Inversions and Figured Bass

A triad has three notes, which means there are three choices for which one goes at the bottom.

The pitches are the same either way, so it remains “the same chord” — but the stability of the sound changes, and so does the melodic line traced by the bass. Handling that difference is what inversion is about.

Three arrangements

Position	Note in the bass	Arrangement	Figured bass
Root position	root	C–E–G	(5⁄3, conventionally omitted)
First inversion	third	E–G–C	6
Second inversion	fifth	G–C–E	6⁄4

The names count how many times the chord has been rotated, not which chord member is in the bass. Move the root up an octave once for first inversion, once more for second.

The figures count intervals above the bass

What do the numbers in figured bass mean? They are intervals from the bass up to the other notes. Misread that and everything downstream becomes confusing.

Take first inversion, E–G–C, where the bass is E.

• E up to G → a 3rd
• E up to C → a 6th

Strictly that should be figured “6⁄3”, but a third is assumed to be present and goes unwritten, leaving only the distinctive 6. That is all the symbol means.

In second inversion, G–C–E, the bass is G.

• G up to C → a 4th
• G up to E → a 6th

Here both numbers are written, giving 6⁄4.

Root position, C–E–G, has a third and a fifth above the bass, so it would be figured 5⁄3 — but since that is the ordinary case, nothing is written at all. Figured bass is a notation that records only departures from the expected.

Check

In figured bass, the number 6 measures the interval from what to what?

Root to bassRoot to thirdBass to rootBass to fifth

Check answer

Inversion changes how stable the chord sounds

All three arrangements contain the same pitches, and their stability differs sharply.

The three arrangements compared

▶Root position C–E–G▶First inversion E–G–C▶Second inversion G–C–E

Check: Every one of these is C, E, and G. Root position is the most settled and can end a phrase. First inversion is lighter and leans forward. Second inversion, with a fourth above the bass, is plainly unstable and cannot finish anything on its own.

bass = root. Maximum stability

Why second inversion is unstable

The reason is the perfect 4th above the bass from Unit 1.

In second inversion, G–C–E, the interval from the bass G to the root C is a perfect 4th. A perfect 4th in isolation is consonant, but a fourth measured against the bass behaves as a dissonance in functional harmony.

That makes second inversion a chord you cannot end on, and consequently it appears in specific places for specific reasons. The most important is immediately before a cadence, where a second-inversion tonic chord is placed ahead of the dominant — the cadential 6⁄4. Unit 4 takes it up.

Second inversion as a way through, not a destination

▶Stopping on second inversion▶I64 → V → I

Check: The first stops on the second-inversion chord, and it does not feel finished. The second continues on to the dominant and the tonic, which shows the second inversion functioning as a point of passage. This shape is one of the standard formulas of classical harmony.

cannot close

Inversions exist to shape the bass line

The practical value of inversions is that they let you design what the bass does.

String every chord together in root position and the bass jumps around between roots. Inversions let it move smoothly instead.

Unit 5 develops this as a technique in earnest. For now, hold onto the idea that inversions are not only about changing the color of a chord — they are the tool for writing a bass line.

Slash chords say the same thing differently

Popular music writes inversions with a slash.

Figured bass	Chord symbol	Arrangement
(root position)	C	C–E–G
6	C/E	E–G–C
6⁄4	C/G	G–C–E

Whatever follows the slash is the bass note, so “C/E” means “a C chord, with E in the bass.”

The two notations record the same fact from different starting assumptions.

• figured bass writes intervals above the bass (the bass is given; everything else is relative to it)
• slash notation writes the name of the bass note (the chord is given; the bass is specified)

Neither is better. They presuppose different things. Figured bass grew out of a way of composing that writes the bass line first (basso continuo), and slash notation grew out of a way of composing that fixes the chords first. The final lesson of this unit returns to that correspondence in more detail.

Check

Which inversion is the chord symbol F/A?

Second inversionThird inversionRoot positionFirst inversion

Check answer

Inversion does not change a chord’s function

One principle to close on. Inverting a chord does not change the role it plays within the key.

C–E–G, E–G–C, and G–C–E are all “the C chord.” In C major, every one of them functions as the tonic. Stability and smoothness change; harmonic analysis treats them as the same chord.

Roman numerals reflect this by keeping the numeral fixed and appending inversion figures instead — I, I6, I64. The root establishes the chord’s identity; the bass establishes its arrangement.

Because of that division of labor, harmonic analysis does not get dragged into the details of voicing. The next lesson adds seventh chords, and the one after that introduces Roman numerals formally.

▶ Confirm the chord tones in the chord finder Check that C is C, E, and G, then keep in mind that those three notes remain the same regardless of which one you put in the bass Chord Finder → ▶ Look for inversions in guitar chords Standard guitar shapes contain more inversions than people expect. Check which note the lowest sounding string is playing and you will find plenty that are not in root position Chord Diagram →