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,[lower-alpha 1] 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 formInterval
vector		Carter
no.		AudioPossible
spacings		Forte
no.		Prime formInterval
vector		Carter's
no.		AudioPossible
spacings
0-1 [] <0,0,0,0,0,0>empty set12-1 [0,1,2,3,4,5,
 6,7,8,9,T,E]		 <C,C,C,C,C,6> Playaggregate
1-1 [0] <0,0,0,0,0,0> PlayPU, P811-1 [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 Playm2, M710-1 [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 PlayM2, m710-2 [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 Playm3, M610-3 [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 PlayM3, m610-4 [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 PlayP4, P510-5 [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 PlayA4, d510-6 [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 PlayViennese trichord9-5B [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 PlayBlues trichord (min. pentatonic subset)[8]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 PlayIt69-8B [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 Playsus. chord9-9 [0,1,2,3,5,
 6,7,8,T]		 <6,7,6,6,8,3> Playblues scale
3-10 [0,3,6] <0,0,2,0,0,1>2 Playdim. chord9-10 [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 Playminor chord9-11B [0,1,2,3,5,
 6,8,9,T]		 <6,6,7,7,7,3> Play...
3-11B [0,4,7] Playmajor chord9-11A [0,1,2,3,5,
 6,7,9,T]		 Play...
3-12 [0,4,8] <0,0,0,3,0,0>1 PlayAug. chord9-12 [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 Playdream chord8-6 [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 Playdistance model8-9 [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 Playall-interval tetrachord8-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 Playalpha chord8-17 [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 Playdim. M7 chord8-18B [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 PlayMm7 chord8-19B [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 PlayM7 chord8-20 [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 Playmu chord8-22B [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 Playquartal chord8-23 [0,1,2,3,
 5,7,8,T]		 <4,6,5,4,7,2> Playbebop scale
4-24 [0,2,4,8] <0,2,0,3,0,1>16 PlayA7 chord8-24 [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 PlayFr68-25 [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 Playminor seventh chord8-26 [0,1,3,4,
 5,7,8,T][lower-alpha 2]		 <4,5,6,5,6,2> Play...
4-27A [0,2,5,8] <0,1,2,1,1,1>29 Playdominant 7th chord8-27B [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 Playdim. 7th chord8-28 [0,1,3,4,
 6,7,9,T]		 <4,4,8,4,4,4> Playoctatonic scale
4-z29A [0,1,3,7] <1,1,1,1,1,1>23 Playall-interval tetrachord8-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 [0,2,3,4,8] 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> PlayFarben chord7-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][lower-alpha 3]		 <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][lower-alpha 4] <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] PlayIn scale7-20A [0,1,2,5,
 6,7,9][lower-alpha 5]		 PlayPersian 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 Playdouble 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]		 Playenigmatic scale
5-25A [0,2,3,5,8] <1,2,3,1,2,1> PlaySeven six chord7-25B [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]		 Playminor Neapolitan scale
5-31A [0,1,3,6,9] <1,1,4,1,1,2> PlayDominant minor ninth chord7-31B [0,1,3,4,
 6,8,9]		 <3,3,6,3,3,3>38 Play...
5-31B [0,2,3,6,9] Playbeta chord7-31A [0,2,3,5,
 6,8,9]		 Play...
5-32A [0,1,4,6,9] <1,1,3,2,2,1> PlayElektra chord, gamma chord7-32B [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]		 Playharmonic 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 PlayM Locrian scale
5-34 [0,2,4,6,9] <0,3,2,2,2,1> PlayDominant ninth chord7-34 [0,1,3,4,
 6,8,T]		 <2,5,4,4,4,2>9 Playhalf dim. scale
5-35 [0,2,4,7,9] <0,3,2,1,4,0> PlayM pentatonic scale7-35 [0,1,3,5,
 6,8,T]		 <2,5,4,3,6,1>7 Playdiatonic 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 Playchromatic 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 PlaySacher hexachord6-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 Playall-trichord hexachord6-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] PlaySchoenberg 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 PlayMajor eleventh chord6-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] Playblues 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][lower-alpha 6] <2,2,4,2,3,2>32 PlayBridge chord6-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 PlayPetrushka chord
6-30B [0,2,3,6,8,9] Play...
6-31A [0,1,4,5,7,9][lower-alpha 7] <2,2,3,4,3,1>8 Play...
6-31B [0,2,4,5,8,9][lower-alpha 8] Play...
6-32 [0,2,4,5,7,9] <1,4,3,2,5,0>6 Playdiatonic hexachord
6-33A [0,2,3,5,7,9] <1,4,3,2,4,1>18 PlayDominant eleventh chord
6-33B [0,2,4,6,7,9] Play...
6-34A [0,1,3,5,7,9] <1,4,2,4,2,2>9 Playmystic 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 Playwhole tone scale

See also

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.
  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.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.