Volume I · Chapter 9
The Rule of the Octave
MUSIC 20A · C-ID MUS 120Chapter quiz →
In the musicianship bookChapter 12: Progressions, First Inversion, and TripletsChapter 13: Minor-Key Progressions
Introduction: The Partimento Tradition
For centuries, composers from Durante to Mozart didn't learn harmony by filling in worksheets. They learned at the keyboard, through partimento: a teacher handed them a bass line, and they improvised the upper voices in real time.
The foundational exercise of that tradition is the Rule of the Octave (regola dell'ottava): a standard way to harmonize a bass line that walks up or down the scale. Its central insight is that in tonal music, the bass scale degree tells you the chord. If you can harmonize a scale in the bass, you have the vocabulary for nearly any stepwise bass line.
Click any example to hear it.
Stable and Passing Bass Notes
- The pillars, 1̂ and 5̂, carry root-position chords: I and V. These are the arrival points.
- Every other degree is a passing note, and passing notes take inverted chords (with a 6 in the figures), which keep the upper voices smooth and avoid parallel fifths between root-position chords a step apart.
- The bass notes next to a pillar point toward it. 7̂ and 2̂ lead to 1̂, so they carry dominant chords (V65 and V43). 4̂ rising to 5̂ carries a predominant (ii65); 4̂ falling to 3̂ carries V42, whose seventh resolves down.
The Ascending Scale
| Bass | Figures | Chord (major key) |
|---|---|---|
| 1̂ | 5/3 | I |
| 2̂ | 6/4/3 | V43 |
| 3̂ | 6 | I6 |
| 4̂ | 6/5 | ii65 |
| 5̂ | 5/3 | V |
| 6̂ | 6 | IV6 |
| 7̂ | 6/5 | V65 |
| 8̂ | 5/3 | I |
Over 2̂ the chord is V43 (not V6, which would put the leading tone in the bass). Over 3̂ it's I6, and over 4̂ the 6/5 chord (ii65) prepares the dominant. Ascending 6̂ takes a plain 6 chord (IV6), and 7̂ takes V65, whose leading tone in the bass rises to 8̂.
The Descending Scale
| Bass | Figures | Chord (major key) |
|---|---|---|
| 8̂ | 5/3 | I |
| 7̂ | 6 | V6 |
| 6̂ | ♯6/4/3 | V43/V |
| 5̂ | 5/3 | V |
| 4̂ | 4/2 | V42 |
| 3̂ | 6 | I6 |
| 2̂ | 6/4/3 | V43 |
| 1̂ | 5/3 | I |
Descending, the logic flips: 7̂ falls toward 5̂, so it takes V6 instead of a leading-tone chord. 6̂ gets a raised 4̂ (♯6 in the figures) that leans into 5̂. And 4̂, falling to 3̂, is the seventh of V42: a perfect example of a chordal seventh resolving down by step.
In Minor
In minor keys the Rule of the Octave is the same, with two adjustments: any chord that contains 7̂ and points to the tonic uses the raised leading tone (an accidental), and the descending scale uses the natural 7̂ in the bass (minor's melodic-minor logic from Chapter 3).
From Rule to Reflex
Learning the Rule of the Octave changes the question from "What chord should I use here?" to "The bass is on 4̂ going up to 5̂, so it's a predominant moving to the dominant." Practice it at the keyboard in several keys, starting the soprano on 1̂, then 3̂, then 5̂, until your hands know it without thinking. It's also the fastest way to harmonize the bass lines you'll write in Chapter 11.
Try It: Rule of the Octave Stepper
Rule of the Octave Stepper
Step through the scale one bass note at a time, or play it all. Say the figure out loud before you click.