This web application provides information on any pitch-class set (or ‘Intervallic Prime Form’), drawing terms and concepts from Jenny McLeod’s and Peter Schat’s Tone Clock Theory.
Information returned includes the label, the Forte Name, hour or hour-group name, tone-clock steering, and the ‘dissonance’ value. Much of this information is drawn from the IPF tables in Jenny McLeod’s unpublished monograph Chromatic Maps* (an expansion of Peter Schat’s work). At the bottom of this page is a glossary explaining some of the terminology.
* Unfortunately Jenny’s writings are currently unpublished, though there are possibilities for future publications. Watch this space.
How to use
Click the keyboard, chromatic circle or pitch-class buttons to enter your pitch-class set. Then scroll down to read the information on the IPF.
Information on selected IPF
| IPF: | |
|---|---|
| Existing name (or section of:)**: | |
| Pitch-Class Set: | |
| Tone Clock Name: | |
| Tone Clock 12-note Steerings: | |
| Other Identities: | |
| Mode subset: | |
| Chromatic Complement: | |
| Interval Vector: | |
| Dissonance value (percentage)***: | |
| Common tones under transposition: |
|
*DISS weightings:
|
ic1 | ic2 | ic3 | ic4 | ic5 | ic6 | |
|---|---|---|---|---|---|---|---|
Sample 12-note steering:
** NB: ‘Existing name’ may only apply to certain voicings/inversions of the set
*** The dissonance value is calculated by taking the weighted sum of the interval vector, where each ic is multiplied by the weightings provided above. This value is then skew-scaled to derive a percentage value from 1–100% to provide a rough measure of the perceptual dissonance of a harmony, from the least to the most dissonant (where 1% is a perfect fifth and 100% is the full chromatic aggregate). Of course, as it operates on pc-sets rather than actual chords, it does not take voicing into account; that said, the ratios still provide a certain useful measure.
GLOSSARY
- 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.