 || Inm7
|27/22/18/15
|P1 n3 P5 m7
|Inm7
|Mohajira:6
|-
|-
!Neutral Major Tetrad
| Neutral major tetrad || {{dash|1/1, 27/22, 3/2, 27/16}} ||  || 0, 9, 18, 23 || P1 ~3 P5 M6 || InM6
|27/22/18/16
|P1 n3 P5 M6
|InM6
|Mohajira:6
|-
|-
!Subminor Major Tetrad
| Subminor major tetrad || {{dash|1/1, 7/6, 3/2, 5/3}} || 6:7:9:10 || 0, 7, 18, 23 || P1 vm3 P5 M6 || IsM6
|6:7:9:10
|P1 s3 P5 M6
|IsM6
|Meantone:9, Nusecond:11
|-
|-
!Dominant
| Dominant || {{dash|1/1, 5/4, 3/2, 9/5}} || 20:25:30:36 || 0, 10, 18, 26 || P1 M3 P5 m7 || I7
|20:25:30:36
|P1 M3 P5 m7
|I7
|Meantone:6
|-
|-
!Mothwellsmic Dominant
| Mothwellsmic dominant || {{dash|1/1, 14/11, 3/2, 7/4}} || 44:56:66:77 || 0, 11, 18, 25 || P1 ^M3 P5 vm7 || ISs7
|42/33/28/24
|P1 S3 P5 s7
|ISs7
|Orwell:8, Squares:10
|-
|-
!Subminor Supermajor Seven
| Subminor supermajor Seven || {{dash|1/1, 7/6, 3/2, 21/11}} ||  || 0, 7, 18, 29 || P1 vm3 P5 ^M7 || IsS7
|21/18/14/11
|P1 s3 P5 S7
|IsS7
|Squares:5, Würschmidt:10
|-
|-
!Augmented Seven
| Augmented seven || {{dash|1/1, 5/4, 25/16, 7/4}} || 16:20:25:28 || 0, 10, 20, 25 || P1 M3 A5 vm7 || Ih7(#5)
|16:20:25:28
|P1 M3 A5 s7
|Ih7(#5)
|Tutone:5, Meantone:10
|-
|-
!Half Augmented
| Half augmented || {{dash|1/1, 5/4, 25/16, 15/8}} || 16:20:25:30 || 0, 10, 20, 28 || P1 M3 A5 M7 || IM7(#5)
|16:20:25:30
|P1 M3 A5 M7
|IM7(#5)
|Meantone:8, Würschmidt:9
|-
|-
!Fully Augmented
| Fully augmented || {{dash|1/1, 5/4, 25/16, 125/64}} ||  || 0, 10, 20, 30 || P1 M3 A5 A7 || I+7
|64:80:100:125
|P1 M3 A5 A7
|I+7
|Würschmidt:3, Tutone:6, Orwell:9
|-
|-
!Half Diminished
| Half diminished || {{dash|1/1, 6/5, 36/25, 9/5}} || 25:30:36:45 || 0, 8, 16, 26 || P1 m3 d5 m7 || Im7(b5)
|36/30/25/20
|P1 m3 d5 m7
|Im7(b5)
|Meantone:6
|-
|-
!Fully Diminished
| Fully diminished || {{dash|1/1, 25/21, 10/7, 12/7}} || 21:25:30:36 || 0, 8, 16, 24 || P1 m3 d5 d7 || I<sup>o</sup>7
|21:25:30:36
|P1 m3 d5 d7
|I<sup>o</sup>7
|Myna:3, Nusecond:6, Meantone:9
|-
|-
!Harmonic Half Diminished
| Harmonic half diminished || {{dash|1/1, 6/5, 7/5, 9/5}} || 5:6:7:9 || 0, 8, 15, 26 || P1 m3 vd5 m7 || Im7(db5)
|5:6:7:9
|P1 m3 vd5 m7
|Im7(db5)
|Meantone:9, Nusecond:11
|-
|-
!Harmonic Fully Diminished
| Harmonic fully diminished || {{dash|1/1, 6/5, 7/5, 17/10}} || 10:12:14:17 || 0, 8, 15, 24 || P1 m3 vd5 d7 || I<sup>o</sup>7(db5)
|10:12:14:17
|P1 m3 vd5 d7
|I<sup>o</sup>7(db5)
|Myna:5, Nusecond:10, A-Team:11
|-
|-
!Subminor Half Diminished
| Subminor half diminished || {{dash|1/1, 7/6, 7/5, 7/4}} ||  || 0, 7, 15, 25 || P1 vm3 vd5 vm7 || Is7(db5)
|7/6/5/4
|P1 s3 vd5 s7
|Is7(db5)
|Myna:10, Meantone:10, Orwell:11
|-
|-
!Augmented 3&7
| Augmented 3&7 || {{dash|1/1, 13/10, 3/2, 39/20}} || 20:26:30:39 || 0, 12, 18, 30 || P1 A3 P5 A7 || I(#3, #7)
|20:26:30:39
|P1 A3 P5 A7
|I(#3,#7)
|Mothra:5, Miracle:10
|-
|-
!Diminished 3&7
| Diminished 3&7 || {{dash|1/1, 15/13, 3/2, 45/26}} || 26:30:39:45 || 0, 6, 18, 24 || P1 d3 P5 d7 || I(bb3, bb7)
|26:30:39:45
|P1 d3 P5 d7
|I(bb3,bb7)
|Mothra:4, Miracle:8
|-
|-
!Doubly Augmented Major Seven
| Doubly augmented major seven || {{dash|1/1, 5/4, 13/8, 15/8}} || 8:10:13:15 || 0, 10, 22, 28 || P1 M3 AA5 M7 || IM7(x5)
|8:10:13:15
|P1 M3 AA5 M7
|IM7(x5)
|Miracle:7, Mohajira:11
|-
|-
!Supermajor Seven Augmented
| Supermajor seven augmented || {{dash|1/1, 9/7, 11/7, 27/14}} || 14:18:22:27 || 0, 11, 20, 29 || P1 ^M3 A5 ^M7 || IS7(#5)
|14:18:22:27
|P1 S3 A5 S7
|IS7(#5)
|Squares:4, Würschmidt:8
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Fifth-Contained Tetrads
! Fifth-contained tetrads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Mu Chord
| Mu chord || {{dash|1/1, 9/8, 5/4, 3/2}} || 8:9:10:12 || 0, 5, 10, 18 || P1 M2 M3 P5 || I(add2)
|8:9:10:12
|P1 M2 M3 P5
|I(add2)
|Meantone:4, Mohajira:8
|-
|-
!Nu Chord
| Nu chord || {{dash|1/1, 6/5, 4/3, 3/2}} || 30:36:40:45 || 0, 8, 13, 18 || P1 m3 P4 P5 || Im(add4)
|12/10/9/8
|P1 m3 P4 P5
|Im(add4)
|Meantone:4, Mohajira:8
|-
|-
!Subminor Tetrad
| Subminor tetrad || {{dash|1/1, 7/6, 4/3, 3/2}} || 6:7:8:9 || 0, 7, 13, 18 || P1 vm3 P4 P5 || Is(add4)
|6:7:8:9
|P1 s3 P4 P5
|Is(add4)
|Mothra:7, Squares:9, Meantone:10
|-
|-
!Supermajor Tetrad
| Supermajor tetrad || {{dash|1/1, 9/8, 9/7, 3/2}} || 56:63:72:84 || 0, 5, 11, 18 || P1 M2 ^M3 P5 || IS(add2)
|9/8/7/6
|P1 M2 S3 P5
|IS(add2)
|Mothra:7, Squares:9, Meantone:10
|-
|-
!Super Second Tetrad
| Super second tetrad || {{dash|1/1, 8/7, 9/7, 3/2}} || 14:16:18:21 || 0, 6, 11, 18 || P1 ^M2 ^M3 P5 || IS(add t2)
|14:16:18:21
|P1 S2 S3 P5
|IS(add t2)
|Mothra:7, Meantone:11
|-
|-
!Sub Fourth Tetrad
| Sub fourth tetrad || {{dash|1/1, 7/6, 21/16, 3/2}} || 48:56:63:72 || 0, 7, 12, 18 || P1 vm3 v4 P5 || Is(add d4)
|21/18/16/14
|P1 s3 v4 P5
|Is(add d4)
|Mothra:7, Meantone:11
|-
|-
!Sus 2/4
| Sus 2/4 || {{dash|1/1, 10/9, 4/3, 3/2}} || 18:20:24:27 || 0, 5, 13, 18 || P1 M2 P4 P5 || Isus(2/4)
|18:20:24:27
|P1 M2 P4 P5
|Isus(2/4)
|Meantone:3, Mohajira:6, Mothra:9
|-
|-
!Add^4
| Add^4 || {{dash|1/1, 5/4, 11/8, 3/2}} || 8:10:11:12 || 0, 10, 14, 18 || P1 M3 ^4 P5 || I(add t4)
|8:10:11:12
|P1 M3 ^4 P5
|I(add t4)
|Mohajira:8, Valentine:9, Orwell:10
|-
|-
!Minor Addv2
| Minor addv2 || {{dash|1/1, 12/11, 6/5, 3/2}} ||  || 0, 4, 8, 18 || P1 ~2 m3 P5 || Im(add d2)
|12/11/10/8
|P1 n2 m3 P5
|Im(add d2)
|Mohajira:8, Valentine:9, Orwell:10
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Split Chords
! Split chords !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Split Chord
| Split chord || {{dash|1/1, 6/5, 5/4, 3/2}} || 20:24:25:30 || 0, 8, 10, 18 || P1 m3 M3 P5 || IMm3
|20:24:25:30
|P1 m3 M3 P5
|IMm3
|Meantone:7, Würschmidt:8, Valentine:9, Myna:10
|-
|-
!Septimal Split Chord
| Septimal split chord || {{dash|1/1, 33/28, 9/7, 3/2}} || 28:33:36:42 || 0, 7, 11, 18 || P1 vm3 ^M3 P5 || ISs3
|28:33:36:42
|P1 s3 S3 P5
|ISs3
|Squares:6, Orwell:7, Nusecond:11
|-
|-
!Yellow/Blue Split Chord
| Yellow/blue split chord || {{dash|1/1, 7/6, 5/4, 3/2}} || 12:14:15:18 || 0, 7, 10, 18 || P1 vm3 M3 P5 || IMs3
|12:14:15:18
|P1 s3 M3 P5
|IMs3
|Meantone:9, Orwell:10
|-
|-
!Green/Red Split Chord
| Green/red split chord || {{dash|1/1, 6/5, 9/7, 3/2}} ||  || 0, 8, 11, 18 || P1 m3 ^M3 P5 || ISm3
|18/15/14/12
|P1 m3 S3 P5
|ISm3
|Meantone:9, Orwell:10
|-
|-
!Wolf Split Chord
| Wolf split chord || {{dash|1/1, 25/21, 9/7, 32/21}} || 21:25:27:32 || 0, 8, 11, 19 || P1 m3 ^M3 ^5 || ISm3(t5)
|21:25:27:32
|P1 m3 S3 ^5
|ISm3(t5)
|Nusecond:7, Joan:8, Würschmidt:9
|-
|-
!Squares Split Chord
| Squares split chord || {{dash|1/1, 27/22, 14/11, 18/11}} || 22:27:28:36 || 0, 9, 11, 22 || P1 ~3 ^M3 AA5 || ISn3(#5)
|22:27:28:36
|P1 n3 S3 A5
|ISn3(#5)
|Squares:3, Würschmidt:6, Joan:9
|-
|-
!DR Split Chord
| DR split chord || {{dash|1/1, 7/6, 5/4, 35/24}} || 24:28:30:35 || 0, 7, 10, 17 || P1 vm3 M3 v5 || IMs3(d5)
|24:28:30:35
|P1 s3 M3 v5
|IMs3(d5)
|Orwell:4, A-Team:8
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Harmonic Subsets
! Harmonic subsets !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!h9 Shell
| h9 shell || {{dash|1/1, 5/4, 7/4, 9/4}} || 4:5:7:9 || 0, 10, 25, 36 || P1 M3 vm7 M9 || Ih9(no5)
|4:5:7:9
|P1 M3 s7 M9
|Ih9$
|Tutone:5, Meantone:10
|-
|-
!Add11 Shell
| Add11 shell || {{dash|1/1, 5/4, 7/4, 11/4}} || 4:5:7:11 || 0, 10, 25, 45 || P1 M3 vm7 ^11 || Ih7t11(no5)
|4:5:7:11
|P1 M3 s7 ^11
|Ih7t11$
|Tutone:9, Valentine:11, Tritonic:12
|-
|-
!Quintal Neutral
| Quintal neutral || {{dash|1/1, 3/2, 9/4, 11/4}} || 4:6:9:11 || 0, 18, 36, 45 || P1 P5 M9 ^11 || I59t11
|4:6:9:11
|P1 P5 M9 ^11
|I59t11
|Mohajira:5, Squares:10
|-
|-
!Altered-13 Shell
| Altered 13 shell || {{dash|1/1, 5/4, 7/4, 13/4}} || 4:5:7:13 || 0, 10, 25, 53 || P1 M3 vm7 ~13 || Ih7d13(no5)
|4:5:7:13
|P1 M3 s7 n13
|Ih7d13$
|Miracle:7
|-
|-
!Add-13
| Add-13 || {{dash|1/1, 5/4, 3/2, 13/4}} || 4:5:6:13 || 0, 10, 18, 53 || P1 M3 P5 ~13 || I(add d13)
|4:5:6:13
|P1 M3 P5 n13
|I(add d13)
|Mohajira:9, Valentine:11
|-
|-
!Altered-17 Shell
| Altered 17 shell || {{dash|1/1, 5/4, 7/4, 17/8}} || 8:10:14:17 || 0, 10, 25, 34 || P1 M3 vm7 m9 || Ih7b9(no5)
|8:10:14:17
|P1 M3 s7 m9
|Ih7b9$
|Miracle:7
|-
|-
!Altered-19 Shell
| Altered 19 shell || {{dash|1/1, 5/4, 7/4, 19/8}} || 8:10:14:19 || 0, 10, 25, 39 || P1 M3 vm7 m10 || Ih7b10(no5)
|8:10:14:19
|P1 M3 s7 m10
|Ih7b10$
|Valentine:8, Myna:10
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Misc Tetrads
! Misc tetrads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!h7#9 Shell
| h7#9 shell || {{dash|1/1, 5/4, 7/4, 7/3}} || 12:15:21:28 || 0, 10, 25, 38 || P1 M3 vm7 A9 || Ih7#9(no5)
|12:15:21:28
|P1 M3 s7 A9
|Ih7#9$
|Miracle:8, Meantone:10
|-
|-
!h7db9 Shell
| h7db9 shell || {{dash|1/1, 5/4, 7/4, 25/12}} || 12:15:21:25 || 0, 10, 25, 33 || P1 M3 vm7 vm9 || Ih7db9(no5)
|12:15:21:25
|P1 M3 s7 s9
|Ih7db9$
|Valentine:8, Meantone:10
|-
|-
!h7d9 Shell
| h7d9 shell || {{dash|1/1, 5/4, 7/4, 35/16}} || 16:20:28:35 || 0, 10, 25, 35 || P1 M3 vm7 ~9 || Ih7d9(no5)
|16:20:28:35
|P1 M3 s7 n9
|Ih7d9$
|Tutone:7, Valentine:8, Miracle:9, Orwell:11
|-
|-
!DRmaj
| DRmaj || {{dash|1/1, 9/8, 5/4, 35/24}} || 24:27:30:35 || 0, 5, 10, 17 || P1 M2 M3 v5 || I(add 2, d5)
|24:27:30:35
|P1 M2 M3 v5
|I(add 2, d5)
|A-Team:6
|-
|-
!DRmin
| DRmin || {{dash|1/1, 7/6, 32/21, 12/7}} || 42:49:64:72 || 0, 7, 19, 24 || P1 vm3 ^5 ^M6 || IsS6(t5)
|42:49:64:72
|P1 s3 ^5 S6
|IsS6(t5)
|A-Team:4, Mothra:8
|-
|-
!DRmindim
| DRmindim || {{dash|1/1, 7/6, 16/11, 56/33}} ||  || 0, 7, 17, 24 || P1 vm3 v5 ^M6 || IsS6(d5)
|66:77:96:112
|P1 s3 v5 S6
|IsS6(d5)
|Orwell:3, A-Team:6, Myna:9
|-
|-
!DRsus
| DRsus || {{dash|1/1, 9/8, 21/16, 35/24}} || 48:54:63:70 || 0, 5, 12, 17 || P1 M2 v4 v5 || Isus(2/d4)(d5)
|48:54:63:70
|P1 M2 v4 v5
|Isus(2/d4)(d5)
|A-Team:4, Mothra:8
|-
|-
!Leading DRsus2
| Leading DRsus2 || {{dash|1/1, 19/17, 19/13, 19/10}} ||  || 0, 5, 17, 29 || P1 M2 v5 ^M7 || IS7sus2(d5)
|19/17/13/10
|P1 M2 v5 S7
|IS7sus2(d5)
|A-Team:5, Mothra:10
|-
|-
!Mothwellsmic Dominant #9 Shell
| Mothwellsmic dominant #9 shell || {{dash|1/1, 14/11, 7/4, 7/3}} ||  || 0, 11, 25, 38 || P1 ^M3 vm7 A9 || ISs7#9(no5)
|14/11/8/6
|P1 S3 s7 A9
|ISs7#9$
|Orwell:8, Mothra:8, Squares:10
|-
|-
!Orgone add9
| Orgone add9 || {{dash|1/1, 11/8, 7/4, 9/4}} || 8:11:14:18 || 0, 14, 25, 36 || P1 ^4 vm7 M9 || Ih9sus(t4)(no5)
|8:11:14:18
|P1 ^4 s7 M9
|Ih9sus(t4)$
|Joan:7, Tutone:9, Squares:10
|-
|-
!Greeley Over-3
| Greeley over-3 || {{dash|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)
|6:7:10:11:(13)
|P1 s3 M6 n7 (n9)
|IsM6n7$
|Nusecond:6(7)
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Other Linear Tetrads
! Other linear tetrads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Slendric Tetrad
| Slendric tetrad || {{dash|1/1, 8/7, 55/42, 3/2}} || 42:48:55:63 || 0, 6, 12, 18 || P1 ^M2 v4 P5 || Isus(t2/d4)
|42:48:55:63
|P1 S2 v4 P5
|Isus(t2/d4)
|Mothra:3, Miracle:6, Valentine:9
|-
|-
!Miracle Cluster
| Miracle cluster || {{dash|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)
|13:14:15:16
|P1 m2 S2 n3
|I(13:14:15:16)
|Miracle:3, Joan:6, Slender:9
|-
|-
!Orwell Tetrad
| Orwell tetrad || {{dash|1/1, 7/6, 11/8, 77/48}} || 48:56:66:77 || 0, 7, 14, 21 || P1 vm3 ^4 m6 || IO
|48:56:66:77
|P1 s3 ^4 m6
|IO
|Orwell:3, A-Team:6, Myna:9
|}
|}


== Pentads ==
== Pentads ==


{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Main Ninth Chords
! Main ninth chords !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Major Nine
| Major nine || {{dash|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
|8:10:12:15:18
|P1 M3 P5 M7 M9
|IM9
|Meantone:5, Mohajira:10
|-
|-
!Harmonic Nine
| Harmonic nine || {{dash|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
|4:5:6:7:9
|P1 M3 P5 s7 M9
|Ih9
|Meantone:10
|-
|-
!Minor Nine
| Minor nine || {{dash|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
|18/15/12/10/8
|P1 m3 P5 m7 M9
|Im9
|Meantone:5, Mohajira:10
|-
|-
!Subminor Nine
| Subminor nine || {{dash|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
|12:14:18:21:27
|P1 s3 P5 s7 M9
|Is9
|Squares:9, Meantone:10, Mothra:10
|-
|-
!Supermajor Nine
| Supermajor nine || {{dash|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
|27/21/18/14/12
|P1 S3 P5 S7 M9
|IS9
|Squares:9, Meantone:10, Mothra:10
|-
|-
!9-over Pentad
| 9-over pentad || {{dash|1/1, 9/7, 3/2, 9/5, 9/4}} ||  || 0, 11, 18, 26, 36 || P1 ^M3 P5 m7 M9 || IS9b7
|9/7/6/5/4
|P1 S3 P5 m7 M9
|IS9b7
|Meantone:10
|-
|-
!Neutral Pentad
| Neutral pentad || {{dash|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
|36:44:54:66:81
|P1 n3 P5 n7 M9
|In9
|Mohajira:4, Squares:8, Miracle:12
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Other Main Pentads
! Other main pentads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Major 6/9
| Major 6/9 || {{dash|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
|12:15:18:20:27
|P1 M3 P5 M6 M9
|I6/9
|Meantone:4, Mohajira:8, Slendric:12
|-
|-
!Minor 7/11
| Minor 7/11 || {{dash|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
|10:12:15:18:27
|P1 m3 P5 m7 P11
|Im7/11
|Meantone:4, Mohajira:8, Slendric:12
|-
|-
!Dominant Nine
| Dominant nine || {{dash|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
|20:25:30:36:45
|P1 M3 P5 m7 M9
|I9
|Meantone:6, Mohajira:12
|-
|-
!Tridecimal Pentad
| Tridecimal pentad || {{dash|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
|6:7:9:11:13
|P1 s3 P5 n7 n9
|Isn7d9
|Squares:12
|-
|-
!Subminor 6/9
| Subminor 6/9 || {{dash|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
|12:14:18:20:27
|P1 s3 P5 M6 M9
|IsM6/9
|Meantone:9
|-
|-
!Subminor 7/11
| Subminor 7/11 || {{dash|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
|24:28:36:42:63
|P1 s3 P5 s7 v11
|Is7d11
|Mothra:7, Meantone:11
|-
|-
!Sub Neutral 11
| Sub neutral 11 || {{dash|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
|12:14:18:22:33
|P1 s3 P5 n7 ^11
|Isn7t11
|Squares:10, Nusecond:12
|-
|-
!Fully Augmented #9
| Fully augmented #9 || {{dash|1/1, 5/4, 25/16, 125/64, 75/32}} ||  || 0, 10, 20, 30, 38 || P1 M3 A5 A7 A9 || I+7#9
|64:80:100:125:150
|P1 M3 A5 A7 A9
|I+7#9
|Orwell:10, Würschmidt:10
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Altered Pentads
! Altered pentads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Harmonic #9
| Harmonic #9 || {{dash|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
|12:15:18:21:28
|P1 M3 P5 s7 A9
|Ih7#9
|Meantone:10
|-
|-
!Harmonic db9
| Harmonic db9 || {{dash|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
|12:15:18:21:25
|P1 M3 P5 s7 s9
|Ih7db9
|Meantone:10, Myna:10
|-
|-
!Altered-13
| Altered 13 || {{dash|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
|4:5:6:7:13
|P1 M3 P5 s7 n13
|Ih7d13
|Miracle:13, Valentine:14
|-
|-
!Altered-13 #9 Shell
| Altered 13 #9 shell || {{dash|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)
|12:15:21:28:39
|P1 M3 s7 A9 n13
|Ih7#9d13$
|Miracle:8
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Split Pentads
! Split pentads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Sub Seventh Split
| Sub seventh split || {{dash|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
|12:14:15:18:21
|P1 s3 M3 P5 s7
|IMs3s7
|Meantone:10, Orwell:11
|-
|-
!Major Seventh Split
| Major seventh split || {{dash|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
|24:28:30:36:45
|P1 s3 M3 P5 M7
|IMs3M7
|Meantone:9, Orwell:10, Würschmidt:10
|-
|-
!Major Sixth Split
| Major sixth split || {{dash|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
|12:14:15:18:20
|P1 s3 M3 P5 M6
|IMs3M6
|Meantone:9, Nusecond:13
|-
|-
!Minor Seventh Split
| Minor seventh split || {{dash|1/1, 6/5, 9/7, 3/2, 9/5}} ||  || 0, 8, 11, 18, 26 || P1 m3 ^M3 P5 m7 || ISm3m7
|18/15/14/12/10
|P1 m3 S3 P5 m7
|ISm3m7
|Meantone:9, Nusecond:13
|-
|-
!Super Seventh Split
| Super seventh split || {{dash|1/1, 6/5, 9/7, 3/2, 27/14}} ||  || 0, 8, 11, 18, 29 || P1 m3 ^M3 P5 ^M7 || ISm3S7
|54/45/42/36/28
|P1 m3 S3 P5 S7
|ISm3S7
|Meantone:9, Würschmidt:10
|-
|-
!Super Sixth Split
| Super sixth split || {{dash|1/1, 6/5, 9/7, 3/2, 12/7}} ||  || 0, 8, 11, 18, 24 || P1 m3 ^M3 P5 ^M6 || ISm3S6
|36/30/28/24/21
|P1 m3 S3 P5 S6
|ISm3S6
|Meantone:10, Orwell:11
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Harmonic Pentads
! Harmonic pentads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Orwell Harmonic
| Orwell harmonic || {{dash|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
|4:5:6:7:11
|P1 M3 P5 s7 ^11
|Ih7t11
|Orwell:11, Valentine:12
|-
|-
!Mohajira Harmonic
| Mohajira harmonic || {{dash|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)
|4:5:6:9:11
|P1 M3 P5 M9 ^11
|Ih11(no7)
|Mohajira:8
|-
|-
!Tutone Harmonic
| Tutone harmonic || {{dash|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)
|4:5:7:9:11
|P1 M3 s7 M9 ^11
|Ih11$
|Tutone:9
|-
|-
!Squares Harmonic
| Squares harmonic || {{dash|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)
|4:6:7:9:11
|P1 P5 s7 M9 ^11
|Ih11(no3)
|Squares:10
|-
|-
!Over-5 Harmonic
| Over-5 harmonic || {{dash|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)
|5:6:7:9:11
|P1 m3 vb5 m7 n9
|Im7d9(db5)
|Squares:12
|-
|-
!Miracle Harmonic
| Miracle harmonic || {{dash|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)
|4:5:7:13:17
|P1 M3 s7 n13 m16
|Ih7d13b16$
|Miracle:8
|-
|-
!A-Team Harmonic
| A-Team harmonic || {{dash|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)
|4:5:13:17:19
|P1 M3 n13 m16 m17
|IMd13b16b17$
|A-Team:11
|-
|-
!Joan Sharp Harmonic
| Joan sharp harmonic || {{dash|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)
|4:7:13:17:19
|P1 s7 n13 m16 m17
|I5s7d13b16b17$
|Joan:8
|-
|-
!Joan Flat Harmonic
| Joan flat harmonic || {{dash|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)
|4:7:9:11:15
|P1 s7 M9 ^11 M14
|I59s7t11M14$
|Joan:7
|-
|-
!Greeley Harmonic
| Greeley harmonic || {{dash|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)
|6:7:10:11:13
|P1 s3 M6 n7 n9
|IsM6n7d9$
|Nusecond:7
|}
|}






{| class="wikitable"
{| class="wikitable" style="text-align: left"
!Other Linear Pentads
! Other linear pentads !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation
!Otonal/Utonal Representation
!Notes
!Notation
!Complexity in Temperaments
|-
|-
!Slendric Pentad
| Slendric pentad || {{dash|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)
|42:48:55:63:72
|P1 S2 v4 P5 S6
|IS6sus(t2,d4)
|Mothra:4, Miracle:8, Valentine:12
|-
|-
!Miracle Cluster
| Miracle cluster || {{dash|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)
|13:14:15:16:17
|P1 m2 S2 n3 v4
|I(13:14:15:16:17)
|Miracle:4, Joan:8, Slender:12
|-
|-
!Orwell Pentad
| Orwell pentad || {{dash|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
|48:56:66:77:90
|P1 s3 ^4 m6 M7
|IOM7
|Orwell:4, A-Team:8, Myna:12
|}
|}




== Other Extended Chords ==
== Other extended chords ==


{| class="wikitable"
{| class="wikitable" style="text-align: left"
!
! !! JI ratios !! Harmonics !! 31edo steps !! Intervals !! Notation !! Comments
!Otonal/Utonal Representation
!Notes
!Notation
!Explanation
|-
|-
!Undecimal Hexad
| Undecimal hexad || {{dash|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.
|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
| Novemdecimal hexad || {{dash|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.
|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.
|-
|-
!?
| ? || {{dash|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.
|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.
|-
|-
!?
| ? || {{dash|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.
|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
| Rast minor parent chord || {{dash|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.
|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
| Graham hexad || {{dash|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.
|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.
|-
|-
!?
| ? || {{dash|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.
|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.
|-
|-
!?
| ? || {{dash|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.
|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.
|-
|-
!?
| ? || {{dash|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.
|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.
|-
|-
!?
| ? || {{dash|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.
|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
| Mothra[6] 5 parent chord || {{dash|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.
|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.
|}
|}


[[Category:31edo]]
[[Category:31edo]]
[[Category:Lists of chords]]
[[Category:Lists of chords]]
Retrieved from "https://en.xen.wiki/w/List_of_31edo_chords"