# Chord Type: 0 1 3 7

## 0 1 3 7 = m add b9 = all-interval tetrachord

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

## Chord Type Fun Facts

0 1 3 7
• Subset of Diminished Scale (0 1 3 4 6 7 9 10)
• Subset of Phrygian Mode (0 1 3 5 7 8 10)

## Modal System Fun Facts

0 1 3 7
• Subset of Diminished Scale
• Subset of Diatonic Modal System
• Subset of Melodic Minor Modal System
• All-Interval Tetrachord
• Subset of Dorian Blues Scale
• Subset of Harmonic Major Modal System

## General Statistics

Cardinality:                     4
Jordan Number:                   4-13
Forte Number:                    4-z29
Forte Prime Form:                [0,1,3,7]
Zeitler Scale Name:
Ian Ring's Scale Page 139

Root Reference:                  0 1 3 7
Tone Stacking:                   0 1 2 4
Interval Stacking:               1 2 4 5
Binary:                          1 1 0 1 0 0 0 1 0 0 0 0
Decimal Value:                   139

Interval Vector:                 1 1 1 1 1 1
Inversional Symmetry:            no
Transpositional Symmetry:        no
Modal-system-invariant under multiplication by: 1
Modal System Balanced:           no

All Transpositions of Chord Type:
• +0= 0 1  3  7 |m add b9 = all-interval tetrachord
+1= 1 2  4  8 |
+2= 2 3  5  9 |
+3= 3 4  6 10 |
+4= 4 5  7 11 |
+5= 0 5  6  8 |
+6= 1 6  7  9 |
+7= 2 7  8 10 |
+8= 3 8  9 11 |
+9= 0 4  9 10 |7/6 no 5th = all-interval tetrachord
+10= 1 5 10 11 |
+11= 0 2  6 11 |
Modes of Chord Type:
• (mode 0) 0: 0 1 3  7 | m add b9 = all-interval tetrachord
(mode 1) 1: 0 2 6 11 |
(mode 2) 3: 0 4 9 10 | 7/6 no 5th = all-interval tetrachord
(mode 3) 7: 0 5 6  8 |
Modes of Chord Type Sorted by Rootedness:
•   1.517(mode 0)0:0 1 3  7 |m add b9 = all-interval tetrachord
1.308(mode 2)3:0 4 9 10 |7/6 no 5th = all-interval tetrachord
.758(mode 1)1:0 2 6 11 |
-.150(mode 3)7:0 5 6  8 |
Inversion at 0:               0 5 9 11
• (mode 0) 0:  0 5 9 11 |
(mode 1) 5:  0 4 6  7 | M add#11 = Jetsons tetrachord = all-interval tetrachord
(mode 2) 9:  0 2 3  8 |
(mode 3) 11: 0 1 6 10 |
Times 7:                      0 1 7 9
• (mode 0) 0: 0 1 7  9 | all-interval tetrachord
(mode 1) 1: 0 6 8 11 |
(mode 2) 7: 0 2 5  6 |
(mode 3) 9: 0 3 4 10 | 7#9 no 5th = Hendrix tetrachord = all-interval tetrachord
Times 5:                      0 3 5 11
• (mode 0) 0:  0 3 5 11 | all-interval tetrachord
(mode 1) 3:  0 2 8  9 |
(mode 2) 5:  0 6 7 10 | 7sus#4 = all-interval tetrachord
(mode 3) 11: 0 1 4  6 |

Modal System:                     0 1 3 7 from root(s) 0 | "minor add b9 modal system"
Modes of Modal System:
• (mode 0) 0: 0 1 3  7 | m add b9 = all-interval tetrachord
(mode 1) 1: 0 2 6 11 |
(mode 2) 3: 0 4 9 10 | 7/6 no 5th = all-interval tetrachord
(mode 3) 7: 0 5 6  8 |

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

## Bright Layer Composition

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

subchroma modal system: 0
0 =  0 =  0:  0
1 =  1 =  1:  0
3 =  3 =  3:  0
7 =  7 =  7:  0

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

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

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

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