Definition
The rule of the octave is the standard harmonization of a scale in the bass, ascending and descending, in which each scale degree corresponds to a fixed chord (indicated with figured-bass figures). It was published under this name by François Campion in the Traité d'accompagnement et de composition selon la règle des octaves (1716), but it was already widespread in Italian practice; in the Neapolitan conservatories it became the basis of partimento study (Fenaroli, 1775). It is how a continuo player knew right away which chord to play when the bass moved by step without figures.
The principle
- Degrees 1 and 5 are stable: they carry the root-position triad (5/3).
- All the other degrees are passing or tension degrees and carry inverted chords (6/3, 6/5, 4/3, 4/2), which almost always belong to the tonic or the dominant.
- The rule distinguishes direction: ascending, degree 4 tends toward 5 (it carries a 6/5), descending, degree 4 comes from 5 and carries a 4/2 chord (V4/2) that resolves to 3.
In C major
Ascending
| Degree | Bass | Figures | Chord | Function |
|---|---|---|---|---|
| 1 | C | 5/3 | C | I |
| 2 | D | 6/4/3 | G7/D | V4/3 |
| 3 | E | 6/3 | C/E | I6 |
| 4 | F | 6/5/3 | Dm7/F | ii6/5 |
| 5 | G | 5/3 | G | V |
| 6 | A | 6/3 | F/A | IV6 |
| 7 | B | 6/5/3 | G7/B | V6/5 |
| 8 | C | 5/3 | C | I |
Descending
| Degree | Bass | Figures | Chord | Function |
|---|---|---|---|---|
| 8 | C | 5/3 | C | I |
| 7 | B | 6/3 | G/B | V6 |
| 6 | A | ♯6/4/3 | D7/A | V4/3 of V |
| 5 | G | 5/3 | G | V |
| 4 | F | 6/4/2 | G7/F | V4/2 |
| 3 | E | 6/3 | C/E | I6 |
| 2 | D | 6/4/3 | G7/D | V4/3 |
| 1 | C | 5/3 | C | I |
Note the F♯ on the descending sixth degree: the rule tonicizes the dominant, as Bach's chorales do.
In A minor
- Ascending: A (5/3, Am) – B (6/4/3, E7/B) – C (6/3, Am/C) – D (6/5, Bø7/D, that is iiø6/5) – E (5/3, E major with G♯) – F (6/3, Dm/F) – G♯ (6/5/3, E7/G♯) – A.
- Descending: A – G (6/3, Em/G or G natural as a passing tone) – F (♯6/4/3: F–A–B–D♯ = the French augmented sixth) – E (5/3, E) – D (4/2, E7/D) – C (6/3) – B (6/4/3) – A.
The fact that the descending sixth degree in minor produces an augmented sixth shows how these "special" chords arise from the voice leading of the bass.
Why it is still studied
- It gives you a sensible default for every note of the scale in the bass: useful when you write a stepwise bass line and do not know which chord to put over it.
- It trains you to recognize that many apparently different chords are inversions of I and V.
- It is the basis of galant schemata such as the Prinner (bass 4–3–2–1) and of countless descending pop bass lines (C–B–A–G–F: "A Whiter Shade of Pale" by Procol Harum, 1967, uses a version of it).
Exercise for a producer
- In FL Studio, program the C scale in the bass in quarter notes, then the chords from the table on a second track (pad or piano).
- Listen to how the descending version "pulls" toward the dominant with the D7/A.
- Reuse just a fragment: the descent C–B–A–G with I – V6 – V4/3/V – V is an elegant half cadence to put at the end of a verse.
- Transpose everything to A minor and try the version with the French sixth before the drop.
Related topics
Partimento and the Neapolitan school, Figured bass, Chord inversions, Galant schemata, Augmented sixth chords.