List of set classes



This is a list of set classes, by Forte number. 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 ten and eleven, respectively, as single characters.

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. This results in two different prime form sets for the same Forte number in a number of cases. The alternative notations for those set classes are listed in the footnotes.

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. Donald Martino had produced tables of hexachords, tetrachords, trichords, and pentachords for combinatoriality in his article, "The Source Set and its Aggregate Formations" (1961).