Principle
In parsimonious (or economical) voice leading, each voice moves by the smallest possible number of half steps from one chord to the next. The farther apart the chords are in key, the more chromatic voice leading is what holds them together. Dmitri Tymoczko (A Geometry of Music, 2011) measures the "distance" between two chords by adding up the half steps traveled by the voices in the best voice leading.
Distances between C major and other triads
| From C (C E G) to | Best voice leading | Total half steps |
|---|---|---|
| Am (A C E) | G → A | 2 |
| Em (B E G) | C → B | 1 |
| Cm (C Eb G) | E → Eb | 1 |
| E (B E G#) | C → B, G → G# | 2 |
| Ab (C Eb Ab) | E → Eb, G → Ab | 2 |
| Abm (Cb Eb Ab) | C → Cb, E → Eb, G → Ab | 3 |
| Db (Db F Ab) | each voice rises by 1 | 3 |
| F# (C# F# A#) | for example C → C#, E → F#, G → A# | 6 |
The chords that are most "distant" on the circle of fifths (C → F#) are also the most distant in voice leading; chromatic mediants (C → E, C → Ab) are very close even though they are harmonically distant.
Guide tones in chains of dominants
E7 – A7 – D7 – G7 (third and seventh of each chord):
- E7: G# and D
- A7: G and C#
- D7: F# and C
- G7: F and B
The two lines G# → G → F# → F and D → C# → C → B descend chromatically: third and seventh swap at every chord. It is the sonic engine of swing and gospel.
Diminished seventh as a "hinge"
From B°7 (B D F Ab), moving a single note down by half step, you reach G7, Bb7, Db7, E7. Moving all the notes by half step in different ways, you reach triads and sixth chords in 8 keys: this is why in the nineteenth century the diminished was the "passe-partout" of modulations.
Chopin, Prelude in E minor, Op. 28 No. 4
Tymoczko uses it as an example of chromatic voice leading: above an almost motionless melody, the left-hand chords change by moving only one voice at a time by a half step, passing through different seventh chords (dominants, half-diminished, diminished) that do not always have a clear tonal function. The result is a slow, inexorable descent.
Practical techniques
- Keep the common tones in the same voice and at the same octave.
- Move by half step the voices that change: prefer the half step to the whole step, the whole step to the third.
- Contrary motion between the bass and the top voice when possible.
- One voice at a time: if a passage is difficult, insert an intermediate chord in which only one note changes (e.g. C → C+ → Am/C → F: C E G, C E G#, C E A, C F A).
- Inner chromatic lines: C – C+ – C6 – C7 (G → G# → A → Bb) is a line cliché built on this principle.
Example in a real song
Creep (Radiohead): G – B – C – Cm. The inner voice D – D# – E – Eb – D (5 → #5 → 6 → b6 → 5 relative to G) is a chromatic line that ties "strange" chords together naturally.
Exercise for the producer
- Choose 4 distant chords (e.g. C – Ab – E – Bb).
- Write them in the Piano roll in root position and listen: they sound "blocky," with leaps.
- Revoice: for each transition look for the voice leading with the fewest total half steps (use the table as a guide).
- Assign each voice to a separate track (4 strings or 4 synth voices) and check that each one is a singable melody.
Related topics
Rules of voice leading, guide tone lines, neo-Riemannian theory, Tonnetz, line cliché, Tristan chord.