Chord inversions by ear

A C major chord is C, E and G, and it stays C major whichever of those notes is at the bottom. What changes is the sound. Musicians name a chord’s position by which of its notes is in the bass, the lowest note, and that position is called its inversion.

Hearing inversions is the step after hearing a chord’s quality, covered in Major vs minor chords. This guide shows the three positions of a triad, what changes inside the chord when you invert it, and what to listen for. Every sound on the page is a real piano you can play, and there are two short drills to try.

Three positions of one chord

A triad has three notes: the root, the third and the fifth. Whichever of them is lowest is the bass, whatever instrument or voice is playing it:

• Root position: the root is in the bass.
• First inversion: the third is in the bass.
• Second inversion: the fifth is in the bass.

The bass is not the same thing as the root. The root of C major is C in all three positions; only the bass moves, from C to E to G. In chord symbols, a slash names the bass: C/E is C major with E at the bottom, and C/G is C major with G at the bottom.

Treating all three as one chord goes back to Jean-Philippe Rameau, who is credited as the first to recognize what a chord’s inversions have in common, in his Treatise on Harmony (1722). By ear you need both ideas at once: it’s the same chord, and you can still tell which of its notes is at the bottom.

What changes inside the chord

The clips here and in Earstep play every chord in close position, with its notes as near together as they go above the bass. In close position a triad is two intervals stacked, and inverting it changes which two:

• Root position is a third with a third on top: C up to E, then E up to G.
• First inversion is a third with a fourth on top: E up to G, then G up to C.
• Second inversion is a fourth with a third on top: G up to C, then C up to E.

The fourth appears because moving the root up an octave turns intervals upside down. Turned over, a third becomes a sixth and a fifth becomes a fourth; a major interval becomes minor, and a perfect one stays perfect. So the major third from C up to E becomes the minor sixth from E up to C, and the perfect fifth from C up to G becomes the perfect fourth from G up to C.

Figured bass, a shorthand from 17th- and 18th-century music that’s still used to label inversions today, names each position by its intervals above the bass:

• Root position has a third and a fifth above the bass, 5/3, and the figure is usually left out.
• First inversion has a third and a sixth, 6/3, shortened to 6.
• Second inversion has a fourth and a sixth, 6/4. It keeps both numbers so it can’t be mistaken for first inversion, and that’s where the name six-four chord comes from.

One warning: in jazz chord symbols, C6 means something else, a C major chord with an added sixth. A figured-bass 6 is a first inversion; a chord-symbol 6 is an extra note.

Earstep draws a chord by overlaying the ratio of every note against the bass, so the three positions draw three different figures. Root position overlays 5:4 and 3:2, first inversion 6:5 and 8:5, and second inversion 4:3 and 5:3. The figures differ for the same reason the sounds do: the notes stand at different distances from the bass.

What to listen for

Naming the root and quality is one question; naming the position is another. These habits help:

1. Find the bass. Listen for the lowest note and sing it. Singing pins it down before the chord fades, and everything else is measured from there.
2. Find the fourth. Root position has none, just two thirds. In first inversion the fourth is on top, between the two upper notes. In second inversion it’s at the bottom, right against the bass. Play or imagine the chord one note at a time from the bottom and listen for where the bigger step comes.
3. Notice how settled it sounds. In Open Music Theory’s table of harmonic intervals, thirds and sixths are consonant and the perfect fourth is dissonant. A first-inversion chord has only a third and a sixth above its bass. A second-inversion chord has a fourth against its bass, and Open Music Theory notes that six-four chords are treated in special ways because of that dissonance. Many listeners hear second inversion as the least settled of the three, as if it were on its way to another chord.

The third clue is an impression, so lean on the first two when you’re unsure. The bass and the fourth don’t depend on how a chord strikes you that day. If the fourth itself is new to you, Perfect fourth vs perfect fifth is a good place to practice it, and Why some intervals sound consonant has more on consonance.

Minor chords work the same way

A minor triad inverts the same way, and the fourth lands in the same places. What changes is the thirds. A minor chord in root position is a minor third with a major third on top, so in first inversion its bottom interval is a major third, from E♭ up to G.

That can fool you into hearing a major chord. The quality comes from the third above the root, not from whatever interval happens to be at the bottom, so name the position from the bass and the fourth, and only then the quality.

Try it

The drill below plays a major chord in one of its three positions, on a root picked at random. Name the position.

That’s level 1 of Inversions in Earstep, “Major chord inversions”. Level 2 does the same for minor chords, level 3 mixes the two for six answers, and level 4 adds the diminished triad for nine. The path opens once you’ve passed level 2 of Triads. Here is level 3, a good test of whether the first two have stuck:

Why augmented chords stay in root position

The diminished triad inverts like major and minor. It stacks two minor thirds, C E♭ G♭, so its outer notes are a tritone apart, 6 semitones. Invert it and the tritone takes the place the fourth has in a major or minor chord: on top in first inversion, at the bottom in second. In major and minor keys the diminished triad usually appears in first inversion, so you may meet it that way more often than in root position.

The augmented triad is different. It stacks two major thirds, 4 semitones each, and a third major third on top would land on the root again, an octave up: three major thirds make exactly one octave. Open Music Theory lists this among the only five ways to divide the octave equally.

So put E at the bottom of C augmented and you get E, G♯ and C. From G♯ up to C is again 4 semitones, so you still hear two major thirds stacked. On a piano those are the very keys of E augmented in root position, spelled E G♯ B♯, where B♯ is the key you know as C. Every inversion of an augmented triad sounds like root position of another augmented triad, so by ear its positions can’t be told apart. That’s why Earstep drills augmented triads in root position only.

Sources

• Open Music Theory: Inversion: the bass determines inversion; root position, first and second inversion; the bass isn’t the root; slash chord symbols.
• Open Music Theory: Figured Bass and Roman Numerals with Figures: 5/3, 6/3 and 6/4 above the bass, and the abbreviated figures for root position and first inversion.
• Open Music Theory: Intervals: how intervals invert, and which harmonic intervals are consonant or dissonant.
• Open Music Theory: Strengthening Endings with Cadential 6/4: six-four chords involve a dissonance, the fourth, with the bass.
• Open Music Theory: Equal Divisions of the Octave: major thirds dividing the octave and outlining an augmented triad.
• Inversion (music), Wikipedia: root position and inverted chords, the intervals above the bass, figured bass and slash chords, and Rameau.
• Second inversion, Wikipedia: the fourth between bass and root as a traditional dissonance, and the six-four name.
• Figured bass, Wikipedia: how figures are used today, and the difference from a C6 chord symbol.
• Triad (music) and Diminished triad, Wikipedia: close position, stacked thirds, and the diminished triad’s usual first inversion.