IPF Finder

v1.0b12 ©2006 Michael Norris

This is a little Javascript program that lets you choose a pitch-class set, and then returns a bunch of information about it, primarily drawn from Jenny McLeod's and Peter Schat's Tone Clock theory. Information returned includes the Intervallic Prime Form (IPF), the Forte Name, and the "dissonance". Much reference is made to Tone Clock theory, drawn from the IPF tables in Jenny McLeod’s “Chromatic Maps”* (based on Peter Schat’s work). At the bottom of this page is a glossary explaining (some) of the terminology. One day I'll get round to explaining everything... :-)


Please tick the notes in the chord then click 'Calculate':

A      A#     B      C      C#     D      D#     E      F      F#     G      G#


Existing name (or section of:)**:
Pitch-Class Set:
Tone Clock Name:
Tone Clock 12-note Steerings:
Other Identities:
Mode subset:
Chromatic Complement:
Interval Vector:
DISS (weighted sum)*:
DISS ratio**:
Common tones under transposition:



*DISS weightings:

   ic1 ic2 ic3 ic4 ic5 ic6

Sample 12-note steering:


* Unfortunately Jenny's writings are currently unpublished, though there are possibilities for future publications. Watch this space.

** NB: existing name may only apply to certain voicings or inversions



  • IPF: The Intervallic Prime Form. Like the "Normal Form" in Forte's writing, but a little easier to work with, IMHO. The most 'compact' form of the pitch-classes, where the intervals between notes are shown (1=semitone, 2=whole tone, etc.). Sometimes an alternative IPF is given in brackets.
  • Existing name: If this set of pitches has an English name it will appear here. I have expanded this section from Chromatic Maps to include chords that are often used in jazz (including so-called "rootless" voicings). If the pitches are a subset of a particular scale, then the scale will appear here parenthesised.
  • Pitch-Class Set: The PC Prime Form taken from Allan Forte's The Structure of Atonal Music.
  • Tone Clock Name: The roman tone-clock names, associating the IPFs with the twelve "hours". Not all IPFs have an associated TC name.
  • Tone Clock 12-note Steerings: Some IPFs can be transposed so that each new set of pitch-classes uniquely combines with the old sets to create the 12 chromatic pitch-classes. For instance, a 3-note chord would be transposed 4 times, while a 4-note chord 3 times. The "base" pitches for these transpositions themselves form a set of interval-classes, which is given here in its tone-clock name.
  • Other Identities: Any other names for this IPF.
  • Mode subset: Taken from Messiaen's modes of limited transpositions. If the IPF forms a subset of one of Messiaen's modes, then this is given here.
  • Chromatic Complement: "Complement" as in set theory. If the notes of the IPF are subtracted from the 12-note chromatic scale, the resulting pitches themselves form an IPF, which appears here.
You are here: Home Software IPF Finder