# 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,[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]

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]
[b]
<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]
[c]
<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][d] <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]
[e]
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][f] <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][g] <2,2,3,4,3,1> 8 Play ...
6-31B [0,2,4,5,8,9][h] 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

## Notes

1. ^ 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]).
2. ^ Forte 8-26: [0,1,2,4,5,7,9,T]
3. ^ Forte 7-z18A: [0,1,2,3,5,8,9]
4. ^ Forte 5-20A: [0,1,3,7,8]
5. ^ Forte 7-20A: [0,1,2,4,7,8,9]
6. ^ Forte 6-z29: [0,1,3,6,8,9]
7. ^ Forte 6-31A: [0,1,3,5,8,9]
8. ^ Forte 6-31B: [0,1,4,6,8,9]

## References

1. ^ Forte, Allen (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
2. ^ Nelson, Paul (2004). "Two Algorithms for Computing the Prime Form", ComposerTools.com.
3. ^ Rahn, John (1980). Basic Atonal Theory. New York: Longman. ISBN 978-0028731605.
4. ^ Straus, Joseph N. (1990). Introduction to Post-Tonal Theory. Prentice-Hall. ISBN 9780131898905.
5. ^ Schiff, David (1983/1998). The Music of Elliott Carter.
6. ^ Carter, Elliott (2002). The Harmony Book, "Appendix 1". ISBN 9780825845949.