B - Set-Class Table

Summary

The following pages contain a complete listing of all of the (Tn/TnI) set-classes (after Allen Forte and John Rahn). A set-class (or SC) is a collection of all the sets of pcs (pcsets) that are related under transposition (Tn), inversion (I), or both (in pc-space). All of the pcsets within a set-class are of the same cardinality.

• 1. The name of a SC consists of two numbers separated by a hyphen in parentheses followed by the “prime form” of the SC written in brackets, e.g., (4-5)[0126]. The first of the hyphenated numbers gives the cardinality of the set-class’s members, and the second number indicates the position of a particular set-class on the list. In this case, SC(4-5)[0126] is the name of the set-class whose cardinality is 4, and is fifth on the list of set-classes of that cardinality. The bracketed “prime form” portion of the SC’s name is simply one of the pcsets included in the current set-class and is in (so-called) normal order. The prime form [0126] is an ordering of one member of the SC (4-5)[0126]. Two SCs, one possessing the complements of the pcsets in the other, have the same number after the hyphen in their names, except with hexachordal set-classes.

• 2. The M/MI column refers to the set-class whose members are related under T_nM or T_nMI to those of the present set-class; the column’s entry gives the first part of the set-class’s name. If there is no entry in this column, then the set-class has sets that map on to each other under T_nM and/or T_nMI.

• 3. Z tells whether or not the SC has a unique interval-class vector (see below). If there is an entry in the column, it indicates the other SC with the same vector. (A vector is shared by only two SCs at most.)

• 4. The ICV (Interval-Class Vector) gives the interval-class content for any set within the current set-class. Seven successive numbers occur within brackets. The leftmost number gives the number of interval-classes of size 0 (ic 0) (and thus, the cardinality of the SC’s members), the second number from the left gives the number of interval-classes of size 1 (ic 1), and so forth until we get to the last (seventh, rightmost) number, which indicates the number of ic 6s in any set within the set-class.