Triad inversions
- Root position (5/3): C = C E G.
- First inversion (6/3, called “sixth chord”): C/E, bass E.
- Second inversion (6/4): C/G, bass G.
Seventh chord inversions
G7 (7), G7/B (6/5), G7/D (4/3), G7/F (4/2 or 2). The bass of G7/F almost always falls to E: G7/F → C/E.
What they are for
- Smooth bass line: C – G/B – Am instead of C – G – Am, the bass descends by step C–B–A.
- Graded stability: the first inversion is less conclusive than root position; useful in the middle of a phrase.
- Pop color: F/A, G/B, C/E are the basis of “gospel” passages on the piano.
The four 6/4 chords of the tradition
The second inversion is unstable and in classical writing appears only in four situations:
- Cadential: C/G – G7 – C. The C/G is actually a G with appoggiaturas (C and E fall to B and D). It is analyzed as V6/4–5/3.
- Passing: C – G/D – C/E, the bass rises C–D–E.
- Neighbor (pedal): C – F/C – C, the bass stays still.
- Arpeggiated: the bass arpeggiates the chord (typical of waltzes).
Real example
“A Whiter Shade of Pale” (Procol Harum, 1967) is in C major and owes its character to a bass line descending by conjunct steps (C–B–A–G–F–E–D…) thanks to the inverted chords. In classical concertos, by contrast, the soloist's cadenza almost always starts from a cadential 6/4 held by the orchestra.