II. Counterpoint and Galant Schemas

Galant schemas – The Rule of the Octave and Harmonizing the Scale with Sequences

The Rule of the Octave

Mark Gotham

Key Takeaways

This chapter discusses harmonisations of the scale using the so-called “rule of the octave” and other sequential configuration. There are many files provided to view or download:

  1. The Rule of the Octave
    • Building the Rule, approaching the ‘Rule’ by incrementally nuancing a succession of parallel 63s: .mscz, .mxl, .pdf
    • Part by Part, taking a closer look at the component parts of the ‘Rule’: .mscz, .mxl.pdf
  2. Harmonising the scale with sequences

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 harmonising 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 63s

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 63 (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 harmonisation of the bass scale using parallel 63 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 53s on the first and last chords to give a sense of closure on the tonic.
  3. Then we also add a 53s 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 7th chords. In one case, this also involves a chromatic alteration for a stronger sense of tonicising 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 63 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. inversion of the right hand harmonisation). Keep practicing each component part separately and in a range of keys to build fluency with and abstraction of the Rule. (NB: 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, centred respectively on the:

  • tonic (first system of each page: ascending on page 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 centred successively on the:

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


Rule of the Octave Part by Part by FourScoreAndMore

Harmonising the Scale with Sequences

File Downloads and online:

NB: 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 harmonisation of bass scales (parallel 6/3 chords).
This section looks at some other sequential harmonisation 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 harmonisation of the scale using parallel 63 chords only.
The following systems, proceed to patterns of:

5-6 patterns

  • Ascending: In the ascending form, we alternate between the 5th and 6th 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 5th and 6th 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 re-start 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 63 chords we started with, and just a delay or offset the top line.

Cycles of Fifths

The cycles 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 is in the same register / octave.
At the end of one such down a fifth, up a fouth, we end up a step lower than where we started, and so we also have a step-wise progression that can be scalic (if diatonic – i.e. not modulating).
We set this out in some of the main forms:

  • Descending 1: with triads only
  • Descending 2: with 7ths 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 re-start 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 4/2 to 6 progressions like the important V42-I6 progression, except that we’ve kept it diatonic here (i.e. without tonicising each key).


Scale Sequences Short by FourScoreAndMore

Assignments

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. (NB: As mentioned above, you can transpose scores in MuseScore with the ‘Notes’ menu: Notes/Transpose).
  2. See if you can memorise 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.

License

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OPEN MUSIC THEORY by Mark Gotham is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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