# Chord Type: 0 1 2 5 7 10 11

## 0 1 2 5 7 10 11 = mela 6 Tanarupi

### Quick Links:

This Chord Type Chord Diagrams in 4ths Tuning
This Chord Type, All Keys -- Notation: (Staff, Treble Clef) Audio: (.mp3)

All Chord Types Arpeggiated in All Keys (Standard Notation, Treble Clef)
All Chord Type Main Pages, Non-Collapsible Index
All Chord Type Main Pages, Collapsible Index

### The information on this page uses the Jordan Chromatic System

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## Chord Type Fun Facts

0 1 2 5 7 10 11
• Inversionally Symmetrical around 0

## Modal System Fun Facts

0 1 2 3 4 7 9
• Inversionally Symmetrical

## General Statistics

Cardinality:                     7
Jordan Number:                   7-6
Forte Number:                    7-z12
Forte Prime Form:                [0,1,2,3,4,7,9]
Zeitler Scale Name:              Epythian
Ian Ring's Scale Page 3239

Root Reference:                  0 1 2 5 7 10 11
Tone Stacking:                   0 1 1 3 2 3 1
Interval Stacking:               1 1 3 2 3 1 1
Binary:                          1 1 1 0 0 1 0 1 0 0 1 1
Decimal Value:                   3239

Interval Vector:                 4 4 4 3 4 2
Inversional Symmetry:            yes (axes of symmetry: 0 6)
Transpositional Symmetry:        no
Melodic Adjacency (0-1):         0.583
Harmonic Adjacency (0-1):        0.583
Modal-system-invariant under multiplication by: 1 5 7 11
Modal System Balanced:           no

All Transpositions of Chord Type:
• +0= 0 1 2 5 7 10 11 |mela 6 Tanarupi
+1= 0 1 2 3 6  8 11 |
+2= 0 1 2 3 4  7  9 |
+3= 1 2 3 4 5  8 10 |
+4= 2 3 4 5 6  9 11 |
+5= 0 3 4 5 6  7 10 |
+6= 1 4 5 6 7  8 11 |
+7= 0 2 5 6 7  8  9 |
+8= 1 3 6 7 8  9 10 |
+9= 2 4 7 8 9 10 11 |
+10= 0 3 5 8 9 10 11 |
+11= 0 1 4 6 9 10 11 |
Modes of Chord Type:
• (mode 0) 0:  0 1 2 5 7 10 11 | mela 6 Tanarupi
(mode 1) 1:  0 1 4 6 9 10 11 |
(mode 2) 2:  0 3 5 8 9 10 11 |
(mode 3) 5:  0 2 5 6 7  8  9 |
(mode 4) 7:  0 3 4 5 6  7 10 |
(mode 5) 10: 0 1 2 3 4  7  9 |
(mode 6) 11: 0 1 2 3 6  8 11 |
Modes of Chord Type Sorted by Rootedness:
Inversion at 0:               0 1 2 5 7 10 11
• (mode 0) 0:  0 1 2 5 7 10 11 | mela 6 Tanarupi
(mode 1) 1:  0 1 4 6 9 10 11 |
(mode 2) 2:  0 3 5 8 9 10 11 |
(mode 3) 5:  0 2 5 6 7  8  9 |
(mode 4) 7:  0 3 4 5 6  7 10 |
(mode 5) 10: 0 1 2 3 4  7  9 |
(mode 6) 11: 0 1 2 3 6  8 11 |
Times 7:                      0 1 2 5 7 10 11
• (mode 0) 0:  0 1 2 5 7 10 11 | mela 6 Tanarupi
(mode 1) 1:  0 1 4 6 9 10 11 |
(mode 2) 2:  0 3 5 8 9 10 11 |
(mode 3) 5:  0 2 5 6 7  8  9 |
(mode 4) 7:  0 3 4 5 6  7 10 |
(mode 5) 10: 0 1 2 3 4  7  9 |
(mode 6) 11: 0 1 2 3 6  8 11 |
Times 5:                      0 1 2 5 7 10 11
• (mode 0) 0:  0 1 2 5 7 10 11 | mela 6 Tanarupi
(mode 1) 1:  0 1 4 6 9 10 11 |
(mode 2) 2:  0 3 5 8 9 10 11 |
(mode 3) 5:  0 2 5 6 7  8  9 |
(mode 4) 7:  0 3 4 5 6  7 10 |
(mode 5) 10: 0 1 2 3 4  7  9 |
(mode 6) 11: 0 1 2 3 6  8 11 |

Modal System:                     0 1 2 3 4 7 9 from root(s) 10 | "Melakarta Tanarupi modal system"
Modes of Modal System:
• (mode 0) 0: 0 1 2 3 4  7  9 |
(mode 1) 1: 0 1 2 3 6  8 11 |
(mode 2) 2: 0 1 2 5 7 10 11 | mela 6 Tanarupi
(mode 3) 3: 0 1 4 6 9 10 11 |
(mode 4) 4: 0 3 5 8 9 10 11 |
(mode 5) 7: 0 2 5 6 7  8  9 |
(mode 6) 9: 0 3 4 5 6  7 10 |

Complement:                    3 4 6 8 9
• (mode 0) 3: 0 1 3 5  6 | locrian pentachord
(mode 1) 4: 0 2 4 5 11 |
(mode 2) 6: 0 2 3 9 10 | m13 no 5th, 11th
(mode 3) 8: 0 1 7 8 10 |
(mode 4) 9: 0 6 7 9 11 |
All but the root (subchroma complement of 0): 1 2 5 7 10 11
• (mode 0) 1:  0 1 4 6 9 10 |
(mode 1) 2:  0 3 5 8 9 11 |
(mode 2) 5:  0 2 5 6 8  9 |
(mode 3) 7:  0 3 4 6 7 10 | 7#9#11
(mode 4) 10: 0 1 3 4 7  9 |
(mode 5) 11: 0 2 3 6 8 11 |

## De-Chromaticizations

• Dechromaticised: 2 5 7 10
• (mode 0) 2:  0 3 5  8 |
(mode 1) 5:  0 2 5  9 |
(mode 2) 7:  0 3 7 10 | m7
(mode 3) 10: 0 4 7  9 | 6
• Dechromaticised but Keep 0       0 2 5 7 10
• (mode 0) 0:  0 2 5 7 10 | 11 no 3rd = yosenpo (yo) ascending = yematebela wofe = Thai mode 3 (MSOTW) = slendro (MSOFW)
(mode 1) 2:  0 3 5 8 10 |
(mode 2) 5:  0 2 5 7  9 | yo scale primary tones = ritsu pentatonic = yosenpo (yo) descending = Thai mode 2 (MSOTW) = ambassel major
(mode 3) 7:  0 3 5 7 10 | minor pentatonic = m11 no 9th = minyo = batti minor = Thai mode 4 (MSOTW)
(mode 4) 10: 0 2 4 7  9 | major pentatonic = 5-note 5ths stack = ryo pentatonic = tizita major
• Dechromaticised but Keep 0 7     0 2 5 7 10
• (mode 0) 0:  0 2 5 7 10 | 11 no 3rd = yosenpo (yo) ascending = yematebela wofe = Thai mode 3 (MSOTW) = slendro (MSOFW)
(mode 1) 2:  0 3 5 8 10 |
(mode 2) 5:  0 2 5 7  9 | yo scale primary tones = ritsu pentatonic = yosenpo (yo) descending = Thai mode 2 (MSOTW) = ambassel major
(mode 3) 7:  0 3 5 7 10 | minor pentatonic = m11 no 9th = minyo = batti minor = Thai mode 4 (MSOTW)
(mode 4) 10: 0 2 4 7  9 | major pentatonic = 5-note 5ths stack = ryo pentatonic = tizita major
• Dechromaticised but Keep 0 3 4 7     0 2 5 7 10
• (mode 0) 0:  0 2 5 7 10 | 11 no 3rd = yosenpo (yo) ascending = yematebela wofe = Thai mode 3 (MSOTW) = slendro (MSOFW)
(mode 1) 2:  0 3 5 8 10 |
(mode 2) 5:  0 2 5 7  9 | yo scale primary tones = ritsu pentatonic = yosenpo (yo) descending = Thai mode 2 (MSOTW) = ambassel major
(mode 3) 7:  0 3 5 7 10 | minor pentatonic = m11 no 9th = minyo = batti minor = Thai mode 4 (MSOTW)
(mode 4) 10: 0 2 4 7  9 | major pentatonic = 5-note 5ths stack = ryo pentatonic = tizita major

• Alt-Dechromaticised: 1 2 10 11
• (mode 0) 1:  0 1 9 10 |
(mode 1) 2:  0 8 9 11 |
(mode 2) 10: 0 1 3  4 | 1st 4 of aux. diminished
(mode 3) 11: 0 2 3 11 | mM9 no 5th
• Alt-Dechromaticised but Keep 0       0 1 2 10 11
• (mode 0) 0:  0 1 2 10 11 |
(mode 1) 1:  0 1 9 10 11 |
(mode 2) 2:  0 8 9 10 11 |
(mode 3) 10: 0 1 2  3  4 | 1st 5 notes of chromatic scale
(mode 4) 11: 0 1 2  3 11 |
• Alt-Dechromaticised but Keep 0 7     0 1 2 7 10 11
• (mode 0) 0:  0 1 2 7 10 11 |
(mode 1) 1:  0 1 6 9 10 11 |
(mode 2) 2:  0 5 8 9 10 11 |
(mode 3) 7:  0 3 4 5  6  7 |
(mode 4) 10: 0 1 2 3  4  9 |
(mode 5) 11: 0 1 2 3  8 11 |
• Alt-Dechromaticised but Keep 0 3 4 7     0 1 2 7 10 11
• (mode 0) 0:  0 1 2 7 10 11 |
(mode 1) 1:  0 1 6 9 10 11 |
(mode 2) 2:  0 5 8 9 10 11 |
(mode 3) 7:  0 3 4 5  6  7 |
(mode 4) 10: 0 1 2 3  4  9 |
(mode 5) 11: 0 1 2 3  8 11 |

## Chromaticizations

• chromaticized:
• N/A
• chromaticized keep 0:
• N/A
• chromaticized keep 0 7:
• N/A
• chromaticized keep 0 3 4 7:
• N/A

• alt-chromaticized:
• N/A
• alt-chromaticized keep 0:
• N/A
• alt-chromaticized keep 0 7:
• N/A
• alt-chromaticized keep 0 3 4 7:
• N/A

## Bright Layer Decomposition

•  order origin root set chord type (as pcset) 1 0 0 0 1 2 5 7 10 11 = 0: 0 1 2 5 7 10 11 = 1: 0 1 4 6 9 10 11 = 2: 0 3 5 8 9 10 11 = 5: 0 2 5 6 7 8 9 = 7: 0 3 4 5 6 7 10 = 10: 0 1 2 3 4 7 9 = 11: 0 1 2 3 6 8 11 1 7 7 0 3 4 5 6 7 10 = 0: 0 3 4 5 6 7 10 = 3: 0 1 2 3 4 7 9 = 4: 0 1 2 3 6 8 11 = 5: 0 1 2 5 7 10 11 = 6: 0 1 4 6 9 10 11 = 7: 0 3 5 8 9 10 11 = 10: 0 2 5 6 7 8 9 1 10 10 0 1 2 3 4 7 9 = 0: 0 1 2 3 4 7 9 = 1: 0 1 2 3 6 8 11 = 2: 0 1 2 5 7 10 11 = 3: 0 1 4 6 9 10 11 = 4: 0 3 5 8 9 10 11 = 7: 0 2 5 6 7 8 9 = 9: 0 3 4 5 6 7 10

## Bright Layer Composition

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

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

subchroma modal system: 0 3
0  5 =  0  5 =  0:  0  5     5:  0  7
1  7 =  1  7 =  1  7:  0  6
2 10 =  2 10 = 10:  0  4     2:  0  8
5 11 =  5 11 =  5 11:  0  6
7  0 =  0  7 =  7:  0  5     0:  0  7
10  1 =  1 10 = 10:  0  3     1:  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  5 =  1  2  5 =  1:  0  1  4     2:  0  3 11
2  5  7 =  2  5  7 =  2:  0  3  5     7:  0  7 10
5  7 10 =  5  7 10 =  7:  0  3 10    10:  0  7  9
7 10 11 =  7 10 11 =  7:  0  3  4
10 11  0 =  0 10 11 = 10:  0  1  2    11:  0  1 11     0:  0 10 11
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  5 =  0  1  5 =  1:  0  4 11     5:  0  7  8
1  2  7 =  1  2  7 =  7:  0  6  7
2  5 10 =  2  5 10 = 10:  0  4  7
5  7 11 =  5  7 11 =  7:  0  4 10
7 10  0 =  0  7 10 =  7:  0  3  5     0:  0  7 10
10 11  1 =  1 10 11 = 10:  0  1  3    11:  0  2 11
11  0  2 =  0  2 11 = 11:  0  1  3     0:  0  2 11

subchroma modal system: 0 1 4
0  1  7 =  0  1  7 =  0:  0  1  7
1  2 10 =  1  2 10 = 10:  0  3  4
2  5 11 =  2  5 11 = 11:  0  3  6     2:  0  3  9
5  7  0 =  0  5  7 =  5:  0  2  7     0:  0  5  7     7:  0  5 10
7 10  1 =  1  7 10 =  7:  0  3  6    10:  0  3  9
10 11  2 =  2 10 11 = 10:  0  1  4    11:  0  3 11
11  0  5 =  0  5 11 =  5:  0  6  7

subchroma modal system: 0 1 5
0  1 10 =  0  1 10 = 10:  0  2  3
1  2 11 =  1  2 11 = 11:  0  2  3
2  5  0 =  0  2  5 =  2:  0  3 10     5:  0  7  9
5  7  1 =  1  5  7 =  1:  0  4  6
7 10  2 =  2  7 10 =  7:  0  3  7    10:  0  4  9
10 11  5 =  5 10 11 = 10:  0  1  7
11  0  7 =  0  7 11 =  7:  0  4  5     0:  0  7 11

subchroma modal system: 0 2 4
0  2  7 =  0  2  7 =  0:  0  2  7     7:  0  5  7     2:  0  5 10
1  5 10 =  1  5 10 = 10:  0  3  7     1:  0  4  9
2  7 11 =  2  7 11 =  7:  0  4  7
5 10  0 =  0  5 10 = 10:  0  2  7     5:  0  5  7     0:  0  5 10
7 11  1 =  1  7 11 =  7:  0  4  6
10  0  2 =  0  2 10 = 10:  0  2  4
11  1  5 =  1  5 11 =  1:  0  4 10

subchroma modal system: 0 1 2 3
0  1  2  5 =  0  1  2  5 =  1:  0  1  4 11     2:  0  3 10 11     5:  0  7  8  9
1  2  5  7 =  1  2  5  7 =  2:  0  3  5 11     7:  0  6  7 10
2  5  7 10 =  2  5  7 10 = 10:  0  4  7  9     7:  0  3  7 10
5  7 10 11 =  5  7 10 11 =  7:  0  3  4 10    10:  0  1  7  9
7 10 11  0 =  0  7 10 11 =  7:  0  3  4  5     0:  0  7 10 11
10 11  0  1 =  0  1 10 11 = 10:  0  1  2  3     0:  0  1 10 11     1:  0  9 10 11
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  7 =  0  1  2  7 =  0:  0  1  2  7     7:  0  5  6  7     2:  0  5 10 11
1  2  5 10 =  1  2  5 10 = 10:  0  3  4  7     1:  0  1  4  9
2  5  7 11 =  2  5  7 11 =  7:  0  4  7 10
5  7 10  0 =  0  5  7 10 =  5:  0  2  5  7    10:  0  2  7  9     7:  0  3  5 10     0:  0  5  7 10
7 10 11  1 =  1  7 10 11 =  7:  0  3  4  6
10 11  0  2 =  0  2 10 11 = 10:  0  1  2  4    11:  0  1  3 11     0:  0  2 10 11
11  0  1  5 =  0  1  5 11 =  1:  0  4 10 11     5:  0  6  7  8

subchroma modal system: 0 1 2 5
0  1  2 10 =  0  1  2 10 = 10:  0  2  3  4
1  2  5 11 =  1  2  5 11 = 11:  0  2  3  6     1:  0  1  4 10     2:  0  3  9 11
2  5  7  0 =  0  2  5  7 =  0:  0  2  5  7     5:  0  2  7  9     2:  0  3  5 10     7:  0  5  7 10
5  7 10  1 =  1  5  7 10 = 10:  0  3  7  9     7:  0  3  6 10
7 10 11  2 =  2  7 10 11 =  7:  0  3  4  7    10:  0  1  4  9
10 11  0  5 =  0  5 10 11 = 10:  0  1  2  7     5:  0  5  6  7     0:  0  5 10 11
11  0  1  7 =  0  1  7 11 =  0:  0  1  7 11     7:  0  4  5  6

subchroma modal system: 0 1 3 4
0  1  5  7 =  0  1  5  7 =  0:  0  1  5  7     5:  0  2  7  8     1:  0  4  6 11
1  2  7 10 =  1  2  7 10 = 10:  0  3  4  9     7:  0  3  6  7
2  5 10 11 =  2  5 10 11 = 10:  0  1  4  7    11:  0  3  6 11
5  7 11  0 =  0  5  7 11 =  5:  0  2  6  7     7:  0  4  5 10     0:  0  5  7 11
7 10  0  1 =  0  1  7 10 =  0:  0  1  7 10     7:  0  3  5  6
10 11  1  2 =  1  2 10 11 = 10:  0  1  3  4    11:  0  2  3 11
11  0  2  5 =  0  2  5 11 = 11:  0  1  3  6     2:  0  3  9 10     5:  0  6  7  9

subchroma modal system: 0 1 3 5
0  1  5 10 =  0  1  5 10 = 10:  0  2  3  7     1:  0  4  9 11     5:  0  5  7  8
1  2  7 11 =  1  2  7 11 =  7:  0  4  6  7
2  5 10  0 =  0  2  5 10 = 10:  0  2  4  7     5:  0  5  7  9
5  7 11  1 =  1  5  7 11 =  1  7:  0  4  6 10
7 10  0  2 =  0  2  7 10 = 10:  0  2  4  9     0:  0  2  7 10     7:  0  3  5  7
10 11  1  5 =  1  5 10 11 = 10:  0  1  3  7     1:  0  4  9 10
11  0  2  7 =  0  2  7 11 =  0:  0  2  7 11     7:  0  4  5  7

subchroma modal system: 0 1 2 3 4
0  1  2  5  7 =  0  1  2  5  7 =  0:  0  1  2  5  7     5:  0  2  7  8  9     7:  0  5  6  7 10
1  2  5  7 10 =  1  2  5  7 10 = 10:  0  3  4  7  9     7:  0  3  6  7 10
2  5  7 10 11 =  2  5  7 10 11 = 10:  0  1  4  7  9     7:  0  3  4  7 10
5  7 10 11  0 =  0  5  7 10 11 = 10:  0  1  2  7  9     7:  0  3  4  5 10     0:  0  5  7 10 11
7 10 11  0  1 =  0  1  7 10 11 =  7:  0  3  4  5  6     0:  0  1  7 10 11
10 11  0  1  2 =  0  1  2 10 11 = 10:  0  1  2  3  4    11:  0  1  2  3 11     2:  0  8  9 10 11
11  0  1  2  5 =  0  1  2  5 11 = 11:  0  1  2  3  6     1:  0  1  4 10 11     2:  0  3  9 10 11     5:  0  6  7  8  9

subchroma modal system: 0 1 2 3 5
0  1  2  5 10 =  0  1  2  5 10 = 10:  0  2  3  4  7     1:  0  1  4  9 11     5:  0  5  7  8  9
1  2  5  7 11 =  1  2  5  7 11 =  1:  0  1  4  6 10     7:  0  4  6  7 10
2  5  7 10  0 =  0  2  5  7 10 = 10:  0  2  4  7  9     5:  0  2  5  7  9     0:  0  2  5  7 10     7:  0  3  5  7 10
5  7 10 11  1 =  1  5  7 10 11 = 10:  0  1  3  7  9     7:  0  3  4  6 10
7 10 11  0  2 =  0  2  7 10 11 = 10:  0  1  2  4  9     7:  0  3  4  5  7     0:  0  2  7 10 11
10 11  0  1  5 =  0  1  5 10 11 = 10:  0  1  2  3  7     1:  0  4  9 10 11
11  0  1  2  7 =  0  1  2  7 11 =  0:  0  1  2  7 11     7:  0  4  5  6  7

subchroma modal system: 0 1 2 4 5
0  1  2  7 10 =  0  1  2  7 10 = 10:  0  2  3  4  9     0:  0  1  2  7 10     7:  0  3  5  6  7
1  2  5 10 11 =  1  2  5 10 11 = 10:  0  1  3  4  7    11:  0  2  3  6 11     1:  0  1  4  9 10
2  5  7 11  0 =  0  2  5  7 11 =  5:  0  2  6  7  9     0:  0  2  5  7 11     7:  0  4  5  7 10
5  7 10  0  1 =  0  1  5  7 10 = 10:  0  2  3  7  9     5:  0  2  5  7  8     0:  0  1  5  7 10     7:  0  3  5  6 10
7 10 11  1  2 =  1  2  7 10 11 = 10:  0  1  3  4  9     7:  0  3  4  6  7
10 11  0  2  5 =  0  2  5 10 11 = 10:  0  1  2  4  7    11:  0  1  3  6 11
11  0  1  5  7 =  0  1  5  7 11 =  5:  0  2  6  7  8     0:  0  1  5  7 11     7:  0  4  5  6 10     1:  0  4  6 10 11

subchroma modal system: 0 1 2 3 4 5
0  1  2  5  7 10 =  0  1  2  5  7 10 = 10:  0  2  3  4  7  9     0:  0  1  2  5  7 10     7:  0  3  5  6  7 10
1  2  5  7 10 11 =  1  2  5  7 10 11 = 10:  0  1  3  4  7  9     7:  0  3  4  6  7 10
2  5  7 10 11  0 =  0  2  5  7 10 11 = 10:  0  1  2  4  7  9     7:  0  3  4  5  7 10     0:  0  2  5  7 10 11
5  7 10 11  0  1 =  0  1  5  7 10 11 = 10:  0  1  2  3  7  9     7:  0  3  4  5  6 10     0:  0  1  5  7 10 11     1:  0  4  6  9 10 11
7 10 11  0  1  2 =  0  1  2  7 10 11 = 10:  0  1  2  3  4  9     0:  0  1  2  7 10 11     7:  0  3  4  5  6  7
10 11  0  1  2  5 =  0  1  2  5 10 11 = 10:  0  1  2  3  4  7    11:  0  1  2  3  6 11     1:  0  1  4  9 10 11
11  0  1  2  5  7 =  0  1  2  5  7 11 =  0:  0  1  2  5  7 11     7:  0  4  5  6  7 10

subchroma modal system: 0 1 2 3 4 5 6
0  1  2  5  7 10 11 =  0  1  2  5  7 10 11 = 10:  0  1  2  3  4  7  9     0:  0  1  2  5  7 10 11     7:  0  3  4  5  6  7 10
1  2  5  7 10 11  0 =  0  1  2  5  7 10 11 = 10:  0  1  2  3  4  7  9     0:  0  1  2  5  7 10 11     7:  0  3  4  5  6  7 10
2  5  7 10 11  0  1 =  0  1  2  5  7 10 11 = 10:  0  1  2  3  4  7  9     0:  0  1  2  5  7 10 11     7:  0  3  4  5  6  7 10
5  7 10 11  0  1  2 =  0  1  2  5  7 10 11 = 10:  0  1  2  3  4  7  9     0:  0  1  2  5  7 10 11     7:  0  3  4  5  6  7 10
7 10 11  0  1  2  5 =  0  1  2  5  7 10 11 = 10:  0  1  2  3  4  7  9     0:  0  1  2  5  7 10 11     7:  0  3  4  5  6  7 10
10 11  0  1  2  5  7 =  0  1  2  5  7 10 11 = 10:  0  1  2  3  4  7  9     0:  0  1  2  5  7 10 11     7:  0  3  4  5  6  7 10
11  0  1  2  5  7 10 =  0  1  2  5  7 10 11 = 10:  0  1  2  3  4  7  9     0:  0  1  2  5  7 10 11     7:  0  3  4  5  6  7 10

## Subset Chord Types By Family

•  Chord Type Roots Unison (Scale Degrees: 1) 0 = root, unison, octave | 0 1 2 5 7 10 11 = 0: 0 1 2 5 7 10 11 = 1: 0 1 4 6 9 10 11 = 2: 0 3 5 8 9 10 11 = 5: 0 2 5 6 7 8 9 = 7: 0 3 4 5 6 7 10 = 10: 0 1 2 3 4 7 9 = 11: 0 1 2 3 6 8 11 2nds / 9ths = 1st 2 notes of diamorphic scale (Scale Degrees: 12) 0 1 = semitone, min. 2nd, min. 9th | 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 2 = maj. 2nd, dim., maj. 9th | 0 5 10 11 = 0: 0 5 10 11 = 5: 0 5 6 7 = 10: 0 1 2 7 = 11: 0 1 6 11 3rds / 10ths (Scale Degrees: 13) 0 3 = aug. 2nd, min. 3rd, aug. 9th | 2 7 10 11 = 2: 0 5 8 9 = 7: 0 3 4 7 = 10: 0 1 4 9 = 11: 0 3 8 11 0 4 = maj. 3rd, maj. 10th, dim. 4th | 1 7 10 = 1: 0 6 9 = 7: 0 3 6 = 10: 0 3 9 4ths / 11ths (Scale Degrees: 14) 0 5 = 4th, 11th, 2 in 4ths | 0 2 5 7 = 0: 0 2 5 7 = 2: 0 3 5 10 = 5: 0 2 7 9 = 7: 0 5 7 10 0 6 = tritone, aug. 4th, dim. 5th, aug. 11th | 1 5 7 11 = 1: 0 4 6 10 = 5: 0 2 6 8 = 7: 0 4 6 10 = 11: 0 2 6 8 5ths / 12ths (Scale Degrees: 15) 0 7 = 5th, 2 in 5ths | 0 5 7 10 = 0: 0 5 7 10 = 5: 0 2 5 7 = 7: 0 3 5 10 = 10: 0 2 7 9 6ths / 13ths (Scale Degrees: 16) 0 8 = aug. 5th, min. 6th, aug. 12th, min. 13th | 2 5 11 = 2: 0 3 9 = 5: 0 6 9 = 11: 0 3 6 0 9 = maj. 6th, maj. 13th, dim. 7th | 1 2 5 10 = 1: 0 1 4 9 = 2: 0 3 8 11 = 5: 0 5 8 9 = 10: 0 3 4 7 7ths / 14ths (Scale Degrees: 17) 0 10 = aug. 6th, min. 7th, aug. 13th | 0 1 2 7 = 0: 0 1 2 7 = 1: 0 1 6 11 = 2: 0 5 10 11 = 7: 0 5 6 7 0 11 = maj. 7th, maj. 14th | 0 1 2 11 = 0: 0 1 2 11 = 1: 0 1 10 11 = 2: 0 9 10 11 = 11: 0 1 2 3 chromatic trichord (Scale Degrees: 122) 0 1 2 = 1st 3 chromatics | 0 10 11 = 0: 0 10 11 = 10: 0 1 2 = 11: 0 1 11 1st 3 notes of diamorphic scale (Scale Degrees: 123) 0 1 3 | 10 11 = 10: 0 1 = 11: 0 11 0 1 4 | 1 10 = 1: 0 9 = 10: 0 3 0 2 3 = min. trichord | 10 11 = 10: 0 1 = 11: 0 11 0 2 4 = maj. trichord | 10 = 10: 0 0 3 4 | 7 10 = 7: 0 3 = 10: 0 9 Sus2 triads (Scale Degrees: 125) 0 1 7 | 0 10 = 0: 0 10 = 10: 0 2 0 2 7 = sus2, 3 in 5ths | 0 5 10 = 0: 0 5 10 = 5: 0 5 7 = 10: 0 2 7 Root with upper and lower neighbors (Scale Degrees: 127) 0 1 11 = root & chr. neighbors | 0 1 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2 0 2 11 | 0 11 = 0: 0 11 = 11: 0 1 Scale Degrees: 134 0 3 5 | 2 7 = 2: 0 5 = 7: 0 7 0 4 5 | 7 = 7: 0 Triads (Scale Degrees: 135) 0 3 6 = dim. | 7 11 = 7: 0 4 = 11: 0 8 0 3 7 = m = minor | 7 10 = 7: 0 3 = 10: 0 9 0 4 6 = Mb5 | 1 7 = 1: 0 6 = 7: 0 6 0 4 7 = M = major | 7 10 = 7: 0 3 = 10: 0 9 6ths chords no 5th (Scale Degrees: 136) 0 3 9 = m6 no 5th | 2 10 = 2: 0 8 = 10: 0 4 0 4 9 = M6 no 5th | 1 10 = 1: 0 9 = 10: 0 3 7th chords no 5th (Scale Degrees: 137) 0 3 10 = m7 no 5th | 2 7 = 2: 0 5 = 7: 0 7 0 3 11 = mM7 no 5th | 2 11 = 2: 0 9 = 11: 0 3 0 4 10 = 7 no 5th | 1 7 = 1: 0 6 = 7: 0 6 0 4 11 = M7 no 5th | 1 = 1: 0 Sus4 Triads (Scale Degrees: 145) 0 5 7 = sus4 | 0 5 7 = 0: 0 5 7 = 5: 0 2 7 = 7: 0 5 10 0 6 7 = sus#4, Viennese trichord | 5 7 = 5: 0 2 = 7: 0 10 7sus chords no 5th (Scale Degrees: 147) 0 5 10 = 3 in 4ths | 0 2 7 = 0: 0 2 7 = 2: 0 5 10 = 7: 0 5 7 6th chords no 3rd (Scale Degrees: 156) 0 7 8 | 5 = 5: 0 0 7 9 | 5 10 = 5: 0 5 = 10: 0 7 7th chords no 3rd (Scale Degrees: 157) 0 7 10 = m power chord | 0 7 = 0: 0 7 = 7: 0 5 0 7 11 = M power chord | 0 = 0: 0 Scale Degrees: 167 0 10 11 | 0 1 2 = 0: 0 1 2 = 1: 0 1 11 = 2: 0 10 11 chromatic tetrachord (Scale Degrees: 1223) 0 1 2 3 = chromatic tetrachord | 10 11 = 10: 0 1 = 11: 0 11 0 1 2 4 | 10 = 10: 0 0 1 3 4 = 1st 4 aux dim. | 10 = 10: 0 0 2 3 4 | 10 = 10: 0 Scale Degrees: 1225 0 1 2 7 | 0 10 = 0: 0 10 = 10: 0 2 1st 3 notes of diamorphic scale (Scale Degrees: 1234) 0 3 4 5 | 7 = 7: 0 Add 9 Chords (Scale Degrees: 1235) 0 1 3 6 = dim. add b9 | 11 = 11: 0 0 1 3 7 = m add b9, all-int | 10 = 10: 0 0 1 4 7 = M add b9 | 10 = 10: 0 0 2 3 6 = dim. add 9 | 11 = 11: 0 0 2 3 7 = m add9 | 10 = 10: 0 0 2 4 7 = add9 , Mu chord | 10 = 10: 0 0 3 4 6 = Mb5 add #9 | 7 = 7: 0 0 3 4 7 = add #9, maj-min chord | 7 10 = 7: 0 3 = 10: 0 9 6/9 chord no 5th (Scale Degrees: 1236) 0 1 4 9 | 1 10 = 1: 0 9 = 10: 0 3 0 2 4 9 | 10 = 10: 0 0 3 4 9 | 10 = 10: 0 9th chords no 5th (Scale Degrees: 1237) 0 1 3 11 = Mm7b9 no 5th | 11 = 11: 0 0 1 4 10 = 7b9 no 5th | 1 = 1: 0 0 1 4 11 = M7b9 no 5th | 1 = 1: 0 0 2 3 11 = mM9 no 5th | 11 = 11: 0 0 3 4 10 = 7#9 no 5th, Hendrix, all-int | 7 = 7: 0 11th chords no 3rd no 7th (Scale Degrees: 1245) 0 1 5 7 | 0 = 0: 0 0 2 5 7 | 0 5 = 0: 0 5 = 5: 0 7 0 2 6 7 | 5 = 5: 0 6/9 chords no 3rd (Scale Degrees: 1256) 0 1 7 9 = all-int | 10 = 10: 0 0 2 7 8 | 5 = 5: 0 0 2 7 9 = 4 in 5ths | 5 10 = 5: 0 5 = 10: 0 7 9th chords no 3rd (Scale Degrees: 1257) 0 1 7 10 = 7b9 no 3rd, -7b9 no 3rd | 0 = 0: 0 0 1 7 11 = M7b5 no 3rd, mM7b9 no 3rd | 0 = 0: 0 0 2 7 10 = 9 no 3rd, m9 no 3rd | 0 = 0: 0 0 2 7 11 = M9 no 3rd, mM9 no 3rd | 0 = 0: 0 13th chords no 3rd no 5th no 11th (Scale Degrees: 1267) 0 1 10 11 | 0 1 = 0: 0 1 = 1: 0 11 0 2 10 11 | 0 = 0: 0 Add 11 Chords (Scale Degrees: 1345) 0 3 5 6 = blues tetrachord | 7 = 7: 0 0 3 5 7 = m add 11 | 7 = 7: 0 0 3 6 7 = m add #11 | 7 = 7: 0 0 4 5 6 = Mb5 add 11 | 7 = 7: 0 0 4 5 7 = M add 11 | 7 = 7: 0 0 4 6 7 = Madd#11, Jetsons, all-int | 7 = 7: 0 11th chords no 5th no 9th (Scale Degrees: 1347) 0 3 5 10 = m11 no 5th 7th 9th, 4 in 4ths | 2 7 = 2: 0 5 = 7: 0 7 0 3 5 11 = all-int | 2 = 2: 0 0 4 5 10 | 7 = 7: 0 6th Chords (Scale Degrees: 1356) 0 3 7 9 = m6 , Tristan chord | 10 = 10: 0 0 4 7 9 = 6 | 10 = 10: 0 7th Chords (Scale Degrees: 1357) 0 3 6 10 = m7b5, Tristan chord, half-dim. 7th | 7 = 7: 0 0 3 6 11 = mM7b5, dim. maj. 7th chord | 11 = 11: 0 0 3 7 10 = m7 | 7 = 7: 0 0 4 6 10 = 7b5, French aug. 6th chord | 1 7 = 1: 0 6 = 7: 0 6 0 4 6 11 = M7b5 | 1 = 1: 0 0 4 7 10 = 7, German aug. 6th chord | 7 = 7: 0 6/7 chords no 5th (Scale Degrees: 1367) 0 3 9 10 = m7/6 no 5th | 2 = 2: 0 0 3 9 11 = mM7/6 no 5th | 2 = 2: 0 0 3 10 11 = mM7#6 no 5th | 2 = 2: 0 0 4 9 10 = 7/6 no 5th, all-int | 1 = 1: 0 0 4 9 11 = M7/6 no 5th | 1 = 1: 0 0 4 10 11 = M7/#6 no 5th | 1 = 1: 0 Scale Degrees: 1445 0 5 6 7 = dream chord | 5 7 = 5: 0 2 = 7: 0 10 Scale Degrees: 1456 0 5 7 8 | 5 = 5: 0 0 5 7 9 | 5 = 5: 0 0 6 7 8 | 5 = 5: 0 0 6 7 9 | 5 = 5: 0 Sus 4 7th Chords (Scale Degrees: 1457) 0 5 7 10 = 7sus4 | 0 7 = 0: 0 7 = 7: 0 5 0 5 7 11 = M7sus4 | 0 = 0: 0 0 6 7 10 = 7sus#4, all-int | 7 = 7: 0 Scale Degrees: 1467 0 5 10 11 | 0 2 = 0: 0 2 = 2: 0 10 Scale Degrees: 1566 0 7 8 9 | 5 = 5: 0 Scale Degrees: 1567 0 7 10 11 | 0 = 0: 0 Scale Degrees: 1667 0 9 10 11 | 1 2 = 1: 0 1 = 2: 0 11 chromatic pentachord (Scale Degrees: 12233) 0 1 2 3 4 = 1st 5 chromatics | 10 = 10: 0 Scale Degrees: 12234 0 1 2 3 6 | 11 = 11: 0 Scale Degrees: 12235 0 1 2 3 7 | 10 = 10: 0 0 1 2 4 7 | 10 = 10: 0 0 1 3 4 7 | 10 = 10: 0 0 2 3 4 7 | 10 = 10: 0 Scale Degrees: 12236 0 1 2 4 9 | 10 = 10: 0 0 1 3 4 9 | 10 = 10: 0 0 2 3 4 9 | 10 = 10: 0 Scale Degrees: 12237 0 1 2 3 11 | 11 = 11: 0 Scale Degrees: 12245 0 1 2 5 7 | 0 = 0: 0 Scale Degrees: 12256 0 1 2 7 9 | 10 = 10: 0 Scale Degrees: 12257 0 1 2 7 10 | 0 = 0: 0 0 1 2 7 11 | 0 = 0: 0 1st 5 notes of diamorphic scale (Scale Degrees: 12345) 0 3 4 5 6 | 7 = 7: 0 0 3 4 5 7 | 7 = 7: 0 0 3 4 6 7 | 7 = 7: 0 11th chords no 5th (Scale Degrees: 12347) 0 3 4 5 10 | 7 = 7: 0 6/9 chords (Scale Degrees: 12356) 0 1 3 7 9 | 10 = 10: 0 0 1 4 7 9 = Elektra chord | 10 = 10: 0 0 2 3 7 9 = m6/9, akebono, Thai1 | 10 = 10: 0 0 2 4 7 9 = maj. pent., 5 in 5ths, ryo, tizita maj. | 10 = 10: 0 0 3 4 7 9 = slendro | 10 = 10: 0 9th chords (Scale Degrees: 12357) 0 1 3 6 11 = mM7b5b9 | 11 = 11: 0 0 1 4 6 10 = 7b5b9 | 1 = 1: 0 0 2 3 6 11 = mM9b5 | 11 = 11: 0 0 3 4 6 10 = 7b5#9 | 7 = 7: 0 0 3 4 7 10 = 7#9 | 7 = 7: 0 13th chords no 5th no 11th (Scale Degrees: 12367) 0 1 4 9 10 = 13b9 no 5th no 11th | 1 = 1: 0 0 1 4 9 11 = M13b9 no 5th no 11th | 1 = 1: 0 0 1 4 10 11 = 7#13b9 no 5th no 11th | 1 = 1: 0 Scale Degrees: 12456 0 2 5 7 8 = kokin joshi | 5 = 5: 0 0 2 5 7 9 = ritsu, yo desc., Thai2, ambassel maj. | 5 = 5: 0 0 2 6 7 8 | 5 = 5: 0 0 2 6 7 9 = Javanese pelog pathet barang | 5 = 5: 0 11th chords no 3rd (Scale Degrees: 12457) 0 1 5 7 10 = Insenpo (Insen), han iwato | 0 = 0: 0 0 1 5 7 11 | 0 = 0: 0 0 2 5 7 10 = 11 no 3rd, yo asc., Thai3, slendro, yematebela wofe | 0 = 0: 0 0 2 5 7 11 = M11 no 3rd, batti maj. | 0 = 0: 0 Scale Degrees: 12566 0 2 7 8 9 | 5 = 5: 0 13th chords no 3rd no 11th (Scale Degrees: 12567) 0 1 7 10 11 | 0 = 0: 0 0 2 7 10 11 | 0 = 0: 0 Scale Degrees: 13445 0 3 5 6 7 = blues pentachord | 7 = 7: 0 0 4 5 6 7 | 7 = 7: 0 11th Chords no 9th (Scale Degrees: 13457) 0 3 5 6 10 = m11b5 no 9th | 7 = 7: 0 0 3 5 7 10 = min. pent., m11 no 9th, minyo, batti min., Thai4 | 7 = 7: 0 0 3 6 7 10 = m7#11 no 9th, batti min. #4 | 7 = 7: 0 0 4 5 6 10 = 11b5 no 9th | 7 = 7: 0 0 4 5 7 10 = 11 no 9th | 7 = 7: 0 0 4 6 7 10 = 7#11 no 9th | 7 = 7: 0 7/6 Chords (Scale Degrees: 13567) 0 4 6 10 11 = M7b5/#6 | 1 = 1: 0 Scale Degrees: 13677 0 3 9 10 11 | 2 = 2: 0 0 4 9 10 11 | 1 = 1: 0 Scale Degrees: 14457 0 5 6 7 10 | 7 = 7: 0 Scale Degrees: 14566 0 5 7 8 9 | 5 = 5: 0 0 6 7 8 9 | 5 = 5: 0 13th chords no 3rd no 9th (Scale Degrees: 14567) 0 5 7 10 11 | 0 = 0: 0 Scale Degrees: 16677 0 8 9 10 11 | 2 = 2: 0 Scale Degrees: 122335 0 1 2 3 4 7 | 10 = 10: 0 Scale Degrees: 122336 0 1 2 3 4 9 | 10 = 10: 0 Scale Degrees: 122356 0 1 2 3 7 9 | 10 = 10: 0 0 1 2 4 7 9 | 10 = 10: 0 0 1 3 4 7 9 | 10 = 10: 0 0 2 3 4 7 9 = maj. blues | 10 = 10: 0 Scale Degrees: 122357 0 1 2 3 6 11 | 11 = 11: 0 Scale Degrees: 122457 0 1 2 5 7 10 | 0 = 0: 0 0 1 2 5 7 11 | 0 = 0: 0 Scale Degrees: 122567 0 1 2 7 10 11 | 0 = 0: 0 Scale Degrees: 123445 0 3 4 5 6 7 | 7 = 7: 0 11th chords = diamorphic scales no 6th (Scale Degrees: 123457) 0 3 4 5 6 10 = 11b5#9 | 7 = 7: 0 0 3 4 5 7 10 = 11#9 | 7 = 7: 0 0 3 4 6 7 10 = 7#9#11 | 7 = 7: 0 Scale Degrees: 123667 0 1 4 9 10 11 | 1 = 1: 0 diamorphic scales no 3rd (Scale Degrees: 124567) 0 1 5 7 10 11 | 0 = 0: 0 0 2 5 7 10 11 | 0 = 0: 0 Scale Degrees: 134457 0 3 5 6 7 10 = min. blues, blues hex. | 7 = 7: 0 0 4 5 6 7 10 | 7 = 7: 0 Scale Degrees: 135667 0 4 6 9 10 11 | 1 = 1: 0 Scale Degrees: 1223356 0 1 2 3 4 7 9 | 10 = 10: 0 Scale Degrees: 1224567 0 1 2 5 7 10 11 = Tanarupi | 0 = 0: 0 Scale Degrees: 1234457 0 3 4 5 6 7 10 | 7 = 7: 0

## Superset Chord Types By Family

•  Chord Type Roots Scale Degrees: 1223356 0 1 2 3 4 7 9 | 10 = 10: 0 Scale Degrees: 1224567 0 1 2 5 7 10 11 = Tanarupi | 0 = 0: 0 Scale Degrees: 1234457 0 3 4 5 6 7 10 | 7 = 7: 0 Scale Degrees: 12223456 0 1 2 3 4 5 7 9 | 10 = 10: 0 0 1 2 3 4 6 7 9 | 10 = 10: 0 Scale Degrees: 12223566 0 1 2 3 4 7 8 9 | 10 = 10: 0 Scale Degrees: 12223567 0 1 2 3 4 7 9 10 | 10 = 10: 0 0 1 2 3 4 7 9 11 | 10 = 10: 0 Scale Degrees: 12234457 0 1 3 4 5 6 7 10 | 7 = 7: 0 0 2 3 4 5 6 7 10 | 7 = 7: 0 diamorphic with supplementary 2nd (Scale Degrees: 12234567) 0 1 2 3 5 7 10 11 | 0 = 0: 0 0 1 2 3 6 7 8 11 | 11 = 11: 0 0 1 2 4 5 7 10 11 | 0 = 0: 0 Scale Degrees: 12235667 0 1 3 4 6 9 10 11 | 1 = 1: 0 Scale Degrees: 12244566 0 1 2 5 6 7 8 9 | 5 = 5: 0 Scale Degrees: 12244567 0 1 2 5 6 7 10 11 | 0 = 0: 0 Scale Degrees: 12245667 0 1 2 5 7 8 10 11 | 0 = 0: 0 0 1 2 5 7 9 10 11 | 0 = 0: 0 Scale Degrees: 12344566 0 2 3 5 6 7 8 9 | 5 = 5: 0 diamorphic with supplementary 4th (Scale Degrees: 12344567) 0 1 4 5 6 7 8 11 | 6 = 6: 0 0 3 4 5 6 7 8 10 | 7 = 7: 0 0 3 4 5 6 7 9 10 | 7 = 7: 0 0 3 4 5 6 7 10 11 | 7 = 7: 0 diamorphic with supplementary 6th (Scale Degrees: 12345667) 0 1 3 6 7 8 9 10 | 4 = 4: 0 0 1 4 6 7 9 10 11 | 1 = 1: 0 0 2 3 5 8 9 10 11 | 2 = 2: 0 Scale Degrees: 12356677 0 2 4 7 8 9 10 11 | 3 = 3: 0 Scale Degrees: 12445667 0 2 5 6 7 8 9 10 | 5 = 5: 0 Scale Degrees: 13456677 0 3 5 7 8 9 10 11 | 2 = 2: 0 Scale Degrees: 122334456 0 1 2 3 4 5 6 7 9 | 10 = 10: 0 Scale Degrees: 122334457 0 1 2 3 4 5 6 7 10 | 7 = 7: 0 Scale Degrees: 122334566 0 1 2 3 4 5 7 8 9 | 10 = 10: 0 0 1 2 3 4 6 7 8 9 | 10 = 10: 0 diamorphic with supplementary 2nd, 3rd (Scale Degrees: 122334567) 0 1 2 3 4 5 6 8 10 = whole tone & locrian | 9 = 9: 0 0 1 2 3 4 5 7 8 10 | 9 = 9: 0 0 1 2 3 4 5 7 9 10 | 10 = 10: 0 0 1 2 3 4 5 7 9 11 | 10 = 10: 0 0 1 2 3 4 5 7 10 11 | 0 = 0: 0 0 1 2 3 4 6 7 8 11 | 11 = 11: 0 0 1 2 3 4 6 7 9 10 | 10 = 10: 0 0 1 2 3 4 6 7 9 11 | 10 = 10: 0 0 1 2 3 4 6 8 10 11 | 11 = 11: 0 Scale Degrees: 122335667 0 1 2 3 4 7 8 9 10 | 10 = 10: 0 0 1 2 3 4 7 8 9 11 | 10 = 10: 0 0 1 2 3 4 7 9 10 11 | 10 = 10: 0 Scale Degrees: 122344566 0 1 2 3 5 6 7 8 9 | 5 = 5: 0 0 1 2 4 5 6 7 8 9 | 5 = 5: 0 0 2 3 4 5 6 7 8 9 | 5 = 5: 0 diamorphic with supplementary 2nd, 4th (Scale Degrees: 122344567) 0 1 2 3 5 6 7 8 11 | 11 = 11: 0 0 1 2 3 5 6 7 10 11 | 0 = 0: 0 0 1 2 3 5 6 8 9 11 | 11 = 11: 0 0 1 2 4 5 6 7 8 11 | 6 = 6: 0 0 1 2 4 5 6 7 10 11 | 0 = 0: 0 0 1 3 4 5 6 7 8 10 | 7 = 7: 0 0 1 3 4 5 6 7 8 11 | 6 = 6: 0 0 1 3 4 5 6 7 9 10 | 7 = 7: 0 0 1 3 4 5 6 7 10 11 | 7 = 7: 0 0 2 3 4 5 6 7 8 10 = whole tone & aeolean | 7 = 7: 0 0 2 3 4 5 6 7 9 10 | 7 = 7: 0 0 2 3 4 5 6 7 9 11 = lydian & mel. min. | 8 = 8: 0 0 2 3 4 5 6 7 10 11 | 7 = 7: 0 diamorphic with supplementary 2nd, 6th (Scale Degrees: 122345667) 0 1 2 3 5 7 8 10 11 = phrygian & harm. min. | 0 = 0: 0 0 1 2 3 5 7 9 10 11 | 0 = 0: 0 0 1 2 3 6 7 8 9 10 | 4 = 4: 0 0 1 2 3 6 7 8 9 11 | 11 = 11: 0 0 1 2 3 6 7 8 10 11 | 11 = 11: 0 0 1 2 4 5 7 8 10 11 | 0 = 0: 0 0 1 2 4 5 7 9 10 11 | 0 = 0: 0 0 1 2 4 6 7 9 10 11 | 1 = 1: 0 0 1 3 4 6 7 8 9 10 | 4 = 4: 0 0 1 3 4 6 7 9 10 11 | 1 = 1: 0 0 2 3 4 5 6 9 10 11 | 8 = 8: 0 Scale Degrees: 122356677 0 2 3 4 7 8 9 10 11 | 3 = 3: 0 Scale Degrees: 122456677 0 1 2 5 7 8 9 10 11 = Kanakangi | 0 = 0: 0 Scale Degrees: 123356677 0 1 2 4 7 8 9 10 11 | 3 = 3: 0 diamorphic with supplementary 4th, 6th (Scale Degrees: 123445667) 0 1 3 5 6 7 8 9 10 | 4 = 4: 0 0 1 4 5 6 7 8 9 11 | 6 = 6: 0 0 2 3 5 6 7 8 9 10 | 5 = 5: 0 0 2 3 5 6 7 8 9 11 | 5 = 5: 0 0 2 3 5 6 8 9 10 11 | 2 = 2: 0 0 2 4 5 6 7 8 9 10 = whole tone & mixolydian | 5 = 5: 0 0 2 4 5 6 7 8 9 11 | 5 = 5: 0 diamorphic with supplementary 4th, 7th (Scale Degrees: 123445677) 0 1 4 5 6 7 8 10 11 | 6 = 6: 0 0 1 4 5 6 7 9 10 11 | 1 = 1: 0 0 3 4 5 6 7 8 9 10 | 7 = 7: 0 0 3 4 5 6 7 8 10 11 | 7 = 7: 0 0 3 4 5 6 7 9 10 11 | 7 = 7: 0 diamorphic with supplementary 6th, 7th (Scale Degrees: 123456677) 0 1 3 5 7 8 9 10 11 | 2 = 2: 0 0 1 3 6 7 8 9 10 11 | 4 = 4: 0 0 1 4 6 7 8 9 10 11 | 1 = 1: 0 0 2 3 5 7 8 9 10 11 = dorian & harm. min., aeolean & mel. min. | 2 = 2: 0 0 2 4 5 7 8 9 10 11 | 3 = 3: 0 0 2 4 6 7 8 9 10 11 = whole tone & lydian | 3 = 3: 0 0 3 4 5 7 8 9 10 11 | 2 = 2: 0 Scale Degrees: 134456667 0 3 5 6 7 8 9 10 11 | 2 = 2: 0 chromatic decachord (Scale Degrees: 1223344566) 0 1 2 3 4 5 6 7 8 9 = 1st 10 chromatics | 5 10 = 5: 0 5 = 10: 0 7 diamorphic with supplementary 2nd, 3rd, 4th (Scale Degrees: 1223344567) 0 1 2 3 4 5 6 7 8 10 = whole tone & phrygian | 7 9 = 7: 0 2 = 9: 0 10 0 1 2 3 4 5 6 7 8 11 | 6 11 = 6: 0 5 = 11: 0 7 0 1 2 3 4 5 6 7 9 10 = auxdim. scale & dorian | 7 10 = 7: 0 3 = 10: 0 9 0 1 2 3 4 5 6 7 9 11 | 8 10 = 8: 0 2 = 10: 0 10 0 1 2 3 4 5 6 7 10 11 | 0 7 = 0: 0 7 = 7: 0 5 diamorphic with supplementary 2nd, 3rd, 6th (Scale Degrees: 1223345667) 0 1 2 3 4 5 6 8 9 10 | 9 = 9: 0 0 1 2 3 4 5 6 8 9 11 | 8 11 = 8: 0 3 = 11: 0 9 0 1 2 3 4 5 6 8 10 11 | 9 11 = 9: 0 2 = 11: 0 10 0 1 2 3 4 5 6 9 10 11 | 1 8 = 1: 0 7 = 8: 0 5 0 1 2 3 4 5 7 8 9 10 = mixophrygian | 9 10 = 9: 0 1 = 10: 0 11 0 1 2 3 4 5 7 8 9 11 = 014589 & mel. min. | 10 = 10: 0 0 1 2 3 4 5 7 8 10 11 | 0 9 = 0: 0 9 = 9: 0 3 0 1 2 3 4 5 7 9 10 11 | 0 10 = 0: 0 10 = 10: 0 2 0 1 2 3 4 5 8 9 10 11 | 2 9 = 2: 0 7 = 9: 0 5 0 1 2 3 4 6 7 8 9 10 | 4 10 = 4: 0 6 = 10: 0 6 0 1 2 3 4 6 7 8 9 11 = 10 in 5ths | 10 11 = 10: 0 1 = 11: 0 11 0 1 2 3 4 6 7 8 10 11 | 11 = 11: 0 0 1 2 3 4 6 7 9 10 11 = auxdim. scale & lydian | 1 10 = 1: 0 9 = 10: 0 3 0 1 2 3 4 6 8 9 10 11 | 1 11 = 1: 0 10 = 11: 0 2 Scale Degrees: 1223356667 0 1 2 3 4 7 8 9 10 11 | 3 10 = 3: 0 7 = 10: 0 5 diamorphic with supplementary 2nd, 4th, 6th (Scale Degrees: 1223445667) 0 1 2 3 5 6 7 8 9 10 = locridorian | 4 5 = 4: 0 1 = 5: 0 11 0 1 2 3 5 6 7 8 9 11 | 5 11 = 5: 0 6 = 11: 0 6 0 1 2 3 5 6 7 8 10 11 = locrian & harm. min. | 0 11 = 0: 0 11 = 11: 0 1 0 1 2 3 5 6 7 9 10 11 = 12569A & mel. min. | 0 = 0: 0 0 1 2 3 5 6 8 9 10 11 = dim. scale & locrian | 2 11 = 2: 0 9 = 11: 0 3 0 1 2 4 5 6 7 8 9 10 | 5 = 5: 0 0 1 2 4 5 6 7 8 9 11 | 5 6 = 5: 0 1 = 6: 0 11 0 1 2 4 5 6 7 8 10 11 | 0 6 = 0: 0 6 = 6: 0 6 0 1 2 4 5 6 7 9 10 11 = 12569A & bebop maj. | 0 1 = 0: 0 1 = 1: 0 11 0 1 2 4 5 6 8 9 10 11 | 1 = 1: 0 0 1 3 4 5 6 7 8 9 10 = auxdim. scale & phrygian, 014589 & auxdim. scale | 4 7 = 4: 0 3 = 7: 0 9 0 1 3 4 5 6 7 8 9 11 | 6 = 6: 0 0 1 3 4 5 6 7 8 10 11 = locrian & aug. scale | 6 7 = 6: 0 1 = 7: 0 11 0 1 3 4 5 6 7 9 10 11 | 1 7 = 1: 0 6 = 7: 0 6 0 2 3 4 5 6 7 8 9 10 | 5 7 = 5: 0 2 = 7: 0 10 0 2 3 4 5 6 7 8 9 11 = lydian & harm. min. | 5 8 = 5: 0 3 = 8: 0 9 0 2 3 4 5 6 7 8 10 11 | 7 = 7: 0 0 2 3 4 5 6 7 9 10 11 = dorelydian, 2367AB & bebop maj. | 7 8 = 7: 0 1 = 8: 0 11 0 2 3 4 5 6 8 9 10 11 | 2 8 = 2: 0 6 = 8: 0 6 diamorphic with supplementary 2nd, 6th, 7th (Scale Degrees: 1223456677) 0 1 2 3 5 7 8 9 10 11 = phrygian & mel. min. | 0 2 = 0: 0 2 = 2: 0 10 0 1 2 3 6 7 8 9 10 11 | 4 11 = 4: 0 7 = 11: 0 5 0 1 2 4 5 7 8 9 10 11 = 014589 & bebop maj., Span. Gypsy & ionian | 0 3 = 0: 0 3 = 3: 0 9 0 1 2 4 6 7 8 9 10 11 | 1 3 = 1: 0 2 = 3: 0 10 0 1 3 4 5 6 8 9 10 11 = 10 in 4ths | 1 2 = 1: 0 1 = 2: 0 11 0 1 3 4 5 7 8 9 10 11 | 2 = 2: 0 0 1 3 4 6 7 8 9 10 11 = 03478B & auxdim. scale | 1 4 = 1: 0 3 = 4: 0 9 0 2 3 4 5 7 8 9 10 11 = ioaeolean, mixolydian & harm. min. | 2 3 = 2: 0 1 = 3: 0 11 0 2 3 4 6 7 8 9 10 11 | 3 = 3: 0 Scale Degrees: 1224456677 0 1 2 5 6 7 8 9 10 11 | 0 5 = 0: 0 5 = 5: 0 7 diamorphic with supplementary 4th, 6th, 7th (Scale Degrees: 1234456677) 0 1 3 5 6 7 8 9 10 11 | 2 4 = 2: 0 2 = 4: 0 10 0 1 4 5 6 7 8 9 10 11 | 1 6 = 1: 0 5 = 6: 0 7 0 2 3 5 6 7 8 9 10 11 = dim. scale & dorian | 2 5 = 2: 0 3 = 5: 0 9 0 2 4 5 6 7 8 9 10 11 = whole tone & ionian | 3 5 = 3: 0 2 = 5: 0 10 0 3 4 5 6 7 8 9 10 11 | 2 7 = 2: 0 5 = 7: 0 7 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 | 4 5 7 9 10 = 4: 0 1 3 5 6 = 5: 0 2 4 5 11 = 7: 0 2 3 9 10 = 9: 0 1 7 8 10 = 10: 0 6 7 9 11 0 1 2 3 4 5 6 7 8 9 11 | 5 6 8 10 11 = 5: 0 1 3 5 6 = 6: 0 2 4 5 11 = 8: 0 2 3 9 10 = 10: 0 1 7 8 10 = 11: 0 6 7 9 11 0 1 2 3 4 5 6 7 8 10 11 | 0 6 7 9 11 = 0: 0 6 7 9 11 = 6: 0 1 3 5 6 = 7: 0 2 4 5 11 = 9: 0 2 3 9 10 = 11: 0 1 7 8 10 0 1 2 3 4 5 6 7 9 10 11 = auxdim. scale & ionian | 0 1 7 8 10 = 0: 0 1 7 8 10 = 1: 0 6 7 9 11 = 7: 0 1 3 5 6 = 8: 0 2 4 5 11 = 10: 0 2 3 9 10 diamorphic with supplementary 2nd, 3rd, 6th, 7th (Scale Degrees: 12233456677) 0 1 2 3 4 5 6 8 9 10 11 = 11 in 4ths | 1 2 8 9 11 = 1: 0 1 7 8 10 = 2: 0 6 7 9 11 = 8: 0 1 3 5 6 = 9: 0 2 4 5 11 = 11: 0 2 3 9 10 0 1 2 3 4 5 7 8 9 10 11 = iophrygian, Spanish Gypsy & dorian, consonant-11 | 0 2 3 9 10 = 0: 0 2 3 9 10 = 2: 0 1 7 8 10 = 3: 0 6 7 9 11 = 9: 0 1 3 5 6 = 10: 0 2 4 5 11 0 1 2 3 4 6 7 8 9 10 11 = 11 in 5ths, most stable 11 chord type | 1 3 4 10 11 = 1: 0 2 3 9 10 = 3: 0 1 7 8 10 = 4: 0 6 7 9 11 = 10: 0 1 3 5 6 = 11: 0 2 4 5 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 | 0 2 4 5 11 = 0: 0 2 4 5 11 = 2: 0 2 3 9 10 = 4: 0 1 7 8 10 = 5: 0 6 7 9 11 = 11: 0 1 3 5 6 0 1 2 4 5 6 7 8 9 10 11 = Northern lights chord | 0 1 3 5 6 = 0: 0 1 3 5 6 = 1: 0 2 4 5 11 = 3: 0 2 3 9 10 = 5: 0 1 7 8 10 = 6: 0 6 7 9 11 0 1 3 4 5 6 7 8 9 10 11 | 1 2 4 6 7 = 1: 0 1 3 5 6 = 2: 0 2 4 5 11 = 4: 0 2 3 9 10 = 6: 0 1 7 8 10 = 7: 0 6 7 9 11 0 2 3 4 5 6 7 8 9 10 11 = aeolydian, whole tone & dorian | 2 3 5 7 8 = 2: 0 1 3 5 6 = 3: 0 2 4 5 11 = 5: 0 2 3 9 10 = 7: 0 1 7 8 10 = 8: 0 6 7 9 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 5 = 0: 0 1 2 5 = 1: 0 1 4 11 = 2: 0 3 10 11 = 5: 0 7 8 9
0 1 2 5 7 = 0: 0 1 2 5 7 = 1: 0 1 4 6 11 = 2: 0 3 5 10 11 = 5: 0 2 7 8 9 = 7: 0 5 6 7 10
0 1 2 5 7 10 = 0: 0 1 2 5 7 10 = 1: 0 1 4 6 9 11 = 2: 0 3 5 8 10 11 = 5: 0 2 5 7 8 9 = 7: 0 3 5 6 7 10 = 10: 0 2 3 4 7 9
0 1 2 5 7 10 11 = 0: 0 1 2 5 7 10 11 = 1: 0 1 4 6 9 10 11 = 2: 0 3 5 8 9 10 11 = 5: 0 2 5 6 7 8 9 = 7: 0 3 4 5 6 7 10 = 10: 0 1 2 3 4 7 9 = 11: 0 1 2 3 6 8 11
0 1 2 5 7 11 = 0: 0 1 2 5 7 11 = 1: 0 1 4 6 10 11 = 2: 0 3 5 9 10 11 = 5: 0 2 6 7 8 9 = 7: 0 4 5 6 7 10 = 11: 0 1 2 3 6 8
0 1 2 5 10 = 0: 0 1 2 5 10 = 1: 0 1 4 9 11 = 2: 0 3 8 10 11 = 5: 0 5 7 8 9 = 10: 0 2 3 4 7
0 1 2 5 10 11 = 0: 0 1 2 5 10 11 = 1: 0 1 4 9 10 11 = 2: 0 3 8 9 10 11 = 5: 0 5 6 7 8 9 = 10: 0 1 2 3 4 7 = 11: 0 1 2 3 6 11
0 1 2 5 11 = 0: 0 1 2 5 11 = 1: 0 1 4 10 11 = 2: 0 3 9 10 11 = 5: 0 6 7 8 9 = 11: 0 1 2 3 6
0 1 2 7 = 0: 0 1 2 7 = 1: 0 1 6 11 = 2: 0 5 10 11 = 7: 0 5 6 7
0 1 2 7 10 = 0: 0 1 2 7 10 = 1: 0 1 6 9 11 = 2: 0 5 8 10 11 = 7: 0 3 5 6 7 = 10: 0 2 3 4 9
0 1 2 7 10 11 = 0: 0 1 2 7 10 11 = 1: 0 1 6 9 10 11 = 2: 0 5 8 9 10 11 = 7: 0 3 4 5 6 7 = 10: 0 1 2 3 4 9 = 11: 0 1 2 3 8 11
0 1 2 7 11 = 0: 0 1 2 7 11 = 1: 0 1 6 10 11 = 2: 0 5 9 10 11 = 7: 0 4 5 6 7 = 11: 0 1 2 3 8
0 1 2 10 = 0: 0 1 2 10 = 1: 0 1 9 11 = 2: 0 8 10 11 = 10: 0 2 3 4
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 11 = 0: 0 1 2 11 = 1: 0 1 10 11 = 2: 0 9 10 11 = 11: 0 1 2 3
0 1 5 = 0: 0 1 5 = 1: 0 4 11 = 5: 0 7 8
0 1 5 7 = 0: 0 1 5 7 = 1: 0 4 6 11 = 5: 0 2 7 8 = 7: 0 5 6 10
0 1 5 7 10 = 0: 0 1 5 7 10 = 1: 0 4 6 9 11 = 5: 0 2 5 7 8 = 7: 0 3 5 6 10 = 10: 0 2 3 7 9
0 1 5 7 10 11 = 0: 0 1 5 7 10 11 = 1: 0 4 6 9 10 11 = 5: 0 2 5 6 7 8 = 7: 0 3 4 5 6 10 = 10: 0 1 2 3 7 9 = 11: 0 1 2 6 8 11
0 1 5 7 11 = 0: 0 1 5 7 11 = 1: 0 4 6 10 11 = 5: 0 2 6 7 8 = 7: 0 4 5 6 10 = 11: 0 1 2 6 8
0 1 5 10 = 0: 0 1 5 10 = 1: 0 4 9 11 = 5: 0 5 7 8 = 10: 0 2 3 7
0 1 5 10 11 = 0: 0 1 5 10 11 = 1: 0 4 9 10 11 = 5: 0 5 6 7 8 = 10: 0 1 2 3 7 = 11: 0 1 2 6 11
0 1 5 11 = 0: 0 1 5 11 = 1: 0 4 10 11 = 5: 0 6 7 8 = 11: 0 1 2 6
0 1 7 = 0: 0 1 7 = 1: 0 6 11 = 7: 0 5 6
0 1 7 10 = 0: 0 1 7 10 = 1: 0 6 9 11 = 7: 0 3 5 6 = 10: 0 2 3 9
0 1 7 10 11 = 0: 0 1 7 10 11 = 1: 0 6 9 10 11 = 7: 0 3 4 5 6 = 10: 0 1 2 3 9 = 11: 0 1 2 8 11
0 1 7 11 = 0: 0 1 7 11 = 1: 0 6 10 11 = 7: 0 4 5 6 = 11: 0 1 2 8
0 1 10 = 0: 0 1 10 = 1: 0 9 11 = 10: 0 2 3
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 11 = 0: 0 1 11 = 1: 0 10 11 = 11: 0 1 2
0 2 = 0: 0 2 = 2: 0 10
0 2 5 = 0: 0 2 5 = 2: 0 3 10 = 5: 0 7 9
0 2 5 7 = 0: 0 2 5 7 = 2: 0 3 5 10 = 5: 0 2 7 9 = 7: 0 5 7 10