This chapter discusses harmonizations of the scale using the so-called "rule of the octave" and other sequential configurations. There are many files provided to view or download:

The Rule of the Octave

Building the Rule, approaching the "Rule" by incrementally nuancing a succession of parallel ^6_3s: .mscz, .mxl, .pdf

Part by Part, taking a closer look at the component parts of the "Rule": .mscz, .mxl, .pdf

Harmonizing the scale with sequences

Open score (one voice per part): .mscz, .mxl, .pdf

Short (piano) score: .mscz, .mxl, .pdf

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 ^6_3s

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 ^6_3 (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.

We begin with a simple harmonization of the bass scale using parallel ^6_3 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.

Next we put in strategic ^5_3s on the first and last chords to give a sense of closure on the tonic.

Then we also add a ^5_3 on the dominant chords of both ascending and descending forms to further nuance the hierarchy (these are important chords too).

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?

Rule of the Octave from ^6_3 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)

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 materia