# Music Interval Inversion: Rules, Examples, and Practice

*2026-10-03*

D4 to F♯4 is a major third. Move D4 up an octave to D5, and the lower-to-upper pair becomes F♯4–D5: a minor sixth. The sharp stays on F. You changed which note is lower, not either note's spelling.

**Interval inversion moves one note by an octave and preserves its spelling. To name the result, check both the interval's size and its quality.**

This lesson uses written intervals in common Western music theory. The worked examples cover seconds through sevenths with ordinary sharps and flats; perfect unisons and octaves appear in the rule table. You'll track the octave move, check letters and semitones, then try a mixed quiz. Writing the pitches gives you a way to catch mistakes that memorizing the rule alone can miss.

![A woman lifts a blue ceramic pitcher above an ochre pitcher that remains on the middle shelf](/blog/interval-inversion.png)

## Show which note moves

For two different pitches less than an octave apart, raise the lower note an octave or lower the upper note an octave to exchange their lower-to-upper order. [Emory's interval-inversion lesson](https://scholarblogs.emory.edu/introtheorycomp/harmony/interval-inversion/) describes these two moves.

Here, every pair is written **lower pitch first**. The numbers identify octave registers: middle C is C4, and the next C above it is C5. An octave move changes the register number while keeping the letter and accidental.

| Starting pair | Move | Result, lower pitch first | Interval change |
| --- | --- | --- | --- |
| D4–F♯4 | Raise D4 to D5 | F♯4–D5 | Major third → minor sixth |
| D4–F♯4 | Lower F♯4 to F♯3 | F♯3–D4 | Major third → minor sixth |

Both answers have the same interval name, in different registers. Raising both original notes gives D5–F♯5, still a major third: neither note has passed the other.

Writing F♯4–D4 also leaves the actual pitches unchanged. Played one after the other, they form a descending major third. The minor sixth above requires an octave move.

Chord inversion asks which chord member is in the bass; see the [triad chord spelling lesson](/blog/triad-chord-spelling/). Melodic inversion reflects a melody's upward and downward motions. Here, we're finding the complementary interval between two spelled notes.

## Use nine for the size, then change the quality

For simple interval inversion, subtract the starting number from nine. The new quality follows a separate rule: major and minor exchange, augmented and diminished exchange, and perfect stays perfect. [Music Theory for the 21st-Century Classroom](https://musictheory.pugetsound.edu/mt21c/InversionOfIntervals.html) shows these relationships.

| Starting size | Inverted size | Check |
| --- | --- | --- |
| Unison, 1 | Octave, 8 | 1 + 8 = 9 |
| Second, 2 | Seventh, 7 | 2 + 7 = 9 |
| Third, 3 | Sixth, 6 | 3 + 6 = 9 |
| Fourth, 4 | Fifth, 5 | 4 + 5 = 9 |

Read each row backward too. A perfect octave becomes a perfect unison when one note moves to the other's register; a perfect unison becomes a perfect octave when one note moves an octave away.

| Starting quality | Inverted quality |
| --- | --- |
| Major, M | Minor, m |
| Minor, m | Major, M |
| Perfect, P | Perfect, P |
| Augmented, A | Diminished, d |
| Diminished, d | Augmented, A |

The capital M and lowercase m matter: **M3 inverts to m6**, while **m3 inverts to M6**. For an augmented fourth, the number changes from 4 to 5 and the quality from augmented to diminished: A4 becomes d5.

Changing the quality label doesn't mean altering a note. Keep F♯ as F♯. Its new relationship to D produces the minor sixth in the opening example.

## Check letters and semitones separately

Count letter names inclusively for the interval number. D4–F♯4 gives D (1), E (2), F (3). The sharp doesn't add a letter position. [Open Music Theory's intervals chapter](https://viva.pressbooks.pub/openmusictheory/chapter/intervals/) explains this distinction between size and quality.

Now read F♯4–D5 upward: **F, G, A, B, C, D**. That's six letter positions. Its eight-semitone distance complements the original four-semitone distance to make an octave.

The letter counts add to **nine** because both intervals include their endpoints. The distances add to **twelve semitones**. Use nine with interval numbers and twelve with semitone counts.

For a check without a keyboard, the natural-note gaps are C–D, D–E, F–G, G–A, and A–B = two semitones each; E–F and B–C = one each. A sharp raises a natural pitch one semitone, and a flat lowers it one. Count the starting pitch as zero.

These worked cases show the pitch move, letter count, and distance together. Each raises the original lower note by an octave.

| Before | After | Letter check after inversion | Semitone check |
| --- | --- | --- | --- |
| F♯3–A3, m3 | A3–F♯4, M6 | A–B–C–D–E–F: 6 | 3 + 9 = 12 |
| B3–E4, P4 | E4–B4, P5 | E–F–G–A–B: 5 | 5 + 7 = 12 |
| A♭3–D4, A4 | D4–A♭4, d5 | D–E–F–G–A: 5 | 6 + 6 = 12 |
| G3–F4, m7 | F4–G4, M2 | F–G: 2 | 10 + 2 = 12 |

In the third row, the augmented fourth and diminished fifth both span six semitones in equal temperament. Their letter counts differ. A distance check alone can't tell them apart.

### The same piano key can give the wrong written answer

Start with **A♭3–E4**, an augmented fifth: five letter positions and eight semitones. Raise A♭3 to A♭4. The result is **E4–A♭4**, a diminished fourth: E–F–G–A gives four positions, and the gap is four semitones. A5 becomes d4.

On an equal-tempered piano, A♭4 and G♯4 share a key. Replacing A♭4 with G♯4 gives **E4–G♯4**, a major third. Its four-semitone gap passes the distance check, but the three-letter count fails the inversion task.

Keep the original spellings. If a note looks unfamiliar in its new position, count the letters before replacing it with a more familiar name.

## Build a larger interval through a smaller one

Inversion also helps you construct intervals. Find the smaller complementary interval in the opposite direction, then move that new note an octave. [Emory's lesson](https://scholarblogs.emory.edu/introtheorycomp/harmony/interval-inversion/) demonstrates this construction method.

Suppose you need a **minor seventh above F♯3**:

1. Invert the requested name: m7 becomes M2.
2. Find a major second **below** F♯3. The letter must be E; E3 is two semitones below F♯3.
3. Raise E3 an octave to **E4**. The finished pair is **F♯3–E4**.
4. Check upward: F–G–A–B–C–D–E gives seven positions, and the distance is ten semitones.

Write the temporary pair separately: E3–F♯3 is M2. Its inversion, F♯3–E4, is m7. This makes it easier to see why you first worked below the given note.

For a **minor sixth below E4**, reverse the direction. The complement of m6 is M3, so find a major third above E4: **G♯4**. Lower that note to **G♯3**. The answer, written lower pitch first, is **G♯3–E4**. G–A–B–C–D–E gives six positions, and the distance is eight semitones.

The given note stays fixed in both constructions. “Above” or “below” tells you where the final new note belongs, even though the temporary smaller interval goes the other way.

## Reduce a compound interval before using nine

A compound interval extends beyond an octave. Remove an octave to reduce its generic number by seven while keeping its quality. [Open Music Theory's compound-interval section](https://viva.pressbooks.pub/openmusictheory/chapter/intervals/) explains the relationship.

Take **D3–F♯4**, a major tenth. Lower F♯4 to F♯3 to get **D3–F♯3**, a major third. Then invert that simple pair by raising D3 to D4: **F♯3–D4**, a minor sixth.

The first octave move reduced the interval; D remained below F♯. The second move exchanged their order. You could instead raise the original D3 to D4, producing D4–F♯4. That also reduces the tenth to a third, and still leaves D below F♯. An octave move only creates the inversion when it puts the notes in the required relationship.

Here, the task is to find the **simple inversion after octave reduction**. Don't calculate 9 − 10. If an exercise asks for specific registers or a compound result, count the resulting interval directly.

## Interval inversion practice with explained answers

Use paper and cover the answers. All pairs are lower pitch first, with no implied key signature. For a pitch-pair inversion, show the requested octave move, write the result lower pitch first, and give its full interval name.

| # | Task |
| --- | --- |
| 1 | Give the inversion of a major sixth. |
| 2 | Give the inversion of a diminished fourth. |
| 3 | Invert E♭3–G3 by raising the lower note. |
| 4 | Invert C♯4–G♯4 by lowering the upper note. |
| 5 | Identify B3–F4, then invert it by raising the lower note. |
| 6 | Construct a major seventh above A♭3 through its smaller inversion. |
| 7 | Construct a minor sixth below E4 through its smaller inversion. |
| 8 | D4–F4 was “inverted” to D5–F5. Diagnose and repair the answer by raising only the original lower note. |
| 9 | A♭3–E4 was inverted to E4–G♯4. Diagnose and repair the spelling. |
| 10 | Reduce C3–E♭4 to a simple interval by lowering the upper note, then invert that simple pair by raising its lower note. |
| 11 | Someone says the inversion of an eight-semitone minor sixth is a one-semitone interval because 9 − 8 = 1. Correct the reasoning. |

### Answers and checks

| # | Answer | Reasoning |
| --- | --- | --- |
| 1 | Minor third, m3 | 9 − 6 = 3; major becomes minor. |
| 2 | Augmented fifth, A5 | 9 − 4 = 5; diminished becomes augmented. |
| 3 | G3–E♭4, minor sixth | E♭3 becomes E♭4. E–F–G gives the original M3, 4 semitones; G–A–B–C–D–E gives m6, 8 semitones. |
| 4 | G♯3–C♯4, perfect fourth | G♯4 becomes G♯3. C–D–E–F–G gives P5, 7 semitones; G–A–B–C gives P4, 5 semitones. |
| 5 | B3–F4 is d5; F4–B4 is A4 | B–C–D–E–F gives five positions; F–G–A–B gives four. Both distances are 6 semitones. B3 becomes B4. |
| 6 | A♭3–G4, major seventh | Find a minor second below A♭3: G3. Raise G3 to G4. A–B–C–D–E–F–G gives 7 positions; the gap is 11 semitones. |
| 7 | G♯3–E4, minor sixth | Find a major third above E4: G♯4. Lower G♯4 to G♯3. G–A–B–C–D–E gives 6 positions; the gap is 8 semitones. |
| 8 | F4–D5, major sixth | Moving both notes preserved the m3. Keep F4 fixed and raise D4 to D5: F–G–A–B–C–D gives six positions, and 3 semitones become 9. |
| 9 | E4–A♭4, diminished fourth | G♯4 respells the moved note and makes a major third. Keep A♭; four letter positions and 4 semitones give d4. |
| 10 | C3–E♭3, m3; then E♭3–C4, M6 | The original m10 reduces to m3. Raise C3 to C4: E–F–G–A–B–C gives six positions, and 3 semitones become 9. |
| 11 | Major third, 4 semitones | Use 9 − 6 = 3 for the interval number, then swap minor to major. For the distance, use 12 − 8 = 4. |

If you missed 3–5, write the moving note's old and new register before naming the result. For 6 or 7, mark where the final note belongs, then write the temporary smaller pair. Questions 9 and 11 need different repairs: one is about spelling, the other about mixing counting systems.

## Make cards for the error you actually made

After working the problems on paper, choose a recurring miss and make a short retrieval prompt. You don't need a card for every row of a rule table.

| Front | Back |
| --- | --- |
| Invert E3–G3 by raising the lower note. Give pitches and interval. | G3–E4, M6. E moves up an octave; m3 becomes M6. |
| Repair the inversion of A♭3–E4 written E4–G♯4. | E4–A♭4, d4. The moved note keeps its A♭ spelling; G♯ makes a third. |
| A m6 spans 8 semitones. Give its inversion's name and semitone distance. | M3, 4 semitones. Use 9 − 6 for the number and 12 − 8 for the distance. |

The [music theory flashcards guide](/blog/music-theory-flashcards/) covers keeping written interval prompts precise. Include registers when the question asks which note moves; a letter-only prompt can hide the mistake you're trying to fix.

Next time, change the starting notes and work the octave move again before checking the name. Show the moved pitch, keep both spellings, and make the letter count agree with the semitone distance.

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