List of set classes
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Set_theory_3-1_in_the_chromatic_circle.svg/330px-Set_theory_3-1_in_the_chromatic_circle.svg.png)
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. The prime form of unsymmetrical sets is marked "A". Inversions are marked "B" (sets not marked "A" or "B" are symmetrical). "T" and "E" are conventionally used in sets to notate ten and eleven, respectively, as single characters. The ordering of sets in the lists is based on the string of numerals in the interval vector treated as an integer, decreasing in value, following the strategy used by Forte in constructing his numbering system. Numbers marked with a "z" refer to a pair of sets with identical interval class content, with one of the pair listed at the end of the respective list when they occur. [The "z" derives from the prefix "zygo"—from the ancient Greek, meaning yoked or paired. Hence: zygosets.]
There are two slightly different methods of obtaining the prime form—an earlier one due to Allen Forte and a later (and generally now more popular) one devised by John Rahn—both often confusingly described as "most packed to the left". However, a more precise description of the Rahn spelling is to select the version that is most dispersed from the right. The precise description of the Forte spelling is to select the version that is most packed to the left within the smallest span. [a] This results in two different prime form sets for the same Forte number in a number of cases. The lists here use the Rahn spelling. The alternative notations for those set classes where the Forte spelling differs 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]
The difference between the interval vector of a set and that of its complement is <X, X, X, X, X, X/2>, where (in base-ten) X = 12 – 2C, and C is the cardinality of the smaller set. In nearly all cases, complements of unsymmetrical sets are inversionally related—i.e. the complement of an "A" version of a set of cardinality C is (usually) the "B" version of the respective set of cardinality 12 – C. The most significant exceptions are the sets 4-14/8-14, 5-11/7-11, and 6-14, which are all closely related in terms of subset/superset structure.
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> | aggregate | ||||
1-1 | [0] | <0,0,0,0,0,0> | PU, P8 | 11-1 | [0,1,2,3,4,5, 6,7,8,9,T] |
<T,T,T,T,T,5> | ... | ||||
2-1 | [0,1] | <1,0,0,0,0,0> | 1 | m2, M7 | 10-1 | [0,1,2,3,4, 5,6,7,8,9] |
<9,8,8,8,8,4> | ... | |||
2-2 | [0,2] | <0,1,0,0,0,0> | 2 | M2, m7 | 10-2 | [0,1,2,3,4, 5,6,7,8,T] |
<8,9,8,8,8,4> | ... | |||
2-3 | [0,3] | <0,0,1,0,0,0> | 3 | m3, M6 | 10-3 | [0,1,2,3,4, 5,6,7,9,T] |
<8,8,9,8,8,4> | ... | |||
2-4 | [0,4] | <0,0,0,1,0,0> | 4 | M3, m6 | 10-4 | [0,1,2,3,4, 5,6,8,9,T] |
<8,8,8,9,8,4> | ... | |||
2-5 | [0,5] | <0,0,0,0,1,0> | 5 | P4, P5 | 10-5 | [0,1,2,3,4, 5,7,8,9,T] |
<8,8,8,8,9,4> | ... | |||
2-6 | [0,6] | <0,0,0,0,0,1> | 6 | A4, d5 | 10-6 | [0,1,2,3,4, 6,7,8,9,T] |
<8,8,8,8,8,5> | ... | |||
3-1 | [0,1,2] | <2,1,0,0,0,0> | 4 | ... | 9-1 | [0,1,2,3,4, 5,6,7,8] |
<8,7,6,6,6,3> | ... | |||
3-2A | [0,1,3] | <1,1,1,0,0,0> | 12 | ... | 9-2B | [0,2,3,4,5, 6,7,8,9] |
<7,7,7,6,6,3> | ... | |||
3-2B | [0,2,3] | ... | 9-2A | [0,1,2,3,4, 5,6,7,9] |
... | ||||||
3-3A | [0,1,4] | <1,0,1,1,0,0> | 11 | ... | 9-3B | [0,1,3,4, 5,6,7,8,9] |
<7,6,7,7,6,3> | ... | |||
3-3B | [0,3,4] | ... | 9-3A | [0,1,2,3,4, 5,6,8,9] |
... | ||||||
3-4A | [0,1,5] | <1,0,0,1,1,0> | 9 | ... | 9-4B | [0,1,2,4,5, 6,7,8,9] |
<7,6,6,7,7,3> | ... | |||
3-4B | [0,4,5] | ... | 9-4A | [0,1,2,3,4, 5,7,8,9] |
... | ||||||
3-5A | [0,1,6] | <1,0,0,0,1,1> | 7 | Viennese trichord | 9-5B | [0,1,2,3,5, 6,7,8,9] |
<7,6,6,6,7,4> | ... | |||
3-5B | [0,5,6] | ... | 9-5A | [0,1,2,3,4, 6,7,8,9] |
... | ||||||
3-6 | [0,2,4] | <0,2,0,1,0,0> | 3 | ... | 9-6 | [0,1,2,3,4, 5,6,8,T] |
<6,8,6,7,6,3> | ... | |||
3-7A | [0,2,5] | <0,1,1,0,1,0> | 10 | ... | 9-7B | [0,1,3,4,5, 6,7,8,T] [b] |
<6,7,7,6,7,3> | ... | |||
3-7B | [0,3,5] | Blues trichord (min. pentatonic subset)[8] | 9-7A | [0,1,2,3,4, 5,7,8,T] |
... | ||||||
3-8A | [0,2,6] | <0,1,0,1,0,1> | 8 | It6 | 9-8B | [0,1,2,4,5, 6,7,8,T] [c] |
<6,7,6,7,6,4> | ... | |||
3-8B | [0,4,6] | ... | 9-8A | [0,1,2,3,4, 6,7,8,T] |
... | ||||||
3-9 | [0,2,7] | <0,1,0,0,2,0> | 5 | sus. chord | 9-9 | [0,1,2,3,5, 6,7,8,T] |
<6,7,6,6,8,3> | blues scale | |||
3-10 | [0,3,6] | <0,0,2,0,0,1> | 2 | dim. chord | 9-10 | [0,1,2,3,4, 6,7,9,T] |
<6,6,8,6,6,4> | ... | |||
3-11A | [0,3,7] | <0,0,1,1,1,0> | 6 | minor chord | 9-11B | [0,1,2,4,5, 6,7,9,T] [d] |
<6,6,7,7,7,3> | ... | |||
3-11B | [0,4,7] | major chord | 9-11A | [0,1,2,3,5, 6,7,9,T] |
... | ||||||
3-12 | [0,4,8] | <0,0,0,3,0,0> | 1 | Aug. chord | 9-12 | [0,1,2,4,5, 6,8,9,T] |
<6,6,6,9,6,3> | ... | |||
4-1 | [0,1,2,3] | <3,2,1,0,0,0> | 1 | ... | 8-1 | [0,1,2,3, 4,5,6,7] |
<7,6,5,4,4,2> | ... | |||
4-2A | [0,1,2,4] | <2,2,1,1,0,0> | 17 | ... | 8-2B | [0,2,3,4, 5,6,7,8] |
<6,6,5,5,4,2> | ... | |||
4-2B | [0,2,3,4] | ... | 8-2A | [0,1,2,3, 4,5,6,8] |
... | ||||||
4-3 | [0,1,3,4] | <2,1,2,1,0,0> | 9 | DSCH motif | 8-3 | [0,1,2,3, 4,5,6,9] |
<6,5,6,5,4,2> | ... | |||
4-4A | [0,1,2,5] | <2,1,1,1,1,0> | 20 | ... | 8-4B | [0,1,3,4, 5,6,7,8] |
<6,5,5,5,5,2> | ... | |||
4-4B | [0,3,4,5] | ... | 8-4A | [0,1,2,3, 4,5,7,8] |
... | ||||||
4-5A | [0,1,2,6] | <2,1,0,1,1,1> | 22 | ... | 8-5B | [0,1,2,4, 5,6,7,8] |
<6,5,4,5,5,3> | ... | |||
4-5B | [0,4,5,6] | ... | 8-5A | [0,1,2,3, 4,6,7,8] |
... | ||||||
4-6 | [0,1,2,7] | <2,1,0,0,2,1> | 6 | dream chord | 8-6 | [0,1,2,3, 5,6,7,8] |
<6,5,4,4,6,3> | ... | |||
4-7 | [0,1,4,5] | <2,0,1,2,1,0> | 8 | ... | 8-7 | [0,1,2,3, 4,5,8,9] |
<6,4,5,6,5,2> | ... | |||
4-8 | [0,1,5,6] | <2,0,0,1,2,1> | 10 | ... | 8-8 | [0,1,2,3, 4,7,8,9] |
<6,4,4,5,6,3> | ... | |||
4-9 | [0,1,6,7] | <2,0,0,0,2,2> | 2 | distance model | 8-9 | [0,1,2,3, 6,7,8,9] |
<6,4,4,4,6,4> | ... | |||
4-10 | [0,2,3,5] | <1,2,2,0,1,0> | 3 | ... | 8-10 | [0,2,3,4, 5,6,7,9] |
<5,6,6,4,5,2> | ... | |||
4-11A | [0,1,3,5] | <1,2,1,1,1,0> | 26 | ... | 8-11B | [0,2,4,5, 6,7,8,9] |
<5,6,5,5,5,2> | ... | |||
4-11B | [0,2,4,5] | ... | 8-11A | [0,1,2,3, 4,5,7,9] |
... | ||||||
4-12A | [0,2,3,6] | <1,1,2,1,0,1> | 28 | ... | 8-12A | [0,1,3,4, 5,6,7,9] |
<5,5,6,5,4,3> | ... | |||
4-12B | [0,3,4,6] | ... | 8-12B | [0,2,3,4, 5,6,8,9] |
... | ||||||
4-13A | [0,1,3,6] | <1,1,2,0,1,1> | 7 | ... | 8-13B | [0,2,3,5, 6,7,8,9] |
<5,5,6,4,5,3> | ... | |||
4-13B | [0,3,5,6] | ... | 8-13A | [0,1,2,3, 4,6,7,9] |
... | ||||||
4-14A | [0,2,3,7] | <1,1,1,1,2,0> | 25 | ... | 8-14A | [0,1,2,4, 5,6,7,9] |
<5,5,5,5,6,2> | ... | |||
4-14B | [0,4,5,7] | ... | 8-14B | [0,2,3,4, 5,7,8,9] |
... | ||||||
4-z15A | [0,1,4,6] | <1,1,1,1,1,1> | 18 | all-interval tetrachord | 8-z15B | [0,1,3,5, 6,7,8,9] |
<5,5,5,5,5,3> | ... | |||
4-z15B | [0,2,5,6] | all-interval tetrachord | 8-z15A | [0,1,2,3, 4,6,8,9] |
... | ||||||
4-16A | [0,1,5,7] | <1,1,0,1,2,1> | 19 | ... | 8-16B | [0,1,2,4, 6,7,8,9] |
<5,5,4,5,6,3> | ... | |||
4-16B | [0,2,6,7] | ... | 8-16A | [0,1,2,3, 5,7,8,9] |
... | ||||||
4-17 | [0,3,4,7] | <1,0,2,2,1,0> | 13 | alpha chord | 8-17 | [0,1,3,4, 5,6,8,9] |
<5,4,6,6,5,2> | ... | |||
4-18A | [0,1,4,7] | <1,0,2,1,1,1> | 21 | dim. M7 chord | 8-18B | [0,1,3,4, 6,7,8,9] |
<5,4,6,5,5,3> | ... | |||
4-18B | [0,3,6,7] | ... | 8-18A | [0,1,2,3, 5,6,8,9] |
... | ||||||
4-19A | [0,1,4,8] | <1,0,1,3,1,0> | 24 | mM7 chord | 8-19B | [0,1,3,4, 5,7,8,9] |
<5,4,5,7,5,2> | ... | |||
4-19B | [0,3,4,8] | ... | 8-19A | [0,1,2,4, 5,6,8,9] |
... | ||||||
4-20 | [0,1,5,8] | <1,0,1,2,2,0> | 15 | M7 chord | 8-20 | [0,1,2,4, 5,7,8,9] |
<5,4,5,6,6,2> | ... | |||
4-21 | [0,2,4,6] | <0,3,0,2,0,1> | 11 | ... | 8-21 | [0,1,2,3, 4,6,8,T] |
<4,7,4,6,4,3> | ... | |||
4-22A | [0,2,4,7] | <0,2,1,1,2,0> | 27 | mu chord | 8-22B | [0,1,3,4, 5,6,8,T] [e] |
<4,6,5,5,6,2> | ... | |||
4-22B | [0,3,5,7] | ... | 8-22A | [0,1,2,3, 5,6,8,T] |
... | ||||||
4-23 | [0,2,5,7] | <0,2,1,0,3,0> | 4 | quartal chord | 8-23 | [0,1,2,3, 5,7,8,T] |
<4,6,5,4,7,2> | bebop scale | |||
4-24 | [0,2,4,8] | <0,2,0,3,0,1> | 16 | A7 chord | 8-24 | [0,1,2,4, 5,6,8,T] |
<4,6,4,7,4,3> | ... | |||
4-25 | [0,2,6,8] | <0,2,0,2,0,2> | 12 | Fr6 | 8-25 | [0,1,2,4, 6,7,8,T] |
<4,6,4,6,4,4> | ... | |||
4-26 | [0,3,5,8] | <0,1,2,1,2,0> | 14 | minor seventh chord | 8-26 | [0,1,3,4, 5,7,8,T][f] |
<4,5,6,5,6,2> | ... | |||
4-27A | [0,2,5,8] | <0,1,2,1,1,1> | 29 | Half-diminished seventh chord | 8-27B | [0,1,3,4, 6,7,8,T] [g] |
<4,5,6,5,5,3> | ... | |||
4-27B | [0,3,6,8] | dominant 7th chord | 8-27A | [0,1,2,4, 5,7,8,T] |
... | ||||||
4-28 | [0,3,6,9] | <0,0,4,0,0,2> | 5 | dim. 7th chord | 8-28 | [0,1,3,4, 6,7,9,T] |
<4,4,8,4,4,4> | octatonic scale | |||
4-z29A | [0,1,3,7] | <1,1,1,1,1,1> | 23 | all-interval tetrachord | 8-z29B | [0,2,3,4, 6,7,8,9] |
<5,5,5,5,5,3> | ... | |||
4-z29B | [0,4,6,7] | all-interval tetrachord | 8-z29A | [0,1,2,3, 5,6,7,9] |
... | ||||||
5-1 | [0,1,2,3,4] | <4,3,2,1,0,0> | ... | 7-1 | [0,1,2,3, 4,5,6] |
<6,5,4,3,2,1> | 1 | ... | |||
5-2A | [0,1,2,3,5] | <3,3,2,1,1,0> | ... | 7-2B | [0,2,3,4, 5,6,7] |
<5,5,4,3,3,1> | 11 | ... | |||
5-2B | [0,2,3,4,5] | ... | 7-2A | [0,1,2,3, 4,5,7] |
... | ||||||
5-3A | [0,1,2,4,5] | <3,2,2,2,1,0> | ... | 7-3B | [0,3,4,5, 6,7,8] |
<5,4,4,4,3,1> | 14 | ... | |||
5-3B | [0,1,3,4,5] | ... | 7-3A | [0,1,2,3, 4,5,8] |
... | ||||||
5-4A | [0,1,2,3,6] | <3,2,2,1,1,1> | ... | 7-4B | [0,1,3,4, 5,6,7] |
<5,4,4,3,3,2> | 12 | ... | |||
5-4B | [0,3,4,5,6] | ... | 7-4A | [0,1,2,3, 4,6,7] |
... | ||||||
5-5A | [0,1,2,3,7] | <3,2,1,1,2,1> | ... | 7-5B | [0,1,2,4, 5,6,7] |
<5,4,3,3,4,2> | 13 | ... | |||
5-5B | [0,4,5,6,7] | ... | 7-5A | [0,1,2,3, 5,6,7] |
... | ||||||
5-6A | [0,1,2,5,6] | <3,1,1,2,2,1> | ... | 7-6B | [0,1,4,5, 6,7,8] |
<5,3,3,4,4,2> | 27 | ... | |||
5-6B | [0,1,4,5,6] | ... | 7-6A | [0,1,2,3, 4,7,8] |
... | ||||||
5-7A | [0,1,2,6,7] | <3,1,0,1,3,2> | ... | 7-7B | [0,1,2,5, 6,7,8] |
<5,3,2,3,5,3> | 30 | ... | |||
5-7B | [0,1,5,6,7] | ... | 7-7A | [0,1,2,3, 6,7,8] |
... | ||||||
5-8 | [0,2,3,4,6] | <2,3,2,2,0,1> | ... | 7-8 | [0,2,3,4, 5,6,8] |
<4,5,4,4,2,2> | 2 | ... | |||
5-9A | [0,1,2,4,6] | <2,3,1,2,1,1> | ... | 7-9B | [0,2,4,5, 6,7,8] |
<4,5,3,4,3,2> | 15 | ... | |||
5-9B | [0,2,4,5,6] | ... | 7-9A | [0,1,2,3, 4,6,8] |
... | ||||||
5-10A | [0,1,3,4,6] | <2,2,3,1,1,1> | ... | 7-10B | [0,2,3,4, 5,6,9] |
<4,4,5,3,3,2> | 19 | ... | |||
5-10B | [0,2,3,5,6] | ... | 7-10A | [0,1,2,3, 4,6,9] |
... | ||||||
5-11A | [0,2,3,4,7] | <2,2,2,2,2,0> | ... | 7-11B | [0,2,3,4, 5,7,8] |
<4,4,4,4,4,1> | 18 | ... | |||
5-11B | [0,3,4,5,7] | ... | 7-11A | [0,1,3,4, 5,6,8] |
... | ||||||
5-z12 | [0,1,3,5,6] | <2,2,2,1,2,1> | ... | 7-z12 | [0,1,2,3, 4,7,9] |
<4,4,4,3,4,2> | 5 | ... | |||
5-13A | [0,1,2,4,8] | <2,2,1,3,1,1> | ... | 7-13B | [0,2,3,4, 6,7,8] |
<4,4,3,5,3,2> | 17 | ... | |||
5-13B | [0,2,3,4,8] | ... | 7-13A | [0,1,2,4, 5,6,8] |
... | ||||||
5-14A | [0,1,2,5,7] | <2,2,1,1,3,1> | ... | 7-14B | [0,1,3,5, 6,7,8] |
<4,4,3,3,5,2> | 28 | ... | |||
5-14B | [0,2,5,6,7] | ... | 7-14A | [0,1,2,3, 5,7,8] |
... | ||||||
5-15 | [0,1,2,6,8] | <2,2,0,2,2,2> | ... | 7-15 | [0,1,2,4, 6,7,8] |
<4,4,2,4,4,3> | 4 | ... | |||
5-16A | [0,1,3,4,7] | <2,1,3,2,1,1> | ... | 7-16B | [0,1,3,4, 5,6,9] |
<4,3,5,4,3,2> | 20 | ... | |||
5-16B | [0,3,4,6,7] | ... | 7-16A | [0,1,2,3, 5,6,9] |
... | ||||||
5-z17 | [0,1,3,4,8] | <2,1,2,3,2,0> | Farben chord | 7-z17 | [0,1,2,4, 5,6,9] |
<4,3,4,5,4,1> | 10 | ... | |||
5-z18A | [0,1,4,5,7] | <2,1,2,2,2,1> | ... | 7-z18A | [0,1,4,5, 6,7,9][h] |
<4,3,4,4,4,2> | 35 | ... | |||
5-z18B | [0,2,3,6,7] | ... | 7-z18B | [0,2,3,4, 5,8,9] [i] |
... | ||||||
5-19A | [0,1,3,6,7] | <2,1,2,1,2,2> | ... | 7-19B | [0,1,2,3, 6,8,9] |
<4,3,4,3,4,3> | 31 | ... | |||
5-19B | [0,1,4,6,7] | ... | 7-19A | [0,1,2,3, 6,7,9] |
... | ||||||
5-20A | [0,1,5,6,8][j] | <2,1,1,2,3,1> | ... | 7-20B | [0,2,3,4, 7,8,9][k] |
<4,3,3,4,5,2> | 34 | ... | |||
5-20B | [0,2,3,7,8][l] | In scale | 7-20A | [0,1,2,5, 6,7,9][m] |
Persian scale | ||||||
5-21A | [0,1,4,5,8] | <2,0,2,4,2,0> | ... | 7-21B | [0,1,3,4, 5,8,9] |
<4,2,4,6,4,1> | 21 | ... | |||
5-21B | [0,3,4,7,8] | ... | 7-21A | [0,1,2,4, 5,8,9] |
... | ||||||
5-22 | [0,1,4,7,8] | <2,0,2,3,2,1> | ... | 7-22 | [0,1,2,5, 6,8,9] |
<4,2,4,5,4,2> | 8 | double harmonic scale | |||
5-23A | [0,2,3,5,7] | <1,3,2,1,3,0> | ... | 7-23B | [0,2,4,5, 6,7,9] |
<3,5,4,3,5,1> | 25 | ... | |||
5-23B | [0,2,4,5,7] | ... | 7-23A | [0,2,3,4, 5,7,9] |
... | ||||||
5-24A | [0,1,3,5,7] | <1,3,1,2,2,1> | ... | 7-24B | [0,2,4,6, 7,8,9] |
<3,5,3,4,4,2> | 22 | enigmatic scale | |||
5-24B | [0,2,4,6,7] | ... | 7-24A | [0,1,2,3, 5,7,9] |
... | ||||||
5-25A | [0,2,3,5,8] | <1,2,3,1,2,1> | Seven six chord | 7-25B | [0,2,3,5, 6,7,9] |
<3,4,5,3,4,2> | 24 | ... | |||
5-25B | [0,3,5,6,8] | ... | 7-25A | [0,2,3,4, 6,7,9] |
... | ||||||
5-26A | [0,2,4,5,8] | <1,2,2,3,1,1> | ... | 7-26A | [0,1,3,4, 5,7,9] |
<3,4,4,5,3,2> | 26 | ... | |||
5-26B | [0,3,4,6,8] | ... | 7-26B | [0,2,4,5, 6,8,9] |
... | ||||||
5-27A | [0,1,3,5,8] | <1,2,2,2,3,0> | ... | 7-27B | [0,2,4,5, 7,8,9] |
<3,4,4,4,5,1> | 23 | ... | |||
5-27B | [0,3,5,7,8] | ... | 7-27A | [0,1,2,4, 5,7,9] |
... | ||||||
5-28A | [0,2,3,6,8] | <1,2,2,2,1,2> | ... | 7-28A | [0,1,3,5, 6,7,9] |
<3,4,4,4,3,3> | 36 | ... | |||
5-28B | [0,2,5,6,8] | ... | 7-28B | [0,2,3,4, 6,8,9] |
... | ||||||
5-29A | [0,1,3,6,8] | <1,2,2,1,3,1> | ... | 7-29B | [0,2,3,5, 7,8,9] |
<3,4,4,3,5,2> | 32 | ... | |||
5-29B | [0,2,5,7,8] | ... | 7-29A | [0,1,2,4, 6,7,9] |
... | ||||||
5-30A | [0,1,4,6,8] | <1,2,1,3,2,1> | ... | 7-30B | [0,1,3,5, 7,8,9] |
<3,4,3,5,4,2> | 37 | ... | |||
5-30B | [0,2,4,7,8] | ... | 7-30A | [0,1,2,4, 6,8,9] |
minor Neapolitan scale | ||||||
5-31A | [0,1,3,6,9] | <1,1,4,1,1,2> | beta chord | 7-31B | [0,2,3,5, 6,8,9] |
<3,3,6,3,3,3> | 38 | Romanian major scale | |||
5-31B | [0,2,3,6,9] | Dominant minor ninth chord | 7-31A | [0,1,3,4, 6,7,9] |
Hungarian major scale | ||||||
5-32A | [0,1,4,6,9] | <1,1,3,2,2,1> | ... | 7-32B | [0,1,3,5, 6,8,9] |
<3,3,5,4,4,2> | 33 | harmonic major scale | |||
5-32B | [0,2,5,6,9][n] | Elektra chord, gamma chord | 7-32A | [0,1,3,4, 6,8,9] |
harmonic minor scale | ||||||
5-33 | [0,2,4,6,8] | <0,4,0,4,0,2> | ... | 7-33 | [0,1,2,4, 6,8,T] |
<2,6,2,6,2,3> | 6 | M Locrian scale | |||
5-34 | [0,2,4,6,9] | <0,3,2,2,2,1> | Dominant ninth chord | 7-34 | [0,1,3,4, 6,8,T] |
<2,5,4,4,4,2> | 9 | altered scale | |||
5-35 | [0,2,4,7,9] | <0,3,2,1,4,0> | M pentatonic scale | 7-35 | [0,1,3,5, 6,8,T] |
<2,5,4,3,6,1> | 7 | diatonic scale | |||
5-z36A | [0,1,2,4,7] | <2,2,2,1,2,1> | ... | 7-z36B | [0,2,3,5, 6,7,8] |
<4,4,4,3,4,2> | 16 | ... | |||
5-z36B | [0,3,5,6,7] | ... | 7-z36A | [0,1,2,3, 5,6,8] |
... | ||||||
5-z37 | [0,3,4,5,8] | <2,1,2,3,2,0> | ... | 7-z37 | [0,1,3,4, 5,7,8] |
<4,3,4,5,4,1> | 3 | ... | |||
5-z38A | [0,1,2,5,8] | <2,1,2,2,2,1> | ... | 7-z38B | [0,1,3,4, 6,7,8] |
<4,3,4,4,4,2> | 29 | ... | |||
5-z38B | [0,3,6,7,8] | ... | 7-z38A | [0,1,2,4, 5,7,8] |
... | ||||||
6-1 | [0,1,2,3,4,5] | <5,4,3,2,1,0> | 4 | chromatic hexachord | |||||||
6-2A | [0,1,2,3,4,6] | <4,4,3,2,1,1> | 19 | ... | |||||||
6-2B | [0,2,3,4,5,6] | ... | |||||||||
6-z3A | [0,1,2,3,5,6] | <4,3,3,2,2,1> | 49 | ... | 6-z36B | [0,3,4,5,6,7] | <4,3,3,2,2,1> | 50 | ... | ||
6-z3B | [0,1,3,4,5,6] | ... | 6-z36A | [0,1,2,3,4,7] | ... | ||||||
6-z4 | [0,1,2,4,5,6] | <4,3,2,3,2,1> | 24 | ... | 6-z37 | [0,1,2,3,4,8] | <4,3,2,3,2,1> | 23 | ... | ||
6-5A | [0,1,2,3,6,7] | <4,2,2,2,3,2> | 16 | ... | |||||||
6-5B | [0,1,4,5,6,7] | ... | |||||||||
6-z6 | [0,1,2,5,6,7] | <4,2,1,2,4,2> | 33 | ... | 6-z38 | [0,1,2,3,7,8] | <4,2,1,2,4,2> | 34 | ... | ||
6-7 | [0,1,2,6,7,8] | <4,2,0,2,4,3> | 7 | ... | |||||||
6-8 | [0,2,3,4,5,7] | <3,4,3,2,3,0> | 5 | ... | |||||||
6-9A | [0,1,2,3,5,7] | <3,4,2,2,3,1> | 20 | ... | |||||||
6-9B | [0,2,4,5,6,7] | ... | |||||||||
6-z10A | [0,1,3,4,5,7] | <3,3,3,3,2,1> | 42 | ... | 6-z39B | [0,3,4,5,6,8] | <3,3,3,3,2,1> | 41 | ... | ||
6-z10B | [0,2,3,4,6,7] | ... | 6-z39A | [0,2,3,4,5,8] | ... | ||||||
6-z11A | [0,1,2,4,5,7] | <3,3,3,2,3,1> | 47 | ... | 6-z40B | [0,3,5,6,7,8] | <3,3,3,2,3,1> | 48 | ... | ||
6-z11B | [0,2,3,5,6,7] | Sacher hexachord | 6-z40A | [0,1,2,3,5,8] | ... | ||||||
6-z12A | [0,1,2,4,6,7] | <3,3,2,2,3,2> | 46 | ... | 6-z41B | [0,2,5,6,7,8] | <3,3,2,2,3,2> | 45 | ... | ||
6-z12B | [0,1,3,5,6,7] | ... | 6-z41A | [0,1,2,3,6,8] | ... | ||||||
6-z13 | [0,1,3,4,6,7] | <3,2,4,2,2,2> | 29 | ... | 6-z42 | [0,1,2,3,6,9] | <3,2,4,2,2,2> | 30 | ... | ||
6-14A | [0,1,3,4,5,8] | <3,2,3,4,3,0> | 3 | ... | |||||||
6-14B | [0,3,4,5,7,8] | ... | |||||||||
6-15A | [0,1,2,4,5,8] | <3,2,3,4,2,1> | 13 | ... | |||||||
6-15B | [0,3,4,6,7,8] | ... | |||||||||
6-16A | [0,1,4,5,6,8] | <3,2,2,4,3,1> | 11 | ... | |||||||
6-16B | [0,2,3,4,7,8] | ... | |||||||||
6-z17A | [0,1,2,4,7,8] | <3,2,2,3,3,2> | 35 | all-trichord hexachord | 6-z43B | [0,2,3,6,7,8] | <3,2,2,3,3,2> | 36 | ... | ||
6-z17B | [0,1,4,6,7,8] | ... | 6-z43A | [0,1,2,5,6,8] | ... | ||||||
6-18A | [0,1,2,5,7,8] | <3,2,2,2,4,2> | 17 | ... | |||||||
6-18B | [0,1,3,6,7,8] | ... | |||||||||
6-z19A | [0,1,3,4,7,8] | <3,1,3,4,3,1> | 37 | ... | 6-z44B | [0,1,4,5,6,9][o] | <3,1,3,4,3,1> | 38 | ... | ||
6-z19B | [0,1,4,5,7,8] | ... | 6-z44A | [0,1,2,5,6,9] | Schoenberg hexachord | ||||||
6-20 | [0,1,4,5,8,9] | <3,0,3,6,3,0> | 2 | "Ode-to-Napoleon" hexachord | |||||||
6-21A | [0,2,3,4,6,8] | <2,4,2,4,1,2> | 12 | ... | |||||||
6-21B | [0,2,4,5,6,8] | ... | |||||||||
6-22A | [0,1,2,4,6,8] | <2,4,1,4,2,2> | 10 | ... | |||||||
6-22B | [0,2,4,6,7,8] | ... | |||||||||
6-z23 | [0,2,3,5,6,8] | <2,3,4,2,2,2> | 27 | ... | 6-z45 | [0,2,3,4,6,9] | <2,3,4,2,2,2> | 28 | ... | ||
6-z24A | [0,1,3,4,6,8] | <2,3,3,3,3,1> | 39 | ... | 6-z46B | [0,2,4,5,6,9] | <2,3,3,3,3,1> | 40 | ... | ||
6-z24B | [0,2,4,5,7,8] | ... | 6-z46A | [0,1,2,4,6,9] | ... | ||||||
6-z25A | [0,1,3,5,6,8] | <2,3,3,2,4,1> | 43 | Major eleventh chord | 6-z47B | [0,2,3,4,7,9] | <2,3,3,2,4,1> | 44 | blues scale | ||
6-z25B | [0,2,3,5,7,8] | ... | 6-z47A | [0,1,2,4,7,9] | ... | ||||||
6-z26 | [0,1,3,5,7,8] | <2,3,2,3,4,1> | 26 | ... | 6-z48 | [0,1,2,5,7,9] | <2,3,2,3,4,1> | 25 | ... | ||
6-27A | [0,1,3,4,6,9] | <2,2,5,2,2,2> | 14 | ... | |||||||
6-27B | [0,2,3,5,6,9] | ... | |||||||||
6-z28 | [0,1,3,5,6,9] | <2,2,4,3,2,2> | 21 | ... | 6-z49 | [0,1,3,4,7,9] | <2,2,4,3,2,2> | 22 | ... | ||
6-z29 | [0,2,3,6,7,9][p] | <2,2,4,2,3,2> | 32 | Bridge chord | 6-z50 | [0,1,4,6,7,9] | <2,2,4,2,3,2> | 31 | ... | ||
6-30A | [0,1,3,6,7,9] | <2,2,4,2,2,3> | 15 | ... | |||||||
6-30B | [0,2,3,6,8,9] | Petrushka chord | |||||||||
6-31A | [0,1,4,5,7,9][q] | <2,2,3,4,3,1> | 8 | ... | |||||||
6-31B | [0,2,4,5,8,9][r] | ... | |||||||||
6-32 | [0,2,4,5,7,9] | <1,4,3,2,5,0> | 6 | diatonic hexachord | |||||||
6-33A | [0,2,3,5,7,9] | <1,4,3,2,4,1> | 18 | ... | |||||||
6-33B | [0,2,4,6,7,9] | Dominant eleventh chord | |||||||||
6-34A | [0,1,3,5,7,9] | <1,4,2,4,2,2> | 9 | mystic chord | |||||||
6-34B | [0,2,4,6,8,9] | Prélude chord | |||||||||
6-35 | [0,2,4,6,8,T] | <0,6,0,6,0,3> | 1 | whole tone scale |
See also
References
Notes
- ^ 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]).
- ^ Forte 9-7B: [0,1,2,3,4,5,7,9,T]
- ^ Forte 9-8B: [0,1,2,3,4,6,8,9,T]
- ^ Forte 9-11B: [0,1,2,3,5,6,8,9,T]
- ^ Forte 8-22B: [0,1,2,3,5,7,9,T]
- ^ Forte 8-26: [0,1,2,4,5,7,9,T]
- ^ Forte 8-27B: [0,1,2,4,6,7,9,T]
- ^ Forte 7-z18A: [0,1,2,3,5,8,9]
- ^ Forte 7-z18B: [0,1,4,6,7,8,9]
- ^ Forte 5-20A: [0,1,3,7,8]
- ^ Forte 7-20B: [0,1,2,5,7,8,9]
- ^ Forte 5-20B: [0,1,5,7,8]
- ^ Forte 7-20A: [0,1,2,4,7,8,9]
- ^ Forte 5-32B: [0,1,4,7,9]
- ^ Forte 6-z44B: [0,1,2,5,8,9]
- ^ Forte 6-z29: [0,1,3,6,8,9]
- ^ Forte 6-31A: [0,1,3,5,8,9]
- ^ Forte 6-31B: [0,1,4,6,8,9]
Sources
- ^ Forte, Allen (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
- ^ Nelson, Paul (2004). "Two Algorithms for Computing the Prime Form", ComposerTools.com.
- ^ Rahn, John (1980). Basic Atonal Theory. New York: Longman. ISBN 978-0028731605.
- ^ Straus, Joseph N. (1990). Introduction to Post-Tonal Theory. Prentice-Hall. ISBN 9780131898905.
- ^ Schiff, David (1983/1998). The Music of Elliott Carter.
- ^ Carter, Elliott (2002). The Harmony Book, "Appendix 1". ISBN 9780825845949.
- ^ Schuijer, Michael (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.97. University of Rochester. ISBN 978-1-58046-270-9.
- ^ Everett, Walter (2008). The Foundations of Rock, p.169. Oxford. ISBN 9780199718702.
External links
- Pitch Class Set Calculator from Mount Allison University
- Chord Analyzer on Lamadeguido.com
Online lists
- Solomon, Larry (2005). "The Table of Pitch Class Sets", SolomonsMusic.net.
- Tucker, Gary (2001). "Table of pc set classes", A Brief Introduction to Pitch-Class Set Analysis.
- Nelson, Paul (2004). "Table of Prime Forms", ComposerTools.com.