pf – determine prime form for successive Humdrum vertical sonorities
pf [inputfile ...] [> outputfile.pf]
The pf command is used to determine the prime form for any of five set-theory related inputs: pitch (semits), pitch-class (pc), normal form (nf), interval-vector (iv), or Fortean set name (pcset).
"Prime form" is a standardized way of representing the symmetrical interval structure for any arbitrary set of pitch-classes. Prime form is the most intervalically compact representation of a pitch-class set, transposed to begin on pitch-class 0 — where inversions are deemed equivalent. By way of example, any major or minor chord, having any root, in any inversion, consisting of any number of notes, with any spelling, will have the prime form: 0,3,7. See REFERENCES below.
When provided with semits or pc inputs, pf treats each input record as a set of pitches. Unisons and other pitch-class duplications have no effect on the output. Rests within a set of pitches are ignored; where an input record consists solely of one or more rests, a null-token is output. The pf command can also accept other set theoretic inputs, such as nf, iv, pcset, as well as pf itself.
The following table identifies the input representations accepted by pf. For descriptions of the various input representations (including pf) refer to Section 2 (Representation Reference) of this reference manual.
It is recommended that output files produced using the pf command should be given names with the distinguishing `.pf' extension.
iv interval-class vector representation nf normal form representation pc pitch-class representation pcset Fortean pitch-class set name pf prime form representation semits equal-tempered semitones with respect to middle C=0 (e.g. 12 = C5) ———— ——————————————————————–
Input representations processed by pf.
The pf command provides only a help option:
h displays a help screen summarizing the command syntax ——– ——————————————————-
Options are specified in the command line.
The following command outputs the prime form for the sets formed by
successive sonorities in the input file
opus24. The input may be
pitches, pitch-classes, Fortean set names, etc.
pf opus24 > opus24.pf
DOS 2.0 and up, with the MKS Toolkit. OS/2 with the MKS Toolkit. UNIX systems supporting the Korn shell or Bourne shell command interpreters, and revised awk (1985).
context (4), **iv (2), iv (4), **nf (2), nf (4), **pc (2), pc (4), **pcset (2), pcset (4), **pf (2), **semits (2), semits (4)
The pf command is a shell script that invokes
Allen Forte, The Structure of Atonal Music. New Haven: Yale University Press, 1973.
John Rahn, Basic Atonal Theory. New York: Longman Inc., 1980.
Straus, J. Introduction to Post-Tonal Theory. Englewood Cliffs, N.J.: Prentice Hall, 1990.
- Pertinent description in the Humdrum User Guide
- Index to Humdrum Commands
- Table for Contents for Humdrum User Guide