Interval Inversion

Core Idea

When an interval is inverted (the lower note moves up an octave), the interval name and quality change predictably. Generic names add to 9 (a 3rd inverts to a 6th). Quality inversions follow a pattern: major becomes minor, perfect stays perfect, augmented becomes diminished. Understanding inversion is crucial for voice leading.

How It's Best Learned

Practice inverting intervals on staff and keyboard, observing name and quality changes. Listen to inverted intervals and hear how sound differs while maintaining the same pitch classes. Memorize quality inversion rules.

Common Misconceptions

Inverted intervals sound completely different (they share pitch content). Perfect intervals don't stay perfect when inverted (they do). Miscounting generic interval names after inversion.

Explainer

You've already learned to measure intervals — to identify both the generic size (second, third, fourth, etc.) and the quality (major, minor, perfect, augmented, diminished) of the distance between two notes. Inversion asks a different question: what happens when you flip an interval? Specifically, when you take the lower note of an interval and move it up an octave — or equivalently, take the upper note down an octave — you produce the inversion of that interval. The same two pitch classes remain involved; only which sits on top has changed.

The generic size of an interval and its inversion always sum to 9. This single fact is the key to inversion: a 2nd inverts to a 7th (2 + 7 = 9), a 3rd inverts to a 6th (3 + 6 = 9), a 4th inverts to a 5th (4 + 5 = 9). The rule works because an octave spans 8 generic scale steps, and when you flip an interval, the two resulting pieces must together cover an octave — but interval counting counts both endpoints, which adds the extra 1. Quality changes follow their own predictable pattern: major becomes minor (and minor becomes major), perfect stays perfect, augmented becomes diminished (and diminished becomes augmented). So a major 3rd (C up to E) inverts to a minor 6th (E up to C). A perfect 5th (C up to G) inverts to a perfect 4th (G up to C). An augmented 4th inverts to a diminished 5th — which is the tritone relationship, symmetric and self-inverting in quality.

Why does this matter? Because in four-voice writing and voice leading, chords appear in different inversions (a term that extends directly from interval inversion), and the intervals between voices shift depending on which chord tone is in the bass. Understanding how interval quality changes when voices flip helps you predict and control the sound of progressions. When composers write counterpoint, they frequently use contrary motion — voices moving in opposite directions — which naturally produces inverted intervals from one beat to the next. Recognizing that a major 6th and a minor 3rd are inversions of each other explains why they feel like mirror images: they contain exactly the same pitch classes, just reordered in register.