Octave, ratios, and distance

Interval Inversions

Explore why every interval and its inversion complete the octave in semitones, cents, and frequency ratios.

Interval inversions

Hear the octave complement

An inversion turns an ascending interval into its octave complement: semitones add to 12 and frequency ratios multiply to 2.

Explore one pair

  1. Choose a starting note.
  2. Choose an inversion pair.
  3. Compare semitones, cents, and ratios.
  4. Hear the interval, then hear its inversion.
Semitone complement
Frequency-ratio complement
Interval
Inversion
Product