Audio: inversion (0:06)

Figure: inversion

inversion plays melody and harmony on a harp. The inversion figure shows that the first bar of the score consists of the intervals of unison and its inversion, the octave. Bars two and three show a melody spanning two octaves that consists of only one note, D.

Inversion in music means the same as it does in real life, turning something upside down. In this instance, we are interested in inverting an interval.

Every interval can be inverted to form another interval. If x:y represents the frequency ratio of an interval, y:x is the frequency ratio of its inversion.

Unison and octave are special cases of inversion. The frequency ratio of unison is 1:1. Invert it and, of course, you get another unison with ratio 1:1. The frequency ratio of an octave is 2:1. Invert it and you get 1:2 which is the frequency ratio of two octaves below. By convention, the inverse of unison 1:1 is the octave 2:1, and the inverse of octave 2:1 is the unison 1:1.

We are now in possession of the two crucial pieces of information needed to construct a tuning system:

  1. The frequency of an octave is always twice that of unison.
  2. Intervals always come in pairs, the interval and its inversion.