This web application uses concepts from Jenny McLeod’s and Peter Schat’s Tone Clock Theory to provide information about a selected pitch-class set (or 'Intervallic Prime Form'). Information returned includes the label, the Forte Name, tone-clock steering, and the ‘dissonance’ value. 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.

Selected pitches:


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* Unfortunately Jenny's writings are currently unpublished, though there are possibilities for future publications.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