Interval Inversion Calculator - Flip Any Interval to Its Inversion

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What inverting an interval means

To invert an interval, you move the lower note up an octave, or the higher note down an octave, so the two notes swap positions. The interval changes, but the two notes stay the same pair. Inversion is how musicians flip a melody upside down, how chords get rearranged, and how bass lines move under a melody.

For example, C up to G is a perfect fifth. Move the C up an octave, and you get G up to C, a perfect fourth. Same notes, different interval. The fifth and the fourth are partners: they always add up to an octave.

The rules of inversion

There are two rules, and they never change. First, the two interval numbers add to nine. A second inverts to a seventh, because two plus seven is nine. A third inverts to a sixth. A fourth inverts to a fifth. An octave inverts to a unison.

Second, the quality flips in a fixed way. Major becomes minor, and minor becomes major. Augmented becomes diminished, and diminished becomes augmented. Perfect stays perfect. So a major third inverts to a minor sixth, and a minor seventh inverts to a major second.

How this calculator works

Pick an interval number from one to eight and pick its quality. The tool gives the inverted interval and its distance in semitones. It also checks the combination: perfect intervals are only the unison, fourth, fifth and octave, so if you pick perfect with a second, it tells you that combination does not exist.

The maths is simple. The inverted number is nine minus the original number. The inverted semitone distance is twelve minus the original distance. The quality flips by the rule above. The tool does the arithmetic, but learning the rules yourself is worth it, because they come up constantly in harmony.

Why inversion matters

Inversion matters most in chords. A C major chord in root position has C at the bottom. Put E at the bottom and it is the same chord in first inversion. Put G at the bottom and it is in second inversion. The chord sounds different in each position, even though the notes are the same, and composers use that difference to make bass lines move smoothly.

Inversion also matters in melodies. Turning a melody upside down, called melodic inversion, is a classic composing technique. A rising major third becomes a falling minor sixth. The shape mirrors, and the music gains a hidden connection that listeners feel even if they cannot name it.

Examples to practise

Work through these by hand, then check with the tool. A perfect fifth inverts to a perfect fourth. A major third inverts to a minor sixth. A minor seventh inverts to a major second. An augmented fourth inverts to a diminished fifth. A major sixth inverts to a minor third.

Notice the pattern: the big intervals become small, and the small intervals become big. That is the whole point. Inversion trades height for depth, and the pair always fits inside one octave together.

Common mistakes

The most common mistake is adding to eight instead of nine. The numbers add to nine because the unison counts as one, not zero. Another mistake is forgetting that major and minor swap: a major second inverts to a minor seventh, not a major seventh. A third mistake is trying to invert a compound interval, like a tenth, directly. Reduce it to a simple interval first, invert that, then add the octave back if you need it.

Use the tool to check your homework and your composing. It is free, runs in your browser, and needs no sign-up.

Interval Inversion Calculator – Flip Any Interval to Its Inversion