List of set classes
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,[a] 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] Donald Martino had produced tables of hexachords, tetrachords, trichords, and pentachords for combinatoriality in his article, "The Source Set and its Aggregate Formations" (1961).[7]
| Forte no. |
Prime form | Interval vector |
Carter 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> | aggregate | ||||
| 1-1 | [0] | <0,0,0,0,0,0> | PU, P8 | 11-1 | [0,1,2,3,4,5, 6,7,8,9,T] |
<T,T,T,T,T,5> | ... | ||||
| 2-1 | [0,1] | <1,0,0,0,0,0> | 1 | m2, M7 | 10-1 | [0,1,2,3,4, 5,6,7,8,9] |
<9,8,8,8,8,4> | ... | |||
| 2-2 | [0,2] | <0,1,0,0,0,0> | 2 | M2, m7 | 10-2 | [0,1,2,3,4, 5,6,7,8,T] |
<8,9,8,8,8,4> | ... | |||
| 2-3 | [0,3] | <0,0,1,0,0,0> | 3 | m3, M6 | 10-3 | [0,1,2,3,4, 5,6,7,9,T] |
<8,8,9,8,8,4> | ... | |||
| 2-4 | [0,4] | <0,0,0,1,0,0> | 4 | M3, m6 | 10-4 | [0,1,2,3,4, 5,6,8,9,T] |
<8,8,8,9,8,4> | ... | |||
| 2-5 | [0,5] | <0,0,0,0,1,0> | 5 | P4, P5 | 10-5 | [0,1,2,3,4, 5,7,8,9,T] |
<8,8,8,8,9,4> | ... | |||
| 2-6 | [0,6] | <0,0,0,0,0,1> | 6 | A4, d5 | 10-6 | [0,1,2,3,4, 6,7,8,9,T] |
<8,8,8,8,8,5> | ... | |||
| 3-1 | [0,1,2] | <2,1,0,0,0,0> | 4 | ... | 9-1 | [0,1,2,3,4, 5,6,7,8] |
<8,7,6,6,6,3> | ... | |||
| 3-2A | [0,1,3] | <1,1,1,0,0,0> | 12 | ... | 9-2A | [0,1,2,3,4, 5,6,7,9] |
<7,7,7,6,6,3> | ... | |||
| 3-2B | [0,2,3] | ... | 9-2B | [0,2,3,4,5, 6,7,8,9] |
... | ||||||
| 3-3A | [0,1,4] | <1,0,1,1,0,0> | 11 | ... | 9-3B | [0,1,3,4, 5,6,7,8,9] |
<7,6,7,7,6,3> | ... | |||
| 3-3B | [0,3,4] | ... | 9-3A | [0,1,2,3,4, 5,6,8,9] |
... | ||||||
| 3-4A | [0,1,5] | <1,0,0,1,1,0> | 9 | ... | 9-4B | [0,1,2,4,5, 6,7,8,9] |
<7,6,6,7,7,3> | ... | |||
| 3-4B | [0,4,5] | ... | 9-4A | [0,1,2,3,4, 5,7,8,9] |
... | ||||||
| 3-5A | [0,1,6] | <1,0,0,0,1,1> | 7 | Viennese trichord | 9-5B | [0,1,2,3,5, 6,7,8,9] |
<7,6,6,6,7,4> | ... | |||
| 3-5B | [0,5,6] | ... | 9-5A | [0,1,2,3,4, 6,7,8,9] |
... | ||||||
| 3-6 | [0,2,4] | <0,2,0,1,0,0> | 3 | ... | 9-6 | [0,1,2,3,4, 5,6,8,T] |
<6,8,6,7,6,3> | ... | |||
| 3-7A | [0,2,5] | <0,1,1,0,1,0> | 10 | Blues trichord (min. pentatonic subset)[8] | 9-7B | [0,1,2,3,4, 5,7,9,T] |
<6,7,7,6,7,3> | ... | |||
| 3-7B | [0,3,5] | ... | 9-7A | [0,1,2,3,4, 5,7,8,T] |
... | ||||||
| 3-8A | [0,2,6] | <0,1,0,1,0,1> | 8 | It6 | 9-8B | [0,1,2,3,4, 6,8,9,T] |
<6,7,6,7,6,4> | ... | |||
| 3-8B | [0,4,6] | ... | 9-8A | [0,1,2,3,4, 6,7,8,T] |
... | ||||||
| 3-9 | [0,2,7] | <0,1,0,0,2,0> | 5 | sus. chord | 9-9 | [0,1,2,3,5, 6,7,8,T] |
<6,7,6,6,8,3> | blues scale | |||
| 3-10 | [0,3,6] | <0,0,2,0,0,1> | 2 | dim. chord | 9-10 | [0,1,2,3,4, 6,7,9,T] |
<6,6,8,6,6,4> | ... | |||
| 3-11A | [0,3,7] | <0,0,1,1,1,0> | 6 | minor chord | 9-11B | [0,1,2,3,5, 6,8,9,T] |
<6,6,7,7,7,3> | ... | |||
| 3-11B | [0,4,7] | major chord | 9-11A | [0,1,2,3,5, 6,7,9,T] |
... | ||||||
| 3-12 | [0,4,8] | <0,0,0,3,0,0> | 1 | Aug. chord | 9-12 | [0,1,2,4,5, 6,8,9,T] |
<6,6,6,9,6,3> | ... | |||
| 4-1 | [0,1,2,3] | <3,2,1,0,0,0> | 1 | ... | 8-1 | [0,1,2,3, 4,5,6,7] |
<7,6,5,4,4,2> | ... | |||
| 4-2A | [0,1,2,4] | <2,2,1,1,0,0> | 17 | ... | 8-2B | [0,2,3,4, 5,6,7,8] |
<6,6,5,5,4,2> | ... | |||
| 4-2B | [0,2,3,4] | ... | 8-2A | [0,1,2,3, 4,5,6,8] |
... | ||||||
| 4-3 | [0,1,3,4] | <2,1,2,1,0,0> | 9 | ... | 8-3 | [0,1,2,3, 4,5,6,9] |
<6,5,6,5,4,2> | ... | |||
| 4-4A | [0,1,2,5] | <2,1,1,1,1,0> | 20 | ... | 8-4B | [0,1,3,4, 5,6,7,8] |
<6,5,5,5,5,2> | ... | |||
| 4-4B | [0,3,4,5] | ... | 8-4A | [0,1,2,3, 4,5,7,8] |
... | ||||||
| 4-5A | [0,1,2,6] | <2,1,0,1,1,1> | 22 | ... | 8-5B | [0,1,2,4, 5,6,7,8] |
<6,5,4,5,5,3> | ... | |||
| 4-5B | [0,4,5,6] | ... | 8-5A | [0,1,2,3, 4,6,7,8] |
... | ||||||
| 4-6 | [0,1,2,7] | <2,1,0,0,2,1> | 6 | dream chord | 8-6 | [0,1,2,3, 5,6,7,8] |
<6,5,4,4,6,3> | ... | |||
| 4-7 | [0,1,4,5] | <2,0,1,2,1,0> | 8 | ... | 8-7 | [0,1,2,3, 4,5,8,9] |
<6,4,5,6,5,2> | ... | |||
| 4-8 | [0,1,5,6] | <2,0,0,1,2,1> | 10 | ... | 8-8 | [0,1,2,3, 4,7,8,9] |
<6,4,4,5,6,3> | ... | |||
| 4-9 | [0,1,6,7] | <2,0,0,0,2,2> | 2 | distance model | 8-9 | [0,1,2,3, 6,7,8,9] |
<6,4,4,4,6,4> | ... | |||
| 4-10 | [0,2,3,5] | <1,2,2,0,1,0> | 3 | ... | 8-10 | [0,2,3,4, 5,6,7,9] |
<5,6,6,4,5,2> | ... | |||
| 4-11A | [0,1,3,5] | <1,2,1,1,1,0> | 26 | ... | 8-11B | [0,2,4,5, 6,7,8,9] |
<5,6,5,5,5,2> | ... | |||
| 4-11B | [0,2,4,5] | ... | 8-11A | [0,1,2,3, 4,5,7,9] |
... | ||||||
| 4-12A | [0,2,3,6] | <1,1,2,1,0,1> | 28 | ... | 8-12A | [0,1,3,4, 5,6,7,9] |
<5,5,6,5,4,3> | ... | |||
| 4-12B | [0,3,4,6] | ... | 8-12B | [0,2,3,4, 5,6,8,9] |
... | ||||||
| 4-13A | [0,1,3,6] | <1,1,2,0,1,1> | 7 | ... | 8-13B | [0,2,3,5, 6,7,8,9] |
<5,5,6,4,5,3> | ... | |||
| 4-13B | [0,3,5,6] | ... | 8-13A | [0,1,2,3, 4,6,7,9] |
... | ||||||
| 4-14A | [0,2,3,7] | <1,1,1,1,2,0> | 25 | ... | 8-14A | [0,1,2,4, 5,6,7,9] |
<5,5,5,5,6,2> | ... | |||
| 4-14B | [0,4,5,7] | ... | 8-14B | [0,2,3,4, 5,7,8,9] |
... | ||||||
| 4-z15A | [0,1,4,6] | <1,1,1,1,1,1> | 18 | all-interval tetrachord | 8-z15B | [0,1,3,5, 6,7,8,9] |
<5,5,5,5,5,3> | ... | |||
| 4-z15B | [0,2,5,6] | ... | 8-z15A | [0,1,2,3, 4,6,8,9] |
... | ||||||
| 4-16A | [0,1,5,7] | <1,1,0,1,2,1> | 19 | ... | 8-16B | [0,1,2,4, 6,7,8,9] |
<5,5,4,5,6,3> | ... | |||
| 4-16B | [0,2,6,7] | ... | 8-16A | [0,1,2,3, 5,7,8,9] |
... | ||||||
| 4-17 | [0,3,4,7] | <1,0,2,2,1,0> | 13 | alpha chord | 8-17 | [0,1,3,4, 5,6,8,9] |
<5,4,6,6,5,2> | ... | |||
| 4-18A | [0,1,4,7] | <1,0,2,1,1,1> | 21 | dim. M7 chord | 8-18B | [0,1,3,4, 6,7,8,9] |
<5,4,6,5,5,3> | ... | |||
| 4-18B | [0,3,6,7] | ... | 8-18A | [0,1,2,3, 5,6,8,9] |
... | ||||||
| 4-19A | [0,1,4,8] | <1,0,1,3,1,0> | 24 | Mm7 chord | 8-19B | [0,1,3,4, 5,7,8,9] |
<5,4,5,7,5,2> | ... | |||
| 4-19B | [0,3,4,8] | ... | 8-19A | [0,1,2,4, 5,6,8,9] |
... | ||||||
| 4-20 | [0,1,5,8] | <1,0,1,2,2,0> | 15 | M7 chord | 8-20 | [0,1,2,4, 5,7,8,9] |
<5,4,5,6,6,2> | ... | |||
| 4-21 | [0,2,4,6] | <0,3,0,2,0,1> | 11 | ... | 8-21 | [0,1,2,3, 4,6,8,T] |
<4,7,4,6,4,3> | ... | |||
| 4-22A | [0,2,4,7] | <0,2,1,1,2,0> | 27 | mu chord | 8-22B | [0,1,2,3, 5,7,9,T] |
<4,6,5,5,6,2> | ... | |||
| 4-22B | [0,3,5,7] | ... | 8-22A | [0,1,2,3, 5,6,8,T] |
... | ||||||
| 4-23 | [0,2,5,7] | <0,2,1,0,3,0> | 4 | quartal chord | 8-23 | [0,1,2,3, 5,7,8,T] |
<4,6,5,4,7,2> | bebop scale | |||
| 4-24 | [0,2,4,8] | <0,2,0,3,0,1> | 16 | A7 chord | 8-24 | [0,1,2,4, 5,6,8,T] |
<4,6,4,7,4,3> | ... | |||
| 4-25 | [0,2,6,8] | <0,2,0,2,0,2> | 12 | Fr6 | 8-25 | [0,1,2,4, 6,7,8,T] |
<4,6,4,6,4,4> | ... | |||
| 4-26 | [0,3,5,8] | <0,1,2,1,2,0> | 14 | minor seventh chord | 8-26 | [0,1,3,4, 5,7,8,T][b] |
<4,5,6,5,6,2> | ... | |||
| 4-27A | [0,2,5,8] | <0,1,2,1,1,1> | 29 | dominant 7th chord | 8-27B | [0,1,2,4, 6,7,9,T] |
<4,5,6,5,5,3> | ... | |||
| 4-27B | [0,3,6,8] | ... | 8-27A | [0,1,2,4, 5,7,8,T] |
... | ||||||
| 4-28 | [0,3,6,9] | <0,0,4,0,0,2> | 5 | dim. 7th chord | 8-28 | [0,1,3,4, 6,7,9,T] |
<4,4,8,4,4,4> | octatonic scale | |||
| 4-z29A | [0,1,3,7] | <1,1,1,1,1,1> | 23 | all-interval tetrachord | 8-z29B | [0,2,3,4, 6,7,8,9] |
<5,5,5,5,5,3> | ... | |||
| 4-z29B | [0,4,6,7] | ... | 8-z29A | [0,1,2,3, 5,6,7,9] |
... | ||||||
| 5-1 | [0,1,2,3,4] | <4,3,2,1,0,0> | ... | 7-1 | [0,1,2,3, 4,5,6] |
<6,5,4,3,2,1> | 1 | ... | |||
| 5-2A | [0,1,2,3,5] | <3,3,2,1,1,0> | ... | 7-2B | [0,2,3,4, 5,6,7] |
<5,5,4,3,3,1> | 11 | ... | |||
| 5-2B | [0,2,3,4,5] | ... | 7-2A | [0,1,2,3, 4,5,7] |
... | ||||||
| 5-3A | [0,1,2,4,5] | <3,2,2,2,1,0> | ... | 7-3B | [0,3,4,5, 6,7,8] |
<5,4,4,4,3,1> | 14 | ... | |||
| 5-3B | [0,1,3,4,5] | ... | 7-3A | [0,1,2,3, 4,5,8] |
... | ||||||
| 5-4A | [0,1,2,3,6] | <3,2,2,1,1,1> | ... | 7-4B | [0,1,3,4, 5,6,7] |
<5,4,4,3,3,2> | 12 | ... | |||
| 5-4B | [0,3,4,5,6] | ... | 7-4A | [0,1,2,3, 4,6,7] |
... | ||||||
| 5-5A | [0,1,2,3,7] | <3,2,1,1,2,1> | ... | 7-5B | [0,1,2,4, 5,6,7] |
<5,4,3,3,4,2> | 13 | ... | |||
| 5-5B | [0,4,5,6,7] | ... | 7-5A | [0,1,2,3, 5,6,7] |
... | ||||||
| 5-6A | [0,1,2,5,6] | <3,1,1,2,2,1> | ... | 7-6B | [0,1,4,5, 6,7,8] |
<5,3,3,4,4,2> | 27 | ... | |||
| 5-6B | [0,1,4,5,6] | ... | 7-6A | [0,1,2,3, 4,7,8] |
... | ||||||
| 5-7A | [0,1,2,6,7] | <3,1,0,1,3,2> | ... | 7-7B | [0,1,2,5, 6,7,8] |
<5,3,2,3,5,3> | 30 | ... | |||
| 5-7B | [0,1,5,6,7] | ... | 7-7A | [0,1,2,3, 6,7,8] |
... | ||||||
| 5-8 | [0,2,3,4,6] | <2,3,2,2,0,1> | ... | 7-8 | [0,2,3,4, 5,6,8] |
<4,5,4,4,2,2> | 2 | ... | |||
| 5-9A | [0,1,2,4,6] | <2,3,1,2,1,1> | ... | 7-9B | [0,2,4,5, 6,7,8] |
<4,5,3,4,3,2> | 15 | ... | |||
| 5-9B | [0,2,4,5,6] | ... | 7-9A | [0,1,2,3, 4,6,8] |
... | ||||||
| 5-10A | [0,1,3,4,6] | <2,2,3,1,1,1> | ... | 7-10B | [0,2,3,4, 5,6,9] |
<4,4,5,3,3,2> | 19 | ... | |||
| 5-10B | [0,2,3,5,6] | ... | 7-10A | [0,1,2,3, 4,6,9] |
... | ||||||
| 5-11A | [0,2,3,4,7] | <2,2,2,2,2,0> | ... | 7-11B | [0,2,3,4, 5,7,8] |
<4,4,4,4,4,1> | 18 | ... | |||
| 5-11B | [0,3,4,5,7] | ... | 7-11A | [0,1,3,4, 5,6,8] |
... | ||||||
| 5-z12 | [0,1,3,5,6] | <2,2,2,1,2,1> | ... | 7-z12 | [0,1,2,3, 4,7,9] |
<4,4,4,3,4,2> | 5 | ... | |||
| 5-13A | [0,1,2,4,8] | <2,2,1,3,1,1> | ... | 7-13B | [0,2,3,4, 6,7,8] |
<4,4,3,5,3,2> | 17 | ... | |||
| 5-13B | [0,2,3,4,8] | ... | 7-13A | [0,1,2,4, 5,6,8] |
... | ||||||
| 5-14A | [0,1,2,5,7] | <2,2,1,1,3,1> | ... | 7-14B | [0,1,3,5, 6,7,8] |
<4,4,3,3,5,2> | 28 | ... | |||
| 5-14B | [0,2,5,6,7] | ... | 7-14A | [0,1,2,3, 5,7,8] |
... | ||||||
| 5-15 | [0,1,2,6,8] | <2,2,0,2,2,2> | ... | 7-15 | [0,1,2,4, 6,7,8] |
<4,4,2,4,4,3> | 4 | ... | |||
| 5-16A | [0,1,3,4,7] | <2,1,3,2,1,1> | ... | 7-16B | [0,1,3,4, 5,6,9] |
<4,3,5,4,3,2> | 20 | ... | |||
| 5-16B | [0,3,4,6,7] | ... | 7-16A | [0,1,2,3, 5,6,9] |
... | ||||||
| 5-z17 | [0,1,3,4,8] | <2,1,2,3,2,0> | Farben chord | 7-z17 | [0,1,2,4, 5,6,9] |
<4,3,4,5,4,1> | 10 | ... | |||
| 5-z18A | [0,1,4,5,7] | <2,1,2,2,2,1> | ... | 7-z18A | [0,1,4,5, 6,7,9][c] |
<4,3,4,4,4,2> | 35 | ... | |||
| 5-z18B | [0,2,3,6,7] | ... | 7-z18B | [0,1,4,6, 7,8,9] |
... | ||||||
| 5-19A | [0,1,3,6,7] | <2,1,2,1,2,2> | ... | 7-19B | [0,1,2,3, 6,8,9] |
<4,3,4,3,4,3> | 31 | ... | |||
| 5-19B | [0,1,4,6,7] | ... | 7-19A | [0,1,2,3, 6,7,9] |
... | ||||||
| 5-20A | [0,1,5,6,8][d] | <2,1,1,2,3,1> | ... | 7-20B | [0,1,2,5, 7,8,9] |
<4,3,3,4,5,2> | 34 | ... | |||
| 5-20B | [0,2,3,7,8] | ... | 7-20A | [0,1,2,5, 6,7,9][e] |
Persian scale | ||||||
| 5-21A | [0,1,4,5,8] | <2,0,2,4,2,0> | ... | 7-21B | [0,1,3,4, 5,8,9] |
<4,2,4,6,4,1> | 21 | ... | |||
| 5-21B | [0,3,4,7,8] | ... | 7-21A | [0,1,2,4, 5,8,9] |
... | ||||||
| 5-22 | [0,1,4,7,8] | <2,0,2,3,2,1> | ... | 7-22 | [0,1,2,5, 6,8,9] |
<4,2,4,5,4,2> | 8 | double harmonic scale | |||
| 5-23A | [0,2,3,5,7] | <1,3,2,1,3,0> | ... | 7-23B | [0,2,4,5, 6,7,9] |
<3,5,4,3,5,1> | 25 | ... | |||
| 5-23B | [0,2,4,5,7] | ... | 7-23A | [0,2,3,4, 5,7,9] |
... | ||||||
| 5-24A | [0,1,3,5,7] | <1,3,1,2,2,1> | ... | 7-24B | [0,2,4,6, 7,8,9] |
<3,5,3,4,4,2> | 22 | ... | |||
| 5-24B | [0,2,4,6,7] | ... | 7-24A | [0,1,2,3, 5,7,9] |
enigmatic scale | ||||||
| 5-25A | [0,2,3,5,8] | <1,2,3,1,2,1> | ... | 7-25B | [0,2,3,5, 6,7,9] |
<3,4,5,3,4,2> | 24 | ... | |||
| 5-25B | [0,3,5,6,8] | ... | 7-25A | [0,2,3,4, 6,7,9] |
... | ||||||
| 5-26A | [0,2,4,5,8] | <1,2,2,3,1,1> | ... | 7-26A | [0,1,3,4, 5,7,9] |
<3,4,4,5,3,2> | 26 | ... | |||
| 5-26B | [0,3,4,6,8] | ... | 7-26B | [0,2,4,5, 6,8,9] |
... | ||||||
| 5-27A | [0,1,3,5,8] | <1,2,2,2,3,0> | ... | 7-27B | [0,2,4,5, 7,8,9] |
<3,4,4,4,5,1> | 23 | ... | |||
| 5-27B | [0,3,5,7,8] | ... | 7-27A | [0,1,2,4, 5,7,9] |
... | ||||||
| 5-28A | [0,2,3,6,8] | <1,2,2,2,1,2> | ... | 7-28A | [0,1,3,5, 6,7,9] |
<3,4,4,4,3,3> | 36 | ... | |||
| 5-28B | [0,2,5,6,8] | ... | 7-28B | [0,2,3,4, 6,8,9] |
... | ||||||
| 5-29A | [0,1,3,6,8] | <1,2,2,1,3,1> | ... | 7-29B | [0,2,3,5, 7,8,9] |
<3,4,4,3,5,2> | 32 | ... | |||
| 5-29B | [0,2,5,7,8] | ... | 7-29A | [0,1,2,4, 6,7,9] |
... | ||||||
| 5-30A | [0,1,4,6,8] | <1,2,1,3,2,1> | ... | 7-30B | [0,1,3,5, 7,8,9] |
<3,4,3,5,4,2> | 37 | ... | |||
| 5-30B | [0,2,4,7,8] | ... | 7-30A | [0,1,2,4, 6,8,9] |
minor Neapolitan scale | ||||||
| 5-31A | [0,1,3,6,9] | <1,1,4,1,1,2> | Dominant minor ninth chord | 7-31B | [0,1,3,4, 6,8,9] |
<3,3,6,3,3,3> | 38 | ... | |||
| 5-31B | [0,2,3,6,9] | beta chord | 7-31A | [0,2,3,5, 6,8,9] |
... | ||||||
| 5-32A | [0,1,4,6,9] | <1,1,3,2,2,1> | Elektra chord, gamma chord | 7-32B | [0,1,3,5, 6,8,9] |
<3,3,5,4,4,2> | 33 | ... | |||
| 5-32B | [0,3,5,8,9] | ... | 7-32A | [0,1,3,4, 6,7,9] |
harmonic minor scale | ||||||
| 5-33 | [0,2,4,6,8] | <0,4,0,4,0,2> | ... | 7-33 | [0,1,2,4, 6,8,T] |
<2,6,2,6,2,3> | 6 | M Locrian scale | |||
| 5-34 | [0,2,4,6,9] | <0,3,2,2,2,1> | Dominant ninth chord | 7-34 | [0,1,3,4, 6,8,T] |
<2,5,4,4,4,2> | 9 | half dim. scale | |||
| 5-35 | [0,2,4,7,9] | <0,3,2,1,4,0> | M pentatonic scale | 7-35 | [0,1,3,5, 6,8,T] |
<2,5,4,3,6,1> | 7 | diatonic scale | |||
| 5-z36A | [0,1,2,4,7] | <2,2,2,1,2,1> | ... | 7-z36B | [0,2,3,5, 6,7,8] |
<4,4,4,3,4,2> | 16 | ... | |||
| 5-z36B | [0,3,5,6,7] | ... | 7-z36A | [0,1,2,3, 5,6,8] |
... | ||||||
| 5-z37 | [0,3,4,5,8] | <2,1,2,3,2,0> | ... | 7-z37 | [0,1,3,4, 5,7,8] |
<4,3,4,5,4,1> | 3 | ... | |||
| 5-z38A | [0,1,2,5,8] | <2,1,2,2,2,1> | ... | 7-z38B | [0,1,3,4, 6,7,8] |
<4,3,4,4,4,2> | 29 | ... | |||
| 5-z38B | [0,3,6,7,8] | ... | 7-z38A | [0,1,2,4, 5,7,8] |
... | ||||||
| 6-1 | [0,1,2,3,4,5] | <5,4,3,2,1,0> | 4 | chromatic hexachord | |||||||
| 6-2A | [0,1,2,3,4,6] | <4,4,3,2,1,1> | 19 | ... | |||||||
| 6-2B | [0,2,3,4,5,6] | ... | |||||||||
| 6-z3A | [0,1,2,3,5,6] | <4,3,3,2,2,1> | 49 | ... | 6-z36B | [0,3,4,5,6,7] | <4,3,3,2,2,1> | 50 | ... | ||
| 6-z3B | [0,1,3,4,5,6] | ... | 6-z36A | [0,1,2,3,4,7] | ... | ||||||
| 6-z4 | [0,1,2,4,5,6] | <4,3,2,3,2,1> | 24 | ... | 6-z37 | [0,1,2,3,4,8] | <4,3,2,3,2,1> | 23 | ... | ||
| 6-5A | [0,1,2,3,6,7] | <4,2,2,2,3,2> | 16 | ... | |||||||
| 6-5B | [0,1,4,5,6,7] | ... | |||||||||
| 6-z6 | [0,1,2,5,6,7] | <4,2,1,2,4,2> | 33 | ... | 6-z38 | [0,1,2,3,7,8] | <4,2,1,2,4,2> | 34 | ... | ||
| 6-7 | [0,1,2,6,7,8] | <4,2,0,2,4,3> | 7 | ... | |||||||
| 6-8 | [0,2,3,4,5,7] | <3,4,3,2,3,0> | 5 | ... | |||||||
| 6-9A | [0,1,2,3,5,7] | <3,4,2,2,3,1> | 20 | ... | |||||||
| 6-9B | [0,2,4,5,6,7] | ... | |||||||||
| 6-z10A | [0,1,3,4,5,7] | <3,3,3,3,2,1> | 42 | ... | 6-z39B | [0,3,4,5,6,8] | <3,3,3,3,2,1> | 41 | ... | ||
| 6-z10B | [0,2,3,4,6,7] | ... | 6-z39A | [0,2,3,4,5,8] | ... | ||||||
| 6-z11A | [0,1,2,4,5,7] | <3,3,3,2,3,1> | 47 | Sacher hexachord | 6-z40B | [0,3,5,6,7,8] | <3,3,3,2,3,1> | 48 | ... | ||
| 6-z11B | [0,2,3,5,6,7] | ... | 6-z40A | [0,1,2,3,5,8] | ... | ||||||
| 6-z12A | [0,1,2,4,6,7] | <3,3,2,2,3,2> | 46 | ... | 6-z41B | [0,2,5,6,7,8] | <3,3,2,2,3,2> | 45 | ... | ||
| 6-z12B | [0,1,3,5,6,7] | ... | 6-z41A | [0,1,2,3,6,8] | ... | ||||||
| 6-z13 | [0,1,3,4,6,7] | <3,2,4,2,2,2> | 29 | ... | 6-z42 | [0,1,2,3,6,9] | <3,2,4,2,2,2> | 30 | ... | ||
| 6-14A | [0,1,3,4,5,8] | <3,2,3,4,3,0> | 3 | ... | |||||||
| 6-14B | [0,3,4,5,7,8] | ... | |||||||||
| 6-15A | [0,1,2,4,5,8] | <3,2,3,4,2,1> | 13 | ... | |||||||
| 6-15B | [0,3,4,6,7,8] | ... | |||||||||
| 6-16A | [0,1,4,5,6,8] | <3,2,2,4,3,1> | 11 | ... | |||||||
| 6-16B | [0,2,3,4,7,8] | ... | |||||||||
| 6-z17A | [0,1,2,4,7,8] | <3,2,2,3,3,2> | 35 | all-trichord hexachord | 6-z43B | [0,2,3,6,7,8] | <3,2,2,3,3,2> | 36 | ... | ||
| 6-z17B | [0,1,4,6,7,8] | ... | 6-z43A | [0,1,2,5,6,8] | ... | ||||||
| 6-18A | [0,1,2,5,7,8] | <3,2,2,2,4,2> | 17 | ... | |||||||
| 6-18B | [0,1,3,6,7,8] | ... | |||||||||
| 6-z19A | [0,1,3,4,7,8] | <3,1,3,4,3,1> | 37 | ... | 6-z44B | [0,3,4,7,8,9] | <3,1,3,4,3,1> | 38 | ... | ||
| 6-z19B | [0,1,4,5,7,8] | ... | 6-z44A | [0,1,2,5,6,9] | Schoenberg hexachord | ||||||
| 6-20 | [0,1,4,5,8,9] | <3,0,3,6,3,0> | 2 | "Ode-to-Napoleon" hexachord | |||||||
| 6-21A | [0,2,3,4,6,8] | <2,4,2,4,1,2> | 12 | ... | |||||||
| 6-21B | [0,2,4,5,6,8] | ... | |||||||||
| 6-22A | [0,1,2,4,6,8] | <2,4,1,4,2,2> | 10 | ... | |||||||
| 6-22B | [0,2,4,6,7,8] | ... | |||||||||
| 6-z23 | [0,2,3,5,6,8] | <2,3,4,2,2,2> | 27 | ... | 6-z45 | [0,2,3,4,6,9] | <2,3,4,2,2,2> | 28 | ... | ||
| 6-z24A | [0,1,3,4,6,8] | <2,3,3,3,3,1> | 39 | ... | 6-z46B | [0,3,5,7,8,9] | <2,3,3,3,3,1> | 40 | ... | ||
| 6-z24B | [0,2,4,5,7,8] | ... | 6-z46A | [0,1,2,4,6,9] | ... | ||||||
| 6-z25A | [0,1,3,5,6,8] | <2,3,3,2,4,1> | 43 | Major eleventh chord | 6-z47B | [0,2,5,7,8,9] | <2,3,3,2,4,1> | 44 | ... | ||
| 6-z25B | [0,2,3,5,7,8] | ... | 6-z47A | [0,1,2,4,7,9] | blues scale | ||||||
| 6-z26 | [0,1,3,5,7,8] | <2,3,2,3,4,1> | 26 | ... | 6-z48 | [0,1,2,5,7,9] | <2,3,2,3,4,1> | 25 | ... | ||
| 6-27A | [0,1,3,4,6,9] | <2,2,5,2,2,2> | 14 | ... | |||||||
| 6-27B | [0,3,5,6,8,9] | ... | |||||||||
| 6-z28 | [0,1,3,5,6,9] | <2,2,4,3,2,2> | 21 | ... | 6-z49 | [0,1,3,4,7,9] | <2,2,4,3,2,2> | 22 | ... | ||
| 6-z29 | [0,2,3,6,7,9][f] | <2,2,4,2,3,2> | 32 | Bridge chord | 6-z50 | [0,1,4,6,7,9] | <2,2,4,2,3,2> | 31 | ... | ||
| 6-30A | [0,1,3,6,7,9] | <2,2,4,2,2,3> | 15 | Petrushka chord | |||||||
| 6-30B | [0,2,3,6,8,9] | ... | |||||||||
| 6-31A | [0,1,4,5,7,9][g] | <2,2,3,4,3,1> | 8 | ... | |||||||
| 6-31B | [0,2,4,5,8,9][h] | ... | |||||||||
| 6-32 | [0,2,4,5,7,9] | <1,4,3,2,5,0> | 6 | diatonic hexachord | |||||||
| 6-33A | [0,2,3,5,7,9] | <1,4,3,2,4,1> | 18 | Dominant eleventh chord | |||||||
| 6-33B | [0,2,4,6,7,9] | ... | |||||||||
| 6-34A | [0,1,3,5,7,9] | <1,4,2,4,2,2> | 9 | mystic chord | |||||||
| 6-34B | [0,2,4,6,8,9] | ... | |||||||||
| 6-35 | [0,2,4,6,8,T] | <0,6,0,6,0,3> | 1 | whole tone scale | |||||||
See also
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.
- ^ Schuijer, Michael (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.97. University of Rochester. ISBN 978-1-58046-270-9.
- ^ Everett, Walter (2008). The Foundations of Rock, p.169. Oxford. ISBN 9780199718702.
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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