pcset – convert Humdrum pitch and pitch-class information to set-theoretic representations
pcset [-c] [-n|p|v] [inputfile ...]
The pcset command is used to generate and convert between various set-theoretic representations.
By default, the output is the Fortean pitch-class set type (pcset). Alternatively, the user may choose to output the corresponding normal form (nf) or the more succinct prime form (pf) or the associated interval-class vector (iv). See REFERENCES below.
In addition to accepting semits or pc inputs, pcset can also process nf, iv, pf or pcset inputs. This permits the user to determine the normal form, prime form or interval-class vector for a given pc-set, or the interval-class vector for a given pc-set, prime form, or normal form, etc.
For all of the above translations, pcset also provides a complementation operator, where output values corresponding to the pitch-class set complement. For example, when the complementation option is invoked, an input consisting of the pitch-classes (0,4,7,10) would produce an output pertinent to the complementary set (1,2,3,5,6,8,9,11). Complementation can be applied to any accepted input type, including normal form, prime form, interval-class vector, and pc-set. Note that if the input consists of all twelve pitch-classes, pcset produces a null token as the set complement.
When provided with semits or pc inputs, pcset 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 pcset command is able to translate any of the representations listed below. For descriptions of the various input representations (including pcset) refer to Section 2 (Representation Reference) of this reference manual.
It is recommended that output files produced using the pcset command should be given names with the distinguishing extensions `.pcs', `.nf' `.pf' or `.iv' — depending on the selected option.
iv interval-class vector representation nf normal form for pitch-class sets 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 pcset.
The pcset command provides the following options:
c generate output for set complement h displays a help screen summarizing the command syntax n output normal form (nf) spine p output prime form (pf) spine v output interval-class vector (iv) spine ——– ——————————————————-
Options are specified in the command line.
By default, the pcset command outputs a pcset representation.
The n option causes pcset to output normal form (nf) data instead of pcset data. "Normal form" is a standard way of representing the interval structure of any arbitrary set of pitch-classes.
The p option causes pcset to output the prime form (pf) for the input. Prime form is analogous to rearranging notes in a chord so that the spelling is in root position, close position, transposed so that the root of the chord is C. By way of example, any major chord (having any root, in any inversion, with any spelling) will have the normal form: 0,4,7 — namely, a given (basic) pitch, plus a pitch 4 semitones above than the basic pitch, plus a pitch 7 semitones above the basic pitch. (See REFERENCES.)
The v option causes interval-class vector information (iv) to be output rather than pcset data. All pitch-class sets can be characterized according to the possible interval-classes that can be constructed. The six-element interval-class vector specifies the abundance of various interval-classes from 1 semitone to 6 semitones. (See REFERENCES.)
Note that the iv command, the nf command, and the pf command
are aliases for
pcset -n and
pcset -p respectively.
The following command outputs the interval-class vectors for the sets
formed by successive sonorities in the input file
pcset -v webern > webern.iv
The following command outputs the Fortean set type for the complement of
the sonorities given in the input file
pcset -c berg > berg.pcs
The following command outputs the normal form representation for sets
formed from successive sonorities in the input file
pcset -n boulez.nf
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 context (4), **iv (2), iv (4), **nf (2), nf (4), **pc (2), pc (4), **pcset (2), **pf (2), pf (4), **semits (2), semits (4)
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