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 sound Play aggregate
1-1 [0] <0,0,0,0,0,0> About this sound Play PU, P8 11-1 [0,1,2,3,4,5,
 6,7,8,9,T]
<T,T,T,T,T,5> About this sound Play ...
2-1 [0,1] <1,0,0,0,0,0> 1 About this sound Play m2, M7 10-1 [0,1,2,3,4,
 5,6,7,8,9]
<9,8,8,8,8,4> About this sound Play ...
2-2 [0,2] <0,1,0,0,0,0> 2 About this sound Play M2, m7 10-2 [0,1,2,3,4,
 5,6,7,8,T]
<8,9,8,8,8,4> About this sound Play ...
2-3 [0,3] <0,0,1,0,0,0> 3 About this sound Play m3, M6 10-3 [0,1,2,3,4,
 5,6,7,9,T]
<8,8,9,8,8,4> About this sound Play ...
2-4 [0,4] <0,0,0,1,0,0> 4 About this sound Play M3, m6 10-4 [0,1,2,3,4,
 5,6,8,9,T]
<8,8,8,9,8,4> About this sound Play ...
2-5 [0,5] <0,0,0,0,1,0> 5 About this sound Play P4, P5 10-5 [0,1,2,3,4,
 5,7,8,9,T]
<8,8,8,8,9,4> About this sound Play ...
2-6 [0,6] <0,0,0,0,0,1> 6 About this sound Play A4, d5 10-6 [0,1,2,3,4,
 6,7,8,9,T]
<8,8,8,8,8,5> About this sound Play ...
3-1 [0,1,2] <2,1,0,0,0,0> 4 About this sound Play ... 9-1 [0,1,2,3,4,
 5,6,7,8]
<8,7,6,6,6,3> About this sound Play ...
3-2A [0,1,3] <1,1,1,0,0,0> 12 About this sound Play ... 9-2A [0,1,2,3,4,
 5,6,7,9]
<7,7,7,6,6,3> About this sound Play ...
3-2B [0,2,3] About this sound Play ... 9-2B [0,2,3,4,5,
 6,7,8,9]
About this sound Play ...
3-3A [0,1,4] <1,0,1,1,0,0> 11 About this sound Play ... 9-3B [0,1,3,4,
 5,6,7,8,9]
<7,6,7,7,6,3> About this sound Play ...
3-3B [0,3,4] About this sound Play ... 9-3A [0,1,2,3,4,
 5,6,8,9]
About this sound Play ...
3-4A [0,1,5] <1,0,0,1,1,0> 9 About this sound Play ... 9-4B [0,1,2,4,5,
 6,7,8,9]
<7,6,6,7,7,3> About this sound Play ...
3-4B [0,4,5] About this sound Play ... 9-4A [0,1,2,3,4,
 5,7,8,9]
About this sound Play ...
3-5A [0,1,6] <1,0,0,0,1,1> 7 About this sound Play Viennese trichord 9-5B [0,1,2,3,5,
 6,7,8,9]
<7,6,6,6,7,4> About this sound Play ...
3-5B [0,5,6] About this sound Play ... 9-5A [0,1,2,3,4,
 6,7,8,9]
About this sound Play ...
3-6 [0,2,4] <0,2,0,1,0,0> 3 About this sound Play ... 9-6 [0,1,2,3,4,
 5,6,8,T]
<6,8,6,7,6,3> About this sound Play ...
3-7A [0,2,5] <0,1,1,0,1,0> 10 About this sound Play Blues trichord (min. pentatonic subset)[8] 9-7B [0,1,2,3,4,
 5,7,9,T]
<6,7,7,6,7,3> About this sound Play ...
3-7B [0,3,5] About this sound Play ... 9-7A [0,1,2,3,4,
 5,7,8,T]
About this sound Play ...
3-8A [0,2,6] <0,1,0,1,0,1> 8 About this sound Play It6 9-8B [0,1,2,3,4,
 6,8,9,T]
<6,7,6,7,6,4> About this sound Play ...
3-8B [0,4,6] About this sound Play ... 9-8A [0,1,2,3,4,
 6,7,8,T]
About this sound Play ...
3-9 [0,2,7] <0,1,0,0,2,0> 5 About this sound Play sus. chord 9-9 [0,1,2,3,5,
 6,7,8,T]
<6,7,6,6,8,3> About this sound Play blues scale
3-10 [0,3,6] <0,0,2,0,0,1> 2 About this sound Play dim. chord 9-10 [0,1,2,3,4,
 6,7,9,T]
<6,6,8,6,6,4> About this sound Play ...
3-11A [0,3,7] <0,0,1,1,1,0> 6 About this sound Play minor chord 9-11B [0,1,2,3,5,
 6,8,9,T]
<6,6,7,7,7,3> About this sound Play ...
3-11B [0,4,7] About this sound Play major chord 9-11A [0,1,2,3,5,
 6,7,9,T]
About this sound Play ...
3-12 [0,4,8] <0,0,0,3,0,0> 1 About this sound Play Aug. chord 9-12 [0,1,2,4,5,
 6,8,9,T]
<6,6,6,9,6,3> About this sound Play ...
4-1 [0,1,2,3] <3,2,1,0,0,0> 1 About this sound Play ... 8-1 [0,1,2,3,
 4,5,6,7]
<7,6,5,4,4,2> About this sound Play ...
4-2A [0,1,2,4] <2,2,1,1,0,0> 17 About this sound Play ... 8-2B [0,2,3,4,
 5,6,7,8]
<6,6,5,5,4,2> About this sound Play ...
4-2B [0,2,3,4] About this sound Play ... 8-2A [0,1,2,3,
 4,5,6,8]
About this sound Play ...
4-3 [0,1,3,4] <2,1,2,1,0,0> 9 About this sound Play ... 8-3 [0,1,2,3,
 4,5,6,9]
<6,5,6,5,4,2> About this sound Play ...
4-4A [0,1,2,5] <2,1,1,1,1,0> 20 About this sound Play ... 8-4B [0,1,3,4,
 5,6,7,8]
<6,5,5,5,5,2> About this sound Play ...
4-4B [0,3,4,5] About this sound Play ... 8-4A [0,1,2,3,
 4,5,7,8]
About this sound Play ...
4-5A [0,1,2,6] <2,1,0,1,1,1> 22 About this sound Play ... 8-5B [0,1,2,4,
 5,6,7,8]
<6,5,4,5,5,3> About this sound Play ...
4-5B [0,4,5,6] About this sound Play ... 8-5A [0,1,2,3,
 4,6,7,8]
About this sound Play ...
4-6 [0,1,2,7] <2,1,0,0,2,1> 6 About this sound Play dream chord 8-6 [0,1,2,3,
 5,6,7,8]
<6,5,4,4,6,3> About this sound Play ...
4-7 [0,1,4,5] <2,0,1,2,1,0> 8 About this sound Play ... 8-7 [0,1,2,3,
 4,5,8,9]
<6,4,5,6,5,2> About this sound Play ...
4-8 [0,1,5,6] <2,0,0,1,2,1> 10 About this sound Play ... 8-8 [0,1,2,3,
 4,7,8,9]
<6,4,4,5,6,3> About this sound Play ...
4-9 [0,1,6,7] <2,0,0,0,2,2> 2 About this sound Play distance model 8-9 [0,1,2,3,
 6,7,8,9]
<6,4,4,4,6,4> About this sound Play ...
4-10 [0,2,3,5] <1,2,2,0,1,0> 3 About this sound Play ... 8-10 [0,2,3,4,
 5,6,7,9]
<5,6,6,4,5,2> About this sound Play ...
4-11A [0,1,3,5] <1,2,1,1,1,0> 26 About this sound Play ... 8-11B [0,2,4,5,
 6,7,8,9]
<5,6,5,5,5,2> About this sound Play ...
4-11B [0,2,4,5] About this sound Play ... 8-11A [0,1,2,3,
 4,5,7,9]
About this sound Play ...
4-12A [0,2,3,6] <1,1,2,1,0,1> 28 About this sound Play ... 8-12A [0,1,3,4,
 5,6,7,9]
<5,5,6,5,4,3> About this sound Play ...
4-12B [0,3,4,6] About this sound Play ... 8-12B [0,2,3,4,
 5,6,8,9]
About this sound Play ...
4-13A [0,1,3,6] <1,1,2,0,1,1> 7 About this sound Play ... 8-13B [0,2,3,5,
 6,7,8,9]
<5,5,6,4,5,3> About this sound Play ...
4-13B [0,3,5,6] About this sound Play ... 8-13A [0,1,2,3,
 4,6,7,9]
About this sound Play ...
4-14A [0,2,3,7] <1,1,1,1,2,0> 25 About this sound Play ... 8-14A [0,1,2,4,
 5,6,7,9]
<5,5,5,5,6,2> About this sound Play ...
4-14B [0,4,5,7] About this sound Play ... 8-14B [0,2,3,4,
 5,7,8,9]
About this sound Play ...
4-z15A [0,1,4,6] <1,1,1,1,1,1> 18 About this sound Play all-interval tetrachord 8-z15B [0,1,3,5,
 6,7,8,9]
<5,5,5,5,5,3> About this sound Play ...
4-z15B [0,2,5,6] About this sound Play ... 8-z15A [0,1,2,3,
 4,6,8,9]
About this sound Play ...
4-16A [0,1,5,7] <1,1,0,1,2,1> 19 About this sound Play ... 8-16B [0,1,2,4,
 6,7,8,9]
<5,5,4,5,6,3> About this sound Play ...
4-16B [0,2,6,7] About this sound Play ... 8-16A [0,1,2,3,
 5,7,8,9]
About this sound Play ...
4-17 [0,3,4,7] <1,0,2,2,1,0> 13 About this sound Play alpha chord 8-17 [0,1,3,4,
 5,6,8,9]
<5,4,6,6,5,2> About this sound Play ...
4-18A [0,1,4,7] <1,0,2,1,1,1> 21 About this sound Play dim. M7 chord 8-18B [0,1,3,4,
 6,7,8,9]
<5,4,6,5,5,3> About this sound Play ...
4-18B [0,3,6,7] About this sound Play ... 8-18A [0,1,2,3,
 5,6,8,9]
About this sound Play ...
4-19A [0,1,4,8] <1,0,1,3,1,0> 24 About this sound Play Mm7 chord 8-19B [0,1,3,4,
 5,7,8,9]
<5,4,5,7,5,2> About this sound Play ...
4-19B [0,3,4,8] About this sound Play ... 8-19A [0,1,2,4,
 5,6,8,9]
About this sound Play ...
4-20 [0,1,5,8] <1,0,1,2,2,0> 15 About this sound Play M7 chord 8-20 [0,1,2,4,
 5,7,8,9]
<5,4,5,6,6,2> About this sound Play ...
4-21 [0,2,4,6] <0,3,0,2,0,1> 11 About this sound Play ... 8-21 [0,1,2,3,
 4,6,8,T]
<4,7,4,6,4,3> About this sound Play ...
4-22A [0,2,4,7] <0,2,1,1,2,0> 27 About this sound Play mu chord 8-22B [0,1,2,3,
 5,7,9,T]
<4,6,5,5,6,2> About this sound Play ...
4-22B [0,3,5,7] About this sound Play ... 8-22A [0,1,2,3,
 5,6,8,T]
About this sound Play ...
4-23 [0,2,5,7] <0,2,1,0,3,0> 4 About this sound Play quartal chord 8-23 [0,1,2,3,
 5,7,8,T]
<4,6,5,4,7,2> About this sound Play bebop scale
4-24 [0,2,4,8] <0,2,0,3,0,1> 16 About this sound Play A7 chord 8-24 [0,1,2,4,
 5,6,8,T]
<4,6,4,7,4,3> About this sound Play ...
4-25 [0,2,6,8] <0,2,0,2,0,2> 12 About this sound Play Fr6 8-25 [0,1,2,4,
 6,7,8,T]
<4,6,4,6,4,4> About this sound Play ...
4-26 [0,3,5,8] <0,1,2,1,2,0> 14 About this sound Play minor seventh chord 8-26 [0,1,3,4,
 5,7,8,T]
[b]
<4,5,6,5,6,2> About this sound Play ...
4-27A [0,2,5,8] <0,1,2,1,1,1> 29 About this sound Play dominant 7th chord 8-27B [0,1,2,4,
 6,7,9,T]
<4,5,6,5,5,3> About this sound Play ...
4-27B [0,3,6,8] About this sound Play ... 8-27A [0,1,2,4,
 5,7,8,T]
About this sound Play ...
4-28 [0,3,6,9] <0,0,4,0,0,2> 5 About this sound Play dim. 7th chord 8-28 [0,1,3,4,
 6,7,9,T]
<4,4,8,4,4,4> About this sound Play octatonic scale
4-z29A [0,1,3,7] <1,1,1,1,1,1> 23 About this sound Play all-interval tetrachord 8-z29B [0,2,3,4,
 6,7,8,9]
<5,5,5,5,5,3> About this sound Play ...
4-z29B [0,4,6,7] About this sound Play ... 8-z29A [0,1,2,3,
 5,6,7,9]
About this sound Play ...
5-1 [0,1,2,3,4] <4,3,2,1,0,0> About this sound Play ... 7-1 [0,1,2,3,
 4,5,6]
<6,5,4,3,2,1> 1 About this sound Play ...
5-2A [0,1,2,3,5] <3,3,2,1,1,0> About this sound Play ... 7-2B [0,2,3,4,
 5,6,7]
<5,5,4,3,3,1> 11 About this sound Play ...
5-2B [0,2,3,4,5] About this sound Play ... 7-2A [0,1,2,3,
 4,5,7]
About this sound Play ...
5-3A [0,1,2,4,5] <3,2,2,2,1,0> About this sound Play ... 7-3B [0,3,4,5,
 6,7,8]
<5,4,4,4,3,1> 14 About this sound Play ...
5-3B [0,1,3,4,5] About this sound Play ... 7-3A [0,1,2,3,
 4,5,8]
About this sound Play ...
5-4A [0,1,2,3,6] <3,2,2,1,1,1> About this sound Play ... 7-4B [0,1,3,4,
 5,6,7]
<5,4,4,3,3,2> 12 About this sound Play ...
5-4B [0,3,4,5,6] About this sound Play ... 7-4A [0,1,2,3,
 4,6,7]
About this sound Play ...
5-5A [0,1,2,3,7] <3,2,1,1,2,1> About this sound Play ... 7-5B [0,1,2,4,
 5,6,7]
<5,4,3,3,4,2> 13 About this sound Play ...
5-5B [0,4,5,6,7] About this sound Play ... 7-5A [0,1,2,3,
 5,6,7]
About this sound Play ...
5-6A [0,1,2,5,6] <3,1,1,2,2,1> About this sound Play ... 7-6B [0,1,4,5,
 6,7,8]
<5,3,3,4,4,2> 27 About this sound Play ...
5-6B [0,1,4,5,6] About this sound Play ... 7-6A [0,1,2,3,
 4,7,8]
About this sound Play ...
5-7A [0,1,2,6,7] <3,1,0,1,3,2> About this sound Play ... 7-7B [0,1,2,5,
 6,7,8]
<5,3,2,3,5,3> 30 About this sound Play ...
5-7B [0,1,5,6,7] About this sound Play ... 7-7A [0,1,2,3,
 6,7,8]
About this sound Play ...
5-8 [0,2,3,4,6] <2,3,2,2,0,1> About this sound Play ... 7-8 [0,2,3,4,
 5,6,8]
<4,5,4,4,2,2> 2 About this sound Play ...
5-9A [0,1,2,4,6] <2,3,1,2,1,1> About this sound Play ... 7-9B [0,2,4,5,
 6,7,8]
<4,5,3,4,3,2> 15 About this sound Play ...
5-9B [0,2,4,5,6] About this sound Play ... 7-9A [0,1,2,3,
 4,6,8]
About this sound Play ...
5-10A [0,1,3,4,6] <2,2,3,1,1,1> About this sound Play ... 7-10B [0,2,3,4,
 5,6,9]
<4,4,5,3,3,2> 19 About this sound Play ...
5-10B [0,2,3,5,6] About this sound Play ... 7-10A [0,1,2,3,
 4,6,9]
About this sound Play ...
5-11A [0,2,3,4,7] <2,2,2,2,2,0> About this sound Play ... 7-11B [0,2,3,4,
 5,7,8]
<4,4,4,4,4,1> 18 About this sound Play ...
5-11B [0,3,4,5,7] About this sound Play ... 7-11A [0,1,3,4,
 5,6,8]
About this sound Play ...
5-z12 [0,1,3,5,6] <2,2,2,1,2,1> About this sound Play ... 7-z12 [0,1,2,3,
 4,7,9]
<4,4,4,3,4,2> 5 About this sound Play ...
5-13A [0,1,2,4,8] <2,2,1,3,1,1> About this sound Play ... 7-13B [0,2,3,4,
 6,7,8]
<4,4,3,5,3,2> 17 About this sound Play ...
5-13B [0,2,3,4,8] About this sound Play ... 7-13A [0,1,2,4,
 5,6,8]
About this sound Play ...
5-14A [0,1,2,5,7] <2,2,1,1,3,1> About this sound Play ... 7-14B [0,1,3,5,
 6,7,8]
<4,4,3,3,5,2> 28 About this sound Play ...
5-14B [0,2,5,6,7] About this sound Play ... 7-14A [0,1,2,3,
 5,7,8]
About this sound Play ...
5-15 [0,1,2,6,8] <2,2,0,2,2,2> About this sound Play ... 7-15 [0,1,2,4,
 6,7,8]
<4,4,2,4,4,3> 4 About this sound Play ...
5-16A [0,1,3,4,7] <2,1,3,2,1,1> About this sound Play ... 7-16B [0,1,3,4,
 5,6,9]
<4,3,5,4,3,2> 20 About this sound Play ...
5-16B [0,3,4,6,7] About this sound Play ... 7-16A [0,1,2,3,
 5,6,9]
About this sound Play ...
5-z17 [0,1,3,4,8] <2,1,2,3,2,0> About this sound Play Farben chord 7-z17 [0,1,2,4,
 5,6,9]
<4,3,4,5,4,1> 10 About this sound Play ...
5-z18A [0,1,4,5,7] <2,1,2,2,2,1> About this sound Play ... 7-z18A [0,1,4,5,
 6,7,9]
[c]
<4,3,4,4,4,2> 35 About this sound Play ...
5-z18B [0,2,3,6,7] About this sound Play ... 7-z18B [0,1,4,6,
 7,8,9]
About this sound Play ...
5-19A [0,1,3,6,7] <2,1,2,1,2,2> About this sound Play ... 7-19B [0,1,2,3,
 6,8,9]
<4,3,4,3,4,3> 31 About this sound Play ...
5-19B [0,1,4,6,7] About this sound Play ... 7-19A [0,1,2,3,
 6,7,9]
About this sound Play ...
5-20A [0,1,5,6,8][d] <2,1,1,2,3,1> About this sound Play ... 7-20B [0,1,2,5,
 7,8,9]
<4,3,3,4,5,2> 34 About this sound Play ...
5-20B [0,2,3,7,8] About this sound Play In scale 7-20A [0,1,2,5,
 6,7,9]
[e]
About this sound Play Persian scale
5-21A [0,1,4,5,8] <2,0,2,4,2,0> About this sound Play ... 7-21B [0,1,3,4,
 5,8,9]
<4,2,4,6,4,1> 21 About this sound Play ...
5-21B [0,3,4,7,8] About this sound Play ... 7-21A [0,1,2,4,
 5,8,9]
About this sound Play ...
5-22 [0,1,4,7,8] <2,0,2,3,2,1> About this sound Play ... 7-22 [0,1,2,5,
 6,8,9]
<4,2,4,5,4,2> 8 About this sound Play double harmonic scale
5-23A [0,2,3,5,7] <1,3,2,1,3,0> About this sound Play ... 7-23B [0,2,4,5,
 6,7,9]
<3,5,4,3,5,1> 25 About this sound Play ...
5-23B [0,2,4,5,7] About this sound Play ... 7-23A [0,2,3,4,
 5,7,9]
About this sound Play ...
5-24A [0,1,3,5,7] <1,3,1,2,2,1> About this sound Play ... 7-24B [0,2,4,6,
 7,8,9]
<3,5,3,4,4,2> 22 About this sound Play ...
5-24B [0,2,4,6,7] About this sound Play ... 7-24A [0,1,2,3,
 5,7,9]
About this sound Play enigmatic scale
5-25A [0,2,3,5,8] <1,2,3,1,2,1> About this sound Play Seven six chord 7-25B [0,2,3,5,
 6,7,9]
<3,4,5,3,4,2> 24 About this sound Play ...
5-25B [0,3,5,6,8] About this sound Play ... 7-25A [0,2,3,4,
 6,7,9]
About this sound Play ...
5-26A [0,2,4,5,8] <1,2,2,3,1,1> About this sound Play ... 7-26A [0,1,3,4,
 5,7,9]
<3,4,4,5,3,2> 26 About this sound Play ...
5-26B [0,3,4,6,8] About this sound Play ... 7-26B [0,2,4,5,
 6,8,9]
About this sound Play ...
5-27A [0,1,3,5,8] <1,2,2,2,3,0> About this sound Play ... 7-27B [0,2,4,5,
 7,8,9]
<3,4,4,4,5,1> 23 About this sound Play ...
5-27B [0,3,5,7,8] About this sound Play ... 7-27A [0,1,2,4,
 5,7,9]
About this sound Play ...
5-28A [0,2,3,6,8] <1,2,2,2,1,2> About this sound Play ... 7-28A [0,1,3,5,
 6,7,9]
<3,4,4,4,3,3> 36 About this sound Play ...
5-28B [0,2,5,6,8] About this sound Play ... 7-28B [0,2,3,4,
 6,8,9]
About this sound Play ...
5-29A [0,1,3,6,8] <1,2,2,1,3,1> About this sound Play ... 7-29B [0,2,3,5,
 7,8,9]
<3,4,4,3,5,2> 32 About this sound Play ...
5-29B [0,2,5,7,8] About this sound Play ... 7-29A [0,1,2,4,
 6,7,9]
About this sound Play ...
5-30A [0,1,4,6,8] <1,2,1,3,2,1> About this sound Play ... 7-30B [0,1,3,5,
 7,8,9]
<3,4,3,5,4,2> 37 About this sound Play ...
5-30B [0,2,4,7,8] About this sound Play ... 7-30A [0,1,2,4,
 6,8,9]
About this sound Play minor Neapolitan scale
5-31A [0,1,3,6,9] <1,1,4,1,1,2> About this sound Play Dominant minor ninth chord 7-31B [0,1,3,4,
 6,8,9]
<3,3,6,3,3,3> 38 About this sound Play ...
5-31B [0,2,3,6,9] About this sound Play beta chord 7-31A [0,2,3,5,
 6,8,9]
About this sound Play ...
5-32A [0,1,4,6,9] <1,1,3,2,2,1> About this sound Play Elektra chord, gamma chord 7-32B [0,1,3,5,
 6,8,9]
<3,3,5,4,4,2> 33 About this sound Play ...
5-32B [0,3,5,8,9] About this sound Play ... 7-32A [0,1,3,4,
 6,7,9]
About this sound Play harmonic minor scale
5-33 [0,2,4,6,8] <0,4,0,4,0,2> About this sound Play ... 7-33 [0,1,2,4,
 6,8,T]
<2,6,2,6,2,3> 6 About this sound Play M Locrian scale
5-34 [0,2,4,6,9] <0,3,2,2,2,1> About this sound Play Dominant ninth chord 7-34 [0,1,3,4,
 6,8,T]
<2,5,4,4,4,2> 9 About this sound Play half dim. scale
5-35 [0,2,4,7,9] <0,3,2,1,4,0> About this sound Play M pentatonic scale 7-35 [0,1,3,5,
 6,8,T]
<2,5,4,3,6,1> 7 About this sound Play diatonic scale
5-z36A [0,1,2,4,7] <2,2,2,1,2,1> About this sound Play ... 7-z36B [0,2,3,5,
 6,7,8]
<4,4,4,3,4,2> 16 About this sound Play ...
5-z36B [0,3,5,6,7] About this sound Play ... 7-z36A [0,1,2,3,
 5,6,8]
About this sound Play ...
5-z37 [0,3,4,5,8] <2,1,2,3,2,0> About this sound Play ... 7-z37 [0,1,3,4,
 5,7,8]
<4,3,4,5,4,1> 3 About this sound Play ...
5-z38A [0,1,2,5,8] <2,1,2,2,2,1> About this sound Play ... 7-z38B [0,1,3,4,
 6,7,8]
<4,3,4,4,4,2> 29 About this sound Play ...
5-z38B [0,3,6,7,8] About this sound Play ... 7-z38A [0,1,2,4,
 5,7,8]
About this sound Play ...
6-1 [0,1,2,3,4,5] <5,4,3,2,1,0> 4 About this sound Play chromatic hexachord
6-2A [0,1,2,3,4,6] <4,4,3,2,1,1> 19 About this sound Play ...
6-2B [0,2,3,4,5,6] About this sound Play ...
6-z3A [0,1,2,3,5,6] <4,3,3,2,2,1> 49 About this sound Play ... 6-z36B [0,3,4,5,6,7] <4,3,3,2,2,1> 50 About this sound Play ...
6-z3B [0,1,3,4,5,6] About this sound Play ... 6-z36A [0,1,2,3,4,7] About this sound Play ...
6-z4 [0,1,2,4,5,6] <4,3,2,3,2,1> 24 About this sound Play ... 6-z37 [0,1,2,3,4,8] <4,3,2,3,2,1> 23 About this sound Play ...
6-5A [0,1,2,3,6,7] <4,2,2,2,3,2> 16 About this sound Play ...
6-5B [0,1,4,5,6,7] About this sound Play ...
6-z6 [0,1,2,5,6,7] <4,2,1,2,4,2> 33 About this sound Play ... 6-z38 [0,1,2,3,7,8] <4,2,1,2,4,2> 34 About this sound Play ...
6-7 [0,1,2,6,7,8] <4,2,0,2,4,3> 7 About this sound Play ...
6-8 [0,2,3,4,5,7] <3,4,3,2,3,0> 5 About this sound Play ...
6-9A [0,1,2,3,5,7] <3,4,2,2,3,1> 20 About this sound Play ...
6-9B [0,2,4,5,6,7] About this sound Play ...
6-z10A [0,1,3,4,5,7] <3,3,3,3,2,1> 42 About this sound Play ... 6-z39B [0,3,4,5,6,8] <3,3,3,3,2,1> 41 About this sound Play ...
6-z10B [0,2,3,4,6,7] About this sound Play ... 6-z39A [0,2,3,4,5,8] About this sound Play ...
6-z11A [0,1,2,4,5,7] <3,3,3,2,3,1> 47 About this sound Play Sacher hexachord 6-z40B [0,3,5,6,7,8] <3,3,3,2,3,1> 48 About this sound Play ...
6-z11B [0,2,3,5,6,7] About this sound Play ... 6-z40A [0,1,2,3,5,8] About this sound Play ...
6-z12A [0,1,2,4,6,7] <3,3,2,2,3,2> 46 About this sound Play ... 6-z41B [0,2,5,6,7,8] <3,3,2,2,3,2> 45 About this sound Play ...
6-z12B [0,1,3,5,6,7] About this sound Play ... 6-z41A [0,1,2,3,6,8] About this sound Play ...
6-z13 [0,1,3,4,6,7] <3,2,4,2,2,2> 29 About this sound Play ... 6-z42 [0,1,2,3,6,9] <3,2,4,2,2,2> 30 About this sound Play ...
6-14A [0,1,3,4,5,8] <3,2,3,4,3,0> 3 About this sound Play ...
6-14B [0,3,4,5,7,8] About this sound Play ...
6-15A [0,1,2,4,5,8] <3,2,3,4,2,1> 13 About this sound Play ...
6-15B [0,3,4,6,7,8] About this sound Play ...
6-16A [0,1,4,5,6,8] <3,2,2,4,3,1> 11 About this sound Play ...
6-16B [0,2,3,4,7,8] About this sound Play ...
6-z17A [0,1,2,4,7,8] <3,2,2,3,3,2> 35 About this sound Play all-trichord hexachord 6-z43B [0,2,3,6,7,8] <3,2,2,3,3,2> 36 About this sound Play ...
6-z17B [0,1,4,6,7,8] About this sound Play ... 6-z43A [0,1,2,5,6,8] About this sound Play ...
6-18A [0,1,2,5,7,8] <3,2,2,2,4,2> 17 About this sound Play ...
6-18B [0,1,3,6,7,8] About this sound Play ...
6-z19A [0,1,3,4,7,8] <3,1,3,4,3,1> 37 About this sound Play ... 6-z44B [0,3,4,7,8,9] <3,1,3,4,3,1> 38 About this sound Play ...
6-z19B [0,1,4,5,7,8] About this sound Play ... 6-z44A [0,1,2,5,6,9] About this sound Play Schoenberg hexachord
6-20 [0,1,4,5,8,9] <3,0,3,6,3,0> 2 About this sound Play "Ode-to-Napoleon" hexachord
6-21A [0,2,3,4,6,8] <2,4,2,4,1,2> 12 About this sound Play ...
6-21B [0,2,4,5,6,8] About this sound Play ...
6-22A [0,1,2,4,6,8] <2,4,1,4,2,2> 10 About this sound Play ...
6-22B [0,2,4,6,7,8] About this sound Play ...
6-z23 [0,2,3,5,6,8] <2,3,4,2,2,2> 27 About this sound Play ... 6-z45 [0,2,3,4,6,9] <2,3,4,2,2,2> 28 About this sound Play ...
6-z24A [0,1,3,4,6,8] <2,3,3,3,3,1> 39 About this sound Play ... 6-z46B [0,3,5,7,8,9] <2,3,3,3,3,1> 40 About this sound Play ...
6-z24B [0,2,4,5,7,8] About this sound Play ... 6-z46A [0,1,2,4,6,9] About this sound Play ...
6-z25A [0,1,3,5,6,8] <2,3,3,2,4,1> 43 About this sound Play Major eleventh chord 6-z47B [0,2,5,7,8,9] <2,3,3,2,4,1> 44 About this sound Play ...
6-z25B [0,2,3,5,7,8] About this sound Play ... 6-z47A [0,1,2,4,7,9] About this sound Play blues scale
6-z26 [0,1,3,5,7,8] <2,3,2,3,4,1> 26 About this sound Play ... 6-z48 [0,1,2,5,7,9] <2,3,2,3,4,1> 25 About this sound Play ...
6-27A [0,1,3,4,6,9] <2,2,5,2,2,2> 14 About this sound Play ...
6-27B [0,3,5,6,8,9] About this sound Play ...
6-z28 [0,1,3,5,6,9] <2,2,4,3,2,2> 21 About this sound Play ... 6-z49 [0,1,3,4,7,9] <2,2,4,3,2,2> 22 About this sound Play ...
6-z29 [0,2,3,6,7,9][f] <2,2,4,2,3,2> 32 About this sound Play Bridge chord 6-z50 [0,1,4,6,7,9] <2,2,4,2,3,2> 31 About this sound Play ...
6-30A [0,1,3,6,7,9] <2,2,4,2,2,3> 15 About this sound Play Petrushka chord
6-30B [0,2,3,6,8,9] About this sound Play ...
6-31A [0,1,4,5,7,9][g] <2,2,3,4,3,1> 8 About this sound Play ...
6-31B [0,2,4,5,8,9][h] About this sound Play ...
6-32 [0,2,4,5,7,9] <1,4,3,2,5,0> 6 About this sound Play diatonic hexachord
6-33A [0,2,3,5,7,9] <1,4,3,2,4,1> 18 About this sound Play Dominant eleventh chord
6-33B [0,2,4,6,7,9] About this sound Play ...
6-34A [0,1,3,5,7,9] <1,4,2,4,2,2> 9 About this sound Play mystic chord
6-34B [0,2,4,6,8,9] About this sound Play ...
6-35 [0,2,4,6,8,T] <0,6,0,6,0,3> 1 About this sound Play 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]