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.[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]

List

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>Playⓘaggregate
1-1[0]<0,0,0,0,0,0>PlayⓘPU, 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>1Playⓘm2, 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>2PlayⓘM2, 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>3Playⓘm3, 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>4PlayⓘM3, 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>5PlayⓘP4, 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>6PlayⓘA4, 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>7PlayⓘViennese 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[0,1,3,4,5,
 6,7,8,T] [lower-alpha 2]		<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>8PlayⓘIt69-8B[0,1,2,4,5,
 6,7,8,T] [lower-alpha 3]		<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>5Playⓘsus. chord9-9[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>2Playⓘdim. 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>6Playⓘminor chord9-11B[0,1,2,4,5,
 6,7,9,T] [lower-alpha 4]		<6,6,7,7,7,3>Playⓘ...
3-11B[0,4,7]Playⓘmajor chord9-11A[0,1,2,3,5,
 6,7,9,T]		Playⓘ...
3-12[0,4,8]<0,0,0,3,0,0>1PlayⓘAug. 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>6Playⓘdream 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>2Playⓘdistance 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>18Playⓘall-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ⓘall-interval tetrachord8-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>13Playⓘalpha 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>21Playⓘdim. 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>24PlayⓘmM7 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>15PlayⓘM7 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>27Playⓘmu chord8-22B[0,1,3,4,
 5,6,8,T] [lower-alpha 5]		<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>4Playⓘquartal chord8-23[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>16PlayⓘA7 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>12PlayⓘFr68-25[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>14Playⓘminor seventh chord8-26[0,1,3,4,
 5,7,8,T][lower-alpha 6]		<4,5,6,5,6,2>Playⓘ...
4-27A[0,2,5,8]<0,1,2,1,1,1>29PlayⓘHalf-diminished seventh chord8-27B[0,1,3,4,
 6,7,8,T] [lower-alpha 7]		<4,5,6,5,5,3>Playⓘ...
4-27B[0,3,6,8]Playⓘdominant 7th chord8-27A[0,1,2,4,
 5,7,8,T]		Playⓘ...
4-28[0,3,6,9]<0,0,4,0,0,2>5Playⓘdim. 7th chord8-28[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>23Playⓘall-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ⓘall-interval tetrachord8-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>PlayⓘFarben 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 8]		<4,3,4,4,4,2>35Playⓘ...
5-z18B[0,2,3,6,7]Playⓘ...7-z18B[0,2,3,4,
 5,8,9] [lower-alpha 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 10]<2,1,1,2,3,1>Playⓘ...7-20B[0,2,3,4,
 7,8,9][lower-alpha 11]		<4,3,3,4,5,2>34Playⓘ...
5-20B[0,2,3,7,8][lower-alpha 12]PlayⓘIn scale7-20A[0,1,2,5,
 6,7,9][lower-alpha 13]		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>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>8Playⓘ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>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>22Playⓘ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 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]		Playⓘminor Neapolitan scale
5-31A[0,1,3,6,9]<1,1,4,1,1,2>Playⓘbeta chord7-31B[0,2,3,5,
 6,8,9]		<3,3,6,3,3,3>38PlayⓘRomanian major scale
5-31B[0,2,3,6,9]PlayⓘDominant minor ninth chord7-31A[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>33Playⓘharmonic major scale
5-32B[0,2,5,6,9][lower-alpha 14]PlayⓘElektra chord, gamma chord7-32A[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>6PlayⓘM Locrian scale
5-34[0,2,4,6,9]<0,3,2,2,2,1>PlayⓘDominant ninth chord7-34[0,1,3,4,
 6,8,T]		<2,5,4,4,4,2>9Playⓘaltered scale
5-35[0,2,4,7,9]<0,3,2,1,4,0>PlayⓘM pentatonic scale7-35[0,1,3,5,
 6,8,T]		<2,5,4,3,6,1>7Playⓘ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>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>4Playⓘchromatic 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]PlayⓘSacher 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>35Playⓘall-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[0,1,4,5,6,9][lower-alpha 15]<3,1,3,4,3,1>38Playⓘ...
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>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[0,2,4,5,6,9]<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>43PlayⓘMajor eleventh chord6-z47B[0,2,3,4,7,9]<2,3,3,2,4,1>44Playⓘ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>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[0,2,3,5,6,9]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 16]<2,2,4,2,3,2>32PlayⓘBridge 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]PlayⓘPetrushka chord
6-31A[0,1,4,5,7,9][lower-alpha 17]<2,2,3,4,3,1>8Playⓘ...
6-31B[0,2,4,5,8,9][lower-alpha 18]Playⓘ...
6-32[0,2,4,5,7,9]<1,4,3,2,5,0>6Playⓘdiatonic hexachord
6-33A[0,2,3,5,7,9]<1,4,3,2,4,1>18Playⓘ...
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>9Playⓘ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>1Playⓘwhole 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 9-7B: [0,1,2,3,4,5,7,9,T]
  3. ↑ Forte 9-8B: [0,1,2,4,5,6,7,8,T]
  4. ↑ Forte 9-11B: [0,1,2,3,5,6,8,9,T]
  5. ↑ Forte 8-22B: [0,1,2,3,5,7,9,T]
  6. ↑ Forte 8-26: [0,1,2,4,5,7,9,T]
  7. ↑ Forte 8-27B: [0,1,2,4,6,7,9,T]
  8. ↑ Forte 7-z18A: [0,1,2,3,5,8,9]
  9. ↑ Forte 7-z18B: [0,1,4,6,7,8,9]
  10. ↑ Forte 5-20A: [0,1,3,7,8]
  11. ↑ Forte 7-20B: [0,1,2,5,7,8,9]
  12. ↑ Forte 5-20B: [0,1,5,7,8]
  13. ↑ Forte 7-20A: [0,1,2,4,7,8,9]
  14. ↑ Forte 5-32B: [0,1,4,7,9]
  15. ↑ Forte 6-z44B: [0,1,2,5,8,9]
  16. ↑ Forte 6-z29: [0,1,3,6,8,9]
  17. ↑ Forte 6-31A: [0,1,3,5,8,9]
  18. ↑ 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.