Chord Type: 0 4 5 6 7 8

0 4 5 6 7 8

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Chord Type: 0 4 5 6 7 8

Chord Type Fun Facts 0 4 5 6 7 8 Inversionally Symmetrical around 0 Modal System Fun Facts 0 1 2 3 4 8 Inversionally Symmetrical General Statistics Cardinality: 6 Jordan Number: 6-4 Forte Number: 6-z37 Forte Prime Form: [0,1,2,3,4,8] Zeitler Scale Name: Kadimic Ian Ring's Scale Page 497 Root Reference: 0 4 5 6 7 8 Tone Stacking: 0 4 1 1 1 1 Interval Stacking: 4 1 1 1 1 4 Binary: 1 0 0 0 1 1 1 1 1 0 0 0 Decimal Value: 497 Interval Vector: 4 3 2 3 2 1 Inversional Symmetry: yes (axes of symmetry: 0 6) Transpositional Symmetry: no Melodic Adjacency (0-1): 0.800 Harmonic Adjacency (0-1): 0.400 Modal-system-invariant under multiplication by: 1 11 Modal System Balanced: no Diachromatic Family: Scale Degrees: 134456 0 3 5 6 7 9 ->0 4 5 6 7 8 0 4 5 6 7 9 All Transpositions of Chord Type: +0= 0 4 5 6 7 8 | +1= 1 5 6 7 8 9 | +2= 2 6 7 8 9 10 | +3= 3 7 8 9 10 11 | +4= 0 4 8 9 10 11 | +5= 0 1 5 9 10 11 | +6= 0 1 2 6 10 11 | +7= 0 1 2 3 7 11 | +8= 0 1 2 3 4 8 | +9= 1 2 3 4 5 9 | +10= 2 3 4 5 6 10 | +11= 3 4 5 6 7 11 | Modes of Chord Type: (mode 0) 0: 0 4 5 6 7 8 | (mode 1) 4: 0 1 2 3 4 8 | (mode 2) 5: 0 1 2 3 7 11 | (mode 3) 6: 0 1 2 6 10 11 | (mode 4) 7: 0 1 5 9 10 11 | (mode 5) 8: 0 4 8 9 10 11 | Modes of Chord Type Sorted by Rootedness: 1.525(mode 2)5:0 1 2 3 7 11 | .958(mode 5)8:0 4 8 9 10 11 | .908(mode 1)4:0 1 2 3 4 8 | .750(mode 3)6:0 1 2 6 10 11 | .683(mode 0)0:0 4 5 6 7 8 | .475(mode 4)7:0 1 5 9 10 11 | Inversion at 0: 0 4 5 6 7 8 (mode 0) 0: 0 4 5 6 7 8 | (mode 1) 4: 0 1 2 3 4 8 | (mode 2) 5: 0 1 2 3 7 11 | (mode 3) 6: 0 1 2 6 10 11 | (mode 4) 7: 0 1 5 9 10 11 | (mode 5) 8: 0 4 8 9 10 11 | Times 7: 0 1 4 6 8 11 (mode 0) 0: 0 1 4 6 8 11 | (mode 1) 1: 0 3 5 7 10 11 | mM7#13 no 9th (mode 2) 4: 0 2 4 7 8 9 | (mode 3) 6: 0 2 5 6 7 10 | (mode 4) 8: 0 3 4 5 8 10 | (mode 5) 11: 0 1 2 5 7 9 | Times 5: 0 1 4 6 8 11 (mode 0) 0: 0 1 4 6 8 11 | (mode 1) 1: 0 3 5 7 10 11 | mM7#13 no 9th (mode 2) 4: 0 2 4 7 8 9 | (mode 3) 6: 0 2 5 6 7 10 | (mode 4) 8: 0 3 4 5 8 10 | (mode 5) 11: 0 1 2 5 7 9 | Modal System: 0 1 2 3 4 8 from root(s) 4 | "" Modes of Modal System: (mode 0) 0: 0 1 2 3 4 8 | (mode 1) 1: 0 1 2 3 7 11 | (mode 2) 2: 0 1 2 6 10 11 | (mode 3) 3: 0 1 5 9 10 11 | (mode 4) 4: 0 4 8 9 10 11 | (mode 5) 8: 0 4 5 6 7 8 | Complement: 1 2 3 9 10 11 (mode 0) 1: 0 1 2 8 9 10 | (mode 1) 2: 0 1 7 8 9 11 | (mode 2) 3: 0 6 7 8 10 11 | (mode 3) 9: 0 1 2 4 5 6 | (mode 4) 10: 0 1 3 4 5 11 | (mode 5) 11: 0 2 3 4 10 11 | All but the root (subchroma complement of 0): 4 5 6 7 8 (mode 0) 4: 0 1 2 3 4 | 1st 5 notes of chromatic scale (mode 1) 5: 0 1 2 3 11 | (mode 2) 6: 0 1 2 10 11 | (mode 3) 7: 0 1 9 10 11 | (mode 4) 8: 0 8 9 10 11 | Web Links JCS Wiki Page for This Chord Type No content as of 2022-5-9. This Chord Type, All Keys -- Notation: (Staff, Treble Clef) Audio: (.mp3) De-Chromaticizations Dechromaticised: 0 4 8 (mode 0) 0: 0 4 8 | + = augmented triad = augmented chord (mode 1) 4: 0 4 8 | + = augmented triad = augmented chord (mode 2) 8: 0 4 8 | + = augmented triad = augmented chord Dechromaticised but Keep 0 0 4 8 (unchanged) (mode 0) 0: 0 4 8 | + = augmented triad = augmented chord (mode 1) 4: 0 4 8 | + = augmented triad = augmented chord (mode 2) 8: 0 4 8 | + = augmented triad = augmented chord Dechromaticised but Keep 0 7 0 4 7 8 (mode 0) 0: 0 4 7 8 | Mb6 (mode 1) 4: 0 3 4 8 | aug. add #9 (mode 2) 7: 0 1 5 9 | (mode 3) 8: 0 4 8 11 | M7#5 Dechromaticised but Keep 0 3 4 7 0 4 7 8 (mode 0) 0: 0 4 7 8 | Mb6 (mode 1) 4: 0 3 4 8 | aug. add #9 (mode 2) 7: 0 1 5 9 | (mode 3) 8: 0 4 8 11 | M7#5 Alt-Dechromaticised: 4 5 6 7 8 (mode 0) 4: 0 1 2 3 4 | 1st 5 notes of chromatic scale (mode 1) 5: 0 1 2 3 11 | (mode 2) 6: 0 1 2 10 11 | (mode 3) 7: 0 1 9 10 11 | (mode 4) 8: 0 8 9 10 11 | Alt-Dechromaticised but Keep 0 0 4 5 6 7 8 (mode 0) 0: 0 4 5 6 7 8 | (mode 1) 4: 0 1 2 3 4 8 | (mode 2) 5: 0 1 2 3 7 11 | (mode 3) 6: 0 1 2 6 10 11 | (mode 4) 7: 0 1 5 9 10 11 | (mode 5) 8: 0 4 8 9 10 11 | Alt-Dechromaticised but Keep 0 7 0 4 5 6 7 8 (mode 0) 0: 0 4 5 6 7 8 | (mode 1) 4: 0 1 2 3 4 8 | (mode 2) 5: 0 1 2 3 7 11 | (mode 3) 6: 0 1 2 6 10 11 | (mode 4) 7: 0 1 5 9 10 11 | (mode 5) 8: 0 4 8 9 10 11 | Alt-Dechromaticised but Keep 0 3 4 7 0 4 5 6 7 8 (mode 0) 0: 0 4 5 6 7 8 | (mode 1) 4: 0 1 2 3 4 8 | (mode 2) 5: 0 1 2 3 7 11 | (mode 3) 6: 0 1 2 6 10 11 | (mode 4) 7: 0 1 5 9 10 11 | (mode 5) 8: 0 4 8 9 10 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: (mode 0) 0: 0 1 4 5 6 7 8 | (mode 1) 1: 0 3 4 5 6 7 11 | (mode 2) 4: 0 1 2 3 4 8 9 | (mode 3) 5: 0 1 2 3 7 8 11 | (mode 4) 6: 0 1 2 6 7 10 11 | mela 42 Raghupriya (mode 5) 7: 0 1 5 6 9 10 11 | (mode 6) 8: 0 4 5 8 9 10 11 | (mode 0) 0: 0 4 5 6 7 8 11 | (mode 1) 4: 0 1 2 3 4 7 8 | (mode 2) 5: 0 1 2 3 6 7 11 | (mode 3) 6: 0 1 2 5 6 10 11 | (mode 4) 7: 0 1 4 5 9 10 11 | (mode 5) 8: 0 3 4 8 9 10 11 | (mode 6) 11: 0 1 5 6 7 8 9 | alt-chromaticized keep 0 7: (mode 0) 0: 0 4 5 6 7 8 11 | (mode 1) 4: 0 1 2 3 4 7 8 | (mode 2) 5: 0 1 2 3 6 7 11 | (mode 3) 6: 0 1 2 5 6 10 11 | (mode 4) 7: 0 1 4 5 9 10 11 | (mode 5) 8: 0 3 4 8 9 10 11 | (mode 6) 11: 0 1 5 6 7 8 9 | (mode 0) 0: 0 1 4 5 6 7 8 | (mode 1) 1: 0 3 4 5 6 7 11 | (mode 2) 4: 0 1 2 3 4 8 9 | (mode 3) 5: 0 1 2 3 7 8 11 | (mode 4) 6: 0 1 2 6 7 10 11 | mela 42 Raghupriya (mode 5) 7: 0 1 5 6 9 10 11 | (mode 6) 8: 0 4 5 8 9 10 11 | (mode 0) 0: 0 3 4 5 6 7 8 10 | (mode 1) 3: 0 1 2 3 4 5 7 9 | (mode 2) 4: 0 1 2 3 4 6 8 11 | (mode 3) 5: 0 1 2 3 5 7 10 11 | (mode 4) 6: 0 1 2 4 6 9 10 11 | (mode 5) 7: 0 1 3 5 8 9 10 11 | (mode 6) 8: 0 2 4 7 8 9 10 11 | (mode 7) 10: 0 2 5 6 7 8 9 10 | (mode 0) 0: 0 1 2 4 5 6 7 8 9 | (mode 1) 1: 0 1 3 4 5 6 7 8 11 | (mode 2) 2: 0 2 3 4 5 6 7 10 11 | (mode 3) 4: 0 1 2 3 4 5 8 9 10 | (mode 4) 5: 0 1 2 3 4 7 8 9 11 | (mode 5) 6: 0 1 2 3 6 7 8 10 11 | (mode 6) 7: 0 1 2 5 6 7 9 10 11 | (mode 7) 8: 0 1 4 5 6 8 9 10 11 | (mode 8) 9: 0 3 4 5 7 8 9 10 11 | (mode 0) 0: 0 3 4 5 6 7 8 10 11 | (mode 1) 3: 0 1 2 3 4 5 7 8 9 | (mode 2) 4: 0 1 2 3 4 6 7 8 11 | (mode 3) 5: 0 1 2 3 5 6 7 10 11 | (mode 4) 6: 0 1 2 4 5 6 9 10 11 | (mode 5) 7: 0 1 3 4 5 8 9 10 11 | (mode 6) 8: 0 2 3 4 7 8 9 10 11 | (mode 7) 10: 0 1 2 5 6 7 8 9 10 | (mode 8) 11: 0 1 4 5 6 7 8 9 11 | alt-chromaticized keep 0 3 4 7: (mode 0) 0: 0 4 5 6 7 8 11 | (mode 1) 4: 0 1 2 3 4 7 8 | (mode 2) 5: 0 1 2 3 6 7 11 | (mode 3) 6: 0 1 2 5 6 10 11 | (mode 4) 7: 0 1 4 5 9 10 11 | (mode 5) 8: 0 3 4 8 9 10 11 | (mode 6) 11: 0 1 5 6 7 8 9 | (mode 0) 0: 0 1 4 5 6 7 8 | (mode 1) 1: 0 3 4 5 6 7 11 | (mode 2) 4: 0 1 2 3 4 8 9 | (mode 3) 5: 0 1 2 3 7 8 11 | (mode 4) 6: 0 1 2 6 7 10 11 | mela 42 Raghupriya (mode 5) 7: 0 1 5 6 9 10 11 | (mode 6) 8: 0 4 5 8 9 10 11 | (mode 0) 0: 0 3 4 5 6 7 8 10 | (mode 1) 3: 0 1 2 3 4 5 7 9 | (mode 2) 4: 0 1 2 3 4 6 8 11 | (mode 3) 5: 0 1 2 3 5 7 10 11 | (mode 4) 6: 0 1 2 4 6 9 10 11 | (mode 5) 7: 0 1 3 5 8 9 10 11 | (mode 6) 8: 0 2 4 7 8 9 10 11 | (mode 7) 10: 0 2 5 6 7 8 9 10 | (mode 0) 0: 0 1 2 4 5 6 7 8 9 | (mode 1) 1: 0 1 3 4 5 6 7 8 11 | (mode 2) 2: 0 2 3 4 5 6 7 10 11 | (mode 3) 4: 0 1 2 3 4 5 8 9 10 | (mode 4) 5: 0 1 2 3 4 7 8 9 11 | (mode 5) 6: 0 1 2 3 6 7 8 10 11 | (mode 6) 7: 0 1 2 5 6 7 9 10 11 | (mode 7) 8: 0 1 4 5 6 8 9 10 11 | (mode 8) 9: 0 3 4 5 7 8 9 10 11 | (mode 0) 0: 0 3 4 5 6 7 8 10 11 | (mode 1) 3: 0 1 2 3 4 5 7 8 9 | (mode 2) 4: 0 1 2 3 4 6 7 8 11 | (mode 3) 5: 0 1 2 3 5 6 7 10 11 | (mode 4) 6: 0 1 2 4 5 6 9 10 11 | (mode 5) 7: 0 1 3 4 5 8 9 10 11 | (mode 6) 8: 0 2 3 4 7 8 9 10 11 | (mode 7) 10: 0 1 2 5 6 7 8 9 10 | (mode 8) 11: 0 1 4 5 6 7 8 9 11 | (mode 0) 0: 0 1 3 4 5 6 7 8 10 | (mode 1) 1: 0 2 3 4 5 6 7 9 11 | lydian & melodic minor (mode 2) 3: 0 1 2 3 4 5 7 9 10 | (mode 3) 4: 0 1 2 3 4 6 8 9 11 | (mode 4) 5: 0 1 2 3 5 7 8 10 11 | phrygian & harmonic minor (mode 5) 6: 0 1 2 4 6 7 9 10 11 | (mode 6) 7: 0 1 3 5 6 8 9 10 11 | (mode 7) 8: 0 2 4 5 7 8 9 10 11 | (mode 8) 10: 0 2 3 5 6 7 8 9 10 | (mode 0) 0: 0 2 4 5 6 7 8 9 11 | (mode 1) 2: 0 2 3 4 5 6 7 9 10 | (mode 2) 4: 0 1 2 3 4 5 7 8 10 | (mode 3) 5: 0 1 2 3 4 6 7 9 11 | (mode 4) 6: 0 1 2 3 5 6 8 10 11 | (mode 5) 7: 0 1 2 4 5 7 9 10 11 | (mode 6) 8: 0 1 3 4 6 8 9 10 11 | (mode 7) 9: 0 2 3 5 7 8 9 10 11 | dorian & harmonic minor = aeolean & melodic minor (mode 8) 11: 0 1 3 5 6 7 8 9 10 | Bright Layer Decomposition order origin root set chord type (as pcset) 1 0 0 0 4 5 6 7 8 = 0: 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 = 5: 0 1 2 3 7 11 = 6: 0 1 2 6 10 11 = 7: 0 1 5 9 10 11 = 8: 0 4 8 9 10 11 1 4 4 0 1 2 3 4 8 = 0: 0 1 2 3 4 8 = 1: 0 1 2 3 7 11 = 2: 0 1 2 6 10 11 = 3: 0 1 5 9 10 11 = 4: 0 4 8 9 10 11 = 8: 0 4 5 6 7 8 1 5 5 0 1 2 3 7 11 = 0: 0 1 2 3 7 11 = 1: 0 1 2 6 10 11 = 2: 0 1 5 9 10 11 = 3: 0 4 8 9 10 11 = 7: 0 4 5 6 7 8 = 11: 0 1 2 3 4 8 1 6 6 0 1 2 6 10 11 = 0: 0 1 2 6 10 11 = 1: 0 1 5 9 10 11 = 2: 0 4 8 9 10 11 = 6: 0 4 5 6 7 8 = 10: 0 1 2 3 4 8 = 11: 0 1 2 3 7 11 1 8 8 0 4 8 9 10 11 = 0: 0 4 8 9 10 11 = 4: 0 4 5 6 7 8 = 8: 0 1 2 3 4 8 = 9: 0 1 2 3 7 11 = 10: 0 1 2 6 10 11 = 11: 0 1 5 9 10 11 Bright Layer Composition order pcset 1 0 4 5 6 7 8 = 0: 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 = 5: 0 1 2 3 7 11 = 6: 0 1 2 6 10 11 = 7: 0 1 5 9 10 11 = 8: 0 4 8 9 10 11 2 0 1 2 3 4 5 6 7 8 11 = 0: 0 1 2 3 4 5 6 7 8 11 = 1: 0 1 2 3 4 5 6 7 10 11 = 2: 0 1 2 3 4 5 6 9 10 11 = 3: 0 1 2 3 4 5 8 9 10 11 = 4: 0 1 2 3 4 7 8 9 10 11 = 5: 0 1 2 3 6 7 8 9 10 11 = 6: 0 1 2 5 6 7 8 9 10 11 = 7: 0 1 4 5 6 7 8 9 10 11 = 8: 0 3 4 5 6 7 8 9 10 11 = 11: 0 1 2 3 4 5 6 7 8 9 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 4 5 6 7 8 subchroma modal system: 0 0 = 0 = 0: 0 4 = 4 = 4: 0 5 = 5 = 5: 0 6 = 6 = 6: 0 7 = 7 = 7: 0 8 = 8 = 8: 0 subchroma modal system: 0 1 0 4 = 0 4 = 0: 0 4 4: 0 8 4 5 = 4 5 = 4: 0 1 5: 0 11 5 6 = 5 6 = 5: 0 1 6: 0 11 6 7 = 6 7 = 6: 0 1 7: 0 11 7 8 = 7 8 = 7: 0 1 8: 0 11 8 0 = 0 8 = 8: 0 4 0: 0 8 subchroma modal system: 0 2 0 5 = 0 5 = 0: 0 5 5: 0 7 4 6 = 4 6 = 4: 0 2 6: 0 10 5 7 = 5 7 = 5: 0 2 7: 0 10 6 8 = 6 8 = 6: 0 2 8: 0 10 7 0 = 0 7 = 7: 0 5 0: 0 7 8 4 = 4 8 = 4: 0 4 8: 0 8 subchroma modal system: 0 3 0 6 = 0 6 = 0 6: 0 6 4 7 = 4 7 = 4: 0 3 7: 0 9 5 8 = 5 8 = 5: 0 3 8: 0 9 6 0 = 0 6 = 0 6: 0 6 7 4 = 4 7 = 4: 0 3 7: 0 9 8 5 = 5 8 = 5: 0 3 8: 0 9 subchroma modal system: 0 1 2 0 4 5 = 0 4 5 = 0: 0 4 5 5: 0 7 11 4 5 6 = 4 5 6 = 4: 0 1 2 5: 0 1 11 6: 0 10 11 5 6 7 = 5 6 7 = 5: 0 1 2 6: 0 1 11 7: 0 10 11 6 7 8 = 6 7 8 = 6: 0 1 2 7: 0 1 11 8: 0 10 11 7 8 0 = 0 7 8 = 8: 0 4 11 0: 0 7 8 8 0 4 = 0 4 8 = 0 4 8: 0 4 8 subchroma modal system: 0 1 3 0 4 6 = 0 4 6 = 0: 0 4 6 4 5 7 = 4 5 7 = 4: 0 1 3 5: 0 2 11 5 6 8 = 5 6 8 = 5: 0 1 3 6: 0 2 11 6 7 0 = 0 6 7 = 0: 0 6 7 7 8 4 = 4 7 8 = 4: 0 3 4 8 0 5 = 0 5 8 = 5: 0 3 7 8: 0 4 9 subchroma modal system: 0 1 4 0 4 7 = 0 4 7 = 0: 0 4 7 4 5 8 = 4 5 8 = 4: 0 1 4 5: 0 3 11 5 6 0 = 0 5 6 = 5: 0 1 7 6 7 4 = 4 6 7 = 4: 0 2 3 7 8 5 = 5 7 8 = 5: 0 2 3 8 0 6 = 0 6 8 = 8: 0 4 10 subchroma modal system: 0 2 4 0 5 7 = 0 5 7 = 5: 0 2 7 0: 0 5 7 7: 0 5 10 4 6 8 = 4 6 8 = 4: 0 2 4 5 7 0 = 0 5 7 = 5: 0 2 7 0: 0 5 7 7: 0 5 10 6 8 4 = 4 6 8 = 4: 0 2 4 7 0 5 = 0 5 7 = 5: 0 2 7 0: 0 5 7 7: 0 5 10 8 4 6 = 4 6 8 = 4: 0 2 4 subchroma modal system: 0 1 2 3 0 4 5 6 = 0 4 5 6 = 5: 0 1 7 11 0: 0 4 5 6 4 5 6 7 = 4 5 6 7 = 4: 0 1 2 3 6: 0 1 10 11 7: 0 9 10 11 5 6 7 8 = 5 6 7 8 = 5: 0 1 2 3 7: 0 1 10 11 8: 0 9 10 11 6 7 8 0 = 0 6 7 8 = 8: 0 4 10 11 0: 0 6 7 8 7 8 0 4 = 0 4 7 8 = 4: 0 3 4 8 0: 0 4 7 8 8: 0 4 8 11 8 0 4 5 = 0 4 5 8 = 5: 0 3 7 11 subchroma modal system: 0 1 2 4 0 4 5 7 = 0 4 5 7 = 5: 0 2 7 11 0: 0 4 5 7 4 5 6 8 = 4 5 6 8 = 4: 0 1 2 4 5: 0 1 3 11 6: 0 2 10 11 5 6 7 0 = 0 5 6 7 = 5: 0 1 2 7 0: 0 5 6 7 7: 0 5 10 11 6 7 8 4 = 4 6 7 8 = 4: 0 2 3 4 7 8 0 5 = 0 5 7 8 = 5: 0 2 3 7 8: 0 4 9 11 0: 0 5 7 8 8 0 4 6 = 0 4 6 8 = 8: 0 4 8 10 subchroma modal system: 0 1 3 4 0 4 6 7 = 0 4 6 7 = 0: 0 4 6 7 4 5 7 8 = 4 5 7 8 = 4: 0 1 3 4 5: 0 2 3 11 5 6 8 0 = 0 5 6 8 = 5: 0 1 3 7 8: 0 4 9 10 6 7 0 4 = 0 4 6 7 = 0: 0 4 6 7 7 8 4 5 = 4 5 7 8 = 4: 0 1 3 4 5: 0 2 3 11 8 0 5 6 = 0 5 6 8 = 5: 0 1 3 7 8: 0 4 9 10 subchroma modal system: 0 1 2 3 4 0 4 5 6 7 = 0 4 5 6 7 = 5: 0 1 2 7 11 0: 0 4 5 6 7 4 5 6 7 8 = 4 5 6 7 8 = 4: 0 1 2 3 4 5: 0 1 2 3 11 8: 0 8 9 10 11 5 6 7 8 0 = 0 5 6 7 8 = 5: 0 1 2 3 7 8: 0 4 9 10 11 6 7 8 0 4 = 0 4 6 7 8 = 4: 0 2 3 4 8 0: 0 4 6 7 8 8: 0 4 8 10 11 7 8 0 4 5 = 0 4 5 7 8 = 4: 0 1 3 4 8 5: 0 2 3 7 11 0: 0 4 5 7 8 8 0 4 5 6 = 0 4 5 6 8 = 4: 0 1 2 4 8 5: 0 1 3 7 11 0: 0 4 5 6 8 8: 0 4 8 9 10 subchroma modal system: 0 1 2 3 4 5 0 4 5 6 7 8 = 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 5: 0 1 2 3 7 11 6: 0 1 2 6 10 11 0: 0 4 5 6 7 8 8: 0 4 8 9 10 11 4 5 6 7 8 0 = 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 5: 0 1 2 3 7 11 6: 0 1 2 6 10 11 0: 0 4 5 6 7 8 8: 0 4 8 9 10 11 5 6 7 8 0 4 = 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 5: 0 1 2 3 7 11 6: 0 1 2 6 10 11 0: 0 4 5 6 7 8 8: 0 4 8 9 10 11 6 7 8 0 4 5 = 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 5: 0 1 2 3 7 11 6: 0 1 2 6 10 11 0: 0 4 5 6 7 8 8: 0 4 8 9 10 11 7 8 0 4 5 6 = 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 5: 0 1 2 3 7 11 6: 0 1 2 6 10 11 0: 0 4 5 6 7 8 8: 0 4 8 9 10 11 8 0 4 5 6 7 = 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 5: 0 1 2 3 7 11 6: 0 1 2 6 10 11 0: 0 4 5 6 7 8 8: 0 4 8 9 10 11 Subset Chord Types by Root Set 0 :0 4 5 0 :0 4 6 0 :0 4 7 0 :0 5 7 0 :0 6 7 0 :0 7 8 0 :0 4 5 6 0 :0 4 5 7 0 :0 4 6 7 0 :0 4 7 8 0 :0 5 6 7 0 :0 5 7 8 0 :0 6 7 8 0 :0 4 5 6 7 0 :0 4 5 6 8 0 :0 4 5 7 8 0 :0 4 6 7 8 0 :0 4 5 6 7 8 0 4 5 6 7 8 :0 0 4 8 :0 4 0 4 8 :0 8 0 4 8 :0 4 8 0 5 :0 7 0 6 :0 6 0 7 :0 5 4 :0 1 4 4 :0 2 4 4 :0 3 4 4 :0 1 2 4 4 :0 1 3 4 4 :0 2 3 4 4 :0 3 4 8 4 :0 1 2 3 4 4 :0 1 2 4 8 4 :0 1 3 4 8 4 :0 2 3 4 8 4 :0 1 2 3 4 8 4 5 :0 3 4 5 :0 1 3 4 5 :0 2 3 4 5 :0 1 2 3 4 5 6:0 2 4 5 6:0 1 2 4 5 6 7 :0 1 5 :0 1 7 5 :0 2 7 5 :0 3 7 5 :0 3 11 5 :0 7 11 5 :0 1 2 7 5 :0 1 3 7 5 :0 2 3 7 5 :0 1 3 11 5 :0 2 3 11 5 :0 1 7 11 5 :0 2 7 11 5 :0 3 7 11 5 :0 1 2 3 7 5 :0 1 2 3 11 5 :0 1 2 7 11 5 :0 1 3 7 11 5 :0 2 3 7 11 5 :0 1 2 3 7 11 5 6 :0 2 11 5 6 7:0 1 11 5 6 7 8 :0 11 6 :0 2 10 11 6 :0 1 2 6 10 11 6 7 :0 1 10 11 6 7 8:0 10 6 7 8:0 10 11 7 :0 5 10 7 :0 5 10 11 7 8 :0 9 7 8 :0 9 10 11 8 :0 4 9 8 :0 4 10 8 :0 4 11 8 :0 4 8 10 8 :0 4 8 11 8 :0 4 9 10 8 :0 4 9 11 8 :0 4 10 11 8 :0 4 8 9 10 8 :0 4 8 10 11 8 :0 4 9 10 11 8 :0 8 9 10 11 8 :0 4 8 9 10 11 Superset Chord Types by Root Set 0 :0 4 5 6 7 8 0 :0 1 4 5 6 7 8 0 :0 2 4 5 6 7 8 0 :0 3 4 5 6 7 8 0 :0 4 5 6 7 8 9 0 :0 4 5 6 7 8 10 0 :0 4 5 6 7 8 11 0 :0 1 2 4 5 6 7 8 0 :0 1 3 4 5 6 7 8 0 :0 2 3 4 5 6 7 8 0 :0 1 4 5 6 7 8 10 0 :0 1 4 5 6 7 8 11 0 :0 2 4 5 6 7 8 10 0 :0 2 4 5 6 7 8 11 0 :0 3 4 5 6 7 8 10 0 :0 4 5 6 7 8 9 10 0 :0 4 5 6 7 8 10 11 0 :0 2 3 4 5 6 7 8 9 0 :0 1 2 4 5 6 7 8 10 0 :0 1 2 4 5 6 7 8 11 0 :0 1 3 4 5 6 7 8 10 0 :0 2 4 5 6 7 8 9 11 0 :0 1 4 5 6 7 8 10 11 0 :0 2 4 5 6 7 8 10 11 0 :0 3 4 5 6 7 8 9 10 0 1 :0 3 4 5 6 7 8 11 0 1 :0 1 3 4 5 6 7 8 11 0 1 :0 2 3 4 5 6 7 8 11 0 1 :0 3 4 5 6 7 8 9 11 0 1 :0 3 4 5 6 7 8 10 11 0 1 :0 1 3 4 5 6 7 8 10 11 0 1 :0 2 3 4 5 6 7 8 9 11 0 1 2 :0 2 3 4 5 6 7 8 10 11 0 1 2 3 4 5 6 7 8 9 10 11:0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 4 5 6 :0 1 2 3 4 5 6 7 8 10 11 0 1 2 8 9 10 :0 2 3 4 5 6 7 8 9 10 11 0 1 3 4 5 11 :0 1 2 3 4 5 6 7 8 9 11 0 1 4 5 :0 1 2 3 4 5 6 7 8 11 0 1 7 8 9 11 :0 1 3 4 5 6 7 8 9 10 11 0 1 8 9 :0 3 4 5 6 7 8 9 10 11 0 1 11 :0 1 3 4 5 6 7 8 9 11 0 2 :0 2 3 4 5 6 7 8 10 0 2 3 4 10 11 :0 1 2 3 4 5 6 7 8 9 10 0 2 4 :0 1 2 3 4 5 6 7 8 10 0 2 10 :0 2 3 4 5 6 7 8 9 10 0 3 4 11 :0 1 2 3 4 5 6 7 8 9 0 4 :0 1 2 3 4 5 6 7 8 0 6 :0 1 2 4 5 6 7 8 10 11 0 6 7 8 10 11 :0 1 2 4 5 6 7 8 9 10 11 0 7 8 11 :0 1 4 5 6 7 8 9 10 11 0 8 :0 4 5 6 7 8 9 10 11 0 8 10 :0 2 4 5 6 7 8 9 10 11 0 10 :0 2 4 5 6 7 8 9 10 0 10 11 :0 1 2 4 5 6 7 8 9 10 0 11 :0 1 4 5 6 7 8 9 0 11 :0 1 2 4 5 6 7 8 9 0 11 :0 1 4 5 6 7 8 9 10 0 11 :0 1 4 5 6 7 8 9 11 0 11 :0 1 2 4 5 6 7 8 9 11 0 11 :0 1 3 4 5 6 7 8 9 10 1 :0 3 4 5 6 7 11 1 :0 1 3 4 5 6 7 11 1 :0 2 3 4 5 6 7 11 1 :0 3 4 5 6 7 9 11 1 :0 3 4 5 6 7 10 11 1 :0 1 3 4 5 6 7 9 11 1 :0 1 3 4 5 6 7 10 11 1 :0 2 3 4 5 6 7 9 11 1 :0 3 4 5 6 7 9 10 11 1 2 :0 2 3 4 5 6 7 10 11 1 2 :0 2 3 4 5 6 7 9 10 11 1 2 3 5 6 7 :0 1 2 3 4 5 6 7 9 10 11 1 2 5 6 :0 1 2 3 4 5 6 7 10 11 1 3 5 :0 1 2 3 4 5 6 7 9 11 1 5 :0 1 2 3 4 5 6 7 11 1 7 :0 1 3 4 5 6 7 9 10 11 2 :0 2 3 4 5 6 10 2 :0 1 2 3 4 5 6 10 2 :0 2 3 4 5 6 7 10 2 :0 2 3 4 5 6 9 10 2 :0 2 3 4 5 6 10 11 2 :0 1 2 3 4 5 6 7 10 2 :0 2 3 4 5 6 7 9 10 2 :0 2 3 4 5 6 9 10 11 2 3 :0 1 2 3 4 5 6 9 10 2 3 :0 1 2 3 4 5 6 7 9 10 2 3 4 :0 1 2 3 4 5 6 8 9 10 2 3 4 6 7 8 :0 1 2 3 4 5 6 8 9 10 11 2 3 6 7 :0 1 2 3 4 5 6 9 10 11 2 4 :0 1 2 3 4 5 6 8 10 2 4 6 :0 1 2 3 4 5 6 8 10 11 2 8 :0 2 3 4 5 6 8 9 10 11 3 :0 1 2 3 4 5 7 9 3 :0 1 2 3 4 5 6 7 9 3 :0 1 2 3 4 5 7 9 10 3 4 :0 1 2 3 4 5 7 8 9 3 4 :0 1 2 3 4 5 6 8 9 11 3 4 :0 1 2 3 4 5 7 8 9 10 3 4 5 :0 1 2 3 4 5 7 8 9 11 3 4 5 7 8 9 :0 1 2 3 4 5 7 8 9 10 11 3 4 7 8 :0 1 2 3 4 5 8 9 10 11 3 5 :0 1 2 3 4 5 7 9 11 3 5 7 :0 1 2 3 4 5 7 9 10 11 4 :0 1 2 3 4 8 4 :0 1 2 3 4 7 8 4 :0 1 2 3 4 8 10 4 :0 1 2 3 4 8 11 4 :0 1 2 3 4 5 7 8 4 :0 1 2 3 4 6 7 8 4 :0 1 2 3 4 7 8 9 4 :0 1 2 3 4 7 8 10 4 :0 1 2 3 4 8 10 11 4 :0 1 2 3 4 6 8 10 4 :0 1 2 3 4 6 7 8 9 4 :0 1 2 3 4 5 7 8 10 4 :0 1 2 3 4 6 7 8 10 4 :0 1 2 3 4 7 8 9 10 4 5 :0 1 2 3 4 7 8 11 4 5 :0 1 2 3 4 5 7 8 11 4 5 :0 1 2 3 4 6 7 8 11 4 5 :0 1 2 3 4 7 8 9 11 4 5 :0 1 2 3 4 7 8 10 11 4 5 :0 1 2 3 4 5 7 8 10 11 4 5 :0 1 2 3 4 6 7 8 9 11 4 5 6 :0 1 2 3 4 6 7 8 10 11 4 5 6 8 9 10 :0 1 2 3 4 6 7 8 9 10 11 4 5 8 9 :0 1 2 3 4 7 8 9 10 11 4 6 :0 1 2 3 4 6 8 10 11 4 6 8 :0 1 2 3 4 6 8 9 10 11 4 10 :0 1 2 3 4 6 7 8 9 10 5 :0 1 2 3 7 11 5 :0 1 2 3 4 7 11 5 :0 1 2 3 5 7 11 5 :0 1 2 3 6 7 11 5 :0 1 2 3 7 8 11 5 :0 1 2 3 7 9 11 5 :0 1 2 3 7 10 11 5 :0 1 2 3 4 5 7 11 5 :0 1 2 3 4 6 7 11 5 :0 1 2 3 4 7 9 11 5 :0 1 2 3 4 7 10 11 5 :0 1 2 3 5 6 7 11 5 :0 1 2 3 5 7 8 11 5 :0 1 2 3 5 7 9 11 5 :0 1 2 3 5 7 10 11 5 :0 1 2 3 6 7 8 11 5 :0 1 2 3 6 7 9 11 5 :0 1 2 3 7 8 9 11 5 :0 1 2 3 7 8 10 11 5 :0 1 2 3 7 9 10 11 5 :0 1 2 3 4 5 7 10 11 5 :0 1 2 3 4 6 7 9 11 5 :0 1 2 3 4 7 9 10 11 5 :0 1 2 3 5 6 7 8 11 5 :0 1 2 3 5 6 7 9 11 5 :0 1 2 3 5 7 8 9 11 5 :0 1 2 3 5 7 8 10 11 5 :0 1 2 3 6 7 8 9 11 5 6 :0 1 2 3 6 7 10 11 5 6 :0 1 2 3 4 6 7 10 11 5 6 :0 1 2 3 5 6 7 10 11 5 6 :0 1 2 3 6 7 8 10 11 5 6 :0 1 2 3 6 7 9 10 11 5 6 :0 1 2 3 4 6 7 9 10 11 5 6 :0 1 2 3 5 6 7 8 10 11 5 6 7 :0 1 2 3 5 6 7 9 10 11 5 6 7 9 10 11 :0 1 2 3 5 6 7 8 9 10 11 5 6 9 10 :0 1 2 3 6 7 8 9 10 11 5 7 :0 1 2 3 5 7 9 10 11 5 7 9 :0 1 2 3 5 7 8 9 10 11 5 9 :0 1 2 3 7 8 9 10 11 5 11 :0 1 2 3 5 6 7 8 9 11 6 :0 1 2 6 10 11 6 :0 1 2 3 6 10 11 6 :0 1 2 4 6 10 11 6 :0 1 2 6 7 10 11 6 :0 1 2 4 6 7 10 11 6 :0 1 2 4 6 8 10 11 6 :0 1 2 5 6 7 10 11 6 :0 1 2 6 7 8 10 11 6 :0 1 2 6 7 9 10 11 6 :0 1 2 4 5 6 7 10 11 6 :0 1 2 4 6 7 8 10 11 6 :0 1 2 4 6 7 9 10 11 6 7 :0 1 2 3 5 6 8 9 10 11 6 7 :0 1 2 4 5 6 7 9 10 11 6 7 8 :0 1 2 4 5 6 8 9 10 11 6 7 10 11 :0 1 2 5 6 7 8 9 10 11 6 8 10 :0 1 2 4 6 7 8 9 10 11 6 10 :0 1 2 6 7 8 9 10 11 7 :0 1 5 7 9 10 11 7 :0 1 3 4 5 9 10 11 7 :0 1 2 5 7 9 10 11 7 :0 1 3 5 6 9 10 11 7 :0 1 3 5 7 9 10 11 7 :0 1 4 5 7 9 10 11 7 :0 1 5 6 7 9 10 11 7 :0 1 5 7 8 9 10 11 7 :0 1 2 4 5 7 9 10 11 7 :0 1 3 4 5 7 9 10 11 7 :0 1 2 5 7 8 9 10 11 7 :0 1 3 5 6 7 9 10 11 7 :0 1 4 5 6 7 9 10 11 7 8 :0 1 4 5 7 8 9 10 11 7 8 :0 1 2 4 5 7 8 9 10 11 7 8 :0 1 3 4 5 6 8 9 10 11 7 8 9 :0 1 3 4 5 7 8 9 10 11 7 9 :0 1 3 5 7 8 9 10 11 7 9 11 :0 1 3 5 6 7 8 9 10 11 8 :0 4 8 9 10 11 8 :0 3 4 8 9 10 11 8 :0 4 7 8 9 10 11 8 :0 1 3 4 8 9 10 11 8 :0 2 3 4 8 9 10 11 8 :0 1 4 7 8 9 10 11 8 :0 2 4 7 8 9 10 11 8 :0 4 5 7 8 9 10 11 8 :0 4 6 7 8 9 10 11 8 :0 1 2 4 7 8 9 10 11 8 :0 1 4 6 7 8 9 10 11 8 :0 2 4 5 7 8 9 10 11 8 9 :0 3 4 7 8 9 10 11 8 9 :0 1 3 4 7 8 9 10 11 8 9 :0 2 3 4 7 8 9 10 11 8 9 :0 3 4 5 7 8 9 10 11 8 9 :0 3 4 6 7 8 9 10 11 8 9 :0 1 3 4 6 7 8 9 10 11 8 9 :0 2 3 4 5 7 8 9 10 11 8 9 10 :0 2 3 4 6 7 8 9 10 11 8 10 :0 2 4 6 7 8 9 10 11 9 :0 3 7 8 9 10 11 9 :0 1 3 7 8 9 10 11 9 :0 2 3 7 8 9 10 11 9 :0 3 5 7 8 9 10 11 9 :0 3 6 7 8 9 10 11 9 :0 1 3 6 7 8 9 10 11 9 :0 2 3 5 7 8 9 10 11 9 :0 3 5 6 7 8 9 10 11 9 10 :0 2 3 6 7 8 9 10 11 9 10 :0 2 3 5 6 7 8 9 10 11 10 :0 2 6 7 8 9 10 10 :0 1 2 6 7 8 9 10 10 :0 2 3 6 7 8 9 10 10 :0 2 4 6 7 8 9 10 10 :0 2 5 6 7 8 9 10 10 :0 2 6 7 8 9 10 11 10 :0 1 2 3 6 7 8 9 10 10 :0 1 2 4 6 7 8 9 10 10 :0 2 3 4 6 7 8 9 10 10 :0 2 3 5 6 7 8 9 10 10 11 :0 1 2 3 5 6 7 8 9 10 11 :0 1 2 5 6 7 8 9 11 :0 1 3 5 6 7 8 9 11 :0 1 2 3 5 6 7 8 9 11 :0 1 3 5 6 7 8 9 10 11 :0 1 3 5 6 7 8 9 11 Subset Chord Types By Family Chord Type Roots Unison (Scale Degrees: 1) 0 = root, unison, octave | 0 4 5 6 7 8 = 0: 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 = 5: 0 1 2 3 7 11 = 6: 0 1 2 6 10 11 = 7: 0 1 5 9 10 11 = 8: 0 4 8 9 10 11 2nds / 9ths = 1st 2 notes of diamorphic scale (Scale Degrees: 12) 0 1 = semitone, min. 2nd, min. 9th |

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

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

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

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

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

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

Chord Type		Roots
Unison (Scale Degrees: 1)
0 = root, unison, octave	\|	0 4 5 6 7 8 = 0: 0 4 5 6 7 8 = 4: 0 1 2 3 4 8 = 5: 0 1 2 3 7 11 = 6: 0 1 2 6 10 11 = 7: 0 1 5 9 10 11 = 8: 0 4 8 9 10 11

2nds / 9ths = 1st 2 notes of diamorphic scale (Scale Degrees: 12)
0 1 = semitone, min. 2nd, min. 9th	\|