List of set classes

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Set 3-1 has three possible versions: [01112T], [011TE1], and [0TT1E1], where subscripts indicate adjacency intervals. The normal form is the smallest "slice of pie" (shaded) or most compact form; in this case, [01112T]. Set theory 3-1 in the chromatic circle fix.svg
Set 3-1 has three possible versions: [01112T], [011TE1], and [0TT1E1], where subscripts indicate adjacency intervals. The normal form is the smallest "slice of pie" (shaded) or most compact form; in this case, [01112T].

This is a list of set classes , by Forte number. [1] In music theory, a set class (an abbreviation of pitch-class-set class) is an ascending collection of pitch classes, transposed to begin at zero. For a list of ordered collections, see this list of tone rows and series.

Contents

Sets are listed with links to their complements. For unsymmetrical sets, the prime form is marked with "A" and the inversion with "B"; sets without either are symmetrical. Sets marked with a "Z" refer to a pair of different set classes with identical interval class content unrelated by inversion, with one of each pair listed at the end of the respective list when they occur. ("Z" is derived from the prefix zygo-, from Ancient Greek ζυγόν, "yoke". Hence: zygosets.) "T" and "E" are conventionally used in sets to notate ten and eleven, respectively, as single characters. Because, for any given set, its interval-class vector is independent of the version (cyclic permutation) considered, for any cardinality, the ordering of sets in the list (except for Z-related sets, as explained below) 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.

There are two slightly different methods of obtaining the prime form—an earlier one by Allen Forte and a later but now generally more popular one 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 most dispersed from the right, whereas the precise description of the Forte spelling is to select the version most packed to the left within the smallest span. [a] In the lists here, the Rahn spelling is used for the 17 out of 352 set classes where the two methods yield different results; the alternative Forte spellings are listed in the footnotes. [3] [4]

Before either (1960–67), however, Elliott Carter had 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 1961 article, "The Source Set and its Aggregate Formations". [7]

The magnitude of the difference between the interval-class vector of a set and that of its complement is X, X, X, X, X, X/2, where (in base-ten) X = 12 – 2C, where C is the smaller set's cardinality. In nearly all cases, complements of unsymmetrical sets are related by inversion—that is, the complement of an "A" version of a set of cardinality C is (usually) the "B" version of the respective complementary 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.

Allen Forte's own rule for numbering is usually applied to determine which zygote appears in the main list and which appears added at the end (with a much larger index number) as well; in other words, the one with the lower number has an equal or lesser minimum span. For example, for the all-interval tetrads, 4-Z15 and 4-Z29, the former has a minimum span of 6 semitones and the latter 7 semitones. Meanwhile, 5-Z17 and 5-Z37 both have a minimum span of 8 semitones, but the former is more packed to the left; adjacency intervals of 1-2-1-4-4 versus 3-1-1-3-4.

However, in the heptads, zygotic pairs with higher numbers have a smaller minimum span. For each of 7-Z12 versus 7-Z36, 7Z-17 versus 7-Z37, and 7-Z18 versus 7-Z38, the first member has a minimum span of 9 semitones and the second member 8 semitones. Clearly, they have been assigned index numbers corresponding to their pentad complements instead of following the general rule.

Additionally, there is one genuine anomaly, in the ordering of the hexads, a clear mistake on Forte's part: 6-Z28 versus 6Z-49. Their minimum span is the same (9), but their adjacency intervals are 1-2-2-1-3-3 versus 1-2-1-3-2-3. According to Forte's own rule, this ordering is incorrect – the set [0,1,3,4,7,9] should have been assigned the lower number 6-Z28, with [0,1,3,5,6,9] given the higher number 6-Z49. To avoid confusion, the original Forte numbering system is retained here for them.

List

Forte no.Prime formInterval vectorCarter no.AudioPossible spacingsComplement
0-1[]<0,0,0,0,0,0> Empty set 12-1
1-1[0]<0,0,0,0,0,0> Play Unison, octave 11-1
2-1[0,1]<1,0,0,0,0,0>1 Play Minor second, major seventh 10-1
2-2[0,2]<0,1,0,0,0,0>2 Play Major second, minor seventh 10-2
2-3[0,3]<0,0,1,0,0,0>3 Play Minor third, major sixth 10-3
2-4[0,4]<0,0,0,1,0,0>4 Play Major third, minor sixth 10-4
2-5[0,5]<0,0,0,0,1,0>5 Play Perfect fourth, perfect fifth 10-5
2-6[0,6]<0,0,0,0,0,1>6 Play Augmented fourth, diminished fifth, tritone 10-6
3-1[0,1,2]<2,1,0,0,0,0>4 Play ... 9-1
3-2A[0,1,3]<1,1,1,0,0,0>12 Play ... 9-2B
3-2B[0,2,3] Play ... 9-2A
3-3A[0,1,4]<1,0,1,1,0,0>11 Play ... 9-3B
3-3B[0,3,4] Play ... 9-3A
3-4A[0,1,5]<1,0,0,1,1,0>9 Play ... 9-4B
3-4B[0,4,5] Play ... 9-4A
3-5A[0,1,6]<1,0,0,0,1,1>7 Play Viennese trichord 9-5B
3-5B[0,5,6] Play Viennese trichord 9-5A
3-6[0,2,4]<0,2,0,1,0,0>3 Play ... 9-6
3-7A[0,2,5]<0,1,1,0,1,0>10 Play ... 9-7B
3-7B[0,3,5] Play Blues trichord (minor pentatonic subset) [8] 9-7A
3-8A[0,2,6]<0,1,0,1,0,1>8 Play Italian sixth chord 9-8B
3-8B[0,4,6] Play ... 9-8A
3-9[0,2,7]<0,1,0,0,2,0>5 Play Suspended chord 9-9
3-10[0,3,6]<0,0,2,0,0,1>2 Play Diminished chord 9-10
3-11A[0,3,7]<0,0,1,1,1,0>6 Play Minor chord, Neapolitan chord 9-11B
3-11B[0,4,7] Play Major chord 9-11A
3-12[0,4,8]<0,0,0,3,0,0>1 Play Augmented chord 9-12
4-1[0,1,2,3]<3,2,1,0,0,0>1 Play BACH motif 8-1
4-2A[0,1,2,4]<2,2,1,1,0,0>17 Play ... 8-2B
4-2B[0,2,3,4] Play ... 8-2A
4-3[0,1,3,4]<2,1,2,1,0,0>9 Play DSCH motif 8-3
4-4A[0,1,2,5]<2,1,1,1,1,0>20 Play ... 8-4B
4-4B[0,3,4,5] Play Chromatic tetrachord 8-4A
4-5A[0,1,2,6]<2,1,0,1,1,1>22 Play ... 8-5B
4-5B[0,4,5,6] Play ... 8-5A
4-6[0,1,2,7]<2,1,0,0,2,1>6 Play Dream chord 8-6
4-7[0,1,4,5]<2,0,1,2,1,0>8 Play ... 8-7
4-8[0,1,5,6]<2,0,0,1,2,1>10 Play ... 8-8
4-9[0,1,6,7]<2,0,0,0,2,2>2 Play Distance model 8-9
4-10[0,2,3,5]<1,2,2,0,1,0>3 Play ... 8-10
4-11A[0,1,3,5]<1,2,1,1,1,0>26 Play ... 8-11B
4-11B[0,2,4,5] Play Diatonic tetrachord 8-11A
4-12A[0,2,3,6]<1,1,2,1,0,1>28 Play ... 8-12A
4-12B[0,3,4,6] Play ... 8-12B
4-13A[0,1,3,6]<1,1,2,0,1,1>7 Play ... 8-13B
4-13B[0,3,5,6] Play ... 8-13A
4-14A[0,2,3,7]<1,1,1,1,2,0>25 Play ... 8-14A
4-14B[0,4,5,7] Play ... 8-14B
4-Z15A[0,1,4,6]<1,1,1,1,1,1>18 Play All-interval tetrachord 8-Z15B
4-Z15B[0,2,5,6] Play All-interval tetrachord 8-Z15A
4-16A[0,1,5,7]<1,1,0,1,2,1>19 Play Major seventh flat five chord 8-16B
4-16B[0,2,6,7] Play ... 8-16A
4-17[0,3,4,7]<1,0,2,2,1,0>13 Play Alpha chord 8-17
4-18A[0,1,4,7]<1,0,2,1,1,1>21 Play Diminished major seventh chord 8-18B
4-18B[0,3,6,7] Play ... 8-18A
4-19A[0,1,4,8]<1,0,1,3,1,0>24 Play Minor major seventh chord 8-19B
4-19B[0,3,4,8] Play Augmented major seventh chord 8-19A
4-20[0,1,5,8]<1,0,1,2,2,0>15 Play Major seventh chord, minor flat sixth chord 8-20
4-21[0,2,4,6]<0,3,0,2,0,1>11 Play ... 8-21
4-22A[0,2,4,7]<0,2,1,1,2,0>27 Play Mu chord 8-22B
4-22B[0,3,5,7] Play ... 8-22A
4-23[0,2,5,7]<0,2,1,0,3,0>4 Play Quartal chord, seventh suspension four chord [9] 8-23
4-24[0,2,4,8]<0,2,0,3,0,1>16 Play Augmented seventh chord 8-24
4-25[0,2,6,8]<0,2,0,2,0,2>12 Play Dominant seventh flat five chord, French sixth chord 8-25
4-26[0,3,5,8]<0,1,2,1,2,0>14 Play Minor seventh chord 8-26
4-27A[0,2,5,8]<0,1,2,1,1,1>29 Play Half-diminished seventh chord, minor sixth chord, Tristan chord 8-27B
4-27B[0,3,6,8] Play Dominant seventh chord, German sixth chord, harmonic seventh chord 8-27A
4-28[0,3,6,9]<0,0,4,0,0,2>5 Play Diminished seventh chord 8-28
4-Z29A[0,1,3,7]<1,1,1,1,1,1>23 Play All-interval tetrachord 8-Z29B
4-Z29B[0,4,6,7] Play All-interval tetrachord 8-Z29A
5-1[0,1,2,3,4]<4,3,2,1,0,0> Play ... 7-1
5-2A[0,1,2,3,5]<3,3,2,1,1,0> Play ... 7-2B
5-2B[0,2,3,4,5] Play ... 7-2A
5-3A[0,1,2,4,5]<3,2,2,2,1,0> Play ... 7-3B
5-3B[0,1,3,4,5] Play ... 7-3A
5-4A[0,1,2,3,6]<3,2,2,1,1,1> Play ... 7-4B
5-4B[0,3,4,5,6] Play ... 7-4A
5-5A[0,1,2,3,7]<3,2,1,1,2,1> Play ... 7-5B
5-5B[0,4,5,6,7] Play ... 7-5A
5-6A[0,1,2,5,6]<3,1,1,2,2,1> Play ... 7-6B
5-6B[0,1,4,5,6] Play ... 7-6A
5-7A[0,1,2,6,7]<3,1,0,1,3,2> Play ... 7-7B
5-7B[0,1,5,6,7] Play ... 7-7A
5-8[0,2,3,4,6]<2,3,2,2,0,1> Play ... 7-8
5-9A[0,1,2,4,6]<2,3,1,2,1,1> Play ... 7-9B
5-9B[0,2,4,5,6] Play ... 7-9A
5-10A[0,1,3,4,6]<2,2,3,1,1,1> Play ... 7-10B
5-10B[0,2,3,5,6] Play ... 7-10A
5-11A[0,2,3,4,7]<2,2,2,2,2,0> Play ... 7-11A
5-11B[0,3,4,5,7] Play ... 7-11B
5-Z12[0,1,3,5,6]<2,2,2,1,2,1> Play ... 7-Z12
5-13A[0,1,2,4,8]<2,2,1,3,1,1> Play ... 7-13B
5-13B[0,2,3,4,8] Play ... 7-13A
5-14A[0,1,2,5,7]<2,2,1,1,3,1> Play ... 7-14B
5-14B[0,2,5,6,7] Play ... 7-14A
5-15[0,1,2,6,8]<2,2,0,2,2,2> Play ... 7-15
5-16A[0,1,3,4,7]<2,1,3,2,1,1> Play ... 7-16B
5-16B[0,3,4,6,7] Play ... 7-16A
5-Z17[0,1,3,4,8]<2,1,2,3,2,0> Play Farben chord, minor major ninth chord 7-Z17
5-Z18A[0,1,4,5,7]<2,1,2,2,2,1> Play ... 7-Z18B
5-Z18B[0,2,3,6,7] Play ... 7-Z18A
5-19A[0,1,3,6,7]<2,1,2,1,2,2> Play ... 7-19B
5-19B[0,1,4,6,7] Play ... 7-19A
5-20A[0,1,5,6,8] [b] <2,1,1,2,3,1> Play Ryukyu scale 7-20B
5-20B[0,2,3,7,8] [c] Play Hirajōshi scale, in scale, iwato scale 7-20A
5-21A[0,1,4,5,8]<2,0,2,4,2,0> Play ... 7-21B
5-21B[0,3,4,7,8] Play ... 7-21A
5-22[0,1,4,7,8]<2,0,2,3,2,1> Play ... 7-22
5-23A[0,2,3,5,7]<1,3,2,1,3,0> Play ... 7-23B
5-23B[0,2,4,5,7] Play ... 7-23A
5-24A[0,1,3,5,7]<1,3,1,2,2,1> Play ... 7-24B
5-24B[0,2,4,6,7] Play ... 7-24A
5-25A[0,2,3,5,8]<1,2,3,1,2,1> Play Half-diminished minor ninth chord 7-25B
5-25B[0,3,5,6,8] Play Seven six chord 7-25A
5-26A[0,2,4,5,8]<1,2,2,3,1,1> Play Half-diminished ninth chord 7-26A
5-26B[0,3,4,6,8] Play Augmented major ninth chord 7-26B
5-27A[0,1,3,5,8]<1,2,2,2,3,0> Play Major ninth chord 7-27B
5-27B[0,3,5,7,8] Play Minor ninth chord 7-27A
5-28A[0,2,3,6,8]<1,2,2,2,1,2> Play ... 7-28A
5-28B[0,2,5,6,8] Play ... 7-28B
5-29A[0,1,3,6,8]<1,2,2,1,3,1> Play ... 7-29B
5-29B[0,2,5,7,8] Play Insen scale, minor sixth ninth chord 7-29A
5-30A[0,1,4,6,8]<1,2,1,3,2,1> Play ... 7-30B
5-30B[0,2,4,7,8] Play Jazz sus chord, Lydian augmented chord 7-30A
5-31A[0,1,3,6,9]<1,1,4,1,1,2> Play Beta chord, diminished minor ninth chord 7-31B
5-31B[0,2,3,6,9] Play Diminished ninth chord, dominant minor ninth chord 7-31A
5-32A[0,1,4,6,9]<1,1,3,2,2,1> Play Dominant seventh sharp ninth chord 7-32B
5-32B[0,2,5,6,9] [d] Play Elektra chord, gamma chord 7-32A
5-33[0,2,4,6,8]<0,4,0,4,0,2> Play Augmented dominant ninth chord, ninth augmented fifth chord, [10] ninth flat fifth chord [10] 7-33
5-34[0,2,4,6,9]<0,3,2,2,2,1> Play Dominant ninth chord 7-34
5-35[0,2,4,7,9]<0,3,2,1,4,0> Play Major pentatonic scale 7-35
5-Z36A[0,1,2,4,7]<2,2,2,1,2,1> Play ... 7-Z36B
5-Z36B[0,3,5,6,7] Play ... 7-Z36A
5-Z37[0,3,4,5,8]<2,1,2,3,2,0> Play ... 7-Z37
5-Z38A[0,1,2,5,8]<2,1,2,2,2,1> Play ... 7-Z38B
5-Z38B[0,3,6,7,8] Play ... 7-Z38A
6-1[0,1,2,3,4,5]<5,4,3,2,1,0>4 Play Chromatic hexachord 6-1
6-2A[0,1,2,3,4,6]<4,4,3,2,1,1>19 Play ... 6-2B
6-2B[0,2,3,4,5,6] Play ... 6-2A
6-Z3A[0,1,2,3,5,6]<4,3,3,2,2,1>49 Play ... 6-Z36B
6-Z3B[0,1,3,4,5,6] Play ... 6-Z36A
6-Z4[0,1,2,4,5,6]<4,3,2,3,2,1>24 Play ... 6-Z37
6-5A[0,1,2,3,6,7]<4,2,2,2,3,2>16 Play ... 6-5B
6-5B[0,1,4,5,6,7] Play ... 6-5A
6-Z6[0,1,2,5,6,7]<4,2,1,2,4,2>33 Play ... 6-Z38
6-7[0,1,2,6,7,8]<4,2,0,2,4,3>7 Play Two-semitone tritone scale 6-7
6-8[0,2,3,4,5,7]<3,4,3,2,3,0>5 Play ... 6-8
6-9A[0,1,2,3,5,7]<3,4,2,2,3,1>20 Play ... 6-9B
6-9B[0,2,4,5,6,7] Play ... 6-9A
6-Z10A[0,1,3,4,5,7]<3,3,3,3,2,1>42 Play ... 6-Z39A
6-Z10B[0,2,3,4,6,7] Play ... 6-Z39B
6-Z11A[0,1,2,4,5,7]<3,3,3,2,3,1>47 Play ... 6-Z40B
6-Z11B[0,2,3,5,6,7] Play Sacher hexachord 6-Z40A
6-Z12A[0,1,2,4,6,7]<3,3,2,2,3,2>46 Play ... 6-Z41B
6-Z12B[0,1,3,5,6,7] Play ... 6-Z41A
6-Z13[0,1,3,4,6,7]<3,2,4,2,2,2>29 Play Istrian scale 6-Z42
6-14A[0,1,3,4,5,8]<3,2,3,4,3,0>3 Play ... 6-14A
6-14B[0,3,4,5,7,8] Play ... 6-14B
6-15A[0,1,2,4,5,8]<3,2,3,4,2,1>13 Play ... 6-15B
6-15B[0,3,4,6,7,8] Play ... 6-15A
6-16A[0,1,4,5,6,8]<3,2,2,4,3,1>11 Play ... 6-16B
6-16B[0,2,3,4,7,8] Play ... 6-16A
6-Z17A[0,1,2,4,7,8]<3,2,2,3,3,2>35 Play All-trichord hexachord 6-Z43B
6-Z17B[0,1,4,6,7,8] Play ... 6-Z43A
6-18A[0,1,2,5,7,8]<3,2,2,2,4,2>17 Play ... 6-18B
6-18B[0,1,3,6,7,8] Play ... 6-18A
6-Z19A[0,1,3,4,7,8]<3,1,3,4,3,1>37 Play ... 6-Z44B
6-Z19B[0,1,4,5,7,8] Play ... 6-Z44A
6-20[0,1,4,5,8,9]<3,0,3,6,3,0>2 Play Augmented scale, "Ode-to-Napoleon" hexachord 6-20
6-21A[0,2,3,4,6,8]<2,4,2,4,1,2>12 Play ... 6-21B
6-21B[0,2,4,5,6,8] Play ... 6-21A
6-22A[0,1,2,4,6,8]<2,4,1,4,2,2>10 Play ... 6-22B
6-22B[0,2,4,6,7,8] Play ... 6-22A
6-Z23[0,2,3,5,6,8]<2,3,4,2,2,2>27 Play ... 6-Z45
6-Z24A[0,1,3,4,6,8]<2,3,3,3,3,1>39 Play Minor major eleventh chord 6-Z46B
6-Z24B[0,2,4,5,7,8] Play Half-diminished eleventh chord 6-Z46A
6-Z25A[0,1,3,5,6,8]<2,3,3,2,4,1>43 Play Major eleventh chord 6-Z47B
6-Z25B[0,2,3,5,7,8] Play ... 6-Z47A
6-Z26[0,1,3,5,7,8]<2,3,2,3,4,1>26 Play Major ninth sharp eleventh chord 6-Z48
6-27A[0,1,3,4,6,9]<2,2,5,2,2,2>14 Play ... 6-27B
6-27B[0,2,3,5,6,9] Play Diminished eleventh chord 6-27A
6-Z28[0,1,3,5,6,9]<2,2,4,3,2,2>21 Play Augmented major eleventh chord 6-Z49
6-Z29[0,2,3,6,7,9] [e] <2,2,4,2,3,2>32 Play Bridge chord 6-Z50
6-30A[0,1,3,6,7,9]<2,2,4,2,2,3>15 Play ... 6-30B
6-30B[0,2,3,6,8,9] Play Petrushka chord, tritone scale 6-30A
6-31A[0,1,4,5,7,9] [f] <2,2,3,4,3,1>8 Play ... 6-31B
6-31B[0,2,4,5,8,9] [g] Play ... 6-31A
6-32[0,2,4,5,7,9]<1,4,3,2,5,0>6 Play Diatonic hexachord, minor eleventh chord 6-32
6-33A[0,2,3,5,7,9]<1,4,3,2,4,1>18 Play ... 6-33B
6-33B[0,2,4,6,7,9] Play Dominant eleventh chord 6-33A
6-34A[0,1,3,5,7,9]<1,4,2,4,2,2>9 Play Mystic chord 6-34B
6-34B[0,2,4,6,8,9] Play Augmented eleventh chord, dominant sharp eleventh chord, Prélude chord 6-34A
6-35[0,2,4,6,8,T]<0,6,0,6,0,3>1 Play Whole tone scale 6-35
6-Z36A[0,1,2,3,4,7]<4,3,3,2,2,1>50 Play ... 6-Z3B
6-Z36B[0,3,4,5,6,7] Play ... 6-Z3A
6-Z37[0,1,2,3,4,8]<4,3,2,3,2,1>23 Play ... 6-Z4
6-Z38[0,1,2,3,7,8]<4,2,1,2,4,2>34 Play ... 6-Z6
6-Z39A[0,2,3,4,5,8]<3,3,3,3,2,1>41 Play ... 6-Z10A
6-Z39B[0,3,4,5,6,8] Play ... 6-Z10B
6-Z40A[0,1,2,3,5,8]<3,3,3,2,3,1>48 Play ... 6-Z11B
6-Z40B[0,3,5,6,7,8] Play ... 6-Z11A
6-Z41A[0,1,2,3,6,8]<3,3,2,2,3,2>45 Play ... 6-Z12B
6-Z41B[0,2,5,6,7,8] Play ... 6-Z12A
6-Z42[0,1,2,3,6,9]<3,2,4,2,2,2>30 Play ... 6-Z13
6-Z43A[0,1,2,5,6,8]<3,2,2,3,3,2>36 Play ... 6-Z17B
6-Z43B[0,2,3,6,7,8] Play ... 6-Z17A
6-Z44A[0,1,2,5,6,9]<3,1,3,4,3,1>38 Play Schoenberg hexachord 6-Z19B
6-Z44B[0,1,4,5,6,9] [h] Play ... 6-Z19A
6-Z45[0,2,3,4,6,9]<2,3,4,2,2,2>28 Play ... 6-Z23
6-Z46A[0,1,2,4,6,9]<2,3,3,3,3,1>40 Play Scale of harmonics 6-Z24B
6-Z46B[0,2,4,5,6,9] Play ... 6-Z24A
6-Z47A[0,1,2,4,7,9]<2,3,3,2,4,1>44 Play ... 6-Z25B
6-Z47B[0,2,3,4,7,9] Play Blues scale 6-Z25A
6-Z48[0,1,2,5,7,9]<2,3,2,3,4,1>25 Play ... 6-Z26
6-Z49[0,1,3,4,7,9]<2,2,4,3,2,2>22 Play ... 6-Z28
6-Z50[0,1,4,6,7,9]<2,2,4,2,3,2>31 Play ... 6-Z29
7-1[0,1,2,3,4,5,6]<6,5,4,3,2,1>1 Play ... 5-1
7-2A[0,1,2,3,4,5,7]<5,5,4,3,3,1>11 Play ... 5-2B
7-2B[0,2,3,4,5,6,7] Play ... 5-2A
7-3A[0,1,2,3,4,5,8]<5,4,4,4,3,1>14 Play ... 5-3B
7-3B[0,3,4,5,6,7,8] Play ... 5-3A
7-4A[0,1,2,3,4,6,7]<5,4,4,3,3,2>12 Play ... 5-4B
7-4B[0,1,3,4,5,6,7] Play ... 5-4A
7-5A[0,1,2,3,5,6,7]<5,4,3,3,4,2>13 Play ... 5-5B
7-5B[0,1,2,4,5,6,7] Play ... 5-5A
7-6A[0,1,2,3,4,7,8]<5,3,3,4,4,2>27 Play ... 5-6B
7-6B[0,1,4,5,6,7,8] Play ... 5-6A
7-7A[0,1,2,3,6,7,8]<5,3,2,3,5,3>30 Play ... 5-7B
7-7B[0,1,2,5,6,7,8] Play ... 5-7A
7-8[0,2,3,4,5,6,8]<4,5,4,4,2,2>2 Play ... 5-8
7-9A[0,1,2,3,4,6,8]<4,5,3,4,3,2>15 Play ... 5-9B
7-9B[0,2,4,5,6,7,8] Play ... 5-9A
7-10A[0,1,2,3,4,6,9]<4,4,5,3,3,2>19 Play ... 5-10B
7-10B[0,2,3,4,5,6,9] Play ... 5-10A
7-11A[0,1,3,4,5,6,8]<4,4,4,4,4,1>18 Play ... 5-11A
7-11B[0,2,3,4,5,7,8] Play ... 5-11B
7-Z12[0,1,2,3,4,7,9]<4,4,4,3,4,2>5 Play ... 5-Z12
7-13A[0,1,2,4,5,6,8]<4,4,3,5,3,2>17 Play ... 5-13B
7-13B[0,2,3,4,6,7,8] Play ... 5-13A
7-14A[0,1,2,3,5,7,8]<4,4,3,3,5,2>28 Play Natural minor scale 5-14B
7-14B[0,1,3,5,6,7,8] Play ... 5-14A
7-15[0,1,2,4,6,7,8]<4,4,2,4,4,3>4 Play ... 5-15
7-16A[0,1,2,3,5,6,9]<4,3,5,4,3,2>20 Play ... 5-16B
7-16B[0,1,3,4,5,6,9] Play ... 5-16A
7-Z17[0,1,2,4,5,6,9]<4,3,4,5,4,1>10 Play ... 5-Z17
7-Z18A[0,1,4,5,6,7,9] [i] <4,3,4,4,4,2>35 Play ... 5-Z18B
7-Z18B[0,2,3,4,5,8,9] [j] Play ... 5-Z18A
7-19A[0,1,2,3,6,7,9]<4,3,4,3,4,3>31 Play ... 5-19B
7-19B[0,1,2,3,6,8,9] Play ... 5-19A
7-20A[0,1,2,5,6,7,9] [k] <4,3,3,4,5,2>34 Play Persian scale 5-20B
7-20B[0,2,3,4,7,8,9] [l] Play ... 5-20A
7-21A[0,1,2,4,5,8,9]<4,2,4,6,4,1>21 Play ... 5-21B
7-21B[0,1,3,4,5,8,9] Play ... 5-21A
7-22[0,1,2,5,6,8,9]<4,2,4,5,4,2>8 Play Double harmonic scale, Hungarian minor scale 5-22
7-23A[0,2,3,4,5,7,9]<3,5,4,3,5,1>25 Play ... 5-23B
7-23B[0,2,4,5,6,7,9] Play ... 5-23A
7-24A[0,1,2,3,5,7,9]<3,5,3,4,4,2>22 Play ... 5-24B
7-24B[0,2,4,6,7,8,9] Play Enigmatic scale 5-24A
7-25A[0,2,3,4,6,7,9]<3,4,5,3,4,2>24 Play ... 5-25B
7-25B[0,2,3,5,6,7,9] Play ... 5-25A
7-26A[0,1,3,4,5,7,9]<3,4,4,5,3,2>26 Play ... 5-26A
7-26B[0,2,4,5,6,8,9] Play ... 5-26B
7-27A[0,1,2,4,5,7,9]<3,4,4,4,5,1>23 Play ... 5-27B
7-27B[0,2,4,5,7,8,9] Play ... 5-27A
7-28A[0,1,3,5,6,7,9]<3,4,4,4,3,3>36 Play ... 5-28A
7-28B[0,2,3,4,6,8,9] Play ... 5-28B
7-29A[0,1,2,4,6,7,9]<3,4,4,3,5,2>32 Play ... 5-29B
7-29B[0,2,3,5,7,8,9] Play ... 5-29A
7-30A[0,1,2,4,6,8,9]<3,4,3,5,4,2>37 Play Augmented thirteenth chord, minor Neapolitan scale 5-30B
7-30B[0,1,3,5,7,8,9] Play ... 5-30A
7-31A[0,1,3,4,6,7,9]<3,3,6,3,3,3>38 Play Hungarian major scale 5-31B
7-31B[0,2,3,5,6,8,9] Play Romanian major scale 5-31A
7-32A[0,1,3,4,6,8,9]<3,3,5,4,4,2>33 Play Augmented major thirteenth chord, harmonic minor scale, Ukrainian Dorian scale 5-32B
7-32B[0,1,3,5,6,8,9] Play Half-diminished thirteenth chord, harmonic major scale 5-32A
7-33[0,1,2,4,6,8,T]<2,6,2,6,2,3>6 Play Major Locrian scale, major Neapolitan scale 5-33
7-34[0,1,3,4,6,8,T]<2,5,4,4,4,2>9 Play Acoustic scale, altered scale, minor major thirteenth chord 5-34
7-35[0,1,3,5,6,8,T]<2,5,4,3,6,1>7 Play Diatonic scale, major thirteenth chord, minor thirteenth chord 5-35
7-Z36A[0,1,2,3,5,6,8]<4,4,4,3,4,2>16 Play ... 5-Z36B
7-Z36B[0,2,3,5,6,7,8] Play ... 5-Z36A
7-Z37[0,1,3,4,5,7,8]<4,3,4,5,4,1>3 Play ... 5-Z37
7-Z38A[0,1,2,4,5,7,8]<4,3,4,4,4,2>29 Play ... 5-Z38B
7-Z38B[0,1,3,4,6,7,8] Play ... 5-Z38A
8-1[0,1,2,3,4,5,6,7]<7,6,5,4,4,2> Play ... 4-1
8-2A[0,1,2,3,4,5,6,8]<6,6,5,5,4,2> Play ... 4-2B
8-2B[0,2,3,4,5,6,7,8] Play ... 4-2A
8-3[0,1,2,3,4,5,6,9]<6,5,6,5,4,2> Play ... 4-3
8-4A[0,1,2,3,4,5,7,8]<6,5,5,5,5,2> Play ... 4-4B
8-4B[0,1,3,4,5,6,7,8] Play ... 4-4A
8-5A[0,1,2,3,4,6,7,8]<6,5,4,5,5,3> Play ... 4-5B
8-5B[0,1,2,4,5,6,7,8] Play ... 4-5A
8-6[0,1,2,3,5,6,7,8]<6,5,4,4,6,3> Play ... 4-6
8-7[0,1,2,3,4,5,8,9]<6,4,5,6,5,2> Play ... 4-7
8-8[0,1,2,3,4,7,8,9]<6,4,4,5,6,3> Play ... 4-8
8-9[0,1,2,3,6,7,8,9]<6,4,4,4,6,4> Play ... 4-9
8-10[0,2,3,4,5,6,7,9]<5,6,6,4,5,2> Play ... 4-10
8-11A[0,1,2,3,4,5,7,9]<5,6,5,5,5,2> Play ... 4-11B
8-11B[0,2,4,5,6,7,8,9] Play ... 4-11A
8-12A[0,1,3,4,5,6,7,9]<5,5,6,5,4,3> Play ... 4-12A
8-12B[0,2,3,4,5,6,8,9] Play ... 4-12B
8-13A[0,1,2,3,4,6,7,9]<5,5,6,4,5,3> Play ... 4-13B
8-13B[0,2,3,5,6,7,8,9] Play ... 4-13A
8-14A[0,1,2,4,5,6,7,9]<5,5,5,5,6,2> Play ... 4-14A
8-14B[0,2,3,4,5,7,8,9] Play ... 4-14B
8-Z15A[0,1,2,3,4,6,8,9]<5,5,5,5,5,3> Play ... 4-Z15B
8-Z15B[0,1,3,5,6,7,8,9] Play ... 4-Z15A
8-16A[0,1,2,3,5,7,8,9]<5,5,4,5,6,3> Play ... 4-16B
8-16B[0,1,2,4,6,7,8,9] Play ... 4-16A
8-17[0,1,3,4,5,6,8,9]<5,4,6,6,5,2> Play ... 4-17
8-18A[0,1,2,3,5,6,8,9]<5,4,6,5,5,3> Play ... 4-18B
8-18B[0,1,3,4,6,7,8,9] Play ... 4-18A
8-19A[0,1,2,4,5,6,8,9]<5,4,5,7,5,2> Play ... 4-19B
8-19B[0,1,3,4,5,7,8,9] Play ... 4-19A
8-20[0,1,2,4,5,7,8,9]<5,4,5,6,6,2> Play ... 4-20
8-21[0,1,2,3,4,6,8,T]<4,7,4,6,4,3> Play ... 4-21
8-22A[0,1,2,3,5,6,8,T]<4,6,5,5,6,2> Play ... 4-22B
8-22B[0,1,3,4,5,6,8,T] [m] Play ... 4-22A
8-23[0,1,2,3,5,7,8,T]<4,6,5,4,7,2> Play Bebop dominant scale, bebop major scale 4-23
8-24[0,1,2,4,5,6,8,T]<4,6,4,7,4,3> Play ... 4-24
8-25[0,1,2,4,6,7,8,T]<4,6,4,6,4,4> Play Seventh flat five diminished scale 4-25
8-26[0,1,3,4,5,7,8,T] [n] <4,5,6,5,6,2> Play Bebop harmonic minor scale 4-26
8-27A[0,1,2,4,5,7,8,T]<4,5,6,5,5,3> Play ... 4-27B
8-27B[0,1,3,4,6,7,8,T] [o] Play Bebop melodic minor scale 4-27A
8-28[0,1,3,4,6,7,9,T]<4,4,8,4,4,4> Play Octatonic scale 4-28
8-Z29A[0,1,2,3,5,6,7,9]<5,5,5,5,5,3> Play ... 4-Z29B
8-Z29B[0,2,3,4,6,7,8,9] Play ... 4-Z29A
9-1[0,1,2,3,4,5,6,7,8]<8,7,6,6,6,3> Play ... 3-1
9-2A[0,1,2,3,4,5,6,7,9]<7,7,7,6,6,3> Play ... 3-2B
9-2B[0,2,3,4,5,6,7,8,9] Play ... 3-2A
9-3A[0,1,2,3,4,5,6,8,9]<7,6,7,7,6,3> Play ... 3-3B
9-3B[0,1,3,4,5,6,7,8,9] Play ... 3-3A
9-4A[0,1,2,3,4,5,7,8,9]<7,6,6,7,7,3> Play ... 3-4B
9-4B[0,1,2,4,5,6,7,8,9] Play ... 3-4A
9-5A[0,1,2,3,4,6,7,8,9]<7,6,6,6,7,4> Play ... 3-5B
9-5B[0,1,2,3,5,6,7,8,9] Play ... 3-5A
9-6[0,1,2,3,4,5,6,8,T]<6,8,6,7,6,3> Play ... 3-6
9-7A[0,1,2,3,4,5,7,8,T]<6,7,7,6,7,3> Play ... 3-7B
9-7B[0,1,3,4,5,6,7,8,T] [p] Play ... 3-7A
9-8A[0,1,2,3,4,6,7,8,T]<6,7,6,7,6,4> Play ... 3-8B
9-8B[0,1,2,4,5,6,7,8,T] [q] Play ... 3-8A
9-9[0,1,2,3,5,6,7,8,T]<6,7,6,6,8,3> Play Blues scale 3-9
9-10[0,1,2,3,4,6,7,9,T]<6,6,8,6,6,4> Play ... 3-10
9-11A[0,1,2,3,5,6,7,9,T]<6,6,7,7,7,3> Play ... 3-11B
9-11B[0,1,2,4,5,6,7,9,T] [r] Play ... 3-11A
9-12[0,1,2,4,5,6,8,9,T]<6,6,6,9,6,3> Play ... 3-12
10-1[0,1,2,3,4,5,6,7,8,9]<9,8,8,8,8,4> Play ... 2-1
10-2[0,1,2,3,4,5,6,7,8,T]<8,9,8,8,8,4> Play ... 2-2
10-3[0,1,2,3,4,5,6,7,9,T]<8,8,9,8,8,4> Play ... 2-3
10-4[0,1,2,3,4,5,6,8,9,T]<8,8,8,9,8,4> Play ... 2-4
10-5[0,1,2,3,4,5,7,8,9,T]<8,8,8,8,9,4> Play ... 2-5
10-6[0,1,2,3,4,6,7,8,9,T]<8,8,8,8,8,5> Play ... 2-6
11-1[0,1,2,3,4,5,6,7,8,9,T]<T,T,T,T,T,5> Play Northern lights chord 1-1
12-1[0,1,2,3,4,5,6,7,8,9,T,E]<C,C,C,C,C,6> Play Aggregate, all-interval twelve-tone row 0-1

See also

References

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 5-20A: [0,1,3,7,8]
  3. Forte 5-20B: [0,1,5,7,8]
  4. Forte 5-32B: [0,1,4,7,9]
  5. Forte 6-Z29: [0,1,3,6,8,9]
  6. Forte 6-31A: [0,1,3,5,8,9]
  7. Forte 6-31B: [0,1,4,6,8,9]
  8. Forte 6-Z44B: [0,1,2,5,8,9]
  9. Forte 7-Z18A: [0,1,2,3,5,8,9]
  10. Forte 7-Z18B: [0,1,4,6,7,8,9]
  11. Forte 7-20A: [0,1,2,4,7,8,9]
  12. Forte 7-20B: [0,1,2,5,7,8,9]
  13. Forte 8-22B: [0,1,2,3,5,7,9,T]
  14. Forte 8-26: [0,1,2,4,5,7,9,T]
  15. Forte 8-27B: [0,1,2,4,6,7,9,T]
  16. Forte 9-7B: [0,1,2,3,4,5,7,9,T]
  17. Forte 9-8B: [0,1,2,3,4,6,8,9,T]
  18. Forte 9-11B: [0,1,2,3,5,6,8,9,T]

Sources

  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.
  9. Pearse, John (1977). The Guitarist's Picture Chord Encyclopedia, p.31. ISBN   0-8256-2199-2.
  10. 1 2 Bay, William (10 April 1971). Encyclopedia of guitar chords. Mel Bay Publications. p. 2. ISBN   978-0-87166-664-2.

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