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List of set classes

From Wikipedia, the free encyclopedia

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] A set class in music theory is a collection of pitch classes. 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

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 [0,1,3,4,5,
 6,7,8,T] [b]		 <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 [0,1,2,4,5,
 6,7,8,T] [c]		 <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 [0,1,2,4,5,
 6,7,9,T] [d]		 <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 [0,1,3,4,
 5,6,8,T] [e]		 <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][f]		 <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 [0,1,3,4,
 6,7,8,T] [g]		 <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][h]		 <4,3,4,4,4,2> 35 Playⓘ ...
5-z18B [0,2,3,6,7] Playⓘ ... 7-z18B [0,2,3,4,
 5,8,9] [i]		 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][j] <2,1,1,2,3,1> Playⓘ ... 7-20B [0,2,3,4,
 7,8,9][k]		 <4,3,3,4,5,2> 34 Playⓘ ...
5-20B [0,2,3,7,8][l] Playⓘ In scale 7-20A [0,1,2,5,
 6,7,9][m]		 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ⓘ Romanian major scale
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 [0,2,5,6,9][n] 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 [0,1,4,5,6,9][o] <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 [0,2,4,5,6,9] <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 [0,2,3,4,7,9] <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 [0,2,3,5,6,9] 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][p] <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][q] <2,2,3,4,3,1> 8 Playⓘ ...
6-31B [0,2,4,5,8,9][r] 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

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: [0,1,2,3,4,6,8,9,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.

External links

This page was last edited on 25 April 2024, at 01:29
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