List of pitch-class sets

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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> About this soundPlay aggregate
1-1 [0] <0,0,0,0,0,0> About this soundPlay PU, P8 11-1 [0,1,2,3,4,5,
 6,7,8,9,T]
<T,T,T,T,T,5> About this soundPlay ...
2-1 [0,1] <1,0,0,0,0,0> 1 About this soundPlay m2, M7 10-1 [0,1,2,3,4,
 5,6,7,8,9]
<9,8,8,8,8,4> About this soundPlay ...
2-2 [0,2] <0,1,0,0,0,0> 2 About this soundPlay M2, m7 10-2 [0,1,2,3,4,
 5,6,7,8,T]
<8,9,8,8,8,4> About this soundPlay ...
2-3 [0,3] <0,0,1,0,0,0> 3 About this soundPlay m3, M6 10-3 [0,1,2,3,4,
 5,6,7,9,T]
<8,8,9,8,8,4> About this soundPlay ...
2-4 [0,4] <0,0,0,1,0,0> 4 About this soundPlay M3, m6 10-4 [0,1,2,3,4,
 5,6,8,9,T]
<8,8,8,9,8,4> About this soundPlay ...
2-5 [0,5] <0,0,0,0,1,0> 5 About this soundPlay P4, P5 10-5 [0,1,2,3,4,
 5,7,8,9,T]
<8,8,8,8,9,4> About this soundPlay ...
2-6 [0,6] <0,0,0,0,0,1> 6 About this soundPlay A4, d5 10-6 [0,1,2,3,4,
 6,7,8,9,T]
<8,8,8,8,8,5> About this soundPlay ...
3-1 [0,1,2] <2,1,0,0,0,0> 4 About this soundPlay ... 9-1 [0,1,2,3,4,
 5,6,7,8]
<8,7,6,6,6,3> About this soundPlay ...
3-2A [0,1,3] <1,1,1,0,0,0> 12 About this soundPlay ... 9-2A [0,1,2,3,4,
 5,6,7,9]
<7,7,7,6,6,3> About this soundPlay ...
3-2B [0,2,3] About this soundPlay ... 9-2B [0,2,3,4,5,
 6,7,8,9]
About this soundPlay ...
3-3A [0,1,4] <1,0,1,1,0,0> 11 About this soundPlay ... 9-3B [0,1,3,4,
 5,6,7,8,9]
<7,6,7,7,6,3> About this soundPlay ...
3-3B [0,3,4] About this soundPlay ... 9-3A [0,1,2,3,4,
 5,6,8,9]
About this soundPlay ...
3-4A [0,1,5] <1,0,0,1,1,0> 9 About this soundPlay ... 9-4B [0,1,2,4,5,
 6,7,8,9]
<7,6,6,7,7,3> About this soundPlay ...
3-4B [0,4,5] About this soundPlay ... 9-4A [0,1,2,3,4,
 5,7,8,9]
About this soundPlay ...
3-5A [0,1,6] <1,0,0,0,1,1> 7 About this soundPlay Viennese trichord 9-5B [0,1,2,3,5,
 6,7,8,9]
<7,6,6,6,7,4> About this soundPlay ...
3-5B [0,5,6] About this soundPlay ... 9-5A [0,1,2,3,4,
 6,7,8,9]
About this soundPlay ...
3-6 [0,2,4] <0,2,0,1,0,0> 3 About this soundPlay ... 9-6 [0,1,2,3,4,
 5,6,8,T]
<6,8,6,7,6,3> About this soundPlay ...
3-7A [0,2,5] <0,1,1,0,1,0> 10 About this soundPlay ... 9-7B [0,1,2,3,4,
 5,7,9,T]
<6,7,7,6,7,3> About this soundPlay ...
3-7B [0,3,5] About this soundPlay Blues trichord (min. pentatonic subset)[8] 9-7A [0,1,2,3,4,
 5,7,8,T]
About this soundPlay ...
3-8A [0,2,6] <0,1,0,1,0,1> 8 About this soundPlay It6 9-8B [0,1,2,3,4,
 6,8,9,T]
<6,7,6,7,6,4> About this soundPlay ...
3-8B [0,4,6] About this soundPlay ... 9-8A [0,1,2,3,4,
 6,7,8,T]
About this soundPlay ...
3-9 [0,2,7] <0,1,0,0,2,0> 5 About this soundPlay sus. chord 9-9 [0,1,2,3,5,
 6,7,8,T]
<6,7,6,6,8,3> About this soundPlay blues scale
3-10 [0,3,6] <0,0,2,0,0,1> 2 About this soundPlay dim. chord 9-10 [0,1,2,3,4,
 6,7,9,T]
<6,6,8,6,6,4> About this soundPlay ...
3-11A [0,3,7] <0,0,1,1,1,0> 6 About this soundPlay minor chord 9-11B [0,1,2,3,5,
 6,8,9,T]
<6,6,7,7,7,3> About this soundPlay ...
3-11B [0,4,7] About this soundPlay major chord 9-11A [0,1,2,3,5,
 6,7,9,T]
About this soundPlay ...
3-12 [0,4,8] <0,0,0,3,0,0> 1 About this soundPlay Aug. chord 9-12 [0,1,2,4,5,
 6,8,9,T]
<6,6,6,9,6,3> About this soundPlay ...
4-1 [0,1,2,3] <3,2,1,0,0,0> 1 About this soundPlay ... 8-1 [0,1,2,3,
 4,5,6,7]
<7,6,5,4,4,2> About this soundPlay ...
4-2A [0,1,2,4] <2,2,1,1,0,0> 17 About this soundPlay ... 8-2B [0,2,3,4,
 5,6,7,8]
<6,6,5,5,4,2> About this soundPlay ...
4-2B [0,2,3,4] About this soundPlay ... 8-2A [0,1,2,3,
 4,5,6,8]
About this soundPlay ...
4-3 [0,1,3,4] <2,1,2,1,0,0> 9 About this soundPlay ... 8-3 [0,1,2,3,
 4,5,6,9]
<6,5,6,5,4,2> About this soundPlay ...
4-4A [0,1,2,5] <2,1,1,1,1,0> 20 About this soundPlay ... 8-4B [0,1,3,4,
 5,6,7,8]
<6,5,5,5,5,2> About this soundPlay ...
4-4B [0,3,4,5] About this soundPlay ... 8-4A [0,1,2,3,
 4,5,7,8]
About this soundPlay ...
4-5A [0,1,2,6] <2,1,0,1,1,1> 22 About this soundPlay ... 8-5B [0,1,2,4,
 5,6,7,8]
<6,5,4,5,5,3> About this soundPlay ...
4-5B [0,4,5,6] About this soundPlay ... 8-5A [0,1,2,3,
 4,6,7,8]
About this soundPlay ...
4-6 [0,1,2,7] <2,1,0,0,2,1> 6 About this soundPlay dream chord 8-6 [0,1,2,3,
 5,6,7,8]
<6,5,4,4,6,3> About this soundPlay ...
4-7 [0,1,4,5] <2,0,1,2,1,0> 8 About this soundPlay ... 8-7 [0,1,2,3,
 4,5,8,9]
<6,4,5,6,5,2> About this soundPlay ...
4-8 [0,1,5,6] <2,0,0,1,2,1> 10 About this soundPlay ... 8-8 [0,1,2,3,
 4,7,8,9]
<6,4,4,5,6,3> About this soundPlay ...
4-9 [0,1,6,7] <2,0,0,0,2,2> 2 About this soundPlay distance model 8-9 [0,1,2,3,
 6,7,8,9]
<6,4,4,4,6,4> About this soundPlay ...
4-10 [0,2,3,5] <1,2,2,0,1,0> 3 About this soundPlay ... 8-10 [0,2,3,4,
 5,6,7,9]
<5,6,6,4,5,2> About this soundPlay ...
4-11A [0,1,3,5] <1,2,1,1,1,0> 26 About this soundPlay ... 8-11B [0,2,4,5,
 6,7,8,9]
<5,6,5,5,5,2> About this soundPlay ...
4-11B [0,2,4,5] About this soundPlay ... 8-11A [0,1,2,3,
 4,5,7,9]
About this soundPlay ...
4-12A [0,2,3,6] <1,1,2,1,0,1> 28 About this soundPlay ... 8-12A [0,1,3,4,
 5,6,7,9]
<5,5,6,5,4,3> About this soundPlay ...
4-12B [0,3,4,6] About this soundPlay ... 8-12B [0,2,3,4,
 5,6,8,9]
About this soundPlay ...
4-13A [0,1,3,6] <1,1,2,0,1,1> 7 About this soundPlay ... 8-13B [0,2,3,5,
 6,7,8,9]
<5,5,6,4,5,3> About this soundPlay ...
4-13B [0,3,5,6] About this soundPlay ... 8-13A [0,1,2,3,
 4,6,7,9]
About this soundPlay ...
4-14A [0,2,3,7] <1,1,1,1,2,0> 25 About this soundPlay ... 8-14A [0,1,2,4,
 5,6,7,9]
<5,5,5,5,6,2> About this soundPlay ...
4-14B [0,4,5,7] About this soundPlay ... 8-14B [0,2,3,4,
 5,7,8,9]
About this soundPlay ...
4-z15A [0,1,4,6] <1,1,1,1,1,1> 18 About this soundPlay all-interval tetrachord 8-z15B [0,1,3,5,
 6,7,8,9]
<5,5,5,5,5,3> About this soundPlay ...
4-z15B [0,2,5,6] About this soundPlay ... 8-z15A [0,1,2,3,
 4,6,8,9]
About this soundPlay ...
4-16A [0,1,5,7] <1,1,0,1,2,1> 19 About this soundPlay ... 8-16B [0,1,2,4,
 6,7,8,9]
<5,5,4,5,6,3> About this soundPlay ...
4-16B [0,2,6,7] About this soundPlay ... 8-16A [0,1,2,3,
 5,7,8,9]
About this soundPlay ...
4-17 [0,3,4,7] <1,0,2,2,1,0> 13 About this soundPlay alpha chord 8-17 [0,1,3,4,
 5,6,8,9]
<5,4,6,6,5,2> About this soundPlay ...
4-18A [0,1,4,7] <1,0,2,1,1,1> 21 About this soundPlay dim. M7 chord 8-18B [0,1,3,4,
 6,7,8,9]
<5,4,6,5,5,3> About this soundPlay ...
4-18B [0,3,6,7] About this soundPlay ... 8-18A [0,1,2,3,
 5,6,8,9]
About this soundPlay ...
4-19A [0,1,4,8] <1,0,1,3,1,0> 24 About this soundPlay mM7 chord 8-19B [0,1,3,4,
 5,7,8,9]
<5,4,5,7,5,2> About this soundPlay ...
4-19B [0,3,4,8] About this soundPlay ... 8-19A [0,1,2,4,
 5,6,8,9]
About this soundPlay ...
4-20 [0,1,5,8] <1,0,1,2,2,0> 15 About this soundPlay M7 chord 8-20 [0,1,2,4,
 5,7,8,9]
<5,4,5,6,6,2> About this soundPlay ...
4-21 [0,2,4,6] <0,3,0,2,0,1> 11 About this soundPlay ... 8-21 [0,1,2,3,
 4,6,8,T]
<4,7,4,6,4,3> About this soundPlay ...
4-22A [0,2,4,7] <0,2,1,1,2,0> 27 About this soundPlay mu chord 8-22B [0,1,2,3,
 5,7,9,T]
<4,6,5,5,6,2> About this soundPlay ...
4-22B [0,3,5,7] About this soundPlay ... 8-22A [0,1,2,3,
 5,6,8,T]
About this soundPlay ...
4-23 [0,2,5,7] <0,2,1,0,3,0> 4 About this soundPlay quartal chord 8-23 [0,1,2,3,
 5,7,8,T]
<4,6,5,4,7,2> About this soundPlay bebop scale
4-24 [0,2,4,8] <0,2,0,3,0,1> 16 About this soundPlay A7 chord 8-24 [0,1,2,4,
 5,6,8,T]
<4,6,4,7,4,3> About this soundPlay ...
4-25 [0,2,6,8] <0,2,0,2,0,2> 12 About this soundPlay Fr6 8-25 [0,1,2,4,
 6,7,8,T]
<4,6,4,6,4,4> About this soundPlay ...
4-26 [0,3,5,8] <0,1,2,1,2,0> 14 About this soundPlay minor seventh chord 8-26 [0,1,3,4,
 5,7,8,T]
[b]
<4,5,6,5,6,2> About this soundPlay ...
4-27A [0,2,5,8] <0,1,2,1,1,1> 29 About this soundPlay Half-diminished seventh chord 8-27B [0,1,2,4,
 6,7,9,T]
<4,5,6,5,5,3> About this soundPlay ...
4-27B [0,3,6,8] About this soundPlay dominant 7th chord 8-27A [0,1,2,4,
 5,7,8,T]
About this soundPlay ...
4-28 [0,3,6,9] <0,0,4,0,0,2> 5 About this soundPlay dim. 7th chord 8-28 [0,1,3,4,
 6,7,9,T]
<4,4,8,4,4,4> About this soundPlay octatonic scale
4-z29A [0,1,3,7] <1,1,1,1,1,1> 23 About this soundPlay all-interval tetrachord 8-z29B [0,2,3,4,
 6,7,8,9]
<5,5,5,5,5,3> About this soundPlay ...
4-z29B [0,4,6,7] About this soundPlay ... 8-z29A [0,1,2,3,
 5,6,7,9]
About this soundPlay ...
5-1 [0,1,2,3,4] <4,3,2,1,0,0> About this soundPlay ... 7-1 [0,1,2,3,
 4,5,6]
<6,5,4,3,2,1> 1 About this soundPlay ...
5-2A [0,1,2,3,5] <3,3,2,1,1,0> About this soundPlay ... 7-2B [0,2,3,4,
 5,6,7]
<5,5,4,3,3,1> 11 About this soundPlay ...
5-2B [0,2,3,4,5] About this soundPlay ... 7-2A [0,1,2,3,
 4,5,7]
About this soundPlay ...
5-3A [0,1,2,4,5] <3,2,2,2,1,0> About this soundPlay ... 7-3B [0,3,4,5,
 6,7,8]
<5,4,4,4,3,1> 14 About this soundPlay ...
5-3B [0,1,3,4,5] About this soundPlay ... 7-3A [0,1,2,3,
 4,5,8]
About this soundPlay ...
5-4A [0,1,2,3,6] <3,2,2,1,1,1> About this soundPlay ... 7-4B [0,1,3,4,
 5,6,7]
<5,4,4,3,3,2> 12 About this soundPlay ...
5-4B [0,3,4,5,6] About this soundPlay ... 7-4A [0,1,2,3,
 4,6,7]
About this soundPlay ...
5-5A [0,1,2,3,7] <3,2,1,1,2,1> About this soundPlay ... 7-5B [0,1,2,4,
 5,6,7]
<5,4,3,3,4,2> 13 About this soundPlay ...
5-5B [0,4,5,6,7] About this soundPlay ... 7-5A [0,1,2,3,
 5,6,7]
About this soundPlay ...
5-6A [0,1,2,5,6] <3,1,1,2,2,1> About this soundPlay ... 7-6B [0,1,4,5,
 6,7,8]
<5,3,3,4,4,2> 27 About this soundPlay ...
5-6B [0,1,4,5,6] About this soundPlay ... 7-6A [0,1,2,3,
 4,7,8]
About this soundPlay ...
5-7A [0,1,2,6,7] <3,1,0,1,3,2> About this soundPlay ... 7-7B [0,1,2,5,
 6,7,8]
<5,3,2,3,5,3> 30 About this soundPlay ...
5-7B [0,1,5,6,7] About this soundPlay ... 7-7A [0,1,2,3,
 6,7,8]
About this soundPlay ...
5-8 [0,2,3,4,6] <2,3,2,2,0,1> About this soundPlay ... 7-8 [0,2,3,4,
 5,6,8]
<4,5,4,4,2,2> 2 About this soundPlay ...
5-9A [0,1,2,4,6] <2,3,1,2,1,1> About this soundPlay ... 7-9B [0,2,4,5,
 6,7,8]
<4,5,3,4,3,2> 15 About this soundPlay ...
5-9B [0,2,4,5,6] About this soundPlay ... 7-9A [0,1,2,3,
 4,6,8]
About this soundPlay ...
5-10A [0,1,3,4,6] <2,2,3,1,1,1> About this soundPlay ... 7-10B [0,2,3,4,
 5,6,9]
<4,4,5,3,3,2> 19 About this soundPlay ...
5-10B [0,2,3,5,6] About this soundPlay ... 7-10A [0,1,2,3,
 4,6,9]
About this soundPlay ...
5-11A [0,2,3,4,7] <2,2,2,2,2,0> About this soundPlay ... 7-11B [0,2,3,4,
 5,7,8]
<4,4,4,4,4,1> 18 About this soundPlay ...
5-11B [0,3,4,5,7] About this soundPlay ... 7-11A [0,1,3,4,
 5,6,8]
About this soundPlay ...
5-z12 [0,1,3,5,6] <2,2,2,1,2,1> About this soundPlay ... 7-z12 [0,1,2,3,
 4,7,9]
<4,4,4,3,4,2> 5 About this soundPlay ...
5-13A [0,1,2,4,8] <2,2,1,3,1,1> About this soundPlay ... 7-13B [0,2,3,4,
 6,7,8]
<4,4,3,5,3,2> 17 About this soundPlay ...
5-13B [0,2,3,4,8] About this soundPlay ... 7-13A [0,1,2,4,
 5,6,8]
About this soundPlay ...
5-14A [0,1,2,5,7] <2,2,1,1,3,1> About this soundPlay ... 7-14B [0,1,3,5,
 6,7,8]
<4,4,3,3,5,2> 28 About this soundPlay ...
5-14B [0,2,5,6,7] About this soundPlay ... 7-14A [0,1,2,3,
 5,7,8]
About this soundPlay ...
5-15 [0,1,2,6,8] <2,2,0,2,2,2> About this soundPlay ... 7-15 [0,1,2,4,
 6,7,8]
<4,4,2,4,4,3> 4 About this soundPlay ...
5-16A [0,1,3,4,7] <2,1,3,2,1,1> About this soundPlay ... 7-16B [0,1,3,4,
 5,6,9]
<4,3,5,4,3,2> 20 About this soundPlay ...
5-16B [0,3,4,6,7] About this soundPlay ... 7-16A [0,1,2,3,
 5,6,9]
About this soundPlay ...
5-z17 [0,1,3,4,8] <2,1,2,3,2,0> About this soundPlay Farben chord 7-z17 [0,1,2,4,
 5,6,9]
<4,3,4,5,4,1> 10 About this soundPlay ...
5-z18A [0,1,4,5,7] <2,1,2,2,2,1> About this soundPlay ... 7-z18A [0,1,4,5,
 6,7,9]
[c]
<4,3,4,4,4,2> 35 About this soundPlay ...
5-z18B [0,2,3,6,7] About this soundPlay ... 7-z18B [0,1,4,6,
 7,8,9]
About this soundPlay ...
5-19A [0,1,3,6,7] <2,1,2,1,2,2> About this soundPlay ... 7-19B [0,1,2,3,
 6,8,9]
<4,3,4,3,4,3> 31 About this soundPlay ...
5-19B [0,1,4,6,7] About this soundPlay ... 7-19A [0,1,2,3,
 6,7,9]
About this soundPlay ...
5-20A [0,1,5,6,8][d] <2,1,1,2,3,1> About this soundPlay ... 7-20B [0,1,2,5,
 7,8,9]
<4,3,3,4,5,2> 34 About this soundPlay ...
5-20B [0,2,3,7,8] About this soundPlay In scale 7-20A [0,1,2,5,
 6,7,9]
[e]
About this soundPlay Persian scale
5-21A [0,1,4,5,8] <2,0,2,4,2,0> About this soundPlay ... 7-21B [0,1,3,4,
 5,8,9]
<4,2,4,6,4,1> 21 About this soundPlay ...
5-21B [0,3,4,7,8] About this soundPlay ... 7-21A [0,1,2,4,
 5,8,9]
About this soundPlay ...
5-22 [0,1,4,7,8] <2,0,2,3,2,1> About this soundPlay ... 7-22 [0,1,2,5,
 6,8,9]
<4,2,4,5,4,2> 8 About this soundPlay double harmonic scale
5-23A [0,2,3,5,7] <1,3,2,1,3,0> About this soundPlay ... 7-23B [0,2,4,5,
 6,7,9]
<3,5,4,3,5,1> 25 About this soundPlay ...
5-23B [0,2,4,5,7] About this soundPlay ... 7-23A [0,2,3,4,
 5,7,9]
About this soundPlay ...
5-24A [0,1,3,5,7] <1,3,1,2,2,1> About this soundPlay ... 7-24B [0,2,4,6,
 7,8,9]
<3,5,3,4,4,2> 22 About this soundPlay enigmatic scale
5-24B [0,2,4,6,7] About this soundPlay ... 7-24A [0,1,2,3,
 5,7,9]
About this soundPlay ...
5-25A [0,2,3,5,8] <1,2,3,1,2,1> About this soundPlay Seven six chord 7-25B [0,2,3,5,
 6,7,9]
<3,4,5,3,4,2> 24 About this soundPlay ...
5-25B [0,3,5,6,8] About this soundPlay ... 7-25A [0,2,3,4,
 6,7,9]
About this soundPlay ...
5-26A [0,2,4,5,8] <1,2,2,3,1,1> About this soundPlay ... 7-26A [0,1,3,4,
 5,7,9]
<3,4,4,5,3,2> 26 About this soundPlay ...
5-26B [0,3,4,6,8] About this soundPlay ... 7-26B [0,2,4,5,
 6,8,9]
About this soundPlay ...
5-27A [0,1,3,5,8] <1,2,2,2,3,0> About this soundPlay ... 7-27B [0,2,4,5,
 7,8,9]
<3,4,4,4,5,1> 23 About this soundPlay ...
5-27B [0,3,5,7,8] About this soundPlay ... 7-27A [0,1,2,4,
 5,7,9]
About this soundPlay ...
5-28A [0,2,3,6,8] <1,2,2,2,1,2> About this soundPlay ... 7-28A [0,1,3,5,
 6,7,9]
<3,4,4,4,3,3> 36 About this soundPlay ...
5-28B [0,2,5,6,8] About this soundPlay ... 7-28B [0,2,3,4,
 6,8,9]
About this soundPlay ...
5-29A [0,1,3,6,8] <1,2,2,1,3,1> About this soundPlay ... 7-29B [0,2,3,5,
 7,8,9]
<3,4,4,3,5,2> 32 About this soundPlay ...
5-29B [0,2,5,7,8] About this soundPlay ... 7-29A [0,1,2,4,
 6,7,9]
About this soundPlay ...
5-30A [0,1,4,6,8] <1,2,1,3,2,1> About this soundPlay ... 7-30B [0,1,3,5,
 7,8,9]
<3,4,3,5,4,2> 37 About this soundPlay ...
5-30B [0,2,4,7,8] About this soundPlay ... 7-30A [0,1,2,4,
 6,8,9]
About this soundPlay minor Neapolitan scale
5-31A [0,1,3,6,9] <1,1,4,1,1,2> About this soundPlay beta chord 7-31B [0,1,3,4,
 6,8,9]
<3,3,6,3,3,3> 38 About this soundPlay harmonic minor scale
5-31B [0,2,3,6,9] About this soundPlay Dominant minor ninth chord 7-31A [0,2,3,5,
 6,8,9]
About this soundPlay ...
5-32A [0,1,4,6,9] <1,1,3,2,2,1> About this soundPlay ... 7-32B [0,1,3,5,
 6,8,9]
<3,3,5,4,4,2> 33 About this soundPlay harmonic major scale
5-32B [0,3,5,8,9] About this soundPlay Elektra chord, gamma chord 7-32A [0,1,3,4,
 6,7,9]
About this soundPlay ...
5-33 [0,2,4,6,8] <0,4,0,4,0,2> About this soundPlay ... 7-33 [0,1,2,4,
 6,8,T]
<2,6,2,6,2,3> 6 About this soundPlay M Locrian scale
5-34 [0,2,4,6,9] <0,3,2,2,2,1> About this soundPlay Dominant ninth chord 7-34 [0,1,3,4,
 6,8,T]
<2,5,4,4,4,2> 9 About this soundPlay half dim. scale
5-35 [0,2,4,7,9] <0,3,2,1,4,0> About this soundPlay M pentatonic scale 7-35 [0,1,3,5,
 6,8,T]
<2,5,4,3,6,1> 7 About this soundPlay diatonic scale
5-z36A [0,1,2,4,7] <2,2,2,1,2,1> About this soundPlay ... 7-z36B [0,2,3,5,
 6,7,8]
<4,4,4,3,4,2> 16 About this soundPlay ...
5-z36B [0,3,5,6,7] About this soundPlay ... 7-z36A [0,1,2,3,
 5,6,8]
About this soundPlay ...
5-z37 [0,3,4,5,8] <2,1,2,3,2,0> About this soundPlay ... 7-z37 [0,1,3,4,
 5,7,8]
<4,3,4,5,4,1> 3 About this soundPlay ...
5-z38A [0,1,2,5,8] <2,1,2,2,2,1> About this soundPlay ... 7-z38B [0,1,3,4,
 6,7,8]
<4,3,4,4,4,2> 29 About this soundPlay ...
5-z38B [0,3,6,7,8] About this soundPlay ... 7-z38A [0,1,2,4,
 5,7,8]
About this soundPlay ...
6-1 [0,1,2,3,4,5] <5,4,3,2,1,0> 4 About this soundPlay chromatic hexachord
6-2A [0,1,2,3,4,6] <4,4,3,2,1,1> 19 About this soundPlay ...
6-2B [0,2,3,4,5,6] About this soundPlay ...
6-z3A [0,1,2,3,5,6] <4,3,3,2,2,1> 49 About this soundPlay ... 6-z36B [0,3,4,5,6,7] <4,3,3,2,2,1> 50 About this soundPlay ...
6-z3B [0,1,3,4,5,6] About this soundPlay ... 6-z36A [0,1,2,3,4,7] About this soundPlay ...
6-z4 [0,1,2,4,5,6] <4,3,2,3,2,1> 24 About this soundPlay ... 6-z37 [0,1,2,3,4,8] <4,3,2,3,2,1> 23 About this soundPlay ...
6-5A [0,1,2,3,6,7] <4,2,2,2,3,2> 16 About this soundPlay ...
6-5B [0,1,4,5,6,7] About this soundPlay ...
6-z6 [0,1,2,5,6,7] <4,2,1,2,4,2> 33 About this soundPlay ... 6-z38 [0,1,2,3,7,8] <4,2,1,2,4,2> 34 About this soundPlay ...
6-7 [0,1,2,6,7,8] <4,2,0,2,4,3> 7 About this soundPlay ...
6-8 [0,2,3,4,5,7] <3,4,3,2,3,0> 5 About this soundPlay ...
6-9A [0,1,2,3,5,7] <3,4,2,2,3,1> 20 About this soundPlay ...
6-9B [0,2,4,5,6,7] About this soundPlay ...
6-z10A [0,1,3,4,5,7] <3,3,3,3,2,1> 42 About this soundPlay ... 6-z39B [0,3,4,5,6,8] <3,3,3,3,2,1> 41 About this soundPlay ...
6-z10B [0,2,3,4,6,7] About this soundPlay ... 6-z39A [0,2,3,4,5,8] About this soundPlay ...
6-z11A [0,1,2,4,5,7] <3,3,3,2,3,1> 47 About this soundPlay ... 6-z40B [0,3,5,6,7,8] <3,3,3,2,3,1> 48 About this soundPlay ...
6-z11B [0,2,3,5,6,7] About this soundPlay Sacher hexachord 6-z40A [0,1,2,3,5,8] About this soundPlay ...
6-z12A [0,1,2,4,6,7] <3,3,2,2,3,2> 46 About this soundPlay ... 6-z41B [0,2,5,6,7,8] <3,3,2,2,3,2> 45 About this soundPlay ...
6-z12B [0,1,3,5,6,7] About this soundPlay ... 6-z41A [0,1,2,3,6,8] About this soundPlay ...
6-z13 [0,1,3,4,6,7] <3,2,4,2,2,2> 29 About this soundPlay ... 6-z42 [0,1,2,3,6,9] <3,2,4,2,2,2> 30 About this soundPlay ...
6-14A [0,1,3,4,5,8] <3,2,3,4,3,0> 3 About this soundPlay ...
6-14B [0,3,4,5,7,8] About this soundPlay ...
6-15A [0,1,2,4,5,8] <3,2,3,4,2,1> 13 About this soundPlay ...
6-15B [0,3,4,6,7,8] About this soundPlay ...
6-16A [0,1,4,5,6,8] <3,2,2,4,3,1> 11 About this soundPlay ...
6-16B [0,2,3,4,7,8] About this soundPlay ...
6-z17A [0,1,2,4,7,8] <3,2,2,3,3,2> 35 About this soundPlay all-trichord hexachord 6-z43B [0,2,3,6,7,8] <3,2,2,3,3,2> 36 About this soundPlay ...
6-z17B [0,1,4,6,7,8] About this soundPlay ... 6-z43A [0,1,2,5,6,8] About this soundPlay ...
6-18A [0,1,2,5,7,8] <3,2,2,2,4,2> 17 About this soundPlay ...
6-18B [0,1,3,6,7,8] About this soundPlay ...
6-z19A [0,1,3,4,7,8] <3,1,3,4,3,1> 37 About this soundPlay ... 6-z44B [0,3,4,7,8,9] <3,1,3,4,3,1> 38 About this soundPlay ...
6-z19B [0,1,4,5,7,8] About this soundPlay ... 6-z44A [0,1,2,5,6,9] About this soundPlay Schoenberg hexachord
6-20 [0,1,4,5,8,9] <3,0,3,6,3,0> 2 About this soundPlay "Ode-to-Napoleon" hexachord
6-21A [0,2,3,4,6,8] <2,4,2,4,1,2> 12 About this soundPlay ...
6-21B [0,2,4,5,6,8] About this soundPlay ...
6-22A [0,1,2,4,6,8] <2,4,1,4,2,2> 10 About this soundPlay ...
6-22B [0,2,4,6,7,8] About this soundPlay ...
6-z23 [0,2,3,5,6,8] <2,3,4,2,2,2> 27 About this soundPlay ... 6-z45 [0,2,3,4,6,9] <2,3,4,2,2,2> 28 About this soundPlay ...
6-z24A [0,1,3,4,6,8] <2,3,3,3,3,1> 39 About this soundPlay ... 6-z46B [0,3,5,7,8,9] <2,3,3,3,3,1> 40 About this soundPlay ...
6-z24B [0,2,4,5,7,8] About this soundPlay ... 6-z46A [0,1,2,4,6,9] About this soundPlay ...
6-z25A [0,1,3,5,6,8] <2,3,3,2,4,1> 43 About this soundPlay Major eleventh chord 6-z47B [0,2,5,7,8,9] <2,3,3,2,4,1> 44 About this soundPlay blues scale
6-z25B [0,2,3,5,7,8] About this soundPlay ... 6-z47A [0,1,2,4,7,9] About this soundPlay ...
6-z26 [0,1,3,5,7,8] <2,3,2,3,4,1> 26 About this soundPlay ... 6-z48 [0,1,2,5,7,9] <2,3,2,3,4,1> 25 About this soundPlay ...
6-27A [0,1,3,4,6,9] <2,2,5,2,2,2> 14 About this soundPlay ...
6-27B [0,3,5,6,8,9] About this soundPlay ...
6-z28 [0,1,3,5,6,9] <2,2,4,3,2,2> 21 About this soundPlay ... 6-z49 [0,1,3,4,7,9] <2,2,4,3,2,2> 22 About this soundPlay ...
6-z29 [0,2,3,6,7,9][f] <2,2,4,2,3,2> 32 About this soundPlay Bridge chord 6-z50 [0,1,4,6,7,9] <2,2,4,2,3,2> 31 About this soundPlay ...
6-30A [0,1,3,6,7,9] <2,2,4,2,2,3> 15 About this soundPlay ...
6-30B [0,2,3,6,8,9] About this soundPlay Petrushka chord
6-31A [0,1,4,5,7,9][g] <2,2,3,4,3,1> 8 About this soundPlay ...
6-31B [0,2,4,5,8,9][h] About this soundPlay ...
6-32 [0,2,4,5,7,9] <1,4,3,2,5,0> 6 About this soundPlay diatonic hexachord
6-33A [0,2,3,5,7,9] <1,4,3,2,4,1> 18 About this soundPlay ...
6-33B [0,2,4,6,7,9] About this soundPlay Dominant eleventh chord
6-34A [0,1,3,5,7,9] <1,4,2,4,2,2> 9 About this soundPlay mystic chord
6-34B [0,2,4,6,8,9] About this soundPlay ...
6-35 [0,2,4,6,8,T] <0,6,0,6,0,3> 1 About this soundPlay whole tone scale

See also[edit]

Notes[edit]

  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[edit]

  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.
  7. ^ Schuijer, Michael (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.97. University of Rochester. ISBN 978-1-58046-270-9.
  8. ^ Everett, Walter (2008). The Foundations of Rock, p.169. Oxford. ISBN 9780199718702.

External links[edit]