# Chord Type: 0 3 6 10

## 0 3 6 10 = m7b5 = Tristan chord = half-diminished 7th chord

### 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

Click here to learn the Jordan Chromatic System
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## Chord Type Fun Facts

0 3 6 10
• Subset of Diminished Scale (0 1 3 4 6 7 9 10)
• Subset of Locrian Mode (0 1 3 5 6 8 10)
• Subset of Dorian Blues Scale (0 2 3 5 6 7 9 10)

## Modal System Fun Facts

0 2 5 8
• Subset of Diminished Scale
• Subset of Diatonic Modal System
• Subset of Harmonic Minor Modal System
• Subset of Melodic Minor Modal System
• Subset of Dorian Blues Scale
• Subset of Harmonic Major Modal System

## General Statistics

Cardinality:                     4
Jordan Number:                   4-37
Forte Number:                    4-27
Forte Prime Form:                [0,2,5,8]
Zeitler Scale Name:              Aeraphic
Ian Ring's Scale Page 1097

Root Reference:                  0 3 6 10
Tone Stacking:                   0 3 3 4
Interval Stacking:               3 3 4 2
Binary:                          1 0 0 1 0 0 1 0 0 0 1 0
Decimal Value:                   1097

Interval Vector:                 0 1 2 1 1 1
Inversional Symmetry:            no
Transpositional Symmetry:        no
Melodic Adjacency (0-1):         0.250
Harmonic Adjacency (0-1):        0.667
Modal-system-invariant under multiplication by: 1
Modal System Balanced:           no

All Transpositions of Chord Type:
• +0= 0 3 6 10 |m7b5 = Tristan chord = half-diminished 7th chord
+1= 1 4 7 11 |
+2= 0 2 5  8 |
+3= 1 3 6  9 |
+4= 2 4 7 10 |
+5= 3 5 8 11 |
+6= 0 4 6  9 |
+7= 1 5 7 10 |
+8= 2 6 8 11 |
+9= 0 3 7  9 |m6 = Tristan chord
+10= 1 4 8 10 |
+11= 2 5 9 11 |
Modes of Chord Type:
• (mode 0) 0:  0 3 6 10 | m7b5 = Tristan chord = half-diminished 7th chord
(mode 1) 3:  0 3 7  9 | m6 = Tristan chord
(mode 2) 6:  0 4 6  9 |
(mode 3) 10: 0 2 5  8 |
Modes of Chord Type Sorted by Rootedness:
•   1.500(mode 1)3:0 3 7  9 |m6 = Tristan chord
1.017(mode 2)6:0 4 6  9 |
.858(mode 0)0:0 3 6 10 |m7b5 = Tristan chord = half-diminished 7th chord
.058(mode 3)10:0 2 5  8 |
Inversion at 0:               0 2 6 9
• (mode 0) 0: 0 2 6  9 |
(mode 1) 2: 0 4 7 10 | 7 = German aug. 6th chord
(mode 2) 6: 0 3 6  8 |
(mode 3) 9: 0 3 5  9 |
Times 7:                      0 6 9 10
• (mode 0) 0:  0 6 9 10 |
(mode 1) 6:  0 3 4  6 | Mb5 add #9
(mode 2) 9:  0 1 3  9 |
(mode 3) 10: 0 2 8 11 |
Times 5:                      0 2 3 6
• (mode 0) 0: 0 2 3  6 | dim. add 9
(mode 1) 2: 0 1 4 10 | 7b9 no 5th
(mode 2) 3: 0 3 9 11 | mM7/6 no 5th
(mode 3) 6: 0 6 8  9 |

Modal System:                     0 2 5 8 from root(s) 10 | "Tristan modal system"
Modes of Modal System:
• (mode 0) 0: 0 2 5  8 |
(mode 1) 2: 0 3 6 10 | m7b5 = Tristan chord = half-diminished 7th chord
(mode 2) 5: 0 3 7  9 | m6 = Tristan chord
(mode 3) 8: 0 4 6  9 |

Complement:                    1 2 4 5 7 8 9 11
• (mode 0) 1:  0 1 3 4 6 7  8 10 |
(mode 1) 2:  0 2 3 5 6 7  9 11 |
(mode 2) 4:  0 1 3 4 5 7  9 10 |
(mode 3) 5:  0 2 3 4 6 8  9 11 |
(mode 4) 7:  0 1 2 4 6 7  9 10 |
(mode 5) 8:  0 1 3 5 6 8  9 11 |
(mode 6) 9:  0 2 4 5 7 8 10 11 | mela 26 Charukesi
(mode 7) 11: 0 2 3 5 6 8  9 10 |
All but the root (subchroma complement of 0): 3 6 10
• (mode 0) 3:  0 3 7 | m = minor triad = minor chord
(mode 1) 6:  0 4 9 | M6 no 5th
(mode 2) 10: 0 5 8 |

## De-Chromaticizations

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

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

## Bright Layer Composition

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

subchroma modal system: 0
0 =  0 =  0:  0
3 =  3 =  3:  0
6 =  6 =  6:  0
10 = 10 = 10:  0

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

subchroma modal system: 0 2
0  6 =  0  6 =  0  6:  0  6
3 10 =  3 10 = 10:  0  5     3:  0  7
6  0 =  0  6 =  0  6:  0  6
10  3 =  3 10 = 10:  0  5     3:  0  7

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

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