Invert an interval and check its new name

First learn to name an interval’s number and quality. Inverting it is a new operation: exchange which written note is lower by moving one of the notes an octave. For an ascending pair smaller than an octave, raising the lower note one octave puts it above the other. Source: Open Music Theory, intervallic inversion.

Use octave labels, with middle C = C4, to make the movement explicit. Keep the letter and any accidental: D♭4 moved up an octave becomes D♭5. It does not become C♯5 merely because those notes can sound alike on a keyboard. We are checking written intervals as well as distances.

The diagrams below are register-order maps, with labels instead of staff notation. Their vertical spacing is not proportional to semitone distance. Work with the named notes; this is a paper exercise and requires no particular instrument technique.

Start with D4 below F♯4. Move only D4 to D5, leaving F♯4 where it was. Now read from the new bottom: F♯4 up to D5. Count letters F–G–A–B–C–D: six, including both ends. Its eight-semitone span confirms a minor sixth.

E4 to A4 spans four letters and five semitones. Move E4 to E5; A4 to E5 spans five letters and seven semitones. The quality remains perfect. Together the original and inverted semitone spans fill an octave: 5 + 7 = 12.

The relationships work in reverse too: a sixth becomes a third, for example. The numbers total nine because interval numbers include endpoints; an octave contains eight letter positions but seven steps between them.

For quality, major exchanges with minor, augmented with diminished, and perfect stays perfect. Thus “a third becomes a sixth” is incomplete until you supply the quality. Source: Music Theory for the 21st-Century Classroom, interval inversion.

Our worked pairs are seconds through sevenths. For a perfect unison, move one copy of the pitch up an octave to obtain a perfect octave; for a perfect octave, moving its lower note up makes the two pitches coincide in a unison. More complex or compound intervals need careful reduction and are outside this exercise.

Take G3–B♭3, a minor third. After raising G3, the pair is B♭3–G4, a major sixth. The number check 3 + 6 = 9 passes. The quality also changes from minor to major. “Minor sixth” would pass the number check but fail the quality check.

Now take C4–F♯4. The letters make a fourth and the span is six semitones, so it is an augmented fourth. Raising C4 gives F♯4–C5, a diminished fifth. Both span six semitones; their different letter counts still require different names. Do not rename F♯ as G♭ during the move.

If both notes moved up an octave, their interval stayed the same: D4–F♯4 became D5–F♯5, still a major third. That is an octave transposition of the pair, not the exchange shown in our diagrams. Circle the note that moves before writing the answer.

For each pair, raise the lower note one octave. Write the resulting pitches in low-to-high order, name their interval, and check the original/inverted number sum.

1. C4–D4.
2. E4–G4.
3. D4–A4.
4. B3–F4.
5. A learner turns F4–A4 into F5–A5 and calls it an inversion. Repair the move.

Check the results

1. D4–C5: minor seventh; the original is a major second, 2 + 7 = 9.
2. G4–E5: major sixth; the original is a minor third, 3 + 6 = 9.
3. A4–D5: perfect fourth; the original is a perfect fifth, 5 + 4 = 9.
4. F4–B4: augmented fourth; the original is a diminished fifth, 5 + 4 = 9.
5. Leave A4 fixed and move F4 to F5: A4–F5, a minor sixth. The starting F4–A4 is a major third.

The interval inversion worksheet (plain text) adds a place to record letter count and semitone span. If the mnemonic and your written notes disagree, recheck the actual pitches; do not change the answer just to make the numbers add up.

This guide exchanges the registers of two notes and measures the resulting interval. Chord inversion instead identifies which chord member is in the bass. Melodic inversion reverses the direction of intervals in a melodic pattern. Those are different questions; successfully solving this worksheet does not establish that you have analysed a chord or transformed a melody. Source: Open Music Theory, chord inversion; source: melodic inversion in twelve-tone theory.

For a useful next check, give a partner only “minor sixth”, ask for its inverted number and quality, then verify the answer with G3–B♭3 and B♭3–G4. A rule and a concrete pitch pair should support the same conclusion.