Chord Type: 0 1 2 3 7 11

0 1 2 3 7 11

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Chord Type: 0 1 2 3 7 11

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: Thydimic Ian Ring's Scale Page 2191 Root Reference: 0 1 2 3 7 11 Tone Stacking: 0 1 1 1 4 4 Interval Stacking: 1 1 1 4 4 1 Binary: 1 1 1 1 0 0 0 1 0 0 0 1 Decimal Value: 2191 Interval Vector: 4 3 2 3 2 1 Inversional Symmetry: yes (axes of symmetry: 1 7) 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: 122357 0 1 2 3 6 11 0 1 2 3 7 10 ->0 1 2 3 7 11 0 1 2 4 6 11 0 1 2 4 7 10 0 1 2 4 7 11 0 1 2 4 8 10 0 1 3 4 7 10 0 1 3 4 7 11 0 1 3 4 8 10 0 1 3 4 8 11 0 2 3 4 6 10 0 2 3 4 6 11 0 2 3 4 7 10 0 2 3 4 7 11 0 2 3 4 8 10 0 2 3 4 8 11 All Transpositions of Chord Type: +0= 0 1 2 3 7 11 | +1= 0 1 2 3 4 8 | +2= 1 2 3 4 5 9 | +3= 2 3 4 5 6 10 | +4= 3 4 5 6 7 11 | +5= 0 4 5 6 7 8 | +6= 1 5 6 7 8 9 | +7= 2 6 7 8 9 10 | +8= 3 7 8 9 10 11 | +9= 0 4 8 9 10 11 | +10= 0 1 5 9 10 11 | +11= 0 1 2 6 10 11 | Modes of Chord Type: (mode 0) 0: 0 1 2 3 7 11 | (mode 1) 1: 0 1 2 6 10 11 | (mode 2) 2: 0 1 5 9 10 11 | (mode 3) 3: 0 4 8 9 10 11 | (mode 4) 7: 0 4 5 6 7 8 | (mode 5) 11: 0 1 2 3 4 8 | Modes of Chord Type Sorted by Rootedness: 1.525(mode 0)0:0 1 2 3 7 11 | .958(mode 3)3:0 4 8 9 10 11 | .908(mode 5)11:0 1 2 3 4 8 | .750(mode 1)1:0 1 2 6 10 11 | .683(mode 4)7:0 4 5 6 7 8 | .475(mode 2)2:0 1 5 9 10 11 | Inversion at 0: 0 1 5 9 10 11 (mode 0) 0: 0 1 5 9 10 11 | (mode 1) 1: 0 4 8 9 10 11 | (mode 2) 5: 0 4 5 6 7 8 | (mode 3) 9: 0 1 2 3 4 8 | (mode 4) 10: 0 1 2 3 7 11 | (mode 5) 11: 0 1 2 6 10 11 | Times 7: 0 1 2 5 7 9 (mode 0) 0: 0 1 2 5 7 9 | (mode 1) 1: 0 1 4 6 8 11 | (mode 2) 2: 0 3 5 7 10 11 | mM7#13 no 9th (mode 3) 5: 0 2 4 7 8 9 | (mode 4) 7: 0 2 5 6 7 10 | (mode 5) 9: 0 3 4 5 8 10 | Times 5: 0 3 5 7 10 11 (mode 0) 0: 0 3 5 7 10 11 | mM7#13 no 9th (mode 1) 3: 0 2 4 7 8 9 | (mode 2) 5: 0 2 5 6 7 10 | (mode 3) 7: 0 3 4 5 8 10 | (mode 4) 10: 0 1 2 5 7 9 | (mode 5) 11: 0 1 4 6 8 11 | Modal System: 0 1 2 3 4 8 from root(s) 11 | "" 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: 4 5 6 8 9 10 (mode 0) 4: 0 1 2 4 5 6 | (mode 1) 5: 0 1 3 4 5 11 | (mode 2) 6: 0 2 3 4 10 11 | (mode 3) 8: 0 1 2 8 9 10 | (mode 4) 9: 0 1 7 8 9 11 | (mode 5) 10: 0 6 7 8 10 11 | All but the root (subchroma complement of 0): 1 2 3 7 11 (mode 0) 1: 0 1 2 6 10 | (mode 1) 2: 0 1 5 9 11 | (mode 2) 3: 0 4 8 10 11 | M7#5/#6 (mode 3) 7: 0 4 6 7 8 | (mode 4) 11: 0 2 3 4 8 | 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: 3 7 11 (mode 0) 3: 0 4 8 | + = augmented triad = augmented chord (mode 1) 7: 0 4 8 | + = augmented triad = augmented chord (mode 2) 11: 0 4 8 | + = augmented triad = augmented chord Dechromaticised but Keep 0 0 3 7 11 (mode 0) 0: 0 3 7 11 | mM7 (mode 1) 3: 0 4 8 9 | (mode 2) 7: 0 4 5 8 | (mode 3) 11: 0 1 4 8 | Dechromaticised but Keep 0 7 0 3 7 11 (mode 0) 0: 0 3 7 11 | mM7 (mode 1) 3: 0 4 8 9 | (mode 2) 7: 0 4 5 8 | (mode 3) 11: 0 1 4 8 | Dechromaticised but Keep 0 3 4 7 0 3 7 11 (mode 0) 0: 0 3 7 11 | mM7 (mode 1) 3: 0 4 8 9 | (mode 2) 7: 0 4 5 8 | (mode 3) 11: 0 1 4 8 | Alt-Dechromaticised: 0 1 2 3 11 (mode 0) 0: 0 1 2 3 11 | (mode 1) 1: 0 1 2 10 11 | (mode 2) 2: 0 1 9 10 11 | (mode 3) 3: 0 8 9 10 11 | (mode 4) 11: 0 1 2 3 4 | 1st 5 notes of chromatic scale Alt-Dechromaticised but Keep 0 0 1 2 3 11 (unchanged) (mode 0) 0: 0 1 2 3 11 | (mode 1) 1: 0 1 2 10 11 | (mode 2) 2: 0 1 9 10 11 | (mode 3) 3: 0 8 9 10 11 | (mode 4) 11: 0 1 2 3 4 | 1st 5 notes of chromatic scale Alt-Dechromaticised but Keep 0 7 0 1 2 3 7 11 (mode 0) 0: 0 1 2 3 7 11 | (mode 1) 1: 0 1 2 6 10 11 | (mode 2) 2: 0 1 5 9 10 11 | (mode 3) 3: 0 4 8 9 10 11 | (mode 4) 7: 0 4 5 6 7 8 | (mode 5) 11: 0 1 2 3 4 8 | Alt-Dechromaticised but Keep 0 3 4 7 0 1 2 3 7 11 (mode 0) 0: 0 1 2 3 7 11 | (mode 1) 1: 0 1 2 6 10 11 | (mode 2) 2: 0 1 5 9 10 11 | (mode 3) 3: 0 4 8 9 10 11 | (mode 4) 7: 0 4 5 6 7 8 | (mode 5) 11: 0 1 2 3 4 8 | 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 2 3 7 8 11 | (mode 1) 1: 0 1 2 6 7 10 11 | mela 42 Raghupriya (mode 2) 2: 0 1 5 6 9 10 11 | (mode 3) 3: 0 4 5 8 9 10 11 | (mode 4) 7: 0 1 4 5 6 7 8 | (mode 5) 8: 0 3 4 5 6 7 11 | (mode 6) 11: 0 1 2 3 4 8 9 | (mode 0) 0: 0 1 2 3 6 7 11 | (mode 1) 1: 0 1 2 5 6 10 11 | (mode 2) 2: 0 1 4 5 9 10 11 | (mode 3) 3: 0 3 4 8 9 10 11 | (mode 4) 6: 0 1 5 6 7 8 9 | (mode 5) 7: 0 4 5 6 7 8 11 | (mode 6) 11: 0 1 2 3 4 7 8 | alt-chromaticized keep 0 7: (mode 0) 0: 0 1 2 3 6 7 11 | (mode 1) 1: 0 1 2 5 6 10 11 | (mode 2) 2: 0 1 4 5 9 10 11 | (mode 3) 3: 0 3 4 8 9 10 11 | (mode 4) 6: 0 1 5 6 7 8 9 | (mode 5) 7: 0 4 5 6 7 8 11 | (mode 6) 11: 0 1 2 3 4 7 8 | (mode 0) 0: 0 1 2 3 7 8 11 | (mode 1) 1: 0 1 2 6 7 10 11 | mela 42 Raghupriya (mode 2) 2: 0 1 5 6 9 10 11 | (mode 3) 3: 0 4 5 8 9 10 11 | (mode 4) 7: 0 1 4 5 6 7 8 | (mode 5) 8: 0 3 4 5 6 7 11 | (mode 6) 11: 0 1 2 3 4 8 9 | (mode 0) 0: 0 1 2 3 5 7 10 11 | (mode 1) 1: 0 1 2 4 6 9 10 11 | (mode 2) 2: 0 1 3 5 8 9 10 11 | (mode 3) 3: 0 2 4 7 8 9 10 11 | (mode 4) 5: 0 2 5 6 7 8 9 10 | (mode 5) 7: 0 3 4 5 6 7 8 10 | (mode 6) 10: 0 1 2 3 4 5 7 9 | (mode 7) 11: 0 1 2 3 4 6 8 11 | (mode 0) 0: 0 1 2 3 4 7 8 9 11 | (mode 1) 1: 0 1 2 3 6 7 8 10 11 | (mode 2) 2: 0 1 2 5 6 7 9 10 11 | (mode 3) 3: 0 1 4 5 6 8 9 10 11 | (mode 4) 4: 0 3 4 5 7 8 9 10 11 | (mode 5) 7: 0 1 2 4 5 6 7 8 9 | (mode 6) 8: 0 1 3 4 5 6 7 8 11 | (mode 7) 9: 0 2 3 4 5 6 7 10 11 | (mode 8) 11: 0 1 2 3 4 5 8 9 10 | (mode 0) 0: 0 1 2 3 5 6 7 10 11 | (mode 1) 1: 0 1 2 4 5 6 9 10 11 | (mode 2) 2: 0 1 3 4 5 8 9 10 11 | (mode 3) 3: 0 2 3 4 7 8 9 10 11 | (mode 4) 5: 0 1 2 5 6 7 8 9 10 | (mode 5) 6: 0 1 4 5 6 7 8 9 11 | (mode 6) 7: 0 3 4 5 6 7 8 10 11 | (mode 7) 10: 0 1 2 3 4 5 7 8 9 | (mode 8) 11: 0 1 2 3 4 6 7 8 11 | alt-chromaticized keep 0 3 4 7: (mode 0) 0: 0 1 2 3 6 7 11 | (mode 1) 1: 0 1 2 5 6 10 11 | (mode 2) 2: 0 1 4 5 9 10 11 | (mode 3) 3: 0 3 4 8 9 10 11 | (mode 4) 6: 0 1 5 6 7 8 9 | (mode 5) 7: 0 4 5 6 7 8 11 | (mode 6) 11: 0 1 2 3 4 7 8 | (mode 0) 0: 0 1 2 3 7 8 11 | (mode 1) 1: 0 1 2 6 7 10 11 | mela 42 Raghupriya (mode 2) 2: 0 1 5 6 9 10 11 | (mode 3) 3: 0 4 5 8 9 10 11 | (mode 4) 7: 0 1 4 5 6 7 8 | (mode 5) 8: 0 3 4 5 6 7 11 | (mode 6) 11: 0 1 2 3 4 8 9 | (mode 0) 0: 0 1 2 3 5 7 10 11 | (mode 1) 1: 0 1 2 4 6 9 10 11 | (mode 2) 2: 0 1 3 5 8 9 10 11 | (mode 3) 3: 0 2 4 7 8 9 10 11 | (mode 4) 5: 0 2 5 6 7 8 9 10 | (mode 5) 7: 0 3 4 5 6 7 8 10 | (mode 6) 10: 0 1 2 3 4 5 7 9 | (mode 7) 11: 0 1 2 3 4 6 8 11 | (mode 0) 0: 0 1 2 3 4 7 8 9 11 | (mode 1) 1: 0 1 2 3 6 7 8 10 11 | (mode 2) 2: 0 1 2 5 6 7 9 10 11 | (mode 3) 3: 0 1 4 5 6 8 9 10 11 | (mode 4) 4: 0 3 4 5 7 8 9 10 11 | (mode 5) 7: 0 1 2 4 5 6 7 8 9 | (mode 6) 8: 0 1 3 4 5 6 7 8 11 | (mode 7) 9: 0 2 3 4 5 6 7 10 11 | (mode 8) 11: 0 1 2 3 4 5 8 9 10 | (mode 0) 0: 0 1 2 3 5 6 7 10 11 | (mode 1) 1: 0 1 2 4 5 6 9 10 11 | (mode 2) 2: 0 1 3 4 5 8 9 10 11 | (mode 3) 3: 0 2 3 4 7 8 9 10 11 | (mode 4) 5: 0 1 2 5 6 7 8 9 10 | (mode 5) 6: 0 1 4 5 6 7 8 9 11 | (mode 6) 7: 0 3 4 5 6 7 8 10 11 | (mode 7) 10: 0 1 2 3 4 5 7 8 9 | (mode 8) 11: 0 1 2 3 4 6 7 8 11 | (mode 0) 0: 0 1 2 3 5 7 8 10 11 | phrygian & harmonic minor (mode 1) 1: 0 1 2 4 6 7 9 10 11 | (mode 2) 2: 0 1 3 5 6 8 9 10 11 | (mode 3) 3: 0 2 4 5 7 8 9 10 11 | (mode 4) 5: 0 2 3 5 6 7 8 9 10 | (mode 5) 7: 0 1 3 4 5 6 7 8 10 | (mode 6) 8: 0 2 3 4 5 6 7 9 11 | lydian & melodic minor (mode 7) 10: 0 1 2 3 4 5 7 9 10 | (mode 8) 11: 0 1 2 3 4 6 8 9 11 | (mode 0) 0: 0 1 2 3 4 6 7 9 11 | (mode 1) 1: 0 1 2 3 5 6 8 10 11 | (mode 2) 2: 0 1 2 4 5 7 9 10 11 | (mode 3) 3: 0 1 3 4 6 8 9 10 11 | (mode 4) 4: 0 2 3 5 7 8 9 10 11 | dorian & harmonic minor = aeolean & melodic minor (mode 5) 6: 0 1 3 5 6 7 8 9 10 | (mode 6) 7: 0 2 4 5 6 7 8 9 11 | (mode 7) 9: 0 2 3 4 5 6 7 9 10 | (mode 8) 11: 0 1 2 3 4 5 7 8 10 | Bright Layer Decomposition order origin root set chord type (as pcset) 1 0 0 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 1 1 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 3 3 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 1 7 7 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 11 11 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 Bright Layer Composition order pcset 1 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 2 0 1 2 3 6 7 8 9 10 11 = 0: 0 1 2 3 6 7 8 9 10 11 = 1: 0 1 2 5 6 7 8 9 10 11 = 2: 0 1 4 5 6 7 8 9 10 11 = 3: 0 3 4 5 6 7 8 9 10 11 = 6: 0 1 2 3 4 5 6 7 8 9 = 7: 0 1 2 3 4 5 6 7 8 11 = 8: 0 1 2 3 4 5 6 7 10 11 = 9: 0 1 2 3 4 5 6 9 10 11 = 10: 0 1 2 3 4 5 8 9 10 11 = 11: 0 1 2 3 4 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 7 11 subchroma modal system: 0 0 = 0 = 0: 0 1 = 1 = 1: 0 2 = 2 = 2: 0 3 = 3 = 3: 0 7 = 7 = 7: 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 7 = 3 7 = 3: 0 4 7: 0 8 7 11 = 7 11 = 7: 0 4 11: 0 8 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 7 = 2 7 = 2: 0 5 7: 0 7 3 11 = 3 11 = 11: 0 4 3: 0 8 7 0 = 0 7 = 7: 0 5 0: 0 7 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 7 = 1 7 = 1 7: 0 6 2 11 = 2 11 = 11: 0 3 2: 0 9 3 0 = 0 3 = 0: 0 3 3: 0 9 7 1 = 1 7 = 1 7: 0 6 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 7 = 2 3 7 = 3: 0 4 11 7: 0 7 8 3 7 11 = 3 7 11 = 3 7 11: 0 4 8 7 11 0 = 0 7 11 = 7: 0 4 5 0: 0 7 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 3 = 0 1 3 = 0: 0 1 3 1: 0 2 11 1 2 7 = 1 2 7 = 7: 0 6 7 2 3 11 = 2 3 11 = 11: 0 3 4 3 7 0 = 0 3 7 = 0: 0 3 7 3: 0 4 9 7 11 1 = 1 7 11 = 7: 0 4 6 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 11 = 1 2 11 = 11: 0 2 3 2 3 0 = 0 2 3 = 0: 0 2 3 3 7 1 = 1 3 7 = 3: 0 4 10 7 11 2 = 2 7 11 = 7: 0 4 7 11 0 3 = 0 3 11 = 11: 0 1 4 0: 0 3 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 3 11 = 1 3 11 = 11: 0 2 4 2 7 0 = 0 2 7 = 0: 0 2 7 7: 0 5 7 2: 0 5 10 3 11 1 = 1 3 11 = 11: 0 2 4 7 0 2 = 0 2 7 = 0: 0 2 7 7: 0 5 7 2: 0 5 10 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 7 = 1 2 3 7 = 3: 0 4 10 11 7: 0 6 7 8 2 3 7 11 = 2 3 7 11 = 11: 0 3 4 8 7: 0 4 7 8 3: 0 4 8 11 3 7 11 0 = 0 3 7 11 = 0: 0 3 7 11 7 11 0 1 = 0 1 7 11 = 0: 0 1 7 11 7: 0 4 5 6 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 3 11 = 1 2 3 11 = 11: 0 2 3 4 2 3 7 0 = 0 2 3 7 = 0: 0 2 3 7 3: 0 4 9 11 7: 0 5 7 8 3 7 11 1 = 1 3 7 11 = 3: 0 4 8 10 7 11 0 2 = 0 2 7 11 = 0: 0 2 7 11 7: 0 4 5 7 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 7 = 0 1 3 7 = 0: 0 1 3 7 3: 0 4 9 10 1 2 7 11 = 1 2 7 11 = 7: 0 4 6 7 2 3 11 0 = 0 2 3 11 = 11: 0 1 3 4 0: 0 2 3 11 3 7 0 1 = 0 1 3 7 = 0: 0 1 3 7 3: 0 4 9 10 7 11 1 2 = 1 2 7 11 = 7: 0 4 6 7 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 7 = 0 1 2 3 7 = 0: 0 1 2 3 7 3: 0 4 9 10 11 1 2 3 7 11 = 1 2 3 7 11 = 11: 0 2 3 4 8 7: 0 4 6 7 8 3: 0 4 8 10 11 2 3 7 11 0 = 0 2 3 7 11 = 11: 0 1 3 4 8 0: 0 2 3 7 11 7: 0 4 5 7 8 3 7 11 0 1 = 0 1 3 7 11 = 11: 0 1 2 4 8 0: 0 1 3 7 11 7: 0 4 5 6 8 3: 0 4 8 9 10 7 11 0 1 2 = 0 1 2 7 11 = 0: 0 1 2 7 11 7: 0 4 5 6 7 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 7 11 = 0 1 2 3 7 11 = 11: 0 1 2 3 4 8 0: 0 1 2 3 7 11 1: 0 1 2 6 10 11 7: 0 4 5 6 7 8 3: 0 4 8 9 10 11 1 2 3 7 11 0 = 0 1 2 3 7 11 = 11: 0 1 2 3 4 8 0: 0 1 2 3 7 11 1: 0 1 2 6 10 11 7: 0 4 5 6 7 8 3: 0 4 8 9 10 11 2 3 7 11 0 1 = 0 1 2 3 7 11 = 11: 0 1 2 3 4 8 0: 0 1 2 3 7 11 1: 0 1 2 6 10 11 7: 0 4 5 6 7 8 3: 0 4 8 9 10 11 3 7 11 0 1 2 = 0 1 2 3 7 11 = 11: 0 1 2 3 4 8 0: 0 1 2 3 7 11 1: 0 1 2 6 10 11 7: 0 4 5 6 7 8 3: 0 4 8 9 10 11 7 11 0 1 2 3 = 0 1 2 3 7 11 = 11: 0 1 2 3 4 8 0: 0 1 2 3 7 11 1: 0 1 2 6 10 11 7: 0 4 5 6 7 8 3: 0 4 8 9 10 11 11 0 1 2 3 7 = 0 1 2 3 7 11 = 11: 0 1 2 3 4 8 0: 0 1 2 3 7 11 1: 0 1 2 6 10 11 7: 0 4 5 6 7 8 3: 0 4 8 9 10 11 Subset Chord Types by Root Set 0 :0 1 7 0 :0 2 7 0 :0 3 7 0 :0 3 11 0 :0 7 11 0 :0 1 2 7 0 :0 1 3 7 0 :0 2 3 7 0 :0 1 3 11 0 :0 2 3 11 0 :0 1 7 11 0 :0 2 7 11 0 :0 3 7 11 0 :0 1 2 3 7 0 :0 1 2 3 11 0 :0 1 2 7 11 0 :0 1 3 7 11 0 :0 2 3 7 11 0 :0 1 2 3 7 11 0 1 :0 2 11 0 1 2 :0 1 11 0 1 2 3 :0 11 0 1 2 3 7 11:0 0 1 2 11 :0 1 0 1 11:0 2 0 1 11:0 1 2 0 7 :0 7 0 11 :0 3 0 11 :0 1 3 0 11 :0 2 3 0 11 :0 1 2 3 1 :0 2 10 11 1 :0 1 2 6 10 11 1 2 :0 1 10 11 1 2 3 :0 10 1 2 3 :0 10 11 1 7 :0 6 2 :0 5 10 2 :0 5 10 11 2 3 :0 9 2 3 :0 9 10 11 2 7 :0 5 3 :0 4 9 3 :0 4 10 3 :0 4 11 3 :0 4 8 10 3 :0 4 8 11 3 :0 4 9 10 3 :0 4 9 11 3 :0 4 10 11 3 :0 4 8 9 10 3 :0 4 8 10 11 3 :0 4 9 10 11 3 :0 8 9 10 11 3 :0 4 8 9 10 11 3 7 11 :0 4 3 7 11 :0 8 3 7 11 :0 4 8 7 :0 4 5 7 :0 4 6 7 :0 4 7 7 :0 5 7 7 :0 6 7 7 :0 7 8 7 :0 4 5 6 7 :0 4 5 7 7 :0 4 6 7 7 :0 4 7 8 7 :0 5 6 7 7 :0 5 7 8 7 :0 6 7 8 7 :0 4 5 6 7 7 :0 4 5 6 8 7 :0 4 5 7 8 7 :0 4 6 7 8 7 :0 4 5 6 7 8 11 :0 1 4 11 :0 2 4 11 :0 3 4 11 :0 1 2 4 11 :0 1 3 4 11 :0 2 3 4 11 :0 3 4 8 11 :0 1 2 3 4 11 :0 1 2 4 8 11 :0 1 3 4 8 11 :0 2 3 4 8 11 :0 1 2 3 4 8 Superset Chord Types by Root Set 0 :0 1 2 3 7 11 0 :0 1 2 3 4 7 11 0 :0 1 2 3 5 7 11 0 :0 1 2 3 6 7 11 0 :0 1 2 3 7 8 11 0 :0 1 2 3 7 9 11 0 :0 1 2 3 7 10 11 0 :0 1 2 3 4 5 7 11 0 :0 1 2 3 4 6 7 11 0 :0 1 2 3 4 7 9 11 0 :0 1 2 3 4 7 10 11 0 :0 1 2 3 5 6 7 11 0 :0 1 2 3 5 7 8 11 0 :0 1 2 3 5 7 9 11 0 :0 1 2 3 5 7 10 11 0 :0 1 2 3 6 7 8 11 0 :0 1 2 3 6 7 9 11 0 :0 1 2 3 7 8 9 11 0 :0 1 2 3 7 8 10 11 0 :0 1 2 3 7 9 10 11 0 :0 1 2 3 4 5 7 10 11 0 :0 1 2 3 4 6 7 9 11 0 :0 1 2 3 4 7 9 10 11 0 :0 1 2 3 5 6 7 8 11 0 :0 1 2 3 5 6 7 9 11 0 :0 1 2 3 5 7 8 9 11 0 :0 1 2 3 5 7 8 10 11 0 :0 1 2 3 6 7 8 9 11 0 1 :0 1 2 3 6 7 10 11 0 1 :0 1 2 3 4 6 7 10 11 0 1 :0 1 2 3 5 6 7 10 11 0 1 :0 1 2 3 6 7 8 10 11 0 1 :0 1 2 3 6 7 9 10 11 0 1 :0 1 2 3 4 6 7 9 10 11 0 1 :0 1 2 3 5 6 7 8 10 11 0 1 2 :0 1 2 3 5 6 7 9 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 5 6 7 8 9 10 11 0 1 2 8 9 10 :0 1 2 3 4 5 6 7 9 10 11 0 1 3 4 5 11 :0 1 2 3 4 6 7 8 9 10 11 0 1 4 5 :0 1 2 3 6 7 8 9 10 11 0 1 7 8 9 11 :0 1 2 3 4 5 6 7 8 10 11 0 1 8 9 :0 1 2 3 4 5 6 7 10 11 0 1 11 :0 1 2 3 4 6 7 8 10 11 0 2 :0 1 2 3 5 7 9 10 11 0 2 3 4 10 11 :0 1 2 3 4 5 7 8 9 10 11 0 2 4 :0 1 2 3 5 7 8 9 10 11 0 2 10 :0 1 2 3 4 5 7 9 10 11 0 3 4 11 :0 1 2 3 4 7 8 9 10 11 0 4 :0 1 2 3 7 8 9 10 11 0 6 :0 1 2 3 5 6 7 8 9 11 0 6 7 8 10 11 :0 1 2 3 4 5 6 7 8 9 11 0 7 8 11 :0 1 2 3 4 5 6 7 8 11 0 8 :0 1 2 3 4 5 6 7 11 0 8 10 :0 1 2 3 4 5 6 7 9 11 0 10 :0 1 2 3 4 5 7 9 11 0 10 11 :0 1 2 3 4 5 7 8 9 11 0 11 :0 1 2 3 4 7 8 11 0 11 :0 1 2 3 4 5 7 8 11 0 11 :0 1 2 3 4 6 7 8 11 0 11 :0 1 2 3 4 7 8 9 11 0 11 :0 1 2 3 4 7 8 10 11 0 11 :0 1 2 3 4 5 7 8 10 11 0 11 :0 1 2 3 4 6 7 8 9 11 1 :0 1 2 6 10 11 1 :0 1 2 3 6 10 11 1 :0 1 2 4 6 10 11 1 :0 1 2 6 7 10 11 1 :0 1 2 4 6 7 10 11 1 :0 1 2 4 6 8 10 11 1 :0 1 2 5 6 7 10 11 1 :0 1 2 6 7 8 10 11 1 :0 1 2 6 7 9 10 11 1 :0 1 2 4 5 6 7 10 11 1 :0 1 2 4 6 7 8 10 11 1 :0 1 2 4 6 7 9 10 11 1 2 :0 1 2 3 5 6 8 9 10 11 1 2 :0 1 2 4 5 6 7 9 10 11 1 2 3 :0 1 2 4 5 6 8 9 10 11 1 2 3 5 6 7 :0 1 2 4 5 6 7 8 9 10 11 1 2 3 9 10 11 :0 1 2 3 4 5 6 8 9 10 11 1 2 5 6 :0 1 2 5 6 7 8 9 10 11 1 2 9 10 :0 1 2 3 4 5 6 9 10 11 1 3 5 :0 1 2 4 6 7 8 9 10 11 1 3 11 :0 1 2 3 4 6 8 9 10 11 1 5 :0 1 2 6 7 8 9 10 11 1 7 :0 1 2 4 5 6 7 8 10 11 1 9 11 :0 1 2 3 4 5 6 8 10 11 1 11 :0 1 2 3 4 6 8 10 11 2 :0 1 5 7 9 10 11 2 :0 1 3 4 5 9 10 11 2 :0 1 2 5 7 9 10 11 2 :0 1 3 5 6 9 10 11 2 :0 1 3 5 7 9 10 11 2 :0 1 4 5 7 9 10 11 2 :0 1 5 6 7 9 10 11 2 :0 1 5 7 8 9 10 11 2 :0 1 2 4 5 7 9 10 11 2 :0 1 3 4 5 7 9 10 11 2 :0 1 2 5 7 8 9 10 11 2 :0 1 3 5 6 7 9 10 11 2 :0 1 4 5 6 7 9 10 11 2 3 :0 1 4 5 7 8 9 10 11 2 3 :0 1 2 4 5 7 8 9 10 11 2 3 :0 1 3 4 5 6 8 9 10 11 2 3 4 :0 1 3 4 5 7 8 9 10 11 2 3 4 6 7 8 :0 1 3 4 5 6 7 8 9 10 11 2 3 6 7 :0 1 4 5 6 7 8 9 10 11 2 3 10 11 :0 1 2 3 4 5 8 9 10 11 2 4 :0 1 3 5 7 8 9 10 11 2 4 6 :0 1 3 5 6 7 8 9 10 11 2 8 :0 1 3 4 5 6 7 9 10 11 3 :0 4 8 9 10 11 3 :0 3 4 8 9 10 11 3 :0 4 7 8 9 10 11 3 :0 1 3 4 8 9 10 11 3 :0 2 3 4 8 9 10 11 3 :0 1 4 7 8 9 10 11 3 :0 2 4 7 8 9 10 11 3 :0 4 5 7 8 9 10 11 3 :0 4 6 7 8 9 10 11 3 :0 1 2 4 7 8 9 10 11 3 :0 1 4 6 7 8 9 10 11 3 :0 2 4 5 7 8 9 10 11 3 4 :0 3 4 7 8 9 10 11 3 4 :0 1 3 4 7 8 9 10 11 3 4 :0 2 3 4 7 8 9 10 11 3 4 :0 3 4 5 7 8 9 10 11 3 4 :0 3 4 6 7 8 9 10 11 3 4 :0 1 3 4 6 7 8 9 10 11 3 4 :0 2 3 4 5 7 8 9 10 11 3 4 5 :0 2 3 4 6 7 8 9 10 11 3 4 5 7 8 9 :0 2 3 4 5 6 7 8 9 10 11 3 4 7 8 :0 3 4 5 6 7 8 9 10 11 3 5 :0 2 4 6 7 8 9 10 11 3 5 7 :0 2 4 5 6 7 8 9 10 11 3 7 :0 4 5 6 7 8 9 10 11 3 9 :0 2 3 4 5 6 8 9 10 11 4 :0 3 7 8 9 10 11 4 :0 1 3 7 8 9 10 11 4 :0 2 3 7 8 9 10 11 4 :0 3 5 7 8 9 10 11 4 :0 3 6 7 8 9 10 11 4 :0 1 3 6 7 8 9 10 11 4 :0 2 3 5 7 8 9 10 11 4 :0 3 5 6 7 8 9 10 11 4 5 :0 2 3 6 7 8 9 10 11 4 5 :0 2 3 5 6 7 8 9 10 11 5 :0 2 6 7 8 9 10 5 :0 1 2 6 7 8 9 10 5 :0 2 3 6 7 8 9 10 5 :0 2 4 6 7 8 9 10 5 :0 2 5 6 7 8 9 10 5 :0 2 6 7 8 9 10 11 5 :0 1 2 3 6 7 8 9 10 5 :0 1 2 4 6 7 8 9 10 5 :0 2 3 4 6 7 8 9 10 5 :0 2 3 5 6 7 8 9 10 5 6 :0 1 2 3 5 6 7 8 9 10 5 6 7 :0 1 2 4 5 6 7 8 9 10 5 6 7 9 10 11 :0 1 2 3 4 5 6 7 8 9 10 5 7 :0 2 4 5 6 7 8 9 10 5 7 9 :0 2 3 4 5 6 7 8 9 10 5 11 :0 1 2 3 4 6 7 8 9 10 6 :0 1 2 5 6 7 8 9 6 :0 1 3 5 6 7 8 9 6 :0 1 2 3 5 6 7 8 9 6 :0 1 3 5 6 7 8 9 10 6 :0 1 3 5 6 7 8 9 11 6 7 :0 1 4 5 6 7 8 9 6 7 :0 1 2 4 5 6 7 8 9 6 7 :0 1 4 5 6 7 8 9 10 6 7 :0 1 4 5 6 7 8 9 11 6 7 :0 1 2 4 5 6 7 8 9 11 6 7 :0 1 3 4 5 6 7 8 9 10 6 7 8 :0 1 3 4 5 6 7 8 9 11 6 7 10 11 :0 1 2 3 4 5 6 7 8 9 7 :0 4 5 6 7 8 7 :0 1 4 5 6 7 8 7 :0 2 4 5 6 7 8 7 :0 3 4 5 6 7 8 7 :0 4 5 6 7 8 9 7 :0 4 5 6 7 8 10 7 :0 4 5 6 7 8 11 7 :0 1 2 4 5 6 7 8 7 :0 1 3 4 5 6 7 8 7 :0 2 3 4 5 6 7 8 7 :0 1 4 5 6 7 8 10 7 :0 1 4 5 6 7 8 11 7 :0 2 4 5 6 7 8 10 7 :0 2 4 5 6 7 8 11 7 :0 3 4 5 6 7 8 10 7 :0 4 5 6 7 8 9 10 7 :0 4 5 6 7 8 10 11 7 :0 2 3 4 5 6 7 8 9 7 :0 1 2 4 5 6 7 8 10 7 :0 1 2 4 5 6 7 8 11 7 :0 1 3 4 5 6 7 8 10 7 :0 2 4 5 6 7 8 9 11 7 :0 1 4 5 6 7 8 10 11 7 :0 2 4 5 6 7 8 10 11 7 :0 3 4 5 6 7 8 9 10 7 8 :0 3 4 5 6 7 8 11 7 8 :0 1 3 4 5 6 7 8 11 7 8 :0 2 3 4 5 6 7 8 11 7 8 :0 3 4 5 6 7 8 9 11 7 8 :0 3 4 5 6 7 8 10 11 7 8 :0 1 3 4 5 6 7 8 10 11 7 8 :0 2 3 4 5 6 7 8 9 11 7 8 9 :0 2 3 4 5 6 7 8 10 11 7 9 :0 2 3 4 5 6 7 8 10 7 9 11 :0 1 2 3 4 5 6 7 8 10 7 11 :0 1 2 3 4 5 6 7 8 8 :0 3 4 5 6 7 11 8 :0 1 3 4 5 6 7 11 8 :0 2 3 4 5 6 7 11 8 :0 3 4 5 6 7 9 11 8 :0 3 4 5 6 7 10 11 8 :0 1 3 4 5 6 7 9 11 8 :0 1 3 4 5 6 7 10 11 8 :0 2 3 4 5 6 7 9 11 8 :0 3 4 5 6 7 9 10 11 8 9 :0 2 3 4 5 6 7 10 11 8 9 :0 2 3 4 5 6 7 9 10 11 9 :0 2 3 4 5 6 10 9 :0 1 2 3 4 5 6 10 9 :0 2 3 4 5 6 7 10 9 :0 2 3 4 5 6 9 10 9 :0 2 3 4 5 6 10 11 9 :0 1 2 3 4 5 6 7 10 9 :0 2 3 4 5 6 7 9 10 9 :0 2 3 4 5 6 9 10 11 9 10 :0 1 2 3 4 5 6 9 10 9 10 :0 1 2 3 4 5 6 7 9 10 9 10 11 :0 1 2 3 4 5 6 8 9 10 9 11 :0 1 2 3 4 5 6 8 10 10 :0 1 2 3 4 5 7 9 10 :0 1 2 3 4 5 6 7 9 10 :0 1 2 3 4 5 7 9 10 10 11 :0 1 2 3 4 5 7 8 9 10 11 :0 1 2 3 4 5 6 8 9 11 10 11 :0 1 2 3 4 5 7 8 9 10 11 :0 1 2 3 4 8 11 :0 1 2 3 4 7 8 11 :0 1 2 3 4 8 10 11 :0 1 2 3 4 8 11 11 :0 1 2 3 4 5 7 8 11 :0 1 2 3 4 6 7 8 11 :0 1 2 3 4 7 8 9 11 :0 1 2 3 4 7 8 10 11 :0 1 2 3 4 8 10 11 11 :0 1 2 3 4 6 8 10 11 :0 1 2 3 4 6 7 8 9 11 :0 1 2 3 4 5 7 8 10 11 :0 1 2 3 4 6 7 8 10 11

order	origin	root set	chord type (as pcset)
1	0	0	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	1	1	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	3	3	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

1	7	7	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	11	11	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

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