Interval Class

Set Theory

In musical set theory, the octave and unison are not treated as intervals (see octave equivalence) and all possible intervals are grouped by inversion into six interval classes, denoted by colors in the intervals table.

1. Minor second / Major seventh
   1 semitone + 11 semitones = 12 semitones (1 octave)
    

2. Major second / Minor seventh
   2 semitones + 10 semitones = 12 semitones (1 octave)
    

3. Minor third / Major sixth
   3 semitones + 9 semitones = 12 semitones (1 octave)
    

4. Major third / Minor sixth
   4 semitones + 8 semitones = 12 semitones (1 octave)
    

5. Perfect fourth / Perfect fifth
   5 semitones + 7 semitones = 12 semitones (1 octave)
    

6. Tritone (its own inversion)
   6 semitones + 6 semitones = 12 semitones (1 octave)

Equal-tempered intervals that share an interval class (six classes above) have mathematically related tuning ratios (a × b = 2, e.g. P4 × P5 = 2, or 4/3 × 3/2 = 2), with the same amount of purity or impurity (tuning error compared to their just-intoned interval peers).

For more on interval classes, see Intervals as Prime Forms.