ResearchFrontier structures and internal systems
Forte Set Class Catalog
Complete listing of all 224 pitch-class set classes in 12-TET, as catalogued by Allen Forte.
Showing 224 of 224 set classes
| Forte # ↑ | Prime Form | IC Vector | Card ↕ | T-Sym ↕ | I-Sym ↕ | Names | Z-Mate | Complement |
|---|---|---|---|---|---|---|---|---|
| 0-1 | [] | <0,0,0,0,0,0> | 0 | Empty set, Null set | 12-1 | |||
| 1-1 | [0] | <0,0,0,0,0,0> | 1 | 1 | Monad, Single note | 11-1 | ||
| 2-1 | [0,1] | <1,0,0,0,0,0> | 2 | 1 | Minor second, Semitone, Half step | 10-1 | ||
| 2-2 | [0,2] | <0,1,0,0,0,0> | 2 | 1 | Major second, Whole tone, Whole step | 10-2 | ||
| 2-3 | [0,3] | <0,0,1,0,0,0> | 2 | 1 | Minor third | 10-3 | ||
| 2-4 | [0,4] | <0,0,0,1,0,0> | 2 | 1 | Major third | 10-4 | ||
| 2-5 | [0,5] | <0,0,0,0,1,0> | 2 | 1 | Perfect fourth, Perfect fifth | 10-5 | ||
| 2-6 | [0,6] | <0,0,0,0,0,1> | 2 | 2 | 2 | Tritone, Augmented fourth, Diminished fifth | 10-6 | |
| 3-1 | [0,1,2] | <2,1,0,0,0,0> | 3 | 1 | Chromatic trichord, Phrygian trichord | 9-1 | ||
| 3-2 | [0,1,3] | <1,1,1,0,0,0> | 3 | Minor second + minor third | 9-2 | |||
| 3-3 | [0,1,4] | <1,0,1,1,0,0> | 3 | Minor second + major third | 9-3 | |||
| 3-4 | [0,1,5] | <1,0,0,1,1,0> | 3 | Minor second + perfect fourth | 9-4 | |||
| 3-5 | [0,1,6] | <1,0,0,0,1,1> | 3 | Viennese trichord, Minor second + tritone | 9-5 | |||
| 3-6 | [0,2,4] | <0,2,0,1,0,0> | 3 | 1 | Whole-tone trichord | 9-6 | ||
| 3-7 | [0,2,5] | <0,1,1,0,1,0> | 3 | Major second + perfect fourth, Quartal trichord | 9-7 | |||
| 3-8 | [0,2,6] | <0,1,0,1,0,1> | 3 | Italian sixth trichord | 9-8 | |||
| 3-9 | [0,2,7] | <0,1,0,0,2,0> | 3 | 1 | Quartal trichord, Stacked fourths | 9-9 | ||
| 3-10 | [0,3,6] | <0,0,2,0,0,1> | 3 | 1 | Diminished trichord | 9-10 | ||
| 3-11 | [0,3,7] | <0,0,1,1,1,0> | 3 | Minor triad, Major triad | 9-11 | |||
| 3-12 | [0,4,8] | <0,0,0,3,0,0> | 3 | 3 | 3 | Augmented triad | 9-12 | |
| 4-1 | [0,1,2,3] | <3,2,1,0,0,0> | 4 | 1 | Chromatic tetrachord | 8-1 | ||
| 4-2 | [0,1,2,4] | <2,2,1,1,0,0> | 4 | - | 8-2 | |||
| 4-3 | [0,1,3,4] | <2,1,2,1,0,0> | 4 | 1 | - | 8-3 | ||
| 4-4 | [0,1,2,5] | <2,1,1,1,1,0> | 4 | - | 8-4 | |||
| 4-5 | [0,1,2,6] | <2,1,0,1,1,1> | 4 | - | 8-5 | |||
| 4-6 | [0,1,2,7] | <2,1,0,0,2,1> | 4 | 1 | - | 8-6 | ||
| 4-7 | [0,1,4,5] | <2,0,1,2,1,0> | 4 | 1 | Arabian tetrachord | 8-7 | ||
| 4-8 | [0,1,5,6] | <2,0,0,1,2,1> | 4 | 1 | - | 8-8 | ||
| 4-9 | [0,1,6,7] | <2,0,0,0,2,2> | 4 | 2 | 2 | - | 8-9 | |
| 4-10 | [0,2,3,5] | <1,2,2,0,1,0> | 4 | 1 | - | 8-10 | ||
| 4-11 | [0,1,3,5] | <1,2,1,1,1,0> | 4 | - | 8-11 | |||
| 4-12 | [0,2,3,6] | <1,1,2,1,0,1> | 4 | - | 8-12 | |||
| 4-13 | [0,1,3,6] | <1,1,2,0,1,1> | 4 | - | 8-13 | |||
| 4-14 | [0,2,3,7] | <1,1,1,1,2,0> | 4 | - | 8-14 | |||
| 4-Z15 | [0,1,4,6] | <1,1,1,1,1,1> | 4 | All-interval tetrachord | 4-Z29 | 8-Z15 | ||
| 4-16 | [0,1,5,7] | <1,1,0,1,2,1> | 4 | - | 8-16 | |||
| 4-17 | [0,3,4,7] | <1,0,2,2,1,0> | 4 | 1 | Major-minor tetrachord | 8-17 | ||
| 4-18 | [0,1,4,7] | <1,0,2,1,1,1> | 4 | Diminished major seventh, Augmented sixth chord | 8-18 | |||
| 4-19 | [0,1,4,8] | <1,0,1,3,1,0> | 4 | Minor major seventh, Augmented triad + minor second | 8-19 | |||
| 4-20 | [0,1,5,8] | <1,0,1,2,2,0> | 4 | 1 | Major seventh chord | 8-20 | ||
| 4-21 | [0,2,4,6] | <0,3,0,2,0,1> | 4 | 1 | Whole-tone tetrachord | 8-21 | ||
| 4-22 | [0,2,4,7] | <0,2,1,1,2,0> | 4 | Major triad + major second, Add9 (no 3rd) | 8-22 | |||
| 4-23 | [0,2,5,7] | <0,2,1,0,3,0> | 4 | 1 | Quartal tetrachord, All-fourths tetrachord | 8-23 | ||
| 4-24 | [0,2,4,8] | <0,2,0,3,0,1> | 4 | 1 | Augmented seventh chord | 8-24 | ||
| 4-25 | [0,2,6,8] | <0,2,0,2,0,2> | 4 | 2 | 2 | French augmented sixth chord | 8-25 | |
| 4-26 | [0,3,5,8] | <0,1,2,1,2,0> | 4 | 1 | Minor seventh chord | 8-26 | ||
| 4-27 | [0,2,5,8] | <0,1,2,1,1,1> | 4 | Dominant seventh chord, Half-diminished seventh | 8-27 | |||
| 4-28 | [0,3,6,9] | <0,0,4,0,0,2> | 4 | 4 | 4 | Diminished seventh chord | 8-28 | |
| 4-Z29 | [0,1,3,7] | <1,1,1,1,1,1> | 4 | All-interval tetrachord | 4-Z15 | 8-Z29 | ||
| 5-1 | [0,1,2,3,4] | <4,3,2,1,0,0> | 5 | 1 | Chromatic pentachord | 7-1 | ||
| 5-2 | [0,1,2,3,5] | <3,3,2,1,1,0> | 5 | - | 7-2 | |||
| 5-3 | [0,1,2,4,5] | <3,2,2,2,1,0> | 5 | - | 7-3 | |||
| 5-4 | [0,1,2,3,6] | <3,2,2,1,1,1> | 5 | - | 7-4 | |||
| 5-5 | [0,1,2,3,7] | <3,2,1,1,2,1> | 5 | - | 7-5 | |||
| 5-6 | [0,1,2,5,6] | <3,1,1,2,2,1> | 5 | - | 7-6 | |||
| 5-7 | [0,1,2,6,7] | <3,1,0,1,3,2> | 5 | - | 7-7 | |||
| 5-8 | [0,2,3,4,6] | <2,3,2,2,0,1> | 5 | 1 | - | 7-8 | ||
| 5-9 | [0,1,2,4,6] | <2,3,1,2,1,1> | 5 | - | 7-9 | |||
| 5-10 | [0,1,3,4,6] | <2,2,3,1,1,1> | 5 | - | 7-10 | |||
| 5-11 | [0,2,3,4,7] | <2,2,2,2,2,0> | 5 | - | 7-11 | |||
| 5-Z12 | [0,1,3,5,6] | <2,2,2,1,2,1> | 5 | 1 | - | 5-Z36 | 7-Z12 | |
| 5-13 | [0,1,2,4,8] | <2,2,1,3,1,1> | 5 | - | 7-13 | |||
| 5-14 | [0,1,2,5,7] | <2,2,1,1,3,1> | 5 | - | 7-14 | |||
| 5-15 | [0,1,2,6,8] | <2,2,0,2,2,2> | 5 | 1 | - | 7-15 | ||
| 5-16 | [0,1,3,4,7] | <2,1,3,2,1,1> | 5 | - | 7-16 | |||
| 5-Z17 | [0,1,3,4,8] | <2,1,2,3,2,0> | 5 | 1 | - | 5-Z37 | 7-Z17 | |
| 5-Z18 | [0,1,4,5,7] | <2,1,2,2,2,1> | 5 | - | 5-Z38 | 7-Z18 | ||
| 5-19 | [0,1,3,6,7] | <2,1,2,1,2,2> | 5 | - | 7-19 | |||
| 5-20 | [0,1,5,6,8] | <2,1,1,2,3,1> | 5 | - | 7-20 | |||
| 5-21 | [0,1,4,5,8] | <2,0,2,4,2,0> | 5 | - | 7-21 | |||
| 5-22 | [0,1,4,7,8] | <2,0,2,3,2,1> | 5 | 1 | - | 7-22 | ||
| 5-23 | [0,2,3,5,7] | <1,3,2,1,3,0> | 5 | - | 7-23 | |||
| 5-24 | [0,1,3,5,7] | <1,3,1,2,2,1> | 5 | - | 7-24 | |||
| 5-25 | [0,2,3,5,8] | <1,2,3,1,2,1> | 5 | - | 7-25 | |||
| 5-26 | [0,2,4,5,8] | <1,2,2,3,1,1> | 5 | - | 7-26 | |||
| 5-27 | [0,1,3,5,8] | <1,2,2,2,3,0> | 5 | - | 7-27 | |||
| 5-28 | [0,2,3,6,8] | <1,2,2,2,1,2> | 5 | - | 7-28 | |||
| 5-29 | [0,1,3,6,8] | <1,2,2,1,3,1> | 5 | - | 7-29 | |||
| 5-30 | [0,1,4,6,8] | <1,2,1,3,2,1> | 5 | - | 7-30 | |||
| 5-31 | [0,1,3,6,9] | <1,1,4,1,1,2> | 5 | - | 7-31 | |||
| 5-32 | [0,1,4,6,9] | <1,1,3,2,2,1> | 5 | - | 7-32 | |||
| 5-33 | [0,2,4,6,8] | <0,4,0,4,0,2> | 5 | 1 | Whole-tone pentachord | 7-33 | ||
| 5-34 | [0,2,4,6,9] | <0,3,2,2,2,1> | 5 | 1 | Dominant ninth chord (no root), Dominant 9 | 7-34 | ||
| 5-35 | [0,2,4,7,9] | <0,3,2,1,4,0> | 5 | 1 | Pentatonic scale, Major pentatonic, Minor pentatonic | 7-35 | ||
| 5-Z36 | [0,1,2,4,7] | <2,2,2,1,2,1> | 5 | - | 5-Z12 | 7-Z36 | ||
| 5-Z37 | [0,3,4,5,8] | <2,1,2,3,2,0> | 5 | 1 | - | 5-Z17 | 7-Z37 | |
| 5-Z38 | [0,1,2,5,8] | <2,1,2,2,2,1> | 5 | - | 5-Z18 | 7-Z38 | ||
| 6-1 | [0,1,2,3,4,5] | <5,4,3,2,1,0> | 6 | 1 | Chromatic hexachord | 6-1 | ||
| 6-2 | [0,1,2,3,4,6] | <4,4,3,2,1,1> | 6 | - | 6-2 | |||
| 6-Z3 | [0,1,2,3,5,6] | <4,3,3,2,2,1> | 6 | - | 6-Z36 | 6-Z36 | ||
| 6-Z4 | [0,1,2,4,5,6] | <4,3,2,3,2,1> | 6 | 1 | - | 6-Z37 | 6-Z37 | |
| 6-5 | [0,1,2,3,6,7] | <4,2,2,2,3,2> | 6 | - | 6-5 | |||
| 6-Z6 | [0,1,2,5,6,7] | <4,2,1,2,4,2> | 6 | 1 | - | 6-Z38 | 6-Z38 | |
| 6-7 | [0,1,2,6,7,8] | <4,2,0,2,4,3> | 6 | 2 | 2 | - | 6-7 | |
| 6-8 | [0,2,3,4,5,7] | <3,4,3,2,3,0> | 6 | 1 | - | 6-8 | ||
| 6-9 | [0,1,2,3,5,7] | <3,4,2,2,3,1> | 6 | - | 6-9 | |||
| 6-Z10 | [0,1,3,4,5,7] | <3,3,3,3,2,1> | 6 | - | 6-Z39 | 6-Z39 | ||
| 6-Z11 | [0,1,2,4,5,7] | <3,3,3,2,3,1> | 6 | - | 6-Z40 | 6-Z40 | ||
| 6-Z12 | [0,1,2,4,6,7] | <3,3,2,2,3,2> | 6 | - | 6-Z41 | 6-Z41 | ||
| 6-Z13 | [0,1,3,4,6,7] | <3,2,4,2,2,2> | 6 | 1 | - | 6-Z42 | 6-Z42 | |
| 6-14 | [0,1,3,4,5,8] | <3,2,3,4,3,0> | 6 | - | 6-14 | |||
| 6-15 | [0,1,2,4,5,8] | <3,2,3,4,2,1> | 6 | - | 6-15 | |||
| 6-16 | [0,1,4,5,6,8] | <3,2,2,4,3,1> | 6 | - | 6-16 | |||
| 6-Z17 | [0,1,2,4,7,8] | <3,2,2,3,3,2> | 6 | - | 6-Z43 | 6-Z43 | ||
| 6-18 | [0,1,2,5,7,8] | <3,2,2,2,4,2> | 6 | - | 6-18 | |||
| 6-Z19 | [0,1,3,4,7,8] | <3,1,3,4,3,1> | 6 | - | 6-Z44 | 6-Z44 | ||
| 6-20 | [0,1,4,5,8,9] | <3,0,3,6,3,0> | 6 | 4 | 4 | Hexatonic scale, Augmented scale | 6-20 | |
| 6-21 | [0,2,3,4,6,8] | <2,4,2,4,1,2> | 6 | - | 6-21 | |||
| 6-22 | [0,1,2,4,6,8] | <2,4,1,4,2,2> | 6 | - | 6-22 | |||
| 6-Z23 | [0,2,3,5,6,8] | <2,3,4,2,2,2> | 6 | 1 | - | 6-Z45 | 6-Z45 | |
| 6-Z24 | [0,1,3,4,6,8] | <2,3,3,3,3,1> | 6 | - | 6-Z46 | 6-Z46 | ||
| 6-Z25 | [0,1,3,5,6,8] | <2,3,3,2,4,1> | 6 | - | 6-Z47 | 6-Z47 | ||
| 6-Z26 | [0,1,3,5,7,8] | <2,3,2,3,4,1> | 6 | 1 | - | 6-Z48 | 6-Z48 | |
| 6-27 | [0,1,3,4,6,9] | <2,2,5,2,2,2> | 6 | - | 6-27 | |||
| 6-Z28 | [0,1,3,5,6,9] | <2,2,4,3,2,2> | 6 | 1 | - | 6-Z49 | 6-Z49 | |
| 6-Z29 | [0,2,3,6,7,9] | <2,2,4,2,3,2> | 6 | 1 | - | 6-Z50 | 6-Z50 | |
| 6-30 | [0,1,3,6,7,9] | <2,2,4,2,2,3> | 6 | 2 | Petrushka chord | 6-30 | ||
| 6-31 | [0,1,4,5,7,9] | <2,2,3,4,3,1> | 6 | - | 6-31 | |||
| 6-32 | [0,2,4,5,7,9] | <1,4,3,2,5,0> | 6 | 1 | Diatonic hexachord, Major hexachord | 6-32 | ||
| 6-33 | [0,2,3,5,7,9] | <1,4,3,2,4,1> | 6 | Dorian hexachord | 6-33 | |||
| 6-34 | [0,1,3,5,7,9] | <1,4,2,4,2,2> | 6 | Mystic chord, Prometheus scale | 6-34 | |||
| 6-35 | [0,2,4,6,8,10] | <0,6,0,6,0,3> | 6 | 6 | 6 | Whole-tone scale | 6-35 | |
| 6-Z36 | [0,1,2,3,4,7] | <4,3,3,2,2,1> | 6 | - | 6-Z3 | 6-Z3 | ||
| 6-Z37 | [0,1,2,3,4,8] | <4,3,2,3,2,1> | 6 | 1 | - | 6-Z4 | 6-Z4 | |
| 6-Z38 | [0,1,2,3,7,8] | <4,2,1,2,4,2> | 6 | 1 | - | 6-Z6 | 6-Z6 | |
| 6-Z39 | [0,2,3,4,5,8] | <3,3,3,3,2,1> | 6 | - | 6-Z10 | 6-Z10 | ||
| 6-Z40 | [0,1,2,3,5,8] | <3,3,3,2,3,1> | 6 | - | 6-Z11 | 6-Z11 | ||
| 6-Z41 | [0,1,2,3,6,8] | <3,3,2,2,3,2> | 6 | - | 6-Z12 | 6-Z12 | ||
| 6-Z42 | [0,1,2,3,6,9] | <3,2,4,2,2,2> | 6 | 1 | - | 6-Z13 | 6-Z13 | |
| 6-Z43 | [0,1,2,5,6,8] | <3,2,2,3,3,2> | 6 | - | 6-Z17 | 6-Z17 | ||
| 6-Z44 | [0,1,2,5,6,9] | <3,1,3,4,3,1> | 6 | - | 6-Z19 | 6-Z19 | ||
| 6-Z45 | [0,2,3,4,6,9] | <2,3,4,2,2,2> | 6 | 1 | - | 6-Z23 | 6-Z23 | |
| 6-Z46 | [0,1,2,4,6,9] | <2,3,3,3,3,1> | 6 | - | 6-Z24 | 6-Z24 | ||
| 6-Z47 | [0,1,2,4,7,9] | <2,3,3,2,4,1> | 6 | - | 6-Z25 | 6-Z25 | ||
| 6-Z48 | [0,1,2,5,7,9] | <2,3,2,3,4,1> | 6 | 1 | - | 6-Z26 | 6-Z26 | |
| 6-Z49 | [0,1,3,4,7,9] | <2,2,4,3,2,2> | 6 | 1 | - | 6-Z28 | 6-Z28 | |
| 6-Z50 | [0,1,4,6,7,9] | <2,2,4,2,3,2> | 6 | 1 | - | 6-Z29 | 6-Z29 | |
| 7-1 | [0,1,2,3,4,5,6] | <6,5,4,3,2,1> | 7 | 1 | Chromatic heptachord | 5-1 | ||
| 7-2 | [0,1,2,3,4,5,7] | <5,5,4,3,3,1> | 7 | - | 5-2 | |||
| 7-3 | [0,1,2,3,4,5,8] | <5,4,4,4,3,1> | 7 | - | 5-3 | |||
| 7-4 | [0,1,2,3,4,6,7] | <5,4,4,3,3,2> | 7 | - | 5-4 | |||
| 7-5 | [0,1,2,3,5,6,7] | <5,4,3,3,4,2> | 7 | - | 5-5 | |||
| 7-6 | [0,1,2,3,4,7,8] | <5,3,3,4,4,2> | 7 | - | 5-6 | |||
| 7-7 | [0,1,2,3,6,7,8] | <5,3,2,3,5,3> | 7 | - | 5-7 | |||
| 7-8 | [0,2,3,4,5,6,8] | <4,5,4,4,2,2> | 7 | 1 | - | 5-8 | ||
| 7-9 | [0,1,2,3,4,6,8] | <4,5,3,4,3,2> | 7 | - | 5-9 | |||
| 7-10 | [0,1,2,3,4,6,9] | <4,4,5,3,3,2> | 7 | - | 5-10 | |||
| 7-11 | [0,1,3,4,5,6,8] | <4,4,4,4,4,1> | 7 | - | 5-11 | |||
| 7-Z12 | [0,1,2,3,4,7,9] | <4,4,4,3,4,2> | 7 | 1 | - | 7-Z36 | 5-Z12 | |
| 7-13 | [0,1,2,4,5,6,8] | <4,4,3,5,3,2> | 7 | - | 5-13 | |||
| 7-14 | [0,1,2,3,5,7,8] | <4,4,3,3,5,2> | 7 | - | 5-14 | |||
| 7-15 | [0,1,2,4,6,7,8] | <4,4,2,4,4,3> | 7 | 1 | - | 5-15 | ||
| 7-16 | [0,1,2,3,5,6,9] | <4,3,5,4,3,2> | 7 | - | 5-16 | |||
| 7-Z17 | [0,1,2,4,5,6,9] | <4,3,4,5,4,1> | 7 | 1 | - | 7-Z37 | 5-Z17 | |
| 7-Z18 | [0,1,4,5,6,7,9] | <4,3,4,4,4,2> | 7 | - | 7-Z38 | 5-Z18 | ||
| 7-19 | [0,1,2,3,6,7,9] | <4,3,4,3,4,3> | 7 | - | 5-19 | |||
| 7-20 | [0,1,2,5,6,7,9] | <4,3,3,4,5,2> | 7 | - | 5-20 | |||
| 7-21 | [0,1,2,4,5,8,9] | <4,2,4,6,4,1> | 7 | - | 5-21 | |||
| 7-22 | [0,1,2,5,6,8,9] | <4,2,4,5,4,2> | 7 | 1 | Hungarian major, Double harmonic | 5-22 | ||
| 7-23 | [0,2,3,4,5,7,9] | <3,5,4,3,5,1> | 7 | - | 5-23 | |||
| 7-24 | [0,1,2,3,5,7,9] | <3,5,3,4,4,2> | 7 | - | 5-24 | |||
| 7-25 | [0,2,3,4,6,7,9] | <3,4,5,3,4,2> | 7 | - | 5-25 | |||
| 7-26 | [0,1,3,4,5,7,9] | <3,4,4,5,3,2> | 7 | - | 5-26 | |||
| 7-27 | [0,1,2,4,5,7,9] | <3,4,4,4,5,1> | 7 | - | 5-27 | |||
| 7-28 | [0,1,3,5,6,7,9] | <3,4,4,4,3,3> | 7 | - | 5-28 | |||
| 7-29 | [0,1,2,4,6,7,9] | <3,4,4,3,5,2> | 7 | - | 5-29 | |||
| 7-30 | [0,1,2,4,6,8,9] | <3,4,3,5,4,2> | 7 | - | 5-30 | |||
| 7-31 | [0,1,3,4,6,7,9] | <3,3,6,3,3,3> | 7 | Hungarian minor | 5-31 | |||
| 7-32 | [0,1,3,4,6,8,9] | <3,3,5,4,4,2> | 7 | Harmonic minor, Harmonic major | 5-32 | |||
| 7-33 | [0,1,2,4,6,8,10] | <2,6,2,6,2,3> | 7 | 1 | Neapolitan major | 5-33 | ||
| 7-34 | [0,1,3,4,6,8,10] | <2,5,4,4,4,2> | 7 | 1 | Melodic minor ascending, Jazz minor | 5-34 | ||
| 7-35 | [0,1,3,5,6,8,10] | <2,5,4,3,6,1> | 7 | 1 | Major scale, Diatonic scale, Ionian | 5-35 | ||
| 7-Z36 | [0,1,2,3,5,6,8] | <4,4,4,3,4,2> | 7 | - | 7-Z12 | 5-Z36 | ||
| 7-Z37 | [0,1,3,4,5,7,8] | <4,3,4,5,4,1> | 7 | 1 | - | 7-Z17 | 5-Z37 | |
| 7-Z38 | [0,1,2,4,5,7,8] | <4,3,4,4,4,2> | 7 | - | 7-Z18 | 5-Z38 | ||
| 8-1 | [0,1,2,3,4,5,6,7] | <7,6,5,4,4,2> | 8 | 1 | Chromatic octachord | 4-1 | ||
| 8-2 | [0,1,2,3,4,5,6,8] | <6,6,5,5,4,2> | 8 | - | 4-2 | |||
| 8-3 | [0,1,2,3,4,5,6,9] | <6,5,6,5,4,2> | 8 | 1 | - | 4-3 | ||
| 8-4 | [0,1,2,3,4,5,7,8] | <6,5,5,5,5,2> | 8 | - | 4-4 | |||
| 8-5 | [0,1,2,3,4,6,7,8] | <6,5,4,5,5,3> | 8 | - | 4-5 | |||
| 8-6 | [0,1,2,3,5,6,7,8] | <6,5,4,4,6,3> | 8 | 1 | - | 4-6 | ||
| 8-7 | [0,1,2,3,4,5,8,9] | <6,4,5,6,5,2> | 8 | 1 | - | 4-7 | ||
| 8-8 | [0,1,2,3,4,7,8,9] | <6,4,4,5,6,3> | 8 | 1 | - | 4-8 | ||
| 8-9 | [0,1,2,3,6,7,8,9] | <6,4,4,4,6,4> | 8 | 2 | 2 | - | 4-9 | |
| 8-10 | [0,2,3,4,5,6,7,9] | <5,6,6,4,5,2> | 8 | 1 | - | 4-10 | ||
| 8-11 | [0,1,2,3,4,5,7,9] | <5,6,5,5,5,2> | 8 | - | 4-11 | |||
| 8-12 | [0,1,3,4,5,6,7,9] | <5,5,6,5,4,3> | 8 | - | 4-12 | |||
| 8-13 | [0,1,2,3,4,6,7,9] | <5,5,6,4,5,3> | 8 | - | 4-13 | |||
| 8-14 | [0,1,2,4,5,6,7,9] | <5,5,5,5,6,2> | 8 | - | 4-14 | |||
| 8-Z15 | [0,1,2,3,4,6,8,9] | <5,5,5,5,5,3> | 8 | - | 8-Z29 | 4-Z15 | ||
| 8-16 | [0,1,2,3,5,7,8,9] | <5,5,4,5,6,3> | 8 | - | 4-16 | |||
| 8-17 | [0,1,3,4,5,6,8,9] | <5,4,6,6,5,2> | 8 | 1 | - | 4-17 | ||
| 8-18 | [0,1,2,3,5,6,8,9] | <5,4,6,5,5,3> | 8 | - | 4-18 | |||
| 8-19 | [0,1,2,4,5,6,8,9] | <5,4,5,7,5,2> | 8 | - | 4-19 | |||
| 8-20 | [0,1,2,4,5,7,8,9] | <5,4,5,6,6,2> | 8 | 1 | - | 4-20 | ||
| 8-21 | [0,1,2,3,4,6,8,10] | <4,7,4,6,4,3> | 8 | 1 | - | 4-21 | ||
| 8-22 | [0,1,2,3,5,6,8,10] | <4,6,5,5,6,2> | 8 | - | 4-22 | |||
| 8-23 | [0,1,2,3,5,7,8,10] | <4,6,5,4,7,2> | 8 | 1 | - | 4-23 | ||
| 8-24 | [0,1,2,4,5,6,8,10] | <4,6,4,7,4,3> | 8 | 1 | - | 4-24 | ||
| 8-25 | [0,1,2,4,6,7,8,10] | <4,6,4,6,4,4> | 8 | 2 | 2 | - | 4-25 | |
| 8-26 | [0,1,3,4,5,7,8,10] | <4,5,6,5,6,2> | 8 | 1 | - | 4-26 | ||
| 8-27 | [0,1,2,4,5,7,8,10] | <4,5,6,5,5,3> | 8 | - | 4-27 | |||
| 8-28 | [0,1,3,4,6,7,9,10] | <4,4,8,4,4,4> | 8 | 4 | 4 | Octatonic scale, Diminished scale | 4-28 | |
| 8-Z29 | [0,1,2,3,5,6,7,9] | <5,5,5,5,5,3> | 8 | - | 8-Z15 | 4-Z29 | ||
| 9-1 | [0,1,2,3,4,5,6,7,8] | <8,7,6,6,6,3> | 9 | 1 | Chromatic nonachord | 3-1 | ||
| 9-2 | [0,1,2,3,4,5,6,7,9] | <7,7,7,6,6,3> | 9 | - | 3-2 | |||
| 9-3 | [0,1,2,3,4,5,6,8,9] | <7,6,7,7,6,3> | 9 | - | 3-3 | |||
| 9-4 | [0,1,2,3,4,5,7,8,9] | <7,6,6,7,7,3> | 9 | - | 3-4 | |||
| 9-5 | [0,1,2,3,4,6,7,8,9] | <7,6,6,6,7,4> | 9 | - | 3-5 | |||
| 9-6 | [0,1,2,3,4,5,6,8,10] | <6,8,6,7,6,3> | 9 | 1 | - | 3-6 | ||
| 9-7 | [0,1,2,3,4,5,7,8,10] | <6,7,7,6,7,3> | 9 | - | 3-7 | |||
| 9-8 | [0,1,2,3,4,6,7,8,10] | <6,7,6,7,6,4> | 9 | - | 3-8 | |||
| 9-9 | [0,1,2,3,5,6,7,8,10] | <6,7,6,6,8,3> | 9 | 1 | - | 3-9 | ||
| 9-10 | [0,1,2,3,4,6,7,9,10] | <6,6,8,6,6,4> | 9 | 1 | - | 3-10 | ||
| 9-11 | [0,1,2,3,5,6,7,9,10] | <6,6,7,7,7,3> | 9 | - | 3-11 | |||
| 9-12 | [0,1,2,4,5,6,8,9,10] | <6,6,6,9,6,3> | 9 | 3 | 3 | - | 3-12 | |
| 10-1 | [0,1,2,3,4,5,6,7,8,9] | <9,8,8,8,8,4> | 10 | 1 | Chromatic decachord | 2-1 | ||
| 10-2 | [0,1,2,3,4,5,6,7,8,10] | <8,9,8,8,8,4> | 10 | 1 | - | 2-2 | ||
| 10-3 | [0,1,2,3,4,5,6,7,9,10] | <8,8,9,8,8,4> | 10 | 1 | - | 2-3 | ||
| 10-4 | [0,1,2,3,4,5,6,8,9,10] | <8,8,8,9,8,4> | 10 | 1 | - | 2-4 | ||
| 10-5 | [0,1,2,3,4,5,7,8,9,10] | <8,8,8,8,9,4> | 10 | 1 | - | 2-5 | ||
| 10-6 | [0,1,2,3,4,6,7,8,9,10] | <8,8,8,8,8,5> | 10 | 2 | 2 | - | 2-6 | |
| 11-1 | [0,1,2,3,4,5,6,7,8,9,10] | <10,10,10,10,10,5> | 11 | 1 | Chromatic undecachord, All but one | 1-1 | ||
| 12-1 | [0,1,2,3,4,5,6,7,8,9,10,11] | <12,12,12,12,12,6> | 12 | 12 | 12 | Chromatic scale, Aggregate, Total chromatic | 0-1 |
T-Sym: Transpositional symmetry (how many transpositions map the set to itself)
I-Sym: Inversional symmetry (how many inversions map the set to itself)
Z-Mate: Z-related set class (same interval vector, different prime form)