Definition
A triad is in second inversion when its fifth is in the bass: above the bass a fourth and a sixth are formed, hence the name six-four chord (figured 6/4). In the tonal style the fourth above the bass is considered dissonant: for this reason the 6/4 is not used freely, but only in four specific situations. In all four the bass is doubled.
1. Cadential six-four
- Succession: I6/4 – V – I (in C: C/G – G – C).
- It falls on the strong beat; the V that follows on the weak beat.
- The sixth falls to the fifth and the fourth to the third (E → D, C → B): above the bass G we have 6/4 → 5/3.
- It is preceded by a predominant: ii6 – I6/4 – V – I or IV – I6/4 – V – I.
- It can be analyzed in two ways: as I in second inversion, or, more consistently with its function, as a V with two appoggiaturas (V6/4–5/3). In both cases the effect is that of a dominant.
2. Passing six-four
- The bass moves by step and the 6/4 sits in the middle: I – V6/4 – I6 (bass C–D–E) or IV – I6/4 – IV6 (bass F–G–A).
- It falls on the weak beat.
- Often the soprano moves in contrary motion to the bass, with a voice exchange (E–D–C in the soprano against C–D–E in the bass).
3. Neighbor (or pedal) six-four
- The bass stays still and the upper voices play a neighbor tone: I – IV6/4 – I (C–E–G → C–F–A → C–E–G) or V – I6/4 – V.
- It falls on the weak beat; it prolongs the main chord like an embroidery.
4. Arpeggiated six-four
- The bass arpeggiates the chord (root, third, fifth): the fifth in the bass does not create real instability because the harmony is always the same.
- Typical of waltzes and marches, where the bass alternates root and fifth.
Practical rules
- Double the bass in all types of 6/4.
- The cadential 6/4 falls on a stronger beat than the V that follows it (for example 6/4 on the first beat, V on the third): never the reverse.
- Approach the bass of the cadential 6/4 by step or from the fourth below (F–G, D–G); do not leap to it from a foreign note.
- Do not use isolated 6/4s without one of the four functions: they sound unstable and “wrong.”
Common mistakes
- Placing the cadential 6/4 on the weak beat: the cadence loses strength.
- Resolving the fourth upward in the cadential.
- Doubling the sixth or the fourth instead of the bass.
- Ending a piece on a I6/4: no stability.
Examples
- Mozart and Beethoven concertos: the orchestra stops with a fermata on the cadential I6/4; the soloist inserts the cadenza and closes it with the trill on the V.
- Bach chorales: ii6–I6/4–V–I cadences in many concluding phrases.
- Strauss waltzes: arpeggiated root–fifth bass in the “oom-pah-pah” accompaniment.
- Gospel and pop: C – F/C – C (I – IV6/4 – I) is the typical plagal embroidery of endings and vamps.
How to use it in composition
- The cadential 6/4 adds solemnity to the final cadence: use it at the end of a piece or an important section.
- The neighbor 6/4 over a pedal (C – F/C – C) is an excellent way to give movement to a long chord without changing the bass.
- The passing 6/4 makes a bass that rises or falls by step flow smoothly.
Exercise
- Write in Bb major the cadence ii6 – I6/4 – V7 – I in four voices.
- Write I – V6/4 – I6 with a voice exchange between soprano and bass.
- In the DAW, create a four-bar vamp with I – IV6/4 – I over a tonic pedal.
Connections
Chord inversions and six and six-four chords; Cadences; Perfect and imperfect authentic cadence; Pedal and ostinato; Solo concerto; The first inversion.