For compatibility with music theory's traditional pitch-class set theory,
whose landmark text is Allen Forte's 1973 The Structure of Atonal Music,
the data set fortenums hard-codes the ordinal positions of 12-equal pitch-class
set classes from Allen Forte's list. This allows us to look up specific set
classes from Forte numbers or vice versa. sc() does the former and
fortenum() does the latter. There's very little need to ever interact with
the file fortenums itself: you should be able to get anything you need from this
data through either sc() or fortenum().
Note that primeform() in musicMCT
uses Rahn's algorithm rather than Forte's for finding a canonical representative
of each set class. Consequently, the entries of fortenums also use Rahn's prime
forms rather than Forte's.
Format
A list of length 12. The nth entry of the list corresponds to set classes of
cardinality n. Each list entry is a vector of character strings; every element
of the vector contains a Rahn prime form as a comma-delimited string. These prime
forms are ordered in the same sequence as Forte's list. Thus, for instance, the
set class of the minor triad is represented by the string "0, 3, 7", which is
the 11th element in fortenums[[3]].