The Rule of the Octave

The “Rule of the Octave” is an important part of the schema/partimento tradition. You might like to think of it as a kind of cheat sheet for harmonizing bass lines: there’s one chord for each scale degree, and you can go a long way by just matching up those bass notes with their corresponding chord.

There are many, subtly different versions of the Rule of the Octave harmonization. The version used here is closely based on that of Fedele Fenaroli (Naples, 1775), with just a couple of modifications to preserve a consistent number of voices throughout (four voices, including the bass) and to avoid any suggestion of parallels.

Approaching the “Rule” from parallel [latex]^6_3[/latex]s

File downloads: .mscz, .mxl, .pdf

Let’s begin by building up our version of the Rule of the Octave from simple principles, starting with parallel [latex]^6_3[/latex] (first inversion) chords. You could also think of this as a matter of moving from a flat to a rich harmonic hierarchy, or else as a “Regolo recipe”: how to make or understand the rule in four easy steps.

1. We begin with a simple harmonization of the bass scale using parallel [latex]^6_3[/latex] chords only. There’s nothing grammatically incorrect about this, but neither does it have much of a sense of hierarchy or variety. In short, it’s not very interesting.
2. Next we put in strategic [latex]^5_3[/latex]s on the first and last chords to give a sense of closure on the tonic.
3. Then we also add a [latex]^5_3[/latex] on the dominant chords of both ascending and descending forms to further nuance the hierarchy (these are important chords too).
4. Finally, we precede each of the tonic and dominant chords (including those in inversion) with seventh chords. In one case, this also involves a chromatic alteration for a stronger sense of tonicizing the dominant. Why do you think we might only make that change this one time, and not anywhere else in the progression?

https://musescore.com/user/30425053/scores/5350123/embed
Rule of the Octave from [latex]^6_3[/latex] by FourScoreAndMore

Examining the Rule part by part

File downloads: .mscz, .mxl, .pdf

Having arrived at the Rule, this second file deconstructs it again so you can practice and engage with it in parts, with any number of voices, and in any position (i.e., any inversion of the right-hand harmonization). Keep practicing each component part separately and in a range of keys to build fluency with and abstraction of the Rule. (Note: you can transpose scores in MuseScore with the Notes menu: Notes/Transpose.)

We begin by combining the bass scale with each of the three upper-voice parts in turn, centered respectively on the:

• tonic (first system of each page: ascending on p. 1; descending on p. 2)
• mediant (second system)
• dominant (third system)
  These systems are annotated with the interval between the upper and lower parts.

We then combine those upper parts into three-note right-hand chords to generate the Rule.
Here the three versions (“positions” in Fenaroli’s language) are given by the inversion of the chord. Again, the top voice is centered successively on the:

• tonic (fourth system)
• mediant (fifth system)
• dominant (sixth system)

https://musescore.com/user/30425053/scores/5350126/embed
Rule of the Octave Part by Part by FourScoreAndMore

Harmonizing the Scale with Sequences

File Downloads and online:

• Open score (one voice per part): .mscz, .mxl, .pdf, link to view the score online
• Short (piano) score: .mscz, .mxl, .pdf, link to view the score online

Note: The open and short-score versions of this material are otherwise identical, so these introductory comments apply equally to both.

As we’ve seen above, the Rule of the Octave can be thought of as in terms of a sequential harmonization of bass scales (parallel [latex]^6_3[/latex] chords). This section looks at some other sequential harmonizations of the bass scale here. Basically, this involves patterns of one or more harmonies which repeat sequentially in the direction of the scale. Some of these work in the same way for both ascending and descending forms; others require some modification.

We begin just as we did before, with a simple harmonization of the scale using parallel [latex]^6_3[/latex] chords only. The following systems proceed to patterns of:

5–6 patterns

• Ascending: In the ascending form, we alternate between the fifth and sixth above each note of the bass line scale.
• Descending: In the descending form, we could do the same note-by-note alternation as the ascending form, or else alternate between the fifth and sixth on separate notes (as in this file).

7–6 patterns: chains of suspensions

• Ascending: 7–6 suspensions involve a descending upper part, so in the ascending form of this pattern, we need to add in a leap up the octave to restart the pattern, so the repeating pattern is more like 7–6–8.
• Descending: Here the descending sequence matches the descending scale, so no modification is necessary. We essentially go back to the parallel [latex]^6_3[/latex] chords we started with, and just delay or offset the top line.

Cycles of fifths

The cycle of fifths is a based on a progression of root motion descending by fifths. Hiding in this pattern is another (usually descending) scalic progression between alternate bass notes. This arises because instead of literally going down two fifths, we usually go down a fifth and up a fourth, which is the equivalent progression, just keeping it in the same register / octave. At the end of one such “down a fifth, up a fourth,” we end up a step lower than where we started, and so we also have a stepwise progression that can be scalic (if it is diatonic—i.e., not modulating).
We set this out in some of the main forms:

• Descending 1: with triads only
• Descending 2: with sevenths and suspensions (cf. 7–6 descending)
• Descending 3: “zigzag” circle-of-fifths (note the outer-voice canon)
  Finally, we set out one version of this in the ascending direction:
• Ascending 1: with 4–3 suspensions

2–3: more chains of suspensions

So far, we’ve used 7–6 and 4–3 suspensions, so that leaves us one more important type: the 2–3 suspension (which is the inversion of 7–6).

• Ascending: Just like the 7–6 suspensions above, for the ascending scale, we need to restart each pattern, so it ends up being 2–3–1 with the upper part, or 9–8–10 with the bass.
• Descending: Again, no restart is needed for the descending form. The 2–3 pattern sets up a series of [latex]^4_2[/latex] to ⁶ progressions like the important V[latex]^4_2[/latex]–I⁶ progression, except that we’ve kept it diatonic here (i.e., without tonicizing each key).

https://musescore.com/user/30425053/scores/5350121/embed
Scale Sequences Short by FourScoreAndMore

The partimenti approach really calls for hands-on practice.

1. Begin by playing through these examples from the files provided, preferably in a range of different keys. (Note: As mentioned above, you can transpose scores in MuseScore with the Notes menu: Notes/Transpose).
2. See if you can memorize the patterns. Test yourself by:
   • writing them out on paper (start with a blank scale)
   • playing them from memory
3. Both with the music and (when you’re ready) from memory, try embellishing these basic patterns.