Chord Type: 0 3 4 7 9 10

0 3 4 7 9 10 = 13#9 no 11th

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Chord Type: 0 3 4 7 9 10

Chord Type Fun Facts 0 3 4 7 9 10 Subset of Diminished Scale (0 1 3 4 6 7 9 10) Modal System Fun Facts 0 1 3 6 7 10 Subset of Diminished Scale Inversionally Symmetrical General Statistics Cardinality: 6 Jordan Number: 6-54 Forte Number: 6-z50 Forte Prime Form: [0,1,4,6,7,9] Zeitler Scale Name: Lorimic Ian Ring's Scale Page 1689 Root Reference: 0 3 4 7 9 10 Tone Stacking: 0 3 1 3 2 1 Interval Stacking: 3 1 3 2 1 2 Binary: 1 0 0 1 1 0 0 1 0 1 1 0 Decimal Value: 1689 Interval Vector: 2 2 4 2 3 2 Inversional Symmetry: yes (axes of symmetry: 3.5 9.5) Transpositional Symmetry: no Melodic Adjacency (0-1): 0.333 Harmonic Adjacency (0-1): 0.600 Modal-system-invariant under multiplication by: 1 11 Modal System Balanced: no Diachromatic Family: 13th chords no 11th = diamorphic scales no 4th (Scale Degrees: 123567) 0 1 3 7 8 10 = mb13b9 no 11th 0 1 3 7 8 11 = mMb13b9 no 11th 0 1 3 7 9 10 = m13b9 no 11th 0 1 3 7 9 11 = mM13b9 no 11th 0 1 3 7 10 11 = mM#13b9 no 11th 0 1 4 7 8 10 = 7b13b9 no 11th 0 1 4 7 8 11 = Mb13b9 no 11th 0 1 4 7 9 10 = 13b9 no 11th 0 1 4 7 9 11 = M13b9 no 11th 0 1 4 7 10 11 = M#13b9 no 11th 0 1 4 8 10 11 = M#13#5b9 no 11th 0 2 3 7 8 10 = mb13 no 11th 0 2 3 7 8 11 = mMb13 no 11th 0 2 3 7 9 10 = m13 no 11th 0 2 3 7 9 11 = mM 13 no 11th 0 2 3 7 10 11 = mM#13 no 11th 0 2 3 8 10 11 = mM#13 no 11th 0 2 4 7 8 10 = 7b13 no 11th 0 2 4 7 8 11 = M7b13 no 11th 0 2 4 7 9 10 = 13 no 11th 0 2 4 7 9 11 = M13 no 11th, Guido hex., 6 in 5ths 0 2 4 7 10 11 = M#13 no 11th 0 2 4 8 9 10 = 13#5 no 11th 0 2 4 8 9 11 = M13#5 no 11th 0 2 4 8 10 11 = M#13#5 no 11th 0 3 4 6 10 11 = M#13b5#9 no 11th 0 3 4 7 8 10 = 7b13#9 no 11th 0 3 4 7 8 11 = Mb13#9 no 11th, aug. scale, type e ACH ->0 3 4 7 9 10 = 13#9 no 11th 0 3 4 7 9 11 = M13#9 no 11th 0 3 4 7 10 11 = M#13#9 no 11th, Schoen. hex 0 3 4 8 9 10 = M#13#5#9 no 11th, all-tri hex 0 3 4 8 9 11 = M13#5#9 no 11th 0 3 4 8 10 11 = M7#5#9 no 11th All Transpositions of Chord Type: +0= 0 3 4 7 9 10 |13#9 no 11th +1= 1 4 5 8 10 11 | +2= 0 2 5 6 9 11 | +3= 0 1 3 6 7 10 |m#11b9 +4= 1 2 4 7 8 11 | +5= 0 2 3 5 8 9 | +6= 1 3 4 6 9 10 | +7= 2 4 5 7 10 11 | +8= 0 3 5 6 8 11 | +9= 0 1 4 6 7 9 | +10= 1 2 5 7 8 10 | +11= 2 3 6 8 9 11 | Modes of Chord Type: (mode 0) 0: 0 3 4 7 9 10 | 13#9 no 11th (mode 1) 3: 0 1 4 6 7 9 | (mode 2) 4: 0 3 5 6 8 11 | (mode 3) 7: 0 2 3 5 8 9 | (mode 4) 9: 0 1 3 6 7 10 | m#11b9 (mode 5) 10: 0 2 5 6 9 11 | Modes of Chord Type Sorted by Rootedness: 1.875(mode 0)0:0 3 4 7 9 10 |13#9 no 11th 1.467(mode 1)3:0 1 4 6 7 9 | 1.308(mode 4)9:0 1 3 6 7 10 |m#11b9 .192(mode 5)10:0 2 5 6 9 11 | .058(mode 3)7:0 2 3 5 8 9 | -.033(mode 2)4:0 3 5 6 8 11 | Inversion at 0: 0 2 3 5 8 9 (mode 0) 0: 0 2 3 5 8 9 | (mode 1) 2: 0 1 3 6 7 10 | m#11b9 (mode 2) 3: 0 2 5 6 9 11 | (mode 3) 5: 0 3 4 7 9 10 | 13#9 no 11th (mode 4) 8: 0 1 4 6 7 9 | (mode 5) 9: 0 3 5 6 8 11 | Times 7: 0 1 3 4 9 10 (mode 0) 0: 0 1 3 4 9 10 | (mode 1) 1: 0 2 3 8 9 11 | (mode 2) 3: 0 1 6 7 9 10 | (mode 3) 4: 0 5 6 8 9 11 | (mode 4) 9: 0 1 3 4 6 7 | Istrian scale (mode 5) 10: 0 2 3 5 6 11 | mM#11 Times 5: 0 2 3 8 9 11 (mode 0) 0: 0 2 3 8 9 11 | (mode 1) 2: 0 1 6 7 9 10 | (mode 2) 3: 0 5 6 8 9 11 | (mode 3) 8: 0 1 3 4 6 7 | Istrian scale (mode 4) 9: 0 2 3 5 6 11 | mM#11 (mode 5) 11: 0 1 3 4 9 10 | Modal System: 0 1 3 6 7 10 from root(s) 9 | "13#9 no 11th modal system = m#11b9 modal system" Modes of Modal System: (mode 0) 0: 0 1 3 6 7 10 | m#11b9 (mode 1) 1: 0 2 5 6 9 11 | (mode 2) 3: 0 3 4 7 9 10 | 13#9 no 11th (mode 3) 6: 0 1 4 6 7 9 | (mode 4) 7: 0 3 5 6 8 11 | (mode 5) 10: 0 2 3 5 8 9 | Complement: 1 2 5 6 8 11 (mode 0) 1: 0 1 4 5 7 10 | 11b9 (mode 1) 2: 0 3 4 6 9 11 | (mode 2) 5: 0 1 3 6 8 9 | (mode 3) 6: 0 2 5 7 8 11 | (mode 4) 8: 0 3 5 6 9 10 | (mode 5) 11: 0 2 3 6 7 9 | Bridge chord All but the root (subchroma complement of 0): 3 4 7 9 10 (mode 0) 3: 0 1 4 6 7 | (mode 1) 4: 0 3 5 6 11 | (mode 2) 7: 0 2 3 8 9 | (mode 3) 9: 0 1 6 7 10 | (mode 4) 10: 0 5 6 9 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: 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 Chromaticizations chromaticized: N/A chromaticized keep 0: (mode 0) 0: 0 3 4 7 8 9 10 | (mode 1) 3: 0 1 4 5 6 7 9 | (mode 2) 4: 0 3 4 5 6 8 11 | M7b13b5#9 (mode 3) 7: 0 1 2 3 5 8 9 | (mode 4) 8: 0 1 2 4 7 8 11 | (mode 5) 9: 0 1 3 6 7 10 11 | mM#13b9#11 = mela 48 Divyamani (mode 6) 10: 0 2 5 6 9 10 11 | (mode 0) 0: 0 1 2 3 4 7 9 10 | (mode 1) 1: 0 1 2 3 6 8 9 11 | (mode 2) 2: 0 1 2 5 7 8 10 11 | (mode 3) 3: 0 1 4 6 7 9 10 11 | (mode 4) 4: 0 3 5 6 8 9 10 11 | (mode 5) 7: 0 2 3 5 6 7 8 9 | (mode 6) 9: 0 1 3 4 5 6 7 10 | (mode 7) 10: 0 2 3 4 5 6 9 11 | chromaticized keep 0 7: (mode 0) 0: 0 3 4 7 9 10 11 | (mode 1) 3: 0 1 4 6 7 8 9 | mela 49 Dhavalambari (mode 2) 4: 0 3 5 6 7 8 11 | (mode 3) 7: 0 2 3 4 5 8 9 | (mode 4) 9: 0 1 2 3 6 7 10 | (mode 5) 10: 0 1 2 5 6 9 11 | (mode 6) 11: 0 1 4 5 8 10 11 | M#13#5b5 = enigmatic ascending (mode 0) 0: 0 3 4 7 8 9 10 | (mode 1) 3: 0 1 4 5 6 7 9 | (mode 2) 4: 0 3 4 5 6 8 11 | M7b13b5#9 (mode 3) 7: 0 1 2 3 5 8 9 | (mode 4) 8: 0 1 2 4 7 8 11 | (mode 5) 9: 0 1 3 6 7 10 11 | mM#13b9#11 = mela 48 Divyamani (mode 6) 10: 0 2 5 6 9 10 11 | (mode 0) 0: 0 3 4 5 6 7 9 10 | (mode 1) 3: 0 1 2 3 4 6 7 9 | (mode 2) 4: 0 1 2 3 5 6 8 11 | (mode 3) 5: 0 1 2 4 5 7 10 11 | (mode 4) 6: 0 1 3 4 6 9 10 11 | (mode 5) 7: 0 2 3 5 8 9 10 11 | (mode 6) 9: 0 1 3 6 7 8 9 10 | (mode 7) 10: 0 2 5 6 7 8 9 11 | (mode 0) 0: 0 1 2 3 4 7 9 10 | (mode 1) 1: 0 1 2 3 6 8 9 11 | (mode 2) 2: 0 1 2 5 7 8 10 11 | (mode 3) 3: 0 1 4 6 7 9 10 11 | (mode 4) 4: 0 3 5 6 8 9 10 11 | (mode 5) 7: 0 2 3 5 6 7 8 9 | (mode 6) 9: 0 1 3 4 5 6 7 10 | (mode 7) 10: 0 2 3 4 5 6 9 11 | chromaticized keep 0 3 4 7: (mode 0) 0: 0 3 4 7 9 10 11 | (mode 1) 3: 0 1 4 6 7 8 9 | mela 49 Dhavalambari (mode 2) 4: 0 3 5 6 7 8 11 | (mode 3) 7: 0 2 3 4 5 8 9 | (mode 4) 9: 0 1 2 3 6 7 10 | (mode 5) 10: 0 1 2 5 6 9 11 | (mode 6) 11: 0 1 4 5 8 10 11 | M#13#5b5 = enigmatic ascending (mode 0) 0: 0 3 4 7 8 9 10 | (mode 1) 3: 0 1 4 5 6 7 9 | (mode 2) 4: 0 3 4 5 6 8 11 | M7b13b5#9 (mode 3) 7: 0 1 2 3 5 8 9 | (mode 4) 8: 0 1 2 4 7 8 11 | (mode 5) 9: 0 1 3 6 7 10 11 | mM#13b9#11 = mela 48 Divyamani (mode 6) 10: 0 2 5 6 9 10 11 | (mode 0) 0: 0 1 2 3 4 7 9 10 | (mode 1) 1: 0 1 2 3 6 8 9 11 | (mode 2) 2: 0 1 2 5 7 8 10 11 | (mode 3) 3: 0 1 4 6 7 9 10 11 | (mode 4) 4: 0 3 5 6 8 9 10 11 | (mode 5) 7: 0 2 3 5 6 7 8 9 | (mode 6) 9: 0 1 3 4 5 6 7 10 | (mode 7) 10: 0 2 3 4 5 6 9 11 | (mode 0) 0: 0 3 4 5 6 7 9 10 | (mode 1) 3: 0 1 2 3 4 6 7 9 | (mode 2) 4: 0 1 2 3 5 6 8 11 | (mode 3) 5: 0 1 2 4 5 7 10 11 | (mode 4) 6: 0 1 3 4 6 9 10 11 | (mode 5) 7: 0 2 3 5 8 9 10 11 | (mode 6) 9: 0 1 3 6 7 8 9 10 | (mode 7) 10: 0 2 5 6 7 8 9 11 | (mode 0) 0: 0 1 2 3 4 5 6 7 9 10 | aux. diminished scale & dorian (mode 1) 1: 0 1 2 3 4 5 6 8 9 11 | (mode 2) 2: 0 1 2 3 4 5 7 8 10 11 | (mode 3) 3: 0 1 2 3 4 6 7 9 10 11 | aux. diminished scale & lydian = 2367AB & aux. diminished scale (mode 4) 4: 0 1 2 3 5 6 8 9 10 11 | diminished scale & locrian (mode 5) 5: 0 1 2 4 5 7 8 9 10 11 | 014589 & bebop major = Spanish Gypsy & ionian (mode 6) 6: 0 1 3 4 6 7 8 9 10 11 | 03478B & aux. diminished scale (mode 7) 7: 0 2 3 5 6 7 8 9 10 11 | diminished scale & dorian = diminished scale & aeolean (mode 8) 9: 0 1 3 4 5 6 7 8 9 10 | aux. diminished scale & phrygian = aux. diminished scale & locrian = 014589 & aux. diminished scale (mode 9) 10: 0 2 3 4 5 6 7 8 9 11 | lydian & harmonic minor = diminished scale & ionian = diminished scale & lydian alt-chromaticized: N/A alt-chromaticized keep 0: N/A alt-chromaticized keep 0 7: N/A alt-chromaticized keep 0 3 4 7: (mode 0) 0: 0 1 3 4 6 7 8 9 10 11 | 03478B & aux. diminished scale (mode 1) 1: 0 2 3 5 6 7 8 9 10 11 | diminished scale & dorian = diminished scale & aeolean (mode 2) 3: 0 1 3 4 5 6 7 8 9 10 | aux. diminished scale & phrygian = aux. diminished scale & locrian = 014589 & aux. diminished scale (mode 3) 4: 0 2 3 4 5 6 7 8 9 11 | lydian & harmonic minor = diminished scale & ionian = diminished scale & lydian (mode 4) 6: 0 1 2 3 4 5 6 7 9 10 | aux. diminished scale & dorian (mode 5) 7: 0 1 2 3 4 5 6 8 9 11 | (mode 6) 8: 0 1 2 3 4 5 7 8 10 11 | (mode 7) 9: 0 1 2 3 4 6 7 9 10 11 | aux. diminished scale & lydian = 2367AB & aux. diminished scale (mode 8) 10: 0 1 2 3 5 6 8 9 10 11 | diminished scale & locrian (mode 9) 11: 0 1 2 4 5 7 8 9 10 11 | 014589 & bebop major = Spanish Gypsy & ionian Bright Layer Decomposition order origin root set chord type (as pcset) 2 0 0 7 0 3 9 = 0: 0 3 9 = 3: 0 6 9 = 9: 0 3 6 1 0 0 0 3 4 7 9 10 = 0: 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 = 4: 0 3 5 6 8 11 = 7: 0 2 3 5 8 9 = 9: 0 1 3 6 7 10 = 10: 0 2 5 6 9 11 1 3 3 0 1 4 6 7 9 = 0: 0 1 4 6 7 9 = 1: 0 3 5 6 8 11 = 4: 0 2 3 5 8 9 = 6: 0 1 3 6 7 10 = 7: 0 2 5 6 9 11 = 9: 0 3 4 7 9 10 2 9 4 9 0 3 6 = 0: 0 3 6 = 3: 0 3 9 = 6: 0 6 9 1 9 9 0 1 3 6 7 10 = 0: 0 1 3 6 7 10 = 1: 0 2 5 6 9 11 = 3: 0 3 4 7 9 10 = 6: 0 1 4 6 7 9 = 7: 0 3 5 6 8 11 = 10: 0 2 3 5 8 9 Bright Layer Composition order pcset 1 0 3 4 7 9 10 = 0: 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 = 4: 0 3 5 6 8 11 = 7: 0 2 3 5 8 9 = 9: 0 1 3 6 7 10 = 10: 0 2 5 6 9 11 2 0 2 3 4 5 7 9 10 11 = 0: 0 2 3 4 5 7 9 10 11 = 2: 0 1 2 3 5 7 8 9 10 = 3: 0 1 2 4 6 7 8 9 11 = 4: 0 1 3 5 6 7 8 10 11 = 5: 0 2 4 5 6 7 9 10 11 = 7: 0 2 3 4 5 7 8 9 10 = 9: 0 1 2 3 5 6 7 8 10 = 10: 0 1 2 4 5 6 7 9 11 = 11: 0 1 3 4 5 6 8 10 11 3 0 2 3 4 5 6 7 9 10 11 = 0: 0 2 3 4 5 6 7 9 10 11 = 2: 0 1 2 3 4 5 7 8 9 10 = 3: 0 1 2 3 4 6 7 8 9 11 = 4: 0 1 2 3 5 6 7 8 10 11 = 5: 0 1 2 4 5 6 7 9 10 11 = 6: 0 1 3 4 5 6 8 9 10 11 = 7: 0 2 3 4 5 7 8 9 10 11 = 9: 0 1 2 3 5 6 7 8 9 10 = 10: 0 1 2 4 5 6 7 8 9 11 = 11: 0 1 3 4 5 6 7 8 10 11 4 0 1 2 3 4 5 6 7 9 10 11 = 0: 0 1 2 3 4 5 6 7 9 10 11 = 1: 0 1 2 3 4 5 6 8 9 10 11 = 2: 0 1 2 3 4 5 7 8 9 10 11 = 3: 0 1 2 3 4 6 7 8 9 10 11 = 4: 0 1 2 3 5 6 7 8 9 10 11 = 5: 0 1 2 4 5 6 7 8 9 10 11 = 6: 0 1 3 4 5 6 7 8 9 10 11 = 7: 0 2 3 4 5 6 7 8 9 10 11 = 9: 0 1 2 3 4 5 6 7 8 9 10 = 10: 0 1 2 3 4 5 6 7 8 9 11 = 11: 0 1 2 3 4 5 6 7 8 10 11 5 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 4 7 9 10 subchroma modal system: 0 0 = 0 = 0: 0 3 = 3 = 3: 0 4 = 4 = 4: 0 7 = 7 = 7: 0 9 = 9 = 9: 0 10 = 10 = 10: 0 subchroma modal system: 0 1 0 3 = 0 3 = 0: 0 3 3: 0 9 3 4 = 3 4 = 3: 0 1 4: 0 11 4 7 = 4 7 = 4: 0 3 7: 0 9 7 9 = 7 9 = 7: 0 2 9: 0 10 9 10 = 9 10 = 9: 0 1 10: 0 11 10 0 = 0 10 = 10: 0 2 0: 0 10 subchroma modal system: 0 2 0 4 = 0 4 = 0: 0 4 4: 0 8 3 7 = 3 7 = 3: 0 4 7: 0 8 4 9 = 4 9 = 4: 0 5 9: 0 7 7 10 = 7 10 = 7: 0 3 10: 0 9 9 0 = 0 9 = 9: 0 3 0: 0 9 10 3 = 3 10 = 10: 0 5 3: 0 7 subchroma modal system: 0 3 0 7 = 0 7 = 7: 0 5 0: 0 7 3 9 = 3 9 = 3 9: 0 6 4 10 = 4 10 = 4 10: 0 6 7 0 = 0 7 = 7: 0 5 0: 0 7 9 3 = 3 9 = 3 9: 0 6 10 4 = 4 10 = 4 10: 0 6 subchroma modal system: 0 1 2 0 3 4 = 0 3 4 = 0: 0 3 4 3 4 7 = 3 4 7 = 3: 0 1 4 4: 0 3 11 4 7 9 = 4 7 9 = 4: 0 3 5 9: 0 7 10 7 9 10 = 7 9 10 = 7: 0 2 3 9 10 0 = 0 9 10 = 9: 0 1 3 10: 0 2 11 10 0 3 = 0 3 10 = 0: 0 3 10 3: 0 7 9 subchroma modal system: 0 1 3 0 3 7 = 0 3 7 = 0: 0 3 7 3: 0 4 9 3 4 9 = 3 4 9 = 9: 0 6 7 4 7 10 = 4 7 10 = 4: 0 3 6 7: 0 3 9 7 9 0 = 0 7 9 = 9: 0 3 10 0: 0 7 9 9 10 3 = 3 9 10 = 3: 0 6 7 10 0 4 = 0 4 10 = 0: 0 4 10 subchroma modal system: 0 1 4 0 3 9 = 0 3 9 = 9: 0 3 6 0: 0 3 9 3 4 10 = 3 4 10 = 3: 0 1 7 4 7 0 = 0 4 7 = 0: 0 4 7 7 9 3 = 3 7 9 = 3: 0 4 6 9 10 4 = 4 9 10 = 9: 0 1 7 10 0 7 = 0 7 10 = 7: 0 3 5 0: 0 7 10 subchroma modal system: 0 2 4 0 4 9 = 0 4 9 = 9: 0 3 7 0: 0 4 9 3 7 10 = 3 7 10 = 3: 0 4 7 4 9 0 = 0 4 9 = 9: 0 3 7 0: 0 4 9 7 10 3 = 3 7 10 = 3: 0 4 7 9 0 4 = 0 4 9 = 9: 0 3 7 0: 0 4 9 10 3 7 = 3 7 10 = 3: 0 4 7 subchroma modal system: 0 1 2 3 0 3 4 7 = 0 3 4 7 = 0: 0 3 4 7 3: 0 1 4 9 3 4 7 9 = 3 4 7 9 = 4: 0 3 5 11 9: 0 6 7 10 4 7 9 10 = 4 7 9 10 = 9: 0 1 7 10 4: 0 3 5 6 7 9 10 0 = 0 7 9 10 = 7: 0 2 3 5 9: 0 1 3 10 10: 0 2 9 11 0: 0 7 9 10 9 10 0 3 = 0 3 9 10 = 9: 0 1 3 6 0: 0 3 9 10 3: 0 6 7 9 10 0 3 4 = 0 3 4 10 = 0: 0 3 4 10 3: 0 1 7 9 subchroma modal system: 0 1 2 4 0 3 4 9 = 0 3 4 9 = 0: 0 3 4 9 9: 0 3 6 7 3 4 7 10 = 3 4 7 10 = 3: 0 1 4 7 4: 0 3 6 11 4 7 9 0 = 0 4 7 9 = 0: 0 4 7 9 9: 0 3 7 10 7 9 10 3 = 3 7 9 10 = 3: 0 4 6 7 9 10 0 4 = 0 4 9 10 = 9: 0 1 3 7 0: 0 4 9 10 10 0 3 7 = 0 3 7 10 = 3: 0 4 7 9 0: 0 3 7 10 subchroma modal system: 0 1 3 4 0 3 7 9 = 0 3 7 9 = 0: 0 3 7 9 9: 0 3 6 10 3 4 9 10 = 3 4 9 10 = 3 9: 0 1 6 7 4 7 10 0 = 0 4 7 10 = 0: 0 4 7 10 7 9 0 3 = 0 3 7 9 = 0: 0 3 7 9 9: 0 3 6 10 9 10 3 4 = 3 4 9 10 = 3 9: 0 1 6 7 10 0 4 7 = 0 4 7 10 = 0: 0 4 7 10 subchroma modal system: 0 1 2 3 4 0 3 4 7 9 = 0 3 4 7 9 = 0: 0 3 4 7 9 9: 0 3 6 7 10 3 4 7 9 10 = 3 4 7 9 10 = 3: 0 1 4 6 7 9: 0 1 6 7 10 4 7 9 10 0 = 0 4 7 9 10 = 9: 0 1 3 7 10 4: 0 3 5 6 8 0: 0 4 7 9 10 7 9 10 0 3 = 0 3 7 9 10 = 9: 0 1 3 6 10 3: 0 4 6 7 9 0: 0 3 7 9 10 9 10 0 3 4 = 0 3 4 9 10 = 9: 0 1 3 6 7 0: 0 3 4 9 10 3: 0 1 6 7 9 10 0 3 4 7 = 0 3 4 7 10 = 3: 0 1 4 7 9 0: 0 3 4 7 10 subchroma modal system: 0 1 2 3 4 5 0 3 4 7 9 10 = 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 9: 0 1 3 6 7 10 0: 0 3 4 7 9 10 3 4 7 9 10 0 = 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 9: 0 1 3 6 7 10 0: 0 3 4 7 9 10 4 7 9 10 0 3 = 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 9: 0 1 3 6 7 10 0: 0 3 4 7 9 10 7 9 10 0 3 4 = 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 9: 0 1 3 6 7 10 0: 0 3 4 7 9 10 9 10 0 3 4 7 = 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 9: 0 1 3 6 7 10 0: 0 3 4 7 9 10 10 0 3 4 7 9 = 0 3 4 7 9 10 = 3: 0 1 4 6 7 9 9: 0 1 3 6 7 10 0: 0 3 4 7 9 10 Subset Chord Types by Root Set 0 :0 3 4 0 :0 4 10 0 :0 3 4 7 0 :0 3 4 9 0 :0 3 4 10 0 :0 3 7 9 0 :0 4 7 10 0 :0 3 9 10 0 :0 4 9 10 0 :0 7 9 10 0 :0 3 4 7 9 0 :0 3 4 7 10 0 :0 3 4 9 10 0 :0 3 7 9 10 0 :0 4 7 9 10 0 :0 3 4 7 9 10 0 3 :0 4 0 3 :0 4 7 0 3 :0 4 9 0 3 :0 7 9 0 3 :0 4 7 9 0 3 4 7 9 10:0 0 3 7 10 :0 9 0 3 9 :0 7 0 4 7 9 :0 3 0 7 :0 3 9 0 9 :0 10 0 9 :0 3 7 0 9 :0 3 10 0 9 :0 7 10 0 9 :0 3 7 10 3 :0 1 4 3 :0 4 6 3 :0 1 4 7 3 :0 1 4 9 3 :0 1 7 9 3 :0 4 6 7 3 :0 6 7 9 3 :0 1 4 6 7 3 :0 1 4 7 9 3 :0 1 6 7 9 3 :0 4 6 7 9 3 :0 1 4 6 7 9 3 4 9 10 :0 6 3 9 :0 1 3 9 :0 1 7 3 9 :0 6 7 3 9 :0 1 6 7 4 :0 3 11 4 :0 3 5 6 4 :0 3 5 11 4 :0 3 6 11 4 :0 3 5 6 8 4 7 :0 8 4 7 :0 3 5 4 7 10 :0 5 4 9 :0 3 6 4 10 :0 11 7 :0 2 3 7 :0 2 3 5 7 10 :0 2 9 :0 1 3 9 :0 1 3 6 9 :0 1 3 7 9 :0 1 3 10 9 :0 1 7 10 9 :0 3 6 7 9 :0 3 6 10 9 :0 6 7 10 9 :0 1 3 6 7 9 :0 1 3 6 10 9 :0 1 3 7 10 9 :0 1 6 7 10 9 :0 3 6 7 10 9 :0 1 3 6 7 10 10 :0 2 11 10 :0 2 9 11 Superset Chord Types by Root Set 0 :0 3 4 7 9 10 0 :0 1 3 4 7 9 10 0 :0 2 3 4 7 9 10 0 :0 3 4 5 7 9 10 0 :0 3 4 6 7 9 10 0 :0 3 4 7 8 9 10 0 :0 3 4 7 9 10 11 0 :0 1 2 3 4 7 9 10 0 :0 1 3 4 5 7 9 10 0 :0 2 3 4 5 7 9 10 0 :0 2 3 4 6 7 9 10 0 :0 1 3 4 7 8 9 10 0 :0 1 3 4 7 9 10 11 0 :0 2 3 4 7 8 9 10 0 :0 2 3 4 7 9 10 11 0 :0 3 4 5 6 7 9 10 0 :0 3 4 5 7 8 9 10 0 :0 3 4 5 7 9 10 11 0 :0 3 4 6 7 8 9 10 0 :0 3 4 6 7 9 10 11 0 :0 3 4 7 8 9 10 11 0 :0 1 2 3 4 5 7 9 10 0 :0 1 2 3 4 7 8 9 10 0 :0 1 2 3 4 7 9 10 11 0 :0 2 3 4 5 6 7 9 10 0 :0 1 3 4 5 7 8 9 10 0 :0 1 3 4 5 7 9 10 11 0 :0 2 3 4 6 7 8 9 10 0 :0 2 3 4 6 7 9 10 11 0 :0 1 3 4 7 8 9 10 11 0 :0 2 3 4 7 8 9 10 11 0 :0 3 4 5 6 7 8 9 10 0 :0 3 4 5 6 7 9 10 11 0 :0 3 4 5 7 8 9 10 11 0 :0 3 4 6 7 8 9 10 11 0 1 :0 2 3 4 6 7 8 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 3 6 8 9 :0 1 2 3 4 6 7 8 9 10 11 0 1 4 5 7 10 :0 2 3 4 5 6 7 8 9 10 11 0 2 3 6 7 9 :0 1 2 3 4 5 6 7 8 9 10 0 2 5 7 8 11 :0 1 2 3 4 5 7 8 9 10 11 0 2 7 :0 1 2 3 4 5 7 8 9 10 0 3 4 6 9 11 :0 1 3 4 5 6 7 8 9 10 11 0 3 5 6 9 10 :0 1 2 3 4 5 6 7 9 10 11 0 3 6 9 :0 1 3 4 6 7 9 10 0 3 6 9 :0 1 2 3 4 6 7 9 10 0 3 6 9 :0 1 3 4 5 6 7 9 10 0 3 6 9 :0 1 3 4 6 7 8 9 10 0 3 6 9 :0 1 3 4 6 7 9 10 11 0 3 6 9 :0 1 2 3 4 5 6 7 9 10 0 3 6 9 :0 1 2 3 4 6 7 8 9 10 0 3 6 9 :0 1 2 3 4 6 7 9 10 11 0 3 6 9 :0 1 3 4 5 6 7 8 9 10 0 3 6 9 :0 1 3 4 5 6 7 9 10 11 0 3 6 9 :0 1 3 4 6 7 8 9 10 11 0 4 :0 3 4 5 6 7 8 9 10 11 0 5 :0 2 3 4 5 7 9 10 11 0 5 :0 1 2 3 4 5 7 9 10 11 0 5 7 :0 2 3 4 5 7 8 9 10 11 0 5 10 :0 2 3 4 5 6 7 9 10 11 0 7 :0 2 3 4 5 7 8 9 10 0 7 :0 2 3 4 5 6 7 8 9 10 0 8 :0 1 2 3 4 7 8 9 10 11 0 11 :0 1 3 4 5 7 8 9 10 11 1 :0 2 3 6 8 9 11 1 :0 2 3 6 7 8 9 11 1 :0 1 2 3 6 7 8 9 11 1 :0 2 3 4 6 7 8 9 11 1 :0 2 3 6 7 8 9 10 11 1 2 4 7 9 10 :0 1 2 3 5 6 7 8 9 10 11 1 3 4 7 8 10 :0 1 2 3 4 5 6 7 8 9 11 1 3 8 :0 1 2 3 4 6 7 8 9 11 1 4 6 7 10 11 :0 1 2 3 4 5 6 8 9 10 11 1 4 7 10 :0 2 3 5 6 8 9 11 1 4 7 10 :0 1 2 3 5 6 8 9 11 1 4 7 10 :0 2 3 5 6 7 8 9 11 1 4 7 10 :0 2 3 5 6 8 9 10 11 1 4 7 10 :0 1 2 3 4 5 6 8 9 11 1 4 7 10 :0 1 2 3 5 6 7 8 9 11 1 4 7 10 :0 1 2 3 5 6 8 9 10 11 1 4 7 10 :0 2 3 4 5 6 7 8 9 11 1 4 7 10 :0 2 3 4 5 6 8 9 10 11 1 4 7 10 :0 2 3 5 6 7 8 9 10 11 1 6 :0 1 2 3 4 6 8 9 10 11 1 9 :0 1 2 3 6 7 8 9 10 11 2 :0 1 2 5 7 8 10 2 :0 1 2 3 5 7 8 10 2 :0 1 2 4 5 7 8 10 2 :0 1 2 5 6 7 8 10 2 :0 1 2 5 7 8 10 11 2 :0 1 2 3 4 5 7 8 10 2 :0 1 2 4 5 6 7 8 10 2 :0 1 2 3 5 7 8 10 11 2 :0 1 2 4 5 7 8 9 10 2 :0 1 2 5 7 8 9 10 11 2 3 :0 1 2 4 5 6 7 8 9 10 2 3 5 8 10 11 :0 1 2 4 5 6 7 8 9 10 11 2 4 5 8 9 11 :0 1 2 3 4 5 6 7 8 10 11 2 4 9 :0 1 2 3 5 6 7 8 10 11 2 5 8 11 :0 1 2 4 5 7 8 10 11 2 5 8 11 :0 1 2 3 4 5 7 8 10 11 2 5 8 11 :0 1 2 4 5 6 7 8 10 11 2 5 8 11 :0 1 2 4 5 7 8 9 10 11 2 7 :0 1 2 3 5 7 8 9 10 2 7 :0 1 2 3 5 7 8 9 10 11 2 7 9 :0 1 2 3 5 6 7 8 9 10 2 9 :0 1 2 3 5 6 7 8 10 2 9 :0 1 2 3 4 5 6 7 8 10 2 10 :0 1 2 5 6 7 8 9 10 11 3 :0 1 4 6 7 9 3 :0 1 2 4 6 7 9 3 :0 1 3 4 6 7 9 3 :0 1 4 5 6 7 9 3 :0 1 4 6 7 8 9 3 :0 1 4 6 7 9 10 3 :0 1 4 6 7 9 11 3 :0 1 2 3 4 6 7 9 3 :0 1 2 4 5 6 7 9 3 :0 1 3 4 5 6 7 9 3 :0 1 2 4 6 7 8 9 3 :0 1 3 4 6 7 8 9 3 :0 1 2 4 6 7 9 10 3 :0 1 2 4 6 7 9 11 3 :0 1 3 4 6 7 9 11 3 :0 1 4 5 6 7 8 9 3 :0 1 4 5 6 7 9 10 3 :0 1 4 5 6 7 9 11 3 :0 1 4 6 7 8 9 10 3 :0 1 4 6 7 8 9 11 3 :0 1 4 6 7 9 10 11 3 :0 1 2 3 4 5 6 7 9 3 :0 1 2 3 4 6 7 8 9 3 :0 1 2 3 4 6 7 9 11 3 :0 1 2 4 5 6 7 8 9 3 :0 1 2 4 5 6 7 9 10 3 :0 1 3 4 5 6 7 9 11 3 :0 1 2 4 6 7 8 9 10 3 :0 1 2 4 6 7 9 10 11 3 :0 1 3 4 6 7 8 9 11 3 :0 1 4 5 6 7 8 9 10 3 :0 1 4 5 6 7 8 9 11 3 :0 1 4 5 6 7 9 10 11 3 :0 1 4 6 7 8 9 10 11 3 4 :0 1 3 4 5 6 7 8 9 11 3 5 10 :0 1 2 4 5 6 7 9 10 11 3 7 :0 1 2 3 4 5 6 7 8 9 3 8 :0 1 2 4 6 7 8 9 11 3 8 :0 1 2 4 6 7 8 9 10 11 3 8 10 :0 1 2 4 5 6 7 8 9 11 3 10 :0 1 2 4 5 6 7 9 11 3 10 :0 1 2 3 4 5 6 7 9 11 3 11 :0 1 4 5 6 7 8 9 10 11 4 :0 1 3 5 6 8 11 4 :0 2 3 5 6 8 11 4 :0 3 4 5 6 8 11 4 :0 3 5 6 7 8 11 4 :0 1 3 5 6 7 8 11 4 :0 2 3 5 6 7 8 11 4 :0 3 4 5 6 7 8 11 4 :0 3 5 6 7 8 9 11 4 :0 3 5 6 7 8 10 11 4 :0 1 2 3 5 6 7 8 11 4 :0 1 3 4 5 6 7 8 11 4 :0 2 3 4 5 6 7 8 11 4 :0 1 3 5 6 7 8 9 11 4 :0 2 3 5 6 7 8 10 11 4 :0 3 4 5 6 7 8 9 11 4 :0 3 4 5 6 7 8 10 11 4 :0 3 5 6 7 8 9 10 11 4 5 :0 2 3 4 5 6 7 8 10 11 4 6 11 :0 1 3 4 5 6 8 9 10 11 4 8 :0 1 2 3 4 5 6 7 8 11 4 9 :0 1 3 5 6 7 8 9 10 11 4 9 11 :0 1 3 4 5 6 7 8 10 11 4 11 :0 1 2 3 4 5 6 8 10 11 5 :0 2 4 5 7 10 11 5 :0 1 2 4 5 7 10 11 5 :0 2 3 4 5 7 10 11 5 :0 2 4 5 6 7 10 11 5 :0 2 4 5 7 8 10 11 5 :0 2 4 5 7 9 10 11 5 :0 1 2 3 4 5 7 10 11 5 :0 1 2 4 5 6 7 10 11 5 :0 2 3 4 5 6 7 10 11 5 :0 1 2 4 5 7 9 10 11 5 :0 2 3 4 5 7 8 10 11 5 :0 2 4 5 6 7 8 10 11 5 :0 2 4 5 7 8 9 10 11 5 9 :0 1 2 3 4 5 6 7 10 11 5 10 :0 2 4 5 6 7 9 10 11 5 10 :0 2 4 5 6 7 8 9 10 11 6 :0 1 3 4 5 6 9 10 6 :0 1 3 4 6 9 10 11 6 :0 1 2 3 4 5 6 9 10 6 7 :0 1 2 3 4 5 6 8 9 10 6 10 :0 1 2 3 4 5 6 9 10 11 7 :0 2 3 5 7 8 9 7 :0 2 3 5 8 9 10 7 :0 2 3 5 8 9 11 7 :0 1 2 3 5 7 8 9 7 :0 2 3 4 5 7 8 9 7 :0 2 3 5 6 7 8 9 7 :0 2 3 5 7 8 9 10 7 :0 2 3 5 7 8 9 11 7 :0 2 3 5 8 9 10 11 7 :0 1 2 3 4 5 7 8 9 7 :0 1 2 3 5 6 7 8 9 7 :0 2 3 4 5 6 7 8 9 7 :0 1 2 3 5 7 8 9 11 7 :0 2 3 4 5 7 8 9 11 7 :0 2 3 5 6 7 8 9 10 7 :0 2 3 5 7 8 9 10 11 7 8 :0 1 2 3 4 5 7 8 9 11 7 11 :0 1 2 3 4 5 8 9 10 11 8 :0 1 2 4 7 8 11 8 :0 1 2 3 4 7 8 11 8 :0 1 2 4 5 7 8 11 8 :0 1 2 4 6 7 8 11 8 :0 1 2 4 7 8 9 11 8 :0 1 2 4 7 8 10 11 8 :0 1 2 3 4 5 7 8 11 8 :0 1 2 3 4 6 7 8 11 8 :0 1 2 3 4 7 8 9 11 8 :0 1 2 3 4 7 8 10 11 8 :0 1 2 4 5 6 7 8 11 8 :0 1 2 4 5 7 8 9 11 8 :0 1 2 4 6 7 8 10 11 8 :0 1 2 4 7 8 9 10 11 8 9 :0 1 2 3 4 6 7 8 10 11 9 :0 1 3 6 7 10 9 :0 1 2 3 6 7 10 9 :0 1 3 4 6 7 10 9 :0 1 3 5 6 7 10 9 :0 1 3 6 7 8 10 9 :0 1 3 6 7 9 10 9 :0 1 3 6 7 10 11 9 :0 1 2 3 4 6 7 10 9 :0 1 2 3 5 6 7 10 9 :0 1 3 4 5 6 7 10 9 :0 1 2 3 6 7 8 10 9 :0 1 2 3 6 7 9 10 9 :0 1 2 3 6 7 10 11 9 :0 1 3 4 6 7 8 10 9 :0 1 3 4 6 7 10 11 9 :0 1 3 5 6 7 9 10 9 :0 1 3 5 6 7 10 11 9 :0 1 3 6 7 8 9 10 9 :0 1 3 6 7 8 10 11 9 :0 1 3 6 7 9 10 11 9 :0 1 2 3 4 5 6 7 10 9 :0 1 2 3 4 6 7 8 10 9 :0 1 2 3 4 6 7 10 11 9 :0 1 2 3 5 6 7 9 10 9 :0 1 2 3 5 6 7 10 11 9 :0 1 3 4 5 6 7 8 10 9 :0 1 3 4 5 6 7 10 11 9 :0 1 2 3 6 7 8 9 10 9 :0 1 2 3 6 7 8 10 11 9 :0 1 2 3 6 7 9 10 11 9 :0 1 3 4 6 7 8 10 11 9 :0 1 3 5 6 7 8 9 10 9 :0 1 3 5 6 7 9 10 11 9 :0 1 3 6 7 8 9 10 11 9 10 :0 1 2 3 5 6 7 9 10 11 10 :0 2 3 5 6 9 11 10 :0 2 4 5 6 9 11 10 :0 1 2 5 6 7 9 11 10 :0 2 3 5 6 7 9 11 10 :0 2 4 5 6 7 9 11 10 :0 2 4 5 6 9 10 11 10 :0 2 5 6 7 9 10 11 10 :0 1 2 3 5 6 7 9 11 10 :0 2 3 4 5 6 7 9 11 10 :0 2 3 4 5 6 9 10 11 10 :0 2 4 5 6 7 8 9 11 10 :0 2 3 5 6 7 9 10 11

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

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

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

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