List_of_pitch-class_sets

List of set classes

List of set classes

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This is a list of set classes 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]

List

More information Forte no., Prime form ...

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. [1]
    Forte, Allen (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
  2. [2]
    Nelson, Paul (2004). "Two Algorithms for Computing the Prime Form", ComposerTools.com.
  3. [3]
    Rahn, John (1980). Basic Atonal Theory. New York: Longman. ISBN 978-0028731605.
  4. [4]
    Straus, Joseph N. (1990). Introduction to Post-Tonal Theory. Prentice-Hall. ISBN 9780131898905.
  5. [5]
    Schiff, David (1983/1998). The Music of Elliott Carter.
  6. [6]
    Carter, Elliott (2002). The Harmony Book, "Appendix 1". ISBN 9780825845949.
  7. [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. [8]
    Everett, Walter (2008). The Foundations of Rock, p.169. Oxford. ISBN 9780199718702.
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