Inverting a musical interval means moving one of its two notes by an octave so the note that was on top ends up on the bottom, or vice versa. The process follows a simple, predictable pattern: subtract the interval number from 9, then swap the quality to its opposite. Once you learn the two rules, you can invert any interval in seconds.
The Two Methods for Inverting
You have two options. Take the bottom note and move it up one octave, so it now sits above the other note. Or take the top note and move it down one octave, placing it below the other note. Either way, you end up with the same inverted interval. If you start with C on the bottom and E on the top (a major 3rd), moving C up an octave puts it above E, giving you E up to C (a minor 6th). The interval flips.
The Rule of Nine
Every interval and its inversion add up to 9. This is the fastest way to find the new interval number without counting notes on a staff. A 3rd becomes a 6th (9 minus 3 equals 6). A 2nd becomes a 7th. A 5th becomes a 4th. The complete set of pairs:
- Unison (1) inverts to an octave (8)
- 2nd inverts to a 7th
- 3rd inverts to a 6th
- 4th inverts to a 5th
- 5th inverts to a 4th
- 6th inverts to a 3rd
- 7th inverts to a 2nd
- Octave (8) inverts to a unison (1)
This rule never changes regardless of the key, the clef, or whether the notes are sharp, flat, or natural. Nine minus the interval number always gives you the inversion.
How the Quality Flips
The number is only half the answer. You also need to swap the interval’s quality according to a fixed pattern: major becomes minor, minor becomes major, augmented becomes diminished, and diminished becomes augmented. Perfect stays perfect.
- Major becomes minor
- Minor becomes major
- Augmented becomes diminished
- Diminished becomes augmented
- Perfect stays perfect
So a major 3rd inverts to a minor 6th. A minor 6th inverts to a major 3rd. A perfect 5th inverts to a perfect 4th. An augmented 4th inverts to a diminished 5th. Both rules work together: apply the Rule of Nine to get the number, then flip the quality.
A Worked Example on the Staff
Say you’re looking at the notes C and A on a staff, with C below and A above. That’s a major 6th. To invert it, move C up one octave. Now A is on the bottom and C is on the top. Apply the rules: 9 minus 6 equals 3, and major becomes minor. The result is a minor 3rd (A up to C). You can verify by counting: A to C is three letter names, and it contains three half steps, which matches a minor 3rd.
This same process works in reverse as a shortcut for building intervals downward. If someone asks you to write a minor 6th below a given note, you can invert it first: a minor 6th becomes a major 3rd. Find the major 3rd above your note, then write that pitch below instead. It’s often faster than counting downward.
The Tritone: A Special Case
The tritone is the one interval that lands exactly in the middle of the octave, spanning six half steps (three whole tones, which is where the name comes from). It can be spelled as an augmented 4th or a diminished 5th, and its inversion reveals why those two names exist.
Take F up to B. That’s an augmented 4th, six half steps. Invert it by moving F up an octave: now you have B up to F, a diminished 5th, also six half steps. The sounds are identical, but the interval number changes from a 4th to a 5th, and the quality changes from augmented to diminished, exactly as the rules predict. The tritone is the only interval where inversion produces something with the same number of half steps. Every other interval changes size when flipped.
What Happens to Consonance
In traditional music theory, intervals are grouped into consonant (stable, resolved-sounding) and dissonant (tense, restless-sounding). The consonant intervals are the perfect unison, perfect octave, perfect 5th, and all major and minor 3rds and 6ths. The dissonant intervals include major and minor 2nds, major and minor 7ths, and all augmented and diminished intervals.
When you invert a consonant interval, you generally get another consonant interval. A major 3rd (consonant) inverts to a minor 6th (also consonant). A perfect 5th inverts to a perfect 4th. That last one comes with a catch, though: the perfect 4th is sometimes treated as consonant and sometimes as dissonant depending on context. When it functions as the inversion of a 5th within a chord, it’s typically considered consonant. When it sits above the bass note of a texture, it’s historically treated as dissonant. This quirk of the perfect 4th is one of the oldest debates in Western music theory.
Dissonant intervals invert to dissonant intervals. A major 2nd becomes a minor 7th, both dissonant. An augmented 4th becomes a diminished 5th, both dissonant. So inversion preserves the basic tension level of an interval even though it changes the specific size and quality.
Why Inversion Matters in Practice
Interval inversion isn’t just an academic exercise. Composers use it constantly. When a melody rises by a minor 3rd, a composer might answer it with a phrase that falls by a major 6th, the inversion, creating a sense of balance. In counterpoint, knowing that a 3rd and a 6th are inversions of each other explains why both are treated as interchangeable consonances when writing two-part music.
It also speeds up your ear training and sight-reading. If you can instantly recognize a major 6th by ear, you already know what a minor 3rd sounds like, just compressed into a smaller space. The two intervals share the same pair of pitch classes, so training one trains the other. The Rule of Nine and the quality swap make the whole system predictable, letting you work with intervals in any direction without starting from scratch each time.