Inversions and figured bass – free music theory course

A chord keeps its name whatever the order of its notes: C–E–G, E–G–C and G–C–E are all C major chords. But the bass note (the lowest one) deeply changes its colour and function. This is the idea of inversion.

Position	Bass note	Example in C	Figures
Root position	root	C – E – G	5/3 (usually omitted)
First inversion	third	E – G – C	6
Second inversion	fifth	G – C – E	6/4 (“six-four”)

M:4/4
L:1/2
K:C
"C"[CEG]2 | "C/E"[EGc]2 | "C/G"[Gce]2 |]

Figured bass

In the Baroque era, the harpsichordist often read only a bass line with numbers above it: the basso continuo. The figures show the intervals above the bass. In first inversion, above E we find G (a third) and C (a sixth): we simply write “6”. In second inversion, above G we find C (a fourth) and E (a sixth): “6/4”, read “six-four”. Root position (third + fifth, “5/3”) is generally left unfigured.

What are inversions for?

They let you connect chords without jumping around. Compare: C – F – G – C all in root position forces big hand shifts. With inversions, each finger moves by one or two semitones:

M:4/4
L:1/4
K:C
"C"[CEG]2 "F/C"[CFA]2 | "G/B"[B,DG]2 "C"[CEG]2 |]

C stays put, E moves up to F, G moves up to A… This is the secret of a smooth accompaniment, and the basis of the voice leading we'll study later.

To identify an inverted chord: mentally rearrange the notes into stacked thirds. The bottom note of that stack is the root. G–C–E → C–E–G: it's C major with the fifth in the bass, so second inversion.

Careful: the second inversion (6/4) is unstable. In classical music it appears only in specific contexts, above all the “cadential six-four” (I6/4 → V → I). Don't end a piece on a 6/4 chord!