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.

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

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.[lower-alpha 1] 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]

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>1Playm2, 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>2PlayM2, 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>3Playm3, 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>4PlayM3, 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>5PlayP4, 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>6PlayA4, 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>4Play...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>12Play...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>11Play...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>9Play...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>7PlayViennese 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>3Play...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>10Play...9-7B[0,1,2,3,4,
 5,7,9,T]		<6,7,7,6,7,3>Play...
3-7B[0,3,5]PlayBlues 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>8PlayIt69-8B[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>5Playsus. 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>2Playdim. 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>6Playminor 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>1PlayAug. 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>1Play...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>17Play...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>9Play...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>20Play...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>22Play...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>6Playdream 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>8Play...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>10Play...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>2Playdistance 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>3Play...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>26Play...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>28Play...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>7Play...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>25Play...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>18Playall-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>19Play...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>13Playalpha 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>21Playdim. 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>24PlaymM7 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>15PlayM7 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>11Play...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>27Playmu 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>4Playquartal 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>16PlayA7 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>12PlayFr68-25[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>14Playminor 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>29PlayHalf-diminished seventh chord8-27B[0,1,2,4,
 6,7,9,T]		<4,5,6,5,5,3>Play...
4-27B[0,3,6,8]Playdominant 7th chord8-27A[0,1,2,4,
 5,7,8,T]		Play...
4-28[0,3,6,9]<0,0,4,0,0,2>5Playdim. 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>23Playall-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>1Play...
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>11Play...
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>14Play...
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>12Play...
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>13Play...
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>27Play...
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>30Play...
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>2Play...
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>15Play...
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>19Play...
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>18Play...
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>5Play...
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>17Play...
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>28Play...
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>4Play...
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>20Play...
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>10Play...
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>35Play...
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>31Play...
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>34Play...
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>21Play...
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>8Playdouble 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>25Play...
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>22Playenigmatic 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>PlaySeven six chord7-25B[0,2,3,5,
 6,7,9]		<3,4,5,3,4,2>24Play...
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>26Play...
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>23Play...
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>36Play...
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>32Play...
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>37Play...
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>Playbeta chord7-31B[0,2,3,5,
 6,8,9]		<3,3,6,3,3,3>38Play...
5-31B[0,2,3,6,9]PlayDominant minor ninth chord7-31A[0,1,3,4,
 6,7,9]		Play...
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>33Playharmonic major scale
5-32B[0,3,5,8,9]PlayElektra chord, gamma chord7-32A[0,1,3,4,
 6,8,9]		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>6PlayM 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>9Playhalf 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>7Playdiatonic 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>16Play...
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>3Play...
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>29Play...
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>4Playchromatic hexachord
6-2A[0,1,2,3,4,6]<4,4,3,2,1,1>19Play...
6-2B[0,2,3,4,5,6]Play...
6-z3A[0,1,2,3,5,6]<4,3,3,2,2,1>49Play...6-z36B[0,3,4,5,6,7]<4,3,3,2,2,1>50Play...
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>24Play...6-z37[0,1,2,3,4,8]<4,3,2,3,2,1>23Play...
6-5A[0,1,2,3,6,7]<4,2,2,2,3,2>16Play...
6-5B[0,1,4,5,6,7]Play...
6-z6[0,1,2,5,6,7]<4,2,1,2,4,2>33Play...6-z38[0,1,2,3,7,8]<4,2,1,2,4,2>34Play...
6-7[0,1,2,6,7,8]<4,2,0,2,4,3>7Play...
6-8[0,2,3,4,5,7]<3,4,3,2,3,0>5Play...
6-9A[0,1,2,3,5,7]<3,4,2,2,3,1>20Play...
6-9B[0,2,4,5,6,7]Play...
6-z10A[0,1,3,4,5,7]<3,3,3,3,2,1>42Play...6-z39B[0,3,4,5,6,8]<3,3,3,3,2,1>41Play...
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>47Play...6-z40B[0,3,5,6,7,8]<3,3,3,2,3,1>48Play...
6-z11B[0,2,3,5,6,7]PlaySacher hexachord6-z40A[0,1,2,3,5,8]Play...
6-z12A[0,1,2,4,6,7]<3,3,2,2,3,2>46Play...6-z41B[0,2,5,6,7,8]<3,3,2,2,3,2>45Play...
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>29Play...6-z42[0,1,2,3,6,9]<3,2,4,2,2,2>30Play...
6-14A[0,1,3,4,5,8]<3,2,3,4,3,0>3Play...
6-14B[0,3,4,5,7,8]Play...
6-15A[0,1,2,4,5,8]<3,2,3,4,2,1>13Play...
6-15B[0,3,4,6,7,8]Play...
6-16A[0,1,4,5,6,8]<3,2,2,4,3,1>11Play...
6-16B[0,2,3,4,7,8]Play...
6-z17A[0,1,2,4,7,8]<3,2,2,3,3,2>35Playall-trichord hexachord6-z43B[0,2,3,6,7,8]<3,2,2,3,3,2>36Play...
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>17Play...
6-18B[0,1,3,6,7,8]Play...
6-z19A[0,1,3,4,7,8]<3,1,3,4,3,1>37Play...6-z44B[0,3,4,7,8,9]<3,1,3,4,3,1>38Play...
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>2Play"Ode-to-Napoleon" hexachord
6-21A[0,2,3,4,6,8]<2,4,2,4,1,2>12Play...
6-21B[0,2,4,5,6,8]Play...
6-22A[0,1,2,4,6,8]<2,4,1,4,2,2>10Play...
6-22B[0,2,4,6,7,8]Play...
6-z23[0,2,3,5,6,8]<2,3,4,2,2,2>27Play...6-z45[0,2,3,4,6,9]<2,3,4,2,2,2>28Play...
6-z24A[0,1,3,4,6,8]<2,3,3,3,3,1>39Play...6-z46B[0,3,5,7,8,9]<2,3,3,3,3,1>40Play...
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>43PlayMajor eleventh chord6-z47B[0,2,5,7,8,9]<2,3,3,2,4,1>44Playblues 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>26Play...6-z48[0,1,2,5,7,9]<2,3,2,3,4,1>25Play...
6-27A[0,1,3,4,6,9]<2,2,5,2,2,2>14Play...
6-27B[0,3,5,6,8,9]Play...
6-z28[0,1,3,5,6,9]<2,2,4,3,2,2>21Play...6-z49[0,1,3,4,7,9]<2,2,4,3,2,2>22Play...
6-z29[0,2,3,6,7,9][lower-alpha 6]<2,2,4,2,3,2>32PlayBridge chord6-z50[0,1,4,6,7,9]<2,2,4,2,3,2>31Play...
6-30A[0,1,3,6,7,9]<2,2,4,2,2,3>15Play...
6-30B[0,2,3,6,8,9]PlayPetrushka chord
6-31A[0,1,4,5,7,9][lower-alpha 7]<2,2,3,4,3,1>8Play...
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>6Playdiatonic hexachord
6-33A[0,2,3,5,7,9]<1,4,3,2,4,1>18Play...
6-33B[0,2,4,6,7,9]PlayDominant eleventh chord
6-34A[0,1,3,5,7,9]<1,4,2,4,2,2>9Playmystic chord
6-34B[0,2,4,6,8,9]Play...
6-35[0,2,4,6,8,T]<0,6,0,6,0,3>1Playwhole 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.
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