Chord Type: 0 1 2 3 4 11

0 1 2 3 4 11

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Modal System Fun Facts

0 1 2 3 4 5
• Inversionally Symmetrical
• Melodic adjacency = 1 (maximum).

General Statistics

Cardinality:                     6
Jordan Number:                   6-1
Forte Number:                    6-1
Forte Prime Form:                [0,1,2,3,4,5]
Zeitler Scale Name:
Ian Ring's Scale Page 2079

Root Reference:                  0 1 2 3 4 11
Tone Stacking:                   0 1 1 1 1 7
Interval Stacking:               1 1 1 1 7 1
Binary:                          1 1 1 1 1 0 0 0 0 0 0 1
Decimal Value:                   2079

Interval Vector:                 5 4 3 2 1 0
Inversional Symmetry:            yes (axes of symmetry: 1.5 7.5)
Transpositional Symmetry:        no
Melodic Adjacency (0-1):         1.000
Harmonic Adjacency (0-1):        0.333
Modal-system-invariant under multiplication by: 1 11
Modal System Balanced:           no

Diachromatic Family:             Scale Degrees: 122337
All Transpositions of Chord Type:
• +0= 0 1 2 3  4 11 |
+1= 0 1 2 3  4  5 |1st 6 notes of chromatic scale = type A all-combinatorial hexachord prime form
+2= 1 2 3 4  5  6 |
+3= 2 3 4 5  6  7 |
+4= 3 4 5 6  7  8 |
+5= 4 5 6 7  8  9 |
+6= 5 6 7 8  9 10 |
+7= 6 7 8 9 10 11 |
+8= 0 7 8 9 10 11 |
+9= 0 1 8 9 10 11 |
+10= 0 1 2 9 10 11 |
+11= 0 1 2 3 10 11 |
Modes of Chord Type:
• (mode 0) 0:  0 1 2 3  4 11 |
(mode 1) 1:  0 1 2 3 10 11 |
(mode 2) 2:  0 1 2 9 10 11 |
(mode 3) 3:  0 1 8 9 10 11 |
(mode 4) 4:  0 7 8 9 10 11 |
(mode 5) 11: 0 1 2 3  4  5 | 1st 6 notes of chromatic scale = type A all-combinatorial hexachord prime form
Modes of Chord Type Sorted by Rootedness:
Inversion at 0:               0 1 8 9 10 11
• (mode 0) 0:  0 1 8 9 10 11 |
(mode 1) 1:  0 7 8 9 10 11 |
(mode 2) 8:  0 1 2 3  4  5 | 1st 6 notes of chromatic scale = type A all-combinatorial hexachord prime form
(mode 3) 9:  0 1 2 3  4 11 |
(mode 4) 10: 0 1 2 3 10 11 |
(mode 5) 11: 0 1 2 9 10 11 |
Times 7:                      0 2 4 5 7 9
• (mode 0) 0: 0 2 4 5 7  9 | type C all-combinatorial hexachord prime form
(mode 1) 2: 0 2 3 5 7 10 | m11
(mode 2) 4: 0 1 3 5 8 10 |
(mode 3) 5: 0 2 4 7 9 11 | M13 no 11th = Guidonian hexachord = 6-note 5ths stack
(mode 4) 7: 0 2 5 7 9 10 |
(mode 5) 9: 0 3 5 7 8 10 | m7b13 no 9th
Times 5:                      0 3 5 7 8 10
• (mode 0) 0:  0 3 5 7 8 10 | m7b13 no 9th
(mode 1) 3:  0 2 4 5 7  9 | type C all-combinatorial hexachord prime form
(mode 2) 5:  0 2 3 5 7 10 | m11
(mode 3) 7:  0 1 3 5 8 10 |
(mode 4) 8:  0 2 4 7 9 11 | M13 no 11th = Guidonian hexachord = 6-note 5ths stack
(mode 5) 10: 0 2 5 7 9 10 |

Modal System:                     0 1 2 3 4 5 from root(s) 11 | "closed hexachord modal system = type A all-combinatorial hexachord modal system"
Modes of Modal System:
• (mode 0) 0: 0 1 2 3  4  5 | 1st 6 notes of chromatic scale = type A all-combinatorial hexachord prime form
(mode 1) 1: 0 1 2 3  4 11 |
(mode 2) 2: 0 1 2 3 10 11 |
(mode 3) 3: 0 1 2 9 10 11 |
(mode 4) 4: 0 1 8 9 10 11 |
(mode 5) 5: 0 7 8 9 10 11 |

Complement:                    5 6 7 8 9 10
• (mode 0) 5:  0 1 2 3  4  5 | 1st 6 notes of chromatic scale = type A all-combinatorial hexachord prime form
(mode 1) 6:  0 1 2 3  4 11 |
(mode 2) 7:  0 1 2 3 10 11 |
(mode 3) 8:  0 1 2 9 10 11 |
(mode 4) 9:  0 1 8 9 10 11 |
(mode 5) 10: 0 7 8 9 10 11 |
All but the root (subchroma complement of 0): 1 2 3 4 11
• (mode 0) 1:  0 1 2  3 10 |
(mode 1) 2:  0 1 2  9 11 |
(mode 2) 3:  0 1 8 10 11 |
(mode 3) 4:  0 7 9 10 11 |
(mode 4) 11: 0 2 3  4  5 |

De-Chromaticizations

• Dechromaticised: 4 11
• (mode 0) 4:  0 7 | perfect 5th = perfect 12th = diminished 6th = 2-note 5ths stack
(mode 1) 11: 0 5 | perfect 4th = perfect 11th = augmented third = 2-note 4ths stack
• Dechromaticised but Keep 0       0 4 11
• (mode 0) 0:  0 4 11 | M7 no 5th
(mode 1) 4:  0 7  8 |
(mode 2) 11: 0 1  5 |
• Dechromaticised but Keep 0 7     N/A
• Dechromaticised but Keep 0 3 4 7     0 3 4 11
• (mode 0) 0:  0 3 4 11 | M7#9 no 5th
(mode 1) 3:  0 1 8  9 |
(mode 2) 4:  0 7 8 11 |
(mode 3) 11: 0 1 4  5 | Greek chromatic tetrachord

• Alt-Dechromaticised: N/A
• Alt-Dechromaticised but Keep 0       N/A
• Alt-Dechromaticised but Keep 0 7     N/A
• Alt-Dechromaticised but Keep 0 3 4 7     N/A

Bright Layer Decomposition

•  order origin root set chord type (as pcset) 1 0 0 0 1 2 3 4 11 = 0: 0 1 2 3 4 11 = 1: 0 1 2 3 10 11 = 2: 0 1 2 9 10 11 = 3: 0 1 8 9 10 11 = 4: 0 7 8 9 10 11 = 11: 0 1 2 3 4 5 1 1 1 0 1 2 3 10 11 = 0: 0 1 2 3 10 11 = 1: 0 1 2 9 10 11 = 2: 0 1 8 9 10 11 = 3: 0 7 8 9 10 11 = 10: 0 1 2 3 4 5 = 11: 0 1 2 3 4 11 1 4 4 0 7 8 9 10 11 = 0: 0 7 8 9 10 11 = 7: 0 1 2 3 4 5 = 8: 0 1 2 3 4 11 = 9: 0 1 2 3 10 11 = 10: 0 1 2 9 10 11 = 11: 0 1 8 9 10 11 1 11 11 0 1 2 3 4 5 = 0: 0 1 2 3 4 5 = 1: 0 1 2 3 4 11 = 2: 0 1 2 3 10 11 = 3: 0 1 2 9 10 11 = 4: 0 1 8 9 10 11 = 5: 0 7 8 9 10 11

Bright Layer Composition

•  order pcset 1 0 1 2 3 4 11 = 0: 0 1 2 3 4 11 = 1: 0 1 2 3 10 11 = 2: 0 1 2 9 10 11 = 3: 0 1 8 9 10 11 = 4: 0 7 8 9 10 11 = 11: 0 1 2 3 4 5 2 0 1 2 3 4 6 7 8 9 10 11 = 0: 0 1 2 3 4 6 7 8 9 10 11 = 1: 0 1 2 3 5 6 7 8 9 10 11 = 2: 0 1 2 4 5 6 7 8 9 10 11 = 3: 0 1 3 4 5 6 7 8 9 10 11 = 4: 0 2 3 4 5 6 7 8 9 10 11 = 6: 0 1 2 3 4 5 6 7 8 9 10 = 7: 0 1 2 3 4 5 6 7 8 9 11 = 8: 0 1 2 3 4 5 6 7 8 10 11 = 9: 0 1 2 3 4 5 6 7 9 10 11 = 10: 0 1 2 3 4 5 6 8 9 10 11 = 11: 0 1 2 3 4 5 7 8 9 10 11 3 0 1 2 3 4 5 6 7 8 9 10 11 = 0: 0 1 2 3 4 5 6 7 8 9 10 11 = 1: 0 1 2 3 4 5 6 7 8 9 10 11 = 2: 0 1 2 3 4 5 6 7 8 9 10 11 = 3: 0 1 2 3 4 5 6 7 8 9 10 11 = 4: 0 1 2 3 4 5 6 7 8 9 10 11 = 5: 0 1 2 3 4 5 6 7 8 9 10 11 = 6: 0 1 2 3 4 5 6 7 8 9 10 11 = 7: 0 1 2 3 4 5 6 7 8 9 10 11 = 8: 0 1 2 3 4 5 6 7 8 9 10 11 = 9: 0 1 2 3 4 5 6 7 8 9 10 11 = 10: 0 1 2 3 4 5 6 7 8 9 10 11 = 11: 0 1 2 3 4 5 6 7 8 9 10 11

Subset Chord Types by Subchroma Modal System

• Subchroma Modal Systems of 0 1 2 3 4 11

subchroma modal system: 0
0 =  0 =  0:  0
1 =  1 =  1:  0
2 =  2 =  2:  0
3 =  3 =  3:  0
4 =  4 =  4:  0
11 = 11 = 11:  0

subchroma modal system: 0 1
0  1 =  0  1 =  0:  0  1     1:  0 11
1  2 =  1  2 =  1:  0  1     2:  0 11
2  3 =  2  3 =  2:  0  1     3:  0 11
3  4 =  3  4 =  3:  0  1     4:  0 11
4 11 =  4 11 = 11:  0  5     4:  0  7
11  0 =  0 11 = 11:  0  1     0:  0 11

subchroma modal system: 0 2
0  2 =  0  2 =  0:  0  2     2:  0 10
1  3 =  1  3 =  1:  0  2     3:  0 10
2  4 =  2  4 =  2:  0  2     4:  0 10
3 11 =  3 11 = 11:  0  4     3:  0  8
4  0 =  0  4 =  0:  0  4     4:  0  8
11  1 =  1 11 = 11:  0  2     1:  0 10

subchroma modal system: 0 3
0  3 =  0  3 =  0:  0  3     3:  0  9
1  4 =  1  4 =  1:  0  3     4:  0  9
2 11 =  2 11 = 11:  0  3     2:  0  9
3  0 =  0  3 =  0:  0  3     3:  0  9
4  1 =  1  4 =  1:  0  3     4:  0  9
11  2 =  2 11 = 11:  0  3     2:  0  9

subchroma modal system: 0 1 2
0  1  2 =  0  1  2 =  0:  0  1  2     1:  0  1 11     2:  0 10 11
1  2  3 =  1  2  3 =  1:  0  1  2     2:  0  1 11     3:  0 10 11
2  3  4 =  2  3  4 =  2:  0  1  2     3:  0  1 11     4:  0 10 11
3  4 11 =  3  4 11 = 11:  0  4  5     4:  0  7 11
4 11  0 =  0  4 11 =  0:  0  4 11     4:  0  7  8
11  0  1 =  0  1 11 = 11:  0  1  2     0:  0  1 11     1:  0 10 11

subchroma modal system: 0 1 3
0  1  3 =  0  1  3 =  0:  0  1  3     1:  0  2 11
1  2  4 =  1  2  4 =  1:  0  1  3     2:  0  2 11
2  3 11 =  2  3 11 = 11:  0  3  4
3  4  0 =  0  3  4 =  0:  0  3  4
4 11  1 =  1  4 11 =  1:  0  3 10     4:  0  7  9
11  0  2 =  0  2 11 = 11:  0  1  3     0:  0  2 11

subchroma modal system: 0 1 4
0  1  4 =  0  1  4 =  0:  0  1  4     1:  0  3 11
1  2 11 =  1  2 11 = 11:  0  2  3
2  3  0 =  0  2  3 =  0:  0  2  3
3  4  1 =  1  3  4 =  1:  0  2  3
4 11  2 =  2  4 11 = 11:  0  3  5     4:  0  7 10
11  0  3 =  0  3 11 = 11:  0  1  4     0:  0  3 11

subchroma modal system: 0 2 4
0  2  4 =  0  2  4 =  0:  0  2  4
1  3 11 =  1  3 11 = 11:  0  2  4
2  4  0 =  0  2  4 =  0:  0  2  4
3 11  1 =  1  3 11 = 11:  0  2  4
4  0  2 =  0  2  4 =  0:  0  2  4
11  1  3 =  1  3 11 = 11:  0  2  4

subchroma modal system: 0 1 2 3
0  1  2  3 =  0  1  2  3 =  0:  0  1  2  3     2:  0  1 10 11     3:  0  9 10 11
1  2  3  4 =  1  2  3  4 =  1:  0  1  2  3     3:  0  1 10 11     4:  0  9 10 11
2  3  4 11 =  2  3  4 11 = 11:  0  3  4  5     4:  0  7 10 11
3  4 11  0 =  0  3  4 11 = 11:  0  1  4  5     0:  0  3  4 11     4:  0  7  8 11
4 11  0  1 =  0  1  4 11 =  0:  0  1  4 11     1:  0  3 10 11     4:  0  7  8  9
11  0  1  2 =  0  1  2 11 = 11:  0  1  2  3     1:  0  1 10 11     2:  0  9 10 11

subchroma modal system: 0 1 2 4
0  1  2  4 =  0  1  2  4 =  0:  0  1  2  4     1:  0  1  3 11     2:  0  2 10 11
1  2  3 11 =  1  2  3 11 = 11:  0  2  3  4
2  3  4  0 =  0  2  3  4 =  0:  0  2  3  4
3  4 11  1 =  1  3  4 11 = 11:  0  2  4  5     1:  0  2  3 10     4:  0  7  9 11
4 11  0  2 =  0  2  4 11 = 11:  0  1  3  5     0:  0  2  4 11     2:  0  2  9 10     4:  0  7  8 10
11  0  1  3 =  0  1  3 11 = 11:  0  1  2  4     0:  0  1  3 11     1:  0  2 10 11

subchroma modal system: 0 1 3 4
0  1  3  4 =  0  1  3  4 =  0:  0  1  3  4     1:  0  2  3 11
1  2  4 11 =  1  2  4 11 = 11:  0  2  3  5     1:  0  1  3 10     2:  0  2  9 11     4:  0  7  9 10
2  3 11  0 =  0  2  3 11 = 11:  0  1  3  4     0:  0  2  3 11
3  4  0  1 =  0  1  3  4 =  0:  0  1  3  4     1:  0  2  3 11
4 11  1  2 =  1  2  4 11 = 11:  0  2  3  5     1:  0  1  3 10     2:  0  2  9 11     4:  0  7  9 10
11  0  2  3 =  0  2  3 11 = 11:  0  1  3  4     0:  0  2  3 11

subchroma modal system: 0 1 2 3 4
0  1  2  3  4 =  0  1  2  3  4 =  0:  0  1  2  3  4     1:  0  1  2  3 11     4:  0  8  9 10 11
1  2  3  4 11 =  1  2  3  4 11 =  1:  0  1  2  3 10     4:  0  7  9 10 11
2  3  4 11  0 =  0  2  3  4 11 = 11:  0  1  3  4  5     0:  0  2  3  4 11     2:  0  1  2  9 10     4:  0  7  8 10 11
3  4 11  0  1 =  0  1  3  4 11 = 11:  0  1  2  4  5     0:  0  1  3  4 11     1:  0  2  3 10 11     4:  0  7  8  9 11
4 11  0  1  2 =  0  1  2  4 11 = 11:  0  1  2  3  5     0:  0  1  2  4 11     1:  0  1  3 10 11     2:  0  2  9 10 11     4:  0  7  8  9 10
11  0  1  2  3 =  0  1  2  3 11 = 11:  0  1  2  3  4     0:  0  1  2  3 11     3:  0  8  9 10 11

subchroma modal system: 0 1 2 3 4 5
0  1  2  3  4 11 =  0  1  2  3  4 11 = 11:  0  1  2  3  4  5     0:  0  1  2  3  4 11     1:  0  1  2  3 10 11     4:  0  7  8  9 10 11
1  2  3  4 11  0 =  0  1  2  3  4 11 = 11:  0  1  2  3  4  5     0:  0  1  2  3  4 11     1:  0  1  2  3 10 11     4:  0  7  8  9 10 11
2  3  4 11  0  1 =  0  1  2  3  4 11 = 11:  0  1  2  3  4  5     0:  0  1  2  3  4 11     1:  0  1  2  3 10 11     4:  0  7  8  9 10 11
3  4 11  0  1  2 =  0  1  2  3  4 11 = 11:  0  1  2  3  4  5     0:  0  1  2  3  4 11     1:  0  1  2  3 10 11     4:  0  7  8  9 10 11
4 11  0  1  2  3 =  0  1  2  3  4 11 = 11:  0  1  2  3  4  5     0:  0  1  2  3  4 11     1:  0  1  2  3 10 11     4:  0  7  8  9 10 11
11  0  1  2  3  4 =  0  1  2  3  4 11 = 11:  0  1  2  3  4  5     0:  0  1  2  3  4 11     1:  0  1  2  3 10 11     4:  0  7  8  9 10 11

Subset Chord Types By Family

•  Chord Type Roots Unison (Scale Degrees: 1) 0 = root, unison, octave | 0 1 2 3 4 11 = 0: 0 1 2 3 4 11 = 1: 0 1 2 3 10 11 = 2: 0 1 2 9 10 11 = 3: 0 1 8 9 10 11 = 4: 0 7 8 9 10 11 = 11: 0 1 2 3 4 5 2nds / 9ths = 1st 2 notes of diamorphic scale (Scale Degrees: 12) 0 1 = semitone, min. 2nd, min. 9th | 0 1 2 3 11 = 0: 0 1 2 3 11 = 1: 0 1 2 10 11 = 2: 0 1 9 10 11 = 3: 0 8 9 10 11 = 11: 0 1 2 3 4 0 2 = maj. 2nd, dim., maj. 9th | 0 1 2 11 = 0: 0 1 2 11 = 1: 0 1 10 11 = 2: 0 9 10 11 = 11: 0 1 2 3 3rds / 10ths (Scale Degrees: 13) 0 3 = aug. 2nd, min. 3rd, aug. 9th | 0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2 0 4 = maj. 3rd, maj. 10th, dim. 4th | 0 11 = 0: 0 11 = 11: 0 1 4ths / 11ths (Scale Degrees: 14) 0 5 = 4th, 11th, 2 in 4ths | 11 = 11: 0 5ths / 12ths (Scale Degrees: 15) 0 7 = 5th, 2 in 5ths | 4 = 4: 0 6ths / 13ths (Scale Degrees: 16) 0 8 = aug. 5th, min. 6th, aug. 12th, min. 13th | 3 4 = 3: 0 1 = 4: 0 11 0 9 = maj. 6th, maj. 13th, dim. 7th | 2 3 4 = 2: 0 1 2 = 3: 0 1 11 = 4: 0 10 11 7ths / 14ths (Scale Degrees: 17) 0 10 = aug. 6th, min. 7th, aug. 13th | 1 2 3 4 = 1: 0 1 2 3 = 2: 0 1 2 11 = 3: 0 1 10 11 = 4: 0 9 10 11 0 11 = maj. 7th, maj. 14th | 0 1 2 3 4 = 0: 0 1 2 3 4 = 1: 0 1 2 3 11 = 2: 0 1 2 10 11 = 3: 0 1 9 10 11 = 4: 0 8 9 10 11 chromatic trichord (Scale Degrees: 122) 0 1 2 = 1st 3 chromatics | 0 1 2 11 = 0: 0 1 2 11 = 1: 0 1 10 11 = 2: 0 9 10 11 = 11: 0 1 2 3 1st 3 notes of diamorphic scale (Scale Degrees: 123) 0 1 3 | 0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2 0 1 4 | 0 11 = 0: 0 11 = 11: 0 1 0 2 3 = min. trichord | 0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2 0 2 4 = maj. trichord | 0 11 = 0: 0 11 = 11: 0 1 0 3 4 | 0 11 = 0: 0 11 = 11: 0 1 Root with upper and lower neighbors (Scale Degrees: 127) 0 1 11 = root & chr. neighbors | 0 1 2 3 = 0: 0 1 2 3 = 1: 0 1 2 11 = 2: 0 1 10 11 = 3: 0 9 10 11 0 2 11 | 0 1 2 = 0: 0 1 2 = 1: 0 1 11 = 2: 0 10 11 Scale Degrees: 134 0 3 5 | 11 = 11: 0 0 4 5 | 11 = 11: 0 7th chords no 5th (Scale Degrees: 137) 0 3 10 = m7 no 5th | 1 = 1: 0 0 3 11 = mM7 no 5th | 0 1 = 0: 0 1 = 1: 0 11 0 4 11 = M7 no 5th | 0 = 0: 0 6th chords no 3rd (Scale Degrees: 156) 0 7 8 | 4 = 4: 0 0 7 9 | 4 = 4: 0 7th chords no 3rd (Scale Degrees: 157) 0 7 10 = m power chord | 4 = 4: 0 0 7 11 = M power chord | 4 = 4: 0 Scale Degrees: 167 0 10 11 | 1 2 3 4 = 1: 0 1 2 3 = 2: 0 1 2 11 = 3: 0 1 10 11 = 4: 0 9 10 11 chromatic tetrachord (Scale Degrees: 1223) 0 1 2 3 = chromatic tetrachord | 0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2 0 1 2 4 | 0 11 = 0: 0 11 = 11: 0 1 0 1 3 4 = 1st 4 aux dim. | 0 11 = 0: 0 11 = 11: 0 1 0 2 3 4 | 0 11 = 0: 0 11 = 11: 0 1 1st 3 notes of diamorphic scale (Scale Degrees: 1234) 0 1 3 5 = Greek diatonic tetrachord | 11 = 11: 0 0 1 4 5 = Greek chromatic tetrachord | 11 = 11: 0 0 2 3 5 = min. tetrachord | 11 = 11: 0 0 2 4 5 = maj. tetrachord | 11 = 11: 0 0 3 4 5 | 11 = 11: 0 9th chords no 5th (Scale Degrees: 1237) 0 1 3 10 = M7b9 no 5th | 1 = 1: 0 0 1 3 11 = Mm7b9 no 5th | 0 1 = 0: 0 1 = 1: 0 11 0 1 4 11 = M7b9 no 5th | 0 = 0: 0 0 2 3 10 = m9 no 5th | 1 = 1: 0 0 2 3 11 = mM9 no 5th | 0 1 = 0: 0 1 = 1: 0 11 0 2 4 11 = M9 no 5th | 0 = 0: 0 0 3 4 11 = M7#9 no 5th | 0 = 0: 0 13th chords no 3rd no 5th no 11th (Scale Degrees: 1267) 0 1 10 11 | 1 2 3 = 1: 0 1 2 = 2: 0 1 11 = 3: 0 10 11 0 2 9 10 | 2 = 2: 0 0 2 9 11 | 2 = 2: 0 0 2 10 11 | 1 2 = 1: 0 1 = 2: 0 11 6/7 chords no 5th (Scale Degrees: 1367) 0 3 10 11 = mM7#6 no 5th | 1 = 1: 0 Scale Degrees: 1566 0 7 8 9 | 4 = 4: 0 Scale Degrees: 1567 0 7 8 10 | 4 = 4: 0 0 7 8 11 | 4 = 4: 0 0 7 9 10 | 4 = 4: 0 0 7 9 11 | 4 = 4: 0 0 7 10 11 | 4 = 4: 0 Scale Degrees: 1667 0 9 10 11 | 2 3 4 = 2: 0 1 2 = 3: 0 1 11 = 4: 0 10 11 chromatic pentachord (Scale Degrees: 12233) 0 1 2 3 4 = 1st 5 chromatics | 0 11 = 0: 0 11 = 11: 0 1 Scale Degrees: 12234 0 1 2 3 5 | 11 = 11: 0 0 1 2 4 5 | 11 = 11: 0 0 1 3 4 5 | 11 = 11: 0 Scale Degrees: 12237 0 1 2 3 10 | 1 = 1: 0 0 1 2 3 11 | 0 1 = 0: 0 1 = 1: 0 11 0 1 2 4 11 | 0 = 0: 0 0 1 3 4 11 | 0 = 0: 0 0 2 3 4 11 | 0 = 0: 0 Scale Degrees: 12267 0 1 2 9 10 | 2 = 2: 0 13th chords no 5th no 11th (Scale Degrees: 12367) 0 1 3 10 11 = mM#13b9 no 5th no 11th | 1 = 1: 0 0 2 3 10 11 = m#13 no 5th no 11th | 1 = 1: 0 Scale Degrees: 12667 0 2 9 10 11 | 2 = 2: 0 Scale Degrees: 15667 0 7 8 9 10 | 4 = 4: 0 0 7 8 9 11 | 4 = 4: 0 0 7 8 10 11 | 4 = 4: 0 0 7 9 10 11 | 4 = 4: 0 Scale Degrees: 16677 0 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 chromatic hexachord (Scale Degrees: 122334) 0 1 2 3 4 5 = 1st 6 chromatics, type A ACH | 11 = 11: 0 Scale Degrees: 122337 0 1 2 3 4 11 | 0 = 0: 0 Scale Degrees: 122367 0 1 2 3 10 11 | 1 = 1: 0 Scale Degrees: 156677 0 7 8 9 10 11 | 4 = 4: 0

Superset Chord Types By Family

•  Chord Type Roots chromatic hexachord (Scale Degrees: 122334) 0 1 2 3 4 5 = 1st 6 chromatics, type A ACH | 11 = 11: 0 Scale Degrees: 122337 0 1 2 3 4 11 | 0 = 0: 0 Scale Degrees: 122367 0 1 2 3 10 11 | 1 = 1: 0 Scale Degrees: 156677 0 7 8 9 10 11 | 4 = 4: 0 chromatic septachord (Scale Degrees: 1223345) 0 1 2 3 4 5 6 = 1st 7 chromatics | 10 11 = 10: 0 1 = 11: 0 11 0 1 2 3 4 5 7 | 11 = 11: 0 Scale Degrees: 1223347 0 1 2 3 4 5 10 | 11 = 11: 0 Scale Degrees: 1223357 0 1 2 3 4 7 11 | 0 = 0: 0 0 1 2 3 4 8 11 | 0 = 0: 0 Scale Degrees: 1223367 0 1 2 3 4 9 11 | 0 = 0: 0 0 1 2 3 4 10 11 | 0 1 = 0: 0 1 = 1: 0 11 Scale Degrees: 1223445 0 2 3 4 5 6 7 | 9 = 9: 0 Scale Degrees: 1223567 0 1 2 3 6 10 11 | 1 = 1: 0 0 1 2 3 7 10 11 | 1 = 1: 0 Scale Degrees: 1223667 0 1 2 4 9 10 11 | 2 = 2: 0 Scale Degrees: 1225667 0 1 2 7 9 10 11 | 2 = 2: 0 Scale Degrees: 1234456 0 3 4 5 6 7 8 | 8 = 8: 0 Scale Degrees: 1256677 0 1 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 2 7 8 9 10 11 | 4 = 4: 0 Scale Degrees: 1344566 0 4 5 6 7 8 9 | 7 = 7: 0 Scale Degrees: 1356677 0 3 7 8 9 10 11 | 4 = 4: 0 0 4 7 8 9 10 11 | 4 = 4: 0 Scale Degrees: 1456677 0 5 7 8 9 10 11 | 4 = 4: 0 0 6 7 8 9 10 11 | 4 5 = 4: 0 1 = 5: 0 11 chromatic octachord (Scale Degrees: 12223445) 0 1 2 3 4 5 6 7 = 1st 8 chromatics | 9 10 11 = 9: 0 1 2 = 10: 0 1 11 = 11: 0 10 11 Scale Degrees: 12223456 0 1 2 3 4 5 7 8 | 11 = 11: 0 0 1 2 3 4 5 7 9 | 11 = 11: 0 Scale Degrees: 12223457 0 1 2 3 4 5 7 10 | 11 = 11: 0 0 1 2 3 4 5 7 11 | 0 11 = 0: 0 11 = 11: 0 1 0 1 2 3 4 6 7 11 | 0 = 0: 0 Scale Degrees: 12223567 0 1 2 3 4 7 8 11 | 0 = 0: 0 0 1 2 3 4 7 9 11 | 0 = 0: 0 0 1 2 3 4 7 10 11 | 0 1 = 0: 0 1 = 1: 0 11 0 1 2 3 4 8 10 11 | 0 1 = 0: 0 1 = 1: 0 11 Scale Degrees: 12223667 0 1 2 3 4 9 10 11 | 0 1 2 = 0: 0 1 2 = 1: 0 1 11 = 2: 0 10 11 Scale Degrees: 12233457 0 1 2 3 4 5 6 10 | 10 11 = 10: 0 1 = 11: 0 11 Scale Degrees: 12234456 0 1 3 4 5 6 7 8 | 8 = 8: 0 Scale Degrees: 12234457 0 2 3 4 5 6 7 10 | 9 = 9: 0 0 2 3 4 5 6 7 11 | 9 = 9: 0 diamorphic with supplementary 2nd (Scale Degrees: 12234567) 0 1 2 3 5 7 10 11 | 1 = 1: 0 0 1 2 3 6 7 10 11 | 1 = 1: 0 Scale Degrees: 12235667 0 1 2 3 7 8 10 11 | 1 = 1: 0 0 1 2 3 7 9 10 11 | 1 2 = 1: 0 1 = 2: 0 11 0 1 2 4 7 9 10 11 | 2 = 2: 0 0 1 3 4 8 9 10 11 | 3 = 3: 0 Scale Degrees: 12245667 0 1 2 5 7 9 10 11 | 2 = 2: 0 0 1 2 6 7 9 10 11 | 2 = 2: 0 Scale Degrees: 12256677 0 1 2 7 8 9 10 11 | 2 3 4 = 2: 0 1 2 = 3: 0 1 11 = 4: 0 10 11 chromatic nonachord (Scale Degrees: 12344456) 0 2 3 4 5 6 7 8 | 8 9 = 8: 0 1 = 9: 0 11 0 2 3 4 5 6 7 9 | 9 = 9: 0 diamorphic with supplementary 4th (Scale Degrees: 12344567) 0 1 4 5 6 7 8 9 | 7 = 7: 0 0 3 4 5 6 7 8 10 | 8 = 8: 0 0 3 4 5 6 7 8 11 | 8 = 8: 0 Scale Degrees: 12356677 0 1 3 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 1 4 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 2 3 7 8 9 10 11 | 4 = 4: 0 0 2 4 7 8 9 10 11 | 4 = 4: 0 0 3 4 7 8 9 10 11 | 4 = 4: 0 Scale Degrees: 12445667 0 2 5 6 7 8 9 10 | 6 = 6: 0 Scale Degrees: 12456677 0 1 5 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 1 6 7 8 9 10 11 | 3 4 5 = 3: 0 1 2 = 4: 0 1 11 = 5: 0 10 11 0 2 5 7 8 9 10 11 | 4 = 4: 0 0 2 6 7 8 9 10 11 | 4 5 = 4: 0 1 = 5: 0 11 Scale Degrees: 13445667 0 3 5 6 7 8 9 10 | 6 = 6: 0 0 4 5 6 7 8 9 10 | 6 7 = 6: 0 1 = 7: 0 11 Scale Degrees: 13456677 0 3 5 7 8 9 10 11 | 4 = 4: 0 0 3 6 7 8 9 10 11 | 4 5 = 4: 0 1 = 5: 0 11 0 4 5 7 8 9 10 11 | 4 = 4: 0 0 4 6 7 8 9 10 11 | 4 5 = 4: 0 1 = 5: 0 11 Scale Degrees: 122334456 0 1 2 3 4 5 6 7 8 = 1st 9chromatics | 8 9 10 11 = 8: 0 1 2 3 = 9: 0 1 2 11 = 10: 0 1 10 11 = 11: 0 9 10 11 0 1 2 3 4 5 6 7 9 | 9 10 11 = 9: 0 1 2 = 10: 0 1 11 = 11: 0 10 11 Scale Degrees: 122334457 0 1 2 3 4 5 6 7 10 | 9 10 11 = 9: 0 1 2 = 10: 0 1 11 = 11: 0 10 11 0 1 2 3 4 5 6 7 11 | 0 9 10 11 = 0: 0 9 10 11 = 9: 0 1 2 3 = 10: 0 1 2 11 = 11: 0 1 10 11 Scale Degrees: 122334566 0 1 2 3 4 5 7 8 9 | 11 = 11: 0 diamorphic with supplementary 2nd, 3rd (Scale Degrees: 122334567) 0 1 2 3 4 5 6 8 10 = whole tone & locrian | 10 11 = 10: 0 1 = 11: 0 11 0 1 2 3 4 5 6 9 10 | 10 11 = 10: 0 1 = 11: 0 11 0 1 2 3 4 5 7 8 10 | 11 = 11: 0 0 1 2 3 4 5 7 8 11 | 0 11 = 0: 0 11 = 11: 0 1 0 1 2 3 4 5 7 9 10 | 11 = 11: 0 0 1 2 3 4 5 7 9 11 | 0 11 = 0: 0 11 = 11: 0 1 0 1 2 3 4 5 7 10 11 | 0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2 0 1 2 3 4 6 7 8 11 | 0 = 0: 0 0 1 2 3 4 6 7 9 11 | 0 = 0: 0 0 1 2 3 4 6 7 10 11 | 0 1 = 0: 0 1 = 1: 0 11 0 1 2 3 4 6 8 10 11 | 0 1 = 0: 0 1 = 1: 0 11 Scale Degrees: 122335667 0 1 2 3 4 7 8 9 11 | 0 = 0: 0 0 1 2 3 4 7 8 10 11 | 0 1 = 0: 0 1 = 1: 0 11 0 1 2 3 4 7 9 10 11 | 0 1 2 = 0: 0 1 2 = 1: 0 1 11 = 2: 0 10 11 Scale Degrees: 122344566 0 1 2 4 5 6 7 8 9 | 7 = 7: 0 0 2 3 4 5 6 7 8 9 | 7 8 9 = 7: 0 1 2 = 8: 0 1 11 = 9: 0 10 11 diamorphic with supplementary 2nd, 4th (Scale Degrees: 122344567) 0 1 2 3 5 6 7 10 11 | 1 = 1: 0 0 1 3 4 5 6 7 8 10 | 8 = 8: 0 0 1 3 4 5 6 7 8 11 | 8 = 8: 0 0 2 3 4 5 6 7 8 10 = whole tone & aeolean | 8 9 = 8: 0 1 = 9: 0 11 0 2 3 4 5 6 7 8 11 | 8 9 = 8: 0 1 = 9: 0 11 0 2 3 4 5 6 7 9 10 | 9 = 9: 0 0 2 3 4 5 6 7 9 11 = lydian & mel. min. | 9 = 9: 0 0 2 3 4 5 6 7 10 11 | 9 = 9: 0 diamorphic with supplementary 2nd, 6th (Scale Degrees: 122345667) 0 1 2 3 5 7 8 10 11 = phrygian & harm. min. | 1 = 1: 0 0 1 2 3 5 7 9 10 11 | 1 2 = 1: 0 1 = 2: 0 11 0 1 2 3 6 7 8 10 11 | 1 = 1: 0 0 1 2 3 6 7 9 10 11 | 1 2 = 1: 0 1 = 2: 0 11 0 1 2 4 5 7 9 10 11 | 2 = 2: 0 0 1 2 4 6 7 9 10 11 | 2 = 2: 0 Scale Degrees: 122356677 0 1 3 4 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 2 3 4 7 8 9 10 11 | 4 = 4: 0 Scale Degrees: 122456677 0 1 2 5 7 8 9 10 11 = Kanakangi | 2 3 4 = 2: 0 1 2 = 3: 0 1 11 = 4: 0 10 11 0 1 2 6 7 8 9 10 11 | 2 3 4 5 = 2: 0 1 2 3 = 3: 0 1 2 11 = 4: 0 1 10 11 = 5: 0 9 10 11 Scale Degrees: 123356677 0 1 2 3 7 8 9 10 11 | 1 2 3 4 = 1: 0 1 2 3 = 2: 0 1 2 11 = 3: 0 1 10 11 = 4: 0 9 10 11 0 1 2 4 7 8 9 10 11 | 2 3 4 = 2: 0 1 2 = 3: 0 1 11 = 4: 0 10 11 diamorphic with supplementary 4th, 6th (Scale Degrees: 123445667) 0 1 3 5 6 7 8 9 10 | 6 = 6: 0 0 1 4 5 6 7 8 9 10 | 6 7 = 6: 0 1 = 7: 0 11 0 1 4 5 6 7 8 9 11 | 7 = 7: 0 0 2 3 5 6 7 8 9 10 | 6 = 6: 0 0 2 4 5 6 7 8 9 10 = whole tone & mixolydian | 6 7 = 6: 0 1 = 7: 0 11 0 2 4 5 6 7 8 9 11 | 7 = 7: 0 diamorphic with supplementary 4th, 7th (Scale Degrees: 123445677) 0 3 4 5 6 7 8 9 10 | 6 7 8 = 6: 0 1 2 = 7: 0 1 11 = 8: 0 10 11 0 3 4 5 6 7 8 9 11 | 7 8 = 7: 0 1 = 8: 0 11 0 3 4 5 6 7 8 10 11 | 8 = 8: 0 diamorphic with supplementary 6th, 7th (Scale Degrees: 123456677) 0 1 3 5 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 1 3 6 7 8 9 10 11 | 3 4 5 = 3: 0 1 2 = 4: 0 1 11 = 5: 0 10 11 0 1 4 5 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 1 4 6 7 8 9 10 11 | 3 4 5 = 3: 0 1 2 = 4: 0 1 11 = 5: 0 10 11 0 2 3 5 7 8 9 10 11 = dorian & harm. min., aeolean & mel. min. | 4 = 4: 0 0 2 3 6 7 8 9 10 11 | 4 5 = 4: 0 1 = 5: 0 11 0 2 4 5 7 8 9 10 11 | 4 = 4: 0 0 2 4 6 7 8 9 10 11 = whole tone & lydian | 4 5 = 4: 0 1 = 5: 0 11 0 3 4 5 7 8 9 10 11 | 4 = 4: 0 0 3 4 6 7 8 9 10 11 | 4 5 = 4: 0 1 = 5: 0 11 Scale Degrees: 134456667 0 3 5 6 7 8 9 10 11 | 4 5 6 = 4: 0 1 2 = 5: 0 1 11 = 6: 0 10 11 Scale Degrees: 134456677 0 4 5 6 7 8 9 10 11 | 4 5 6 7 = 4: 0 1 2 3 = 5: 0 1 2 11 = 6: 0 1 10 11 = 7: 0 9 10 11 chromatic decachord (Scale Degrees: 1223344566) 0 1 2 3 4 5 6 7 8 9 = 1st 10 chromatics | 7 8 9 10 11 = 7: 0 1 2 3 4 = 8: 0 1 2 3 11 = 9: 0 1 2 10 11 = 10: 0 1 9 10 11 = 11: 0 8 9 10 11 diamorphic with supplementary 2nd, 3rd, 4th (Scale Degrees: 1223344567) 0 1 2 3 4 5 6 7 8 10 = whole tone & phrygian | 8 9 10 11 = 8: 0 1 2 3 = 9: 0 1 2 11 = 10: 0 1 10 11 = 11: 0 9 10 11 0 1 2 3 4 5 6 7 8 11 | 0 8 9 10 11 = 0: 0 8 9 10 11 = 8: 0 1 2 3 4 = 9: 0 1 2 3 11 = 10: 0 1 2 10 11 = 11: 0 1 9 10 11 0 1 2 3 4 5 6 7 9 10 = auxdim. scale & dorian | 9 10 11 = 9: 0 1 2 = 10: 0 1 11 = 11: 0 10 11 0 1 2 3 4 5 6 7 9 11 | 0 9 10 11 = 0: 0 9 10 11 = 9: 0 1 2 3 = 10: 0 1 2 11 = 11: 0 1 10 11 0 1 2 3 4 5 6 7 10 11 | 0 1 9 10 11 = 0: 0 1 9 10 11 = 1: 0 8 9 10 11 = 9: 0 1 2 3 4 = 10: 0 1 2 3 11 = 11: 0 1 2 10 11 diamorphic with supplementary 2nd, 3rd, 6th (Scale Degrees: 1223345667) 0 1 2 3 4 5 6 8 9 10 | 10 11 = 10: 0 1 = 11: 0 11 0 1 2 3 4 5 6 8 9 11 | 0 10 11 = 0: 0 10 11 = 10: 0 1 2 = 11: 0 1 11 0 1 2 3 4 5 6 8 10 11 | 0 1 10 11 = 0: 0 1 10 11 = 1: 0 9 10 11 = 10: 0 1 2 3 = 11: 0 1 2 11 0 1 2 3 4 5 6 9 10 11 | 0 1 2 10 11 = 0: 0 1 2 10 11 = 1: 0 1 9 10 11 = 2: 0 8 9 10 11 = 10: 0 1 2 3 4 = 11: 0 1 2 3 11 0 1 2 3 4 5 7 8 9 10 = mixophrygian | 11 = 11: 0 0 1 2 3 4 5 7 8 9 11 = 014589 & mel. min. | 0 11 = 0: 0 11 = 11: 0 1 0 1 2 3 4 5 7 8 10 11 | 0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2 0 1 2 3 4 5 7 9 10 11 | 0 1 2 11 = 0: 0 1 2 11 = 1: 0 1 10 11 = 2: 0 9 10 11 = 11: 0 1 2 3 0 1 2 3 4 5 8 9 10 11 | 0 1 2 3 11 = 0: 0 1 2 3 11 = 1: 0 1 2 10 11 = 2: 0 1 9 10 11 = 3: 0 8 9 10 11 = 11: 0 1 2 3 4 0 1 2 3 4 6 7 8 9 11 = 10 in 5ths | 0 = 0: 0 0 1 2 3 4 6 7 8 10 11 | 0 1 = 0: 0 1 = 1: 0 11 0 1 2 3 4 6 7 9 10 11 = auxdim. scale & lydian | 0 1 2 = 0: 0 1 2 = 1: 0 1 11 = 2: 0 10 11 0 1 2 3 4 6 8 9 10 11 | 0 1 2 3 = 0: 0 1 2 3 = 1: 0 1 2 11 = 2: 0 1 10 11 = 3: 0 9 10 11 Scale Degrees: 1223356667 0 1 2 3 4 7 8 9 10 11 | 0 1 2 3 4 = 0: 0 1 2 3 4 = 1: 0 1 2 3 11 = 2: 0 1 2 10 11 = 3: 0 1 9 10 11 = 4: 0 8 9 10 11 diamorphic with supplementary 2nd, 4th, 6th (Scale Degrees: 1223445667) 0 1 2 3 5 6 7 8 9 10 = locridorian | 6 = 6: 0 0 1 2 3 5 6 7 8 10 11 = locrian & harm. min. | 1 = 1: 0 0 1 2 3 5 6 7 9 10 11 = 12569A & mel. min. | 1 2 = 1: 0 1 = 2: 0 11 0 1 2 3 5 6 8 9 10 11 = dim. scale & locrian | 1 2 3 = 1: 0 1 2 = 2: 0 1 11 = 3: 0 10 11 0 1 2 4 5 6 7 8 9 10 | 6 7 = 6: 0 1 = 7: 0 11 0 1 2 4 5 6 7 8 9 11 | 7 = 7: 0 0 1 2 4 5 6 7 9 10 11 = 12569A & bebop maj. | 2 = 2: 0 0 1 2 4 5 6 8 9 10 11 | 2 3 = 2: 0 1 = 3: 0 11 0 1 3 4 5 6 7 8 9 10 = auxdim. scale & phrygian, 014589 & auxdim. scale | 6 7 8 = 6: 0 1 2 = 7: 0 1 11 = 8: 0 10 11 0 1 3 4 5 6 7 8 9 11 | 7 8 = 7: 0 1 = 8: 0 11 0 1 3 4 5 6 7 8 10 11 = locrian & aug. scale | 8 = 8: 0 0 2 3 4 5 6 7 8 9 10 | 6 7 8 9 = 6: 0 1 2 3 = 7: 0 1 2 11 = 8: 0 1 10 11 = 9: 0 9 10 11 0 2 3 4 5 6 7 8 9 11 = lydian & harm. min. | 7 8 9 = 7: 0 1 2 = 8: 0 1 11 = 9: 0 10 11 0 2 3 4 5 6 7 8 10 11 | 8 9 = 8: 0 1 = 9: 0 11 0 2 3 4 5 6 7 9 10 11 = dorelydian, 2367AB & bebop maj. | 9 = 9: 0 diamorphic with supplementary 2nd, 6th, 7th (Scale Degrees: 1223456677) 0 1 2 3 5 7 8 9 10 11 = phrygian & mel. min. | 1 2 3 4 = 1: 0 1 2 3 = 2: 0 1 2 11 = 3: 0 1 10 11 = 4: 0 9 10 11 0 1 2 3 6 7 8 9 10 11 | 1 2 3 4 5 = 1: 0 1 2 3 4 = 2: 0 1 2 3 11 = 3: 0 1 2 10 11 = 4: 0 1 9 10 11 = 5: 0 8 9 10 11 0 1 2 4 5 7 8 9 10 11 = 014589 & bebop maj., Span. Gypsy & ionian | 2 3 4 = 2: 0 1 2 = 3: 0 1 11 = 4: 0 10 11 0 1 2 4 6 7 8 9 10 11 | 2 3 4 5 = 2: 0 1 2 3 = 3: 0 1 2 11 = 4: 0 1 10 11 = 5: 0 9 10 11 0 1 3 4 5 6 8 9 10 11 = 10 in 4ths | 3 = 3: 0 0 1 3 4 5 7 8 9 10 11 | 3 4 = 3: 0 1 = 4: 0 11 0 1 3 4 6 7 8 9 10 11 = 03478B & auxdim. scale | 3 4 5 = 3: 0 1 2 = 4: 0 1 11 = 5: 0 10 11 0 2 3 4 5 7 8 9 10 11 = ioaeolean, mixolydian & harm. min. | 4 = 4: 0 0 2 3 4 6 7 8 9 10 11 | 4 5 = 4: 0 1 = 5: 0 11 Scale Degrees: 1224456677 0 1 2 5 6 7 8 9 10 11 | 2 3 4 5 6 = 2: 0 1 2 3 4 = 3: 0 1 2 3 11 = 4: 0 1 2 10 11 = 5: 0 1 9 10 11 = 6: 0 8 9 10 11 diamorphic with supplementary 4th, 6th, 7th (Scale Degrees: 1234456677) 0 1 3 5 6 7 8 9 10 11 | 3 4 5 6 = 3: 0 1 2 3 = 4: 0 1 2 11 = 5: 0 1 10 11 = 6: 0 9 10 11 0 1 4 5 6 7 8 9 10 11 | 3 4 5 6 7 = 3: 0 1 2 3 4 = 4: 0 1 2 3 11 = 5: 0 1 2 10 11 = 6: 0 1 9 10 11 = 7: 0 8 9 10 11 0 2 3 5 6 7 8 9 10 11 = dim. scale & dorian | 4 5 6 = 4: 0 1 2 = 5: 0 1 11 = 6: 0 10 11 0 2 4 5 6 7 8 9 10 11 = whole tone & ionian | 4 5 6 7 = 4: 0 1 2 3 = 5: 0 1 2 11 = 6: 0 1 10 11 = 7: 0 9 10 11 0 3 4 5 6 7 8 9 10 11 | 4 5 6 7 8 = 4: 0 1 2 3 4 = 5: 0 1 2 3 11 = 6: 0 1 2 10 11 = 7: 0 1 9 10 11 = 8: 0 8 9 10 11 chromatic unidecachord = diamorphic with supplementary 2nd, 3rd, 4th, 6th (Scale Degrees: 12233445667) 0 1 2 3 4 5 6 7 8 9 10 = mixolocrian, 1st 11 chromatics | 6 7 8 9 10 11 = 6: 0 1 2 3 4 5 = 7: 0 1 2 3 4 11 = 8: 0 1 2 3 10 11 = 9: 0 1 2 9 10 11 = 10: 0 1 8 9 10 11 = 11: 0 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 11 | 0 7 8 9 10 11 = 0: 0 7 8 9 10 11 = 7: 0 1 2 3 4 5 = 8: 0 1 2 3 4 11 = 9: 0 1 2 3 10 11 = 10: 0 1 2 9 10 11 = 11: 0 1 8 9 10 11 0 1 2 3 4 5 6 7 8 10 11 | 0 1 8 9 10 11 = 0: 0 1 8 9 10 11 = 1: 0 7 8 9 10 11 = 8: 0 1 2 3 4 5 = 9: 0 1 2 3 4 11 = 10: 0 1 2 3 10 11 = 11: 0 1 2 9 10 11 0 1 2 3 4 5 6 7 9 10 11 = auxdim. scale & ionian | 0 1 2 9 10 11 = 0: 0 1 2 9 10 11 = 1: 0 1 8 9 10 11 = 2: 0 7 8 9 10 11 = 9: 0 1 2 3 4 5 = 10: 0 1 2 3 4 11 = 11: 0 1 2 3 10 11 diamorphic with supplementary 2nd, 3rd, 6th, 7th (Scale Degrees: 12233456677) 0 1 2 3 4 5 6 8 9 10 11 = 11 in 4ths | 0 1 2 3 10 11 = 0: 0 1 2 3 10 11 = 1: 0 1 2 9 10 11 = 2: 0 1 8 9 10 11 = 3: 0 7 8 9 10 11 = 10: 0 1 2 3 4 5 = 11: 0 1 2 3 4 11 0 1 2 3 4 5 7 8 9 10 11 = iophrygian, Spanish Gypsy & dorian, consonant-11 | 0 1 2 3 4 11 = 0: 0 1 2 3 4 11 = 1: 0 1 2 3 10 11 = 2: 0 1 2 9 10 11 = 3: 0 1 8 9 10 11 = 4: 0 7 8 9 10 11 = 11: 0 1 2 3 4 5 0 1 2 3 4 6 7 8 9 10 11 = 11 in 5ths, most stable 11 chord type | 0 1 2 3 4 5 = 0: 0 1 2 3 4 5 = 1: 0 1 2 3 4 11 = 2: 0 1 2 3 10 11 = 3: 0 1 2 9 10 11 = 4: 0 1 8 9 10 11 = 5: 0 7 8 9 10 11 diamorphic with supplementary 2nd, 4th, 6th, 7th (Scale Degrees: 12234456677) 0 1 2 3 5 6 7 8 9 10 11 = locrian & mel. min., dim. & phrygian | 1 2 3 4 5 6 = 1: 0 1 2 3 4 5 = 2: 0 1 2 3 4 11 = 3: 0 1 2 3 10 11 = 4: 0 1 2 9 10 11 = 5: 0 1 8 9 10 11 = 6: 0 7 8 9 10 11 0 1 2 4 5 6 7 8 9 10 11 = Northern lights chord | 2 3 4 5 6 7 = 2: 0 1 2 3 4 5 = 3: 0 1 2 3 4 11 = 4: 0 1 2 3 10 11 = 5: 0 1 2 9 10 11 = 6: 0 1 8 9 10 11 = 7: 0 7 8 9 10 11 0 1 3 4 5 6 7 8 9 10 11 | 3 4 5 6 7 8 = 3: 0 1 2 3 4 5 = 4: 0 1 2 3 4 11 = 5: 0 1 2 3 10 11 = 6: 0 1 2 9 10 11 = 7: 0 1 8 9 10 11 = 8: 0 7 8 9 10 11 0 2 3 4 5 6 7 8 9 10 11 = aeolydian, whole tone & dorian | 4 5 6 7 8 9 = 4: 0 1 2 3 4 5 = 5: 0 1 2 3 4 11 = 6: 0 1 2 3 10 11 = 7: 0 1 2 9 10 11 = 8: 0 1 8 9 10 11 = 9: 0 7 8 9 10 11 chromatic Scale = diamorphic with supplementary 2nd, 3rd, 4th, 6th, 7th (Scale Degrees: 122334456677) 0 1 2 3 4 5 6 7 8 9 10 11 = chromatic, dodecachord, 12 in 4ths, 12 in 5ths | 0 1 2 3 4 5 6 7 8 9 10 11 = 0: 0 1 2 3 4 5 6 7 8 9 10 11 = 1: 0 1 2 3 4 5 6 7 8 9 10 11 = 2: 0 1 2 3 4 5 6 7 8 9 10 11 = 3: 0 1 2 3 4 5 6 7 8 9 10 11 = 4: 0 1 2 3 4 5 6 7 8 9 10 11 = 5: 0 1 2 3 4 5 6 7 8 9 10 11 = 6: 0 1 2 3 4 5 6 7 8 9 10 11 = 7: 0 1 2 3 4 5 6 7 8 9 10 11 = 8: 0 1 2 3 4 5 6 7 8 9 10 11 = 9: 0 1 2 3 4 5 6 7 8 9 10 11 = 10: 0 1 2 3 4 5 6 7 8 9 10 11 = 11: 0 1 2 3 4 5 6 7 8 9 10 11

Subset Pitch Class Sets

• 0 = 0: 0
0 1 = 0: 0 1 = 1: 0 11
0 1 2 = 0: 0 1 2 = 1: 0 1 11 = 2: 0 10 11
0 1 2 3 = 0: 0 1 2 3 = 1: 0 1 2 11 = 2: 0 1 10 11 = 3: 0 9 10 11
0 1 2 3 4 = 0: 0 1 2 3 4 = 1: 0 1 2 3 11 = 2: 0 1 2 10 11 = 3: 0 1 9 10 11 = 4: 0 8 9 10 11
0 1 2 3 4 11 = 0: 0 1 2 3 4 11 = 1: 0 1 2 3 10 11 = 2: 0 1 2 9 10 11 = 3: 0 1 8 9 10 11 = 4: 0 7 8 9 10 11 = 11: 0 1 2 3 4 5
0 1 2 3 11 = 0: 0 1 2 3 11 = 1: 0 1 2 10 11 = 2: 0 1 9 10 11 = 3: 0 8 9 10 11 = 11: 0 1 2 3 4
0 1 2 4 = 0: 0 1 2 4 = 1: 0 1 3 11 = 2: 0 2 10 11 = 4: 0 8 9 10
0 1 2 4 11 = 0: 0 1 2 4 11 = 1: 0 1 3 10 11 = 2: 0 2 9 10 11 = 4: 0 7 8 9 10 = 11: 0 1 2 3 5
0 1 2 11 = 0: 0 1 2 11 = 1: 0 1 10 11 = 2: 0 9 10 11 = 11: 0 1 2 3
0 1 3 = 0: 0 1 3 = 1: 0 2 11 = 3: 0 9 10
0 1 3 4 = 0: 0 1 3 4 = 1: 0 2 3 11 = 3: 0 1 9 10 = 4: 0 8 9 11
0 1 3 4 11 = 0: 0 1 3 4 11 = 1: 0 2 3 10 11 = 3: 0 1 8 9 10 = 4: 0 7 8 9 11 = 11: 0 1 2 4 5
0 1 3 11 = 0: 0 1 3 11 = 1: 0 2 10 11 = 3: 0 8 9 10 = 11: 0 1 2 4
0 1 4 = 0: 0 1 4 = 1: 0 3 11 = 4: 0 8 9
0 1 4 11 = 0: 0 1 4 11 = 1: 0 3 10 11 = 4: 0 7 8 9 = 11: 0 1 2 5
0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2
0 2 = 0: 0 2 = 2: 0 10
0 2 3 = 0: 0 2 3 = 2: 0 1 10 = 3: 0 9 11
0 2 3 4 = 0: 0 2 3 4 = 2: 0 1 2 10 = 3: 0 1 9 11 = 4: 0 8 10 11
0 2 3 4 11 = 0: 0 2 3 4 11 = 2: 0 1 2 9 10 = 3: 0 1 8 9 11 = 4: 0 7 8 10 11 = 11: 0 1 3 4 5
0 2 3 11 = 0: 0 2 3 11 = 2: 0 1 9 10 = 3: 0 8 9 11 = 11: 0 1 3 4
0 2 4 = 0: 0 2 4 = 2: 0 2 10 = 4: 0 8 10
0 2 4 11 = 0: 0 2 4 11 = 2: 0 2 9 10 = 4: 0 7 8 10 = 11: 0 1 3 5
0 2 11 = 0: 0 2 11 = 2: 0 9 10 = 11: 0 1 3
0 3 = 0: 0 3 = 3: 0 9
0 3 4 = 0: 0 3 4 = 3: 0 1 9 = 4: 0 8 11
0 3 4 11 = 0: 0 3 4 11 = 3: 0 1 8 9 = 4: 0 7 8 11 = 11: 0 1 4 5
0 3 11 = 0: 0 3 11 = 3: 0 8 9 = 11: 0 1 4