Interval inversion

What it means

In the inversion of an interval, the lower note is placed an octave higher — or, equivalently, the upper one an octave lower. From the distance C–E becomes E–C, from the third thus the sixth. Two rules hold without exception: the numbers of interval and inversion add up to nine, and the designation reverses — major becomes minor, minor becomes major, augmented becomes diminished, diminished becomes augmented, perfect remains perfect.

Musical use

The practical usefulness is considerable. Whoever hears the smaller intervals securely gains access to the larger ones by way of inversion: a sixth that is hard to hit can be thought of as an inverted third. The rule likewise simplifies determination in the notation.

For the study of composition it is also revealing. Third and sixth are both imperfect consonances and may be led in parallel; fifth and fourth belong together, the fourth above the bass being treated as dissonant although its inversion, the fifth, is consonant. Second and seventh are both dissonant — the same relationship of tension in a different register, the wide seventh sounding more open than the close second.

Interval inversion is to be distinguished from chord inversion: there a chord changes its position and keeps its name; here a two-note sonority is turned over and changes its designation. In counterpoint the double leading of voices rests on the same principle.

In inversion the numbers always add up to nine: the third becomes the sixth, the fourth the fifth. The quality reverses, major becomes minor, augmented becomes diminished, perfect remains perfect. This rule is the basis of double counterpoint, in which two voices exchange their position.

Performance practice

Use the rule when singing: a wide leap can be hit securely by way of its inversion — the sixth upward thought as a third downward. Practise intervals therefore always in pairs, with their inversion. And, when analysing, check wide intervals by reducing them to their simple form.