iv — determine interval-class vectors for successive vertical sonorities for Humdrum inputs


` iv [inputfile …] [> outputfile.iv]`


The iv command is used to determine the interval-class vector for any of five set-theory related inputs: pitch (semits), pitch-class (pc), normal form (nf), prime form (pf), or Fortean set name (pcset). An interval-class vector is a six-element numerical list that indicates the abundance of various interval-classes (from 1 semitone to 6 semitones) for some pitch-class set. See REFERENCES below.

When provided with semits or pc inputs, iv 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 iv command is able to translate any of the representations listed below. For descriptions of the various input representations (including iv) refer to Section 2 (Representation Reference) of this reference manual.

It is recommended that output files produced using the iv command should be given names with the distinguishing `.iv' 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 iv.


The iv 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 interval-class vectors for successive sonorities in the input file opus24. The input may be pitches, pitch-classes, normal forms, Fortean set names, etc.

` iv opus24 > opus24.iv`


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), **nf (2), nf (4), **pc (2), pc (4), **pcset (2), pcset (4), **pf (2), pf (4), **semits (2), semits (4)


The iv command is a shell script that invokes pcset -v.



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.