List of set classes

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Set 3-1 has three possible rotations/inversions, the normal form of which is the smallest pie or most compact form

This is a list of set classes 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). "T" and "E" are conventionally used in sets to notate 10 and 11, respectively, as single characters.

There are two slightly different methods of obtaining a normal form.[a] This results in two different normal form sets for the same Forte number in a few cases. The alternative notation for those chords are listed in the 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]

List[edit]

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> 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 Blues trichord (min. pentatonic subset)[8] 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 all-interval tetrachord 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 alpha chord 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 [0,3,4,8] 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 Half-diminished seventh 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 dominant 7th chord 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 all-interval tetrachord 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 [0,2,3,4,8] 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 In scale 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 enigmatic scale
5-24B [0,2,4,6,7] Play ... 7-24A [0,1,2,3,
 5,7,9]
Play ...
5-25A [0,2,3,5,8] <1,2,3,1,2,1> Play Seven six chord 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 beta chord 7-31B [0,2,3,5,
 6,8,9]
<3,3,6,3,3,3> 38 Play ...
5-31B [0,2,3,6,9] Play Dominant minor ninth chord 7-31A [0,1,3,4,
 6,7,9]
Play Hungarian major scale
5-32A [0,1,4,6,9] <1,1,3,2,2,1> Play ... 7-32B [0,1,3,5,
 6,8,9]
<3,3,5,4,4,2> 33 Play harmonic major scale
5-32B [0,3,5,8,9] Play Elektra chord, gamma chord 7-32A [0,1,3,4,
 6,8,9]
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 Dominant ninth chord 7-34 [0,1,3,4,
 6,8,T]
<2,5,4,4,4,2> 9 Play altered 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 ... 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 Sacher hexachord 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 Major eleventh chord 6-z47B [0,2,5,7,8,9] <2,3,3,2,4,1> 44 Play blues scale
6-z25B [0,2,3,5,7,8] Play ... 6-z47A [0,1,2,4,7,9] Play ...
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 ...
6-30B [0,2,3,6,8,9] Play Petrushka chord
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 Dominant eleventh chord
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[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]