List of pitch class sets
This is a list of pitch class sets by Forte number.[1] For a list of ordered collections, see: list of tone rows and series.
Sets are listed next to their complements. Inversions are marked "B" (sets not marked "A" or "B" are symmetrical). 10, 11, and 12 are listed as "T", "E", and "C".
In the five instances they differ,[lower-alpha 1] the prime forms given are Rahn's (also used by Straus) rather than Forte's, which are given in footnotes.[3][4]
Elliott Carter had earlier (1960-67) produced a numbered listing of pitch class sets, or "chords", as Carter referred to them, for his own use.[5][6]
Forte no. | Prime form | Interval vector | Carter's no. | Audio | Possible spacings | Forte no. | Prime form | Interval vector | Carter's no. | Audio | Possible spacings |
---|---|---|---|---|---|---|---|---|---|---|---|
0-1 | [] | <0,0,0,0,0,0> | empty set | 12-1 | [0,1,2,3,4,5, 6,7,8,9,T,E] | <C,C,C,C,C,6> | Play | aggregate | |||
1-1 | [0] | <0,0,0,0,0,0> | Play | PU, P8 | 11-1 | [0,1,2,3,4,5, 6,7,8,9,T] | <T,T,T,T,T,5> | Play | ... | ||
2-1 | [0,1] | <1,0,0,0,0,0> | 1 | Play | m2, M7 | 10-1 | [0,1,2,3,4, 5,6,7,8,9] | <9,8,8,8,8,4> | Play | ... | |
2-2 | [0,2] | <0,1,0,0,0,0> | 2 | Play | M2, m7 | 10-2 | [0,1,2,3,4, 5,6,7,8,T] | <8,9,8,8,8,4> | Play | ... | |
2-3 | [0,3] | <0,0,1,0,0,0> | 3 | Play | m3, M6 | 10-3 | [0,1,2,3,4, 5,6,7,9,T] | <8,8,9,8,8,4> | Play | ... | |
2-4 | [0,4] | <0,0,0,1,0,0> | 4 | Play | M3, m6 | 10-4 | [0,1,2,3,4, 5,6,8,9,T] | <8,8,8,9,8,4> | Play | ... | |
2-5 | [0,5] | <0,0,0,0,1,0> | 5 | Play | P4, P5 | 10-5 | [0,1,2,3,4, 5,7,8,9,T] | <8,8,8,8,9,4> | Play | ... | |
2-6 | [0,6] | <0,0,0,0,0,1> | 6 | Play | A4, d5 | 10-6 | [0,1,2,3,4, 6,7,8,9,T] | <8,8,8,8,8,5> | Play | ... | |
3-1 | [0,1,2] | <2,1,0,0,0,0> | 4 | Play | ... | 9-1 | [0,1,2,3,4, 5,6,7,8] | <8,7,6,6,6,3> | Play | ... | |
3-2A | [0,1,3] | <1,1,1,0,0,0> | 12 | Play | ... | 9-2A | [0,1,2,3,4, 5,6,7,9] | <7,7,7,6,6,3> | Play | ... | |
3-2B | [0,2,3] | Play | ... | 9-2B | [0,2,3,4,5, 6,7,8,9] | Play | ... | ||||
3-3A | [0,1,4] | <1,0,1,1,0,0> | 11 | Play | ... | 9-3B | [0,1,3,4, 5,6,7,8,9] | <7,6,7,7,6,3> | Play | ... | |
3-3B | [0,3,4] | Play | ... | 9-3A | [0,1,2,3,4, 5,6,8,9] | Play | ... | ||||
3-4A | [0,1,5] | <1,0,0,1,1,0> | 9 | Play | ... | 9-4B | [0,1,2,4,5, 6,7,8,9] | <7,6,6,7,7,3> | Play | ... | |
3-4B | [0,4,5] | Play | ... | 9-4A | [0,1,2,3,4, 5,7,8,9] | Play | ... | ||||
3-5A | [0,1,6] | <1,0,0,0,1,1> | 7 | Play | Viennese trichord | 9-5B | [0,1,2,3,5, 6,7,8,9] | <7,6,6,6,7,4> | Play | ... | |
3-5B | [0,5,6] | Play | ... | 9-5A | [0,1,2,3,4, 6,7,8,9] | Play | ... | ||||
3-6 | [0,2,4] | <0,2,0,1,0,0> | 3 | Play | ... | 9-6 | [0,1,2,3,4, 5,6,8,T] | <6,8,6,7,6,3> | Play | ... | |
3-7A | [0,2,5] | <0,1,1,0,1,0> | 10 | Play | ... | 9-7B | [0,1,2,3,4, 5,7,9,T] | <6,7,7,6,7,3> | Play | ... | |
3-7B | [0,3,5] | Play | ... | 9-7A | [0,1,2,3,4, 5,7,8,T] | Play | ... | ||||
3-8A | [0,2,6] | <0,1,0,1,0,1> | 8 | Play | It6 | 9-8B | [0,1,2,3,4, 6,8,9,T] | <6,7,6,7,6,4> | Play | ... | |
3-8B | [0,4,6] | Play | ... | 9-8A | [0,1,2,3,4, 6,7,8,T] | Play | ... | ||||
3-9 | [0,2,7] | <0,1,0,0,2,0> | 5 | Play | sus. chord | 9-9 | [0,1,2,3,5, 6,7,8,T] | <6,7,6,6,8,3> | Play | blues scale | |
3-10 | [0,3,6] | <0,0,2,0,0,1> | 2 | Play | dim. chord | 9-10 | [0,1,2,3,4, 6,7,9,T] | <6,6,8,6,6,4> | Play | ... | |
3-11A | [0,3,7] | <0,0,1,1,1,0> | 6 | Play | minor chord | 9-11B | [0,1,2,3,5, 6,8,9,T] | <6,6,7,7,7,3> | Play | ... | |
3-11B | [0,4,7] | Play | major chord | 9-11A | [0,1,2,3,5, 6,7,9,T] | Play | ... | ||||
3-12 | [0,4,8] | <0,0,0,3,0,0> | 1 | Play | Aug. chord | 9-12 | [0,1,2,4,5, 6,8,9,T] | <6,6,6,9,6,3> | Play | ... | |
4-1 | [0,1,2,3] | <3,2,1,0,0,0> | 1 | Play | ... | 8-1 | [0,1,2,3, 4,5,6,7] | <7,6,5,4,4,2> | Play | ... | |
4-2A | [0,1,2,4] | <2,2,1,1,0,0> | 17 | Play | ... | 8-2B | [0,2,3,4, 5,6,7,8] | <6,6,5,5,4,2> | Play | ... | |
4-2B | [0,2,3,4] | Play | ... | 8-2A | [0,1,2,3, 4,5,6,8] | Play | ... | ||||
4-3 | [0,1,3,4] | <2,1,2,1,0,0> | 9 | Play | ... | 8-3 | [0,1,2,3, 4,5,6,9] | <6,5,6,5,4,2> | Play | ... | |
4-4A | [0,1,2,5] | <2,1,1,1,1,0> | 20 | Play | ... | 8-4B | [0,1,3,4, 5,6,7,8] | <6,5,5,5,5,2> | Play | ... | |
4-4B | [0,3,4,5] | Play | ... | 8-4A | [0,1,2,3, 4,5,7,8] | Play | ... | ||||
4-5A | [0,1,2,6] | <2,1,0,1,1,1> | 22 | Play | ... | 8-5B | [0,1,2,4, 5,6,7,8] | <6,5,4,5,5,3> | Play | ... | |
4-5B | [0,4,5,6] | Play | ... | 8-5A | [0,1,2,3, 4,6,7,8] | Play | ... | ||||
4-6 | [0,1,2,7] | <2,1,0,0,2,1> | 6 | Play | dream chord | 8-6 | [0,1,2,3, 5,6,7,8] | <6,5,4,4,6,3> | Play | ... | |
4-7 | [0,1,4,5] | <2,0,1,2,1,0> | 8 | Play | ... | 8-7 | [0,1,2,3, 4,5,8,9] | <6,4,5,6,5,2> | Play | ... | |
4-8 | [0,1,5,6] | <2,0,0,1,2,1> | 10 | Play | ... | 8-8 | [0,1,2,3, 4,7,8,9] | <6,4,4,5,6,3> | Play | ... | |
4-9 | [0,1,6,7] | <2,0,0,0,2,2> | 2 | Play | distance model | 8-9 | [0,1,2,3, 6,7,8,9] | <6,4,4,4,6,4> | Play | ... | |
4-10 | [0,2,3,5] | <1,2,2,0,1,0> | 3 | Play | ... | 8-10 | [0,2,3,4, 5,6,7,9] | <5,6,6,4,5,2> | Play | ... | |
4-11A | [0,1,3,5] | <1,2,1,1,1,0> | 26 | Play | ... | 8-11B | [0,2,4,5, 6,7,8,9] | <5,6,5,5,5,2> | Play | ... | |
4-11B | [0,2,4,5] | Play | ... | 8-11A | [0,1,2,3, 4,5,7,9] | Play | ... | ||||
4-12A | [0,2,3,6] | <1,1,2,1,0,1> | 28 | Play | ... | 8-12A | [0,1,3,4, 5,6,7,9] | <5,5,6,5,4,3> | Play | ... | |
4-12B | [0,3,4,6] | Play | ... | 8-12B | [0,2,3,4, 5,6,8,9] | Play | ... | ||||
4-13A | [0,1,3,6] | <1,1,2,0,1,1> | 7 | Play | ... | 8-13B | [0,2,3,5, 6,7,8,9] | <5,5,6,4,5,3> | Play | ... | |
4-13B | [0,3,5,6] | Play | ... | 8-13A | [0,1,2,3, 4,6,7,9] | Play | ... | ||||
4-14A | [0,2,3,7] | <1,1,1,1,2,0> | 25 | Play | ... | 8-14A | [0,1,2,4, 5,6,7,9] | <5,5,5,5,6,2> | Play | ... | |
4-14B | [0,4,5,7] | Play | ... | 8-14B | [0,2,3,4, 5,7,8,9] | Play | ... | ||||
4-z15A | [0,1,4,6] | <1,1,1,1,1,1> | 18 | Play | all-interval tetrachord | 8-z15B | [0,1,3,5, 6,7,8,9] | <5,5,5,5,5,3> | Play | ... | |
4-z15B | [0,2,5,6] | Play | ... | 8-z15A | [0,1,2,3, 4,6,8,9] | Play | ... | ||||
4-16A | [0,1,5,7] | <1,1,0,1,2,1> | 19 | Play | ... | 8-16B | [0,1,2,4, 6,7,8,9] | <5,5,4,5,6,3> | Play | ... | |
4-16B | [0,2,6,7] | Play | ... | 8-16A | [0,1,2,3, 5,7,8,9] | Play | ... | ||||
4-17 | [0,3,4,7] | <1,0,2,2,1,0> | 13 | Play | ... | 8-17 | [0,1,3,4, 5,6,8,9] | <5,4,6,6,5,2> | Play | ... | |
4-18A | [0,1,4,7] | <1,0,2,1,1,1> | 21 | Play | dim. M7 chord | 8-18B | [0,1,3,4, 6,7,8,9] | <5,4,6,5,5,3> | Play | ... | |
4-18B | [0,3,6,7] | Play | ... | 8-18A | [0,1,2,3, 5,6,8,9] | Play | ... | ||||
4-19A | [0,1,4,8] | <1,0,1,3,1,0> | 24 | Play | Mm7 chord | 8-19B | [0,1,3,4, 5,7,8,9] | <5,4,5,7,5,2> | Play | ... | |
4-19B | [0,4,7,8] | Play | ... | 8-19A | [0,1,2,4, 5,6,8,9] | Play | ... | ||||
4-20 | [0,1,5,8] | <1,0,1,2,2,0> | 15 | Play | M7 chord | 8-20 | [0,1,2,4, 5,7,8,9] | <5,4,5,6,6,2> | Play | ... | |
4-21 | [0,2,4,6] | <0,3,0,2,0,1> | 11 | Play | ... | 8-21 | [0,1,2,3, 4,6,8,T] | <4,7,4,6,4,3> | Play | ... | |
4-22A | [0,2,4,7] | <0,2,1,1,2,0> | 27 | Play | mu chord | 8-22B | [0,1,2,3, 5,7,9,T] | <4,6,5,5,6,2> | Play | ... | |
4-22B | [0,3,5,7] | Play | ... | 8-22A | [0,1,2,3, 5,6,8,T] | Play | ... | ||||
4-23 | [0,2,5,7] | <0,2,1,0,3,0> | 4 | Play | quartal chord | 8-23 | [0,1,2,3, 5,7,8,T] | <4,6,5,4,7,2> | Play | bebop scale | |
4-24 | [0,2,4,8] | <0,2,0,3,0,1> | 16 | Play | A7 chord | 8-24 | [0,1,2,4, 5,6,8,T] | <4,6,4,7,4,3> | Play | ... | |
4-25 | [0,2,6,8] | <0,2,0,2,0,2> | 12 | Play | Fr6 | 8-25 | [0,1,2,4, 6,7,8,T] | <4,6,4,6,4,4> | Play | ... | |
4-26 | [0,3,5,8] | <0,1,2,1,2,0> | 14 | Play | minor seventh chord | 8-26 | [0,1,3,4, 5,7,8,T][lower-alpha 2] | <4,5,6,5,6,2> | Play | ... | |
4-27A | [0,2,5,8] | <0,1,2,1,1,1> | 29 | Play | dominant 7th chord | 8-27B | [0,1,2,4, 6,7,9,T] | <4,5,6,5,5,3> | Play | ... | |
4-27B | [0,3,6,8] | Play | ... | 8-27A | [0,1,2,4, 5,7,8,T] | Play | ... | ||||
4-28 | [0,3,6,9] | <0,0,4,0,0,2> | 5 | Play | dim. 7th chord | 8-28 | [0,1,3,4, 6,7,9,T] | <4,4,8,4,4,4> | Play | octatonic scale | |
4-z29A | [0,1,3,7] | <1,1,1,1,1,1> | 23 | Play | all-interval tetrachord | 8-z29B | [0,2,3,4, 6,7,8,9] | <5,5,5,5,5,3> | Play | ... | |
4-z29B | [0,4,6,7] | Play | ... | 8-z29A | [0,1,2,3, 5,6,7,9] | Play | ... | ||||
5-1 | [0,1,2,3,4] | <4,3,2,1,0,0> | Play | ... | 7-1 | [0,1,2,3, 4,5,6] | <6,5,4,3,2,1> | 1 | Play | ... | |
5-2A | [0,1,2,3,5] | <3,3,2,1,1,0> | Play | ... | 7-2B | [0,2,3,4, 5,6,7] | <5,5,4,3,3,1> | 11 | Play | ... | |
5-2B | [0,2,3,4,5] | Play | ... | 7-2A | [0,1,2,3, 4,5,7] | Play | ... | ||||
5-3A | [0,1,2,4,5] | <3,2,2,2,1,0> | Play | ... | 7-3B | [0,3,4,5, 6,7,8] | <5,4,4,4,3,1> | 14 | Play | ... | |
5-3B | [0,1,3,4,5] | Play | ... | 7-3A | [0,1,2,3, 4,5,8] | Play | ... | ||||
5-4A | [0,1,2,3,6] | <3,2,2,1,1,1> | Play | ... | 7-4B | [0,1,3,4, 5,6,7] | <5,4,4,3,3,2> | 12 | Play | ... | |
5-4B | [0,3,4,5,6] | Play | ... | 7-4A | [0,1,2,3, 4,6,7] | Play | ... | ||||
5-5A | [0,1,2,3,7] | <3,2,1,1,2,1> | Play | ... | 7-5B | [0,1,2,4, 5,6,7] | <5,4,3,3,4,2> | 13 | Play | ... | |
5-5B | [0,4,5,6,7] | Play | ... | 7-5A | [0,1,2,3, 5,6,7] | Play | ... | ||||
5-6A | [0,1,2,5,6] | <3,1,1,2,2,1> | Play | ... | 7-6B | [0,1,4,5, 6,7,8] | <5,3,3,4,4,2> | 27 | Play | ... | |
5-6B | [0,1,4,5,6] | Play | ... | 7-6A | [0,1,2,3, 4,7,8] | Play | ... | ||||
5-7A | [0,1,2,6,7] | <3,1,0,1,3,2> | Play | ... | 7-7B | [0,1,2,5, 6,7,8] | <5,3,2,3,5,3> | 30 | Play | ... | |
5-7B | [0,1,5,6,7] | Play | ... | 7-7A | [0,1,2,3, 6,7,8] | Play | ... | ||||
5-8 | [0,2,3,4,6] | <2,3,2,2,0,1> | Play | ... | 7-8 | [0,2,3,4, 5,6,8] | <4,5,4,4,2,2> | 2 | Play | ... | |
5-9A | [0,1,2,4,6] | <2,3,1,2,1,1> | Play | ... | 7-9B | [0,2,4,5, 6,7,8] | <4,5,3,4,3,2> | 15 | Play | ... | |
5-9B | [0,2,4,5,6] | Play | ... | 7-9A | [0,1,2,3, 4,6,8] | Play | ... | ||||
5-10A | [0,1,3,4,6] | <2,2,3,1,1,1> | Play | ... | 7-10B | [0,2,3,4, 5,6,9] | <4,4,5,3,3,2> | 19 | Play | ... | |
5-10B | [0,2,3,5,6] | Play | ... | 7-10A | [0,1,2,3, 4,6,9] | Play | ... | ||||
5-11A | [0,2,3,4,7] | <2,2,2,2,2,0> | Play | ... | 7-11B | [0,2,3,4, 5,7,8] | <4,4,4,4,4,1> | 18 | Play | ... | |
5-11B | [0,3,4,5,7] | Play | ... | 7-11A | [0,1,3,4, 5,6,8] | Play | ... | ||||
5-z12 | [0,1,3,5,6] | <2,2,2,1,2,1> | Play | ... | 7-z12 | [0,1,2,3, 4,7,9] | <4,4,4,3,4,2> | 5 | Play | ... | |
5-13A | [0,1,2,4,8] | <2,2,1,3,1,1> | Play | ... | 7-13B | [0,2,3,4, 6,7,8] | <4,4,3,5,3,2> | 17 | Play | ... | |
5-13B | [0,4,6,7,8] | Play | ... | 7-13A | [0,1,2,4, 5,6,8] | Play | ... | ||||
5-14A | [0,1,2,5,7] | <2,2,1,1,3,1> | Play | ... | 7-14B | [0,1,3,5, 6,7,8] | <4,4,3,3,5,2> | 28 | Play | ... | |
5-14B | [0,2,5,6,7] | Play | ... | 7-14A | [0,1,2,3, 5,7,8] | Play | ... | ||||
5-15 | [0,1,2,6,8] | <2,2,0,2,2,2> | Play | ... | 7-15 | [0,1,2,4, 6,7,8] | <4,4,2,4,4,3> | 4 | Play | ... | |
5-16A | [0,1,3,4,7] | <2,1,3,2,1,1> | Play | ... | 7-16B | [0,1,3,4, 5,6,9] | <4,3,5,4,3,2> | 20 | Play | ... | |
5-16B | [0,3,4,6,7] | Play | ... | 7-16A | [0,1,2,3, 5,6,9] | Play | ... | ||||
5-z17 | [0,1,3,4,8] | <2,1,2,3,2,0> | Play | Farben chord | 7-z17 | [0,1,2,4, 5,6,9] | <4,3,4,5,4,1> | 10 | Play | ... | |
5-z18A | [0,1,4,5,7] | <2,1,2,2,2,1> | Play | ... | 7-z18A | [0,1,4,5, 6,7,9][lower-alpha 3] | <4,3,4,4,4,2> | 35 | Play | ... | |
5-z18B | [0,2,3,6,7] | Play | ... | 7-z18B | [0,1,4,6, 7,8,9] | Play | ... | ||||
5-19A | [0,1,3,6,7] | <2,1,2,1,2,2> | Play | ... | 7-19B | [0,1,2,3, 6,8,9] | <4,3,4,3,4,3> | 31 | Play | ... | |
5-19B | [0,1,4,6,7] | Play | ... | 7-19A | [0,1,2,3, 6,7,9] | Play | ... | ||||
5-20A | [0,1,5,6,8][lower-alpha 4] | <2,1,1,2,3,1> | Play | ... | 7-20B | [0,1,2,5, 7,8,9] | <4,3,3,4,5,2> | 34 | Play | ... | |
5-20B | [0,2,3,7,8] | Play | ... | 7-20A | [0,1,2,5, 6,7,9][lower-alpha 5] | Play | Persian scale | ||||
5-21A | [0,1,4,5,8] | <2,0,2,4,2,0> | Play | ... | 7-21B | [0,1,3,4, 5,8,9] | <4,2,4,6,4,1> | 21 | Play | ... | |
5-21B | [0,3,4,7,8] | Play | ... | 7-21A | [0,1,2,4, 5,8,9] | Play | ... | ||||
5-22 | [0,1,4,7,8] | <2,0,2,3,2,1> | Play | ... | 7-22 | [0,1,2,5, 6,8,9] | <4,2,4,5,4,2> | 8 | Play | double harmonic scale | |
5-23A | [0,2,3,5,7] | <1,3,2,1,3,0> | Play | ... | 7-23B | [0,2,4,5, 6,7,9] | <3,5,4,3,5,1> | 25 | Play | ... | |
5-23B | [0,2,4,5,7] | Play | ... | 7-23A | [0,2,3,4, 5,7,9] | Play | ... | ||||
5-24A | [0,1,3,5,7] | <1,3,1,2,2,1> | Play | ... | 7-24B | [0,2,4,6, 7,8,9] | <3,5,3,4,4,2> | 22 | Play | ... | |
5-24B | [0,2,4,6,7] | Play | ... | 7-24A | [0,1,2,3, 5,7,9] | Play | enigmatic scale | ||||
5-25A | [0,2,3,5,8] | <1,2,3,1,2,1> | Play | ... | 7-25B | [0,2,3,5, 6,7,9] | <3,4,5,3,4,2> | 24 | Play | ... | |
5-25B | [0,3,5,6,8] | Play | ... | 7-25A | [0,2,3,4, 6,7,9] | Play | ... | ||||
5-26A | [0,2,4,5,8] | <1,2,2,3,1,1> | Play | ... | 7-26A | [0,1,3,4, 5,7,9] | <3,4,4,5,3,2> | 26 | Play | ... | |
5-26B | [0,3,4,6,8] | Play | ... | 7-26B | [0,2,4,5, 6,8,9] | Play | ... | ||||
5-27A | [0,1,3,5,8] | <1,2,2,2,3,0> | Play | ... | 7-27B | [0,2,4,5, 7,8,9] | <3,4,4,4,5,1> | 23 | Play | ... | |
5-27B | [0,3,5,7,8] | Play | ... | 7-27A | [0,1,2,4, 5,7,9] | Play | ... | ||||
5-28A | [0,2,3,6,8] | <1,2,2,2,1,2> | Play | ... | 7-28A | [0,1,3,5, 6,7,9] | <3,4,4,4,3,3> | 36 | Play | ... | |
5-28B | [0,2,5,6,8] | Play | ... | 7-28B | [0,2,3,4, 6,8,9] | Play | ... | ||||
5-29A | [0,1,3,6,8] | <1,2,2,1,3,1> | Play | ... | 7-29B | [0,2,3,5, 7,8,9] | <3,4,4,3,5,2> | 32 | Play | ... | |
5-29B | [0,2,5,7,8] | Play | ... | 7-29A | [0,1,2,4, 6,7,9] | Play | ... | ||||
5-30A | [0,1,4,6,8] | <1,2,1,3,2,1> | Play | ... | 7-30B | [0,1,3,5, 7,8,9] | <3,4,3,5,4,2> | 37 | Play | ... | |
5-30B | [0,2,4,7,8] | Play | ... | 7-30A | [0,1,2,4, 6,8,9] | Play | minor Neapolitan scale | ||||
5-31A | [0,1,3,6,9] | <1,1,4,1,1,2> | Play | ... | 7-31B | [0,1,3,4, 6,8,9] | <3,3,6,3,3,3> | 38 | Play | ... | |
5-31B | [0,2,3,6,9] | Play | ... | 7-31A | [0,2,3,5, 6,8,9] | Play | ... | ||||
5-32A | [0,1,4,6,9] | <1,1,3,2,2,1> | Play | Elektra chord | 7-32B | [0,1,3,5, 6,8,9] | <3,3,5,4,4,2> | 33 | Play | ... | |
5-32B | [0,3,5,8,9] | Play | ... | 7-32A | [0,1,3,4, 6,7,9] | Play | harmonic minor scale | ||||
5-33 | [0,2,4,6,8] | <0,4,0,4,0,2> | Play | ... | 7-33 | [0,1,2,4, 6,8,T] | <2,6,2,6,2,3> | 6 | Play | M Locrian scale | |
5-34 | [0,2,4,6,9] | <0,3,2,2,2,1> | Play | ... | 7-34 | [0,1,3,4, 6,8,T] | <2,5,4,4,4,2> | 9 | Play | half dim. scale | |
5-35 | [0,2,4,7,9] | <0,3,2,1,4,0> | Play | M pentatonic scale | 7-35 | [0,1,3,5, 6,8,T] | <2,5,4,3,6,1> | 7 | Play | diatonic scale | |
5-z36A | [0,1,2,4,7] | <2,2,2,1,2,1> | Play | ... | 7-z36B | [0,2,3,5, 6,7,8] | <4,4,4,3,4,2> | 16 | Play | ... | |
5-z36B | [0,3,5,6,7] | Play | ... | 7-z36A | [0,1,2,3, 5,6,8] | Play | ... | ||||
5-z37 | [0,3,4,5,8] | <2,1,2,3,2,0> | Play | ... | 7-z37 | [0,1,3,4, 5,7,8] | <4,3,4,5,4,1> | 3 | Play | ... | |
5-z38A | [0,1,2,5,8] | <2,1,2,2,2,1> | Play | ... | 7-z38B | [0,1,3,4, 6,7,8] | <4,3,4,4,4,2> | 29 | Play | ... | |
5-z38B | [0,3,6,7,8] | Play | ... | 7-z38A | [0,1,2,4, 5,7,8] | Play | ... | ||||
6-1 | [0,1,2,3,4,5] | <5,4,3,2,1,0> | 4 | Play | chromatic hexachord | ||||||
6-2A | [0,1,2,3,4,6] | <4,4,3,2,1,1> | 19 | Play | ... | ||||||
6-2B | [0,2,3,4,5,6] | Play | ... | ||||||||
6-z3A | [0,1,2,3,5,6] | <4,3,3,2,2,1> | 49 | Play | ... | 6-z36B | [0,3,4,5,6,7] | <4,3,3,2,2,1> | 50 | Play | ... |
6-z3B | [0,1,3,4,5,6] | Play | ... | 6-z36A | [0,1,2,3,4,7] | Play | ... | ||||
6-z4 | [0,1,2,4,5,6] | <4,3,2,3,2,1> | 24 | Play | ... | 6-z37 | [0,1,2,3,4,8] | <4,3,2,3,2,1> | 23 | Play | ... |
6-5A | [0,1,2,3,6,7] | <4,2,2,2,3,2> | 16 | Play | ... | ||||||
6-5B | [0,1,4,5,6,7] | Play | ... | ||||||||
6-z6 | [0,1,2,5,6,7] | <4,2,1,2,4,2> | 33 | Play | ... | 6-z38 | [0,1,2,3,7,8] | <4,2,1,2,4,2> | 34 | Play | ... |
6-7 | [0,1,2,6,7,8] | <4,2,0,2,4,3> | 7 | Play | ... | ||||||
6-8 | [0,2,3,4,5,7] | <3,4,3,2,3,0> | 5 | Play | ... | ||||||
6-9A | [0,1,2,3,5,7] | <3,4,2,2,3,1> | 20 | Play | ... | ||||||
6-9B | [0,2,4,5,6,7] | Play | ... | ||||||||
6-z10A | [0,1,3,4,5,7] | <3,3,3,3,2,1> | 42 | Play | ... | 6-z39B | [0,3,4,5,6,8] | <3,3,3,3,2,1> | 41 | Play | ... |
6-z10B | [0,2,3,4,6,7] | Play | ... | 6-z39A | [0,2,3,4,5,8] | Play | ... | ||||
6-z11A | [0,1,2,4,5,7] | <3,3,3,2,3,1> | 47 | Play | Sacher hexachord | 6-z40B | [0,3,5,6,7,8] | <3,3,3,2,3,1> | 48 | Play | ... |
6-z11B | [0,2,3,5,6,7] | Play | ... | 6-z40A | [0,1,2,3,5,8] | Play | ... | ||||
6-z12A | [0,1,2,4,6,7] | <3,3,2,2,3,2> | 46 | Play | ... | 6-z41B | [0,2,5,6,7,8] | <3,3,2,2,3,2> | 45 | Play | ... |
6-z12B | [0,1,3,5,6,7] | Play | ... | 6-z41A | [0,1,2,3,6,8] | Play | ... | ||||
6-z13 | [0,1,3,4,6,7] | <3,2,4,2,2,2> | 29 | Play | ... | 6-z42 | [0,1,2,3,6,9] | <3,2,4,2,2,2> | 30 | Play | ... |
6-14A | [0,1,3,4,5,8] | <3,2,3,4,3,0> | 3 | Play | ... | ||||||
6-14B | [0,3,4,5,7,8] | Play | ... | ||||||||
6-15A | [0,1,2,4,5,8] | <3,2,3,4,2,1> | 13 | Play | ... | ||||||
6-15B | [0,3,4,6,7,8] | Play | ... | ||||||||
6-16A | [0,1,4,5,6,8] | <3,2,2,4,3,1> | 11 | Play | ... | ||||||
6-16B | [0,2,3,4,7,8] | Play | ... | ||||||||
6-z17A | [0,1,2,4,7,8] | <3,2,2,3,3,2> | 35 | Play | all-trichord hexachord | 6-z43B | [0,2,3,6,7,8] | <3,2,2,3,3,2> | 36 | Play | ... |
6-z17B | [0,1,4,6,7,8] | Play | ... | 6-z43A | [0,1,2,5,6,8] | Play | ... | ||||
6-18A | [0,1,2,5,7,8] | <3,2,2,2,4,2> | 17 | Play | ... | ||||||
6-18B | [0,1,3,6,7,8] | Play | ... | ||||||||
6-z19A | [0,1,3,4,7,8] | <3,1,3,4,3,1> | 37 | Play | ... | 6-z44B | [0,3,4,7,8,9] | <3,1,3,4,3,1> | 38 | Play | ... |
6-z19B | [0,1,4,5,7,8] | Play | ... | 6-z44A | [0,1,2,5,6,9] | Play | Schoenberg hexachord | ||||
6-20 | [0,1,4,5,8,9] | <3,0,3,6,3,0> | 2 | Play | "Ode-to-Napoleon" hexachord | ||||||
6-21A | [0,2,3,4,6,8] | <2,4,2,4,1,2> | 12 | Play | ... | ||||||
6-21B | [0,2,4,5,6,8] | Play | ... | ||||||||
6-22A | [0,1,2,4,6,8] | <2,4,1,4,2,2> | 10 | Play | ... | ||||||
6-22B | [0,2,4,6,7,8] | Play | ... | ||||||||
6-z23 | [0,2,3,5,6,8] | <2,3,4,2,2,2> | 27 | Play | ... | 6-z45 | [0,2,3,4,6,9] | <2,3,4,2,2,2> | 28 | Play | ... |
6-z24A | [0,1,3,4,6,8] | <2,3,3,3,3,1> | 39 | Play | ... | 6-z46B | [0,3,5,7,8,9] | <2,3,3,3,3,1> | 40 | Play | ... |
6-z24B | [0,2,4,5,7,8] | Play | ... | 6-z46A | [0,1,2,4,6,9] | Play | ... | ||||
6-z25A | [0,1,3,5,6,8] | <2,3,3,2,4,1> | 43 | Play | ... | 6-z47B | [0,2,5,7,8,9] | <2,3,3,2,4,1> | 44 | Play | ... |
6-z25B | [0,2,3,5,7,8] | Play | ... | 6-z47A | [0,1,2,4,7,9] | Play | blues scale | ||||
6-z26 | [0,1,3,5,7,8] | <2,3,2,3,4,1> | 26 | Play | ... | 6-z48 | [0,1,2,5,7,9] | <2,3,2,3,4,1> | 25 | Play | ... |
6-27A | [0,1,3,4,6,9] | <2,2,5,2,2,2> | 14 | Play | ... | ||||||
6-27B | [0,3,5,6,8,9] | Play | ... | ||||||||
6-z28 | [0,1,3,5,6,9] | <2,2,4,3,2,2> | 21 | Play | ... | 6-z49 | [0,1,3,4,7,9] | <2,2,4,3,2,2> | 22 | Play | ... |
6-z29 | [0,2,3,6,7,9][lower-alpha 6] | <2,2,4,2,3,2> | 32 | Play | Bridge chord | 6-z50 | [0,1,4,6,7,9] | <2,2,4,2,3,2> | 31 | Play | ... |
6-30A | [0,1,3,6,7,9] | <2,2,4,2,2,3> | 15 | Play | Petrushka chord | ||||||
6-30B | [0,2,3,6,8,9] | Play | ... | ||||||||
6-31A | [0,1,4,5,7,9][lower-alpha 7] | <2,2,3,4,3,1> | 8 | Play | ... | ||||||
6-31B | [0,2,4,5,8,9][lower-alpha 8] | Play | ... | ||||||||
6-32 | [0,2,4,5,7,9] | <1,4,3,2,5,0> | 6 | Play | diatonic hexachord | ||||||
6-33A | [0,2,3,5,7,9] | <1,4,3,2,4,1> | 18 | Play | ... | ||||||
6-33B | [0,2,4,6,7,9] | Play | ... | ||||||||
6-34A | [0,1,3,5,7,9] | <1,4,2,4,2,2> | 9 | Play | mystic chord | ||||||
6-34B | [0,2,4,6,8,9] | Play | ... | ||||||||
6-35 | [0,2,4,6,8,T] | <0,6,0,6,0,3> | 1 | Play | whole tone scale |
See also
- Interval vector
- List of chords
- Z-relation
Notes
- ↑ Forte and Rahn both list prime forms as the most left-packed possible version of a set. However, Forte packs from the left and Rahn packs from the right ("making the small numbers smaller," versus making, "the larger numbers ... smaller"[2]).
- ↑ Forte 8-26: [0,1,2,4,5,7,9,T]
- ↑ Forte 7-z18A: [0,1,2,3,5,8,9]
- ↑ Forte 5-20A: [0,1,3,7,8]
- ↑ Forte 7-20A: [0,1,2,4,7,8,9]
- ↑ Forte 6-z29: [0,1,3,6,8,9]
- ↑ Forte 6-31A: [0,1,3,5,8,9]
- ↑ Forte 6-31B: [0,1,4,6,8,9]
References
- ↑ Forte, Allen (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
- ↑ Nelson, Paul (2004). "Two Algorithms for Computing the Prime Form", ComposerTools.com.
- ↑ Rahn, John (1980). Basic Atonal Theory. New York: Longman. ISBN 978-0028731605.
- ↑ Straus, Joseph N. (1990). Introduction to Post-Tonal Theory. Prentice-Hall. ISBN 9780131898905.
- ↑ Schiff, David (1983/1998). The Music of Elliott Carter.
- ↑ Carter, Elliott (2002). The Harmony Book, "Appendix 1". ISBN 9780825845949.
External links
- Solomon, Larry (2005). "The Table of Pitch Class Sets", SolomonsMusic.net.
- Tucker, Gary (2001). "Table of pc set classes", A Brief Introduction to Pitch-Class Set Analysis.
- Nelson, Paul (2004). "Table of Prime Forms", ComposerTools.com.
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