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IntervalOctaveInterval NumberPerfect IntervalsCounterpoint

Inversion carries more than one meaning, so separate them first:

• Interval inversion: move the lower note up an octave (or the upper note down) and see the distance reversed.
• Melodic inversion: turn a melody upside down, so rising intervals become falling ones.
• Chord inversion: change which chord tone is in the bass — that belongs to chord inversion.

This entry covers the first only.

One rule, half the memorising

Degrees add up to 9; major ↔ minor; augmented ↔ diminished; perfect stays perfect.

Master everything up to a fifth and derive the rest by subtraction: if a minor sixth will not come to mind, recall its major-third inversion.

Why "perfect" is the one that does not flip

Because the perfect family has no major or minor label to flip. A perfect interval can only become augmented or diminished — and a perfect interval stays perfect when inverted (perfect fourth ↔ perfect fifth; the octave inverts into itself). That asymmetry is a useful clue: major and minor come from small differences in size, while perfect intervals are judged by a different standard.

Diagram: they add up to 9

Listen: one interval, two directions

Hear the major third, then its inverted minor sixth — the very same pair of pitches, with a different note underneath.

Common misconceptions

• "Inversion means reversing the order of notes." That is one kind of melodic inversion. Interval inversion moves one note by an octave and changes no order.
• "A major interval inverts to a major interval." Major becomes minor and minor becomes major. Only perfect intervals stay perfect.
• "The degrees add up to 8." They add to 9, because both endpoints are counted in each direction.
• "An augmented fourth inverts to a diminished fourth." It inverts to a diminished fifth: take 9 minus the original degree, then swap augmented for diminished.

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Sources

• 转位口诀（度数相加为九、大↔小、增↔减、纯仍为纯），为通行乐理表述
• 旋律转位与和声转位两个义项的区分，属乐理与对位写作常识

Used for fact-checking only; all prose is original.