It’s parti(mento) time!

There’s been a resurgence of attention lately to the position of practice in the teaching of music theory, both in the sense of ‘practical’ keyboard skills and the ‘practice’ of the composers we study. This has centred on reviving sets of ‘schemas’ based on short, ‘partimento’ bass lines that Eighteenth-Century musicians learned as stock-in-trade prototypes for improvisation and composition (the distinction between the two being much more slight for musicians of the time than we sometime suppose today).

For further reading on this fascinating topic, we highly recommend this excellent website by the modern master of this historical practice in teaching, Robert Gjerdingen. We’ve no wish to duplicate that fine resource; instead, we’ll focus here as usual on the complementary provision of interactive resources that you can download and adjust for your own purposes.

Downloads

Check out the files here on our MuseScore page where you can play them online and download them in your preferred format (mscz, xml, PDF). NB: you need a (free) account to download files. Further explanation of each component part follows this overview.

The Rule of the Octave

  • Building the Rule: Approaching the ‘Rule’ by incrementally nuancing a succession of parallel 63s
  • Part by Part: Taking a closer look at the component parts of the ‘Rule’.

Harmonising the scale with sequences

Partimenti Prototypes: Representations of canonical schemas

Schema Scores: Templates for pieces based on combinations of schemas.

More about those files

Rule of the Octave

The ‘Rule of the Octave’ is a kind of cheat sheet for harmonising diatonic music: there’s one chord for each scale degree and you can go a long way by just plugging them in on top of the bass line. The version of the harmonisation used here is closely based on that of Fedele Fenaroli (Naples 1775), but with a couple of modifications to preserve a consistent number of voices throughout (4vv, including the bass) and to avoid any suggestion of parallels.

File 1: Approaching the ‘Rule’ from parallel 63s

This section builds up a version of the Rule of the Octave by proceeding in incremental steps from parallel 63s to the rule proper. 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.

  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 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 7ths. 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?

File 2: Examining the Rule Part by Part

Having arrived at the ‘Rule’, this second file deconstructs it again so you can practice in parts, with any number of voices, and in any ‘position’ (inversion of the right hand harmonisation). Keep practicing each component part 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)

Harmonising the Scale with Sequences

(NB: The open and short score versions of this material are otherwise identical so these introductory comments apply equally to both.)

We begin once again with a simple harmonisation of the scale using parallel 63 chords only, before proceeding to:

5-6

  • Ascending: 5-6 on each bass notes
  • Descending: 5-6 on alternating bass notes

7-6: Chains of Suspensions

  • Ascending: 7-6 (and 8 to re-start the pattern)
  • Descending: essentially parallel 63 chords with a delayed top line

Cycles of 5ths (scale connects alternate bass notes)

  • Descending 1: Triads only
  • Descending 2: with 7ths and suspensions (cf. 7-6 descending)
  • Descending 3: ‘Zigzag’ circle-of-fifths (note the outer-voice canon)
  • One Ascending form with 4-3 suspensions

2-3: More Chains of Suspensions

  • Ascending: with re-starts, like in the 7-6 ascending pattern.
  • Descending: 2-3 in a V42-I6 harmonic pattern, but diatonic (i.e. without tonicisations).

Partimeti Prototypes: Representations of canonical schemas

These documents provides a set of schemas, with the constituent parts set out as prototypically as is possible in musical notation: that is, with melody and figured bass lines, along with (in the first file’s case) chords in a middle part based on an automatic realisation of those figures.

More truly prototypical is the following list of information for each schema:

Name When Melodic line Bass line Metre Harmony (figures)
Romanesca Opening [1, 5, 1, 1] [1, 7, 6, 3] S W S W [5, 6, 5, 6]
Do-Re-Mi Opening [1, 2, 3] [1, 7, 1] S W S [5, 6, 5]
Sol-Fa-Mi Opening [5, 4, 4, 3] [1, 2, 7, 1] W S W S [5, 5, ‘6,5’, 5]
Meyer Opening [1, 7, 4, 3] [1, 2, 7, 1] W S W S [5, ‘6,4,3’, ‘6,5’, 5]
Prinner Answer/Process/Transition [6, 5, 4, 3] [4, 3, 2, 1] S W S W [5, 6, 7, 6, 5]
Modulating Prinner Answer/Process/Transition, e.g. end of A [3, 2, 1, 7] [8, 7, 6, 5] S W S W [5, 6, 7, ‘#6’, 5]
Fonte Answer/Process/Transition, e.g. start of B [5, 4, 4, 3] [‘#1’, 2, 7, 1] W S W S [‘6,5’, 5, ‘6,5’, 5]
Monte Answer/Process/Transition, e.g. start of B [‘1’, ‘b7’, ‘6’, ‘2’, ‘1’, ‘7’] [3, 4, ‘#4’, 5] W S W S [6, 5, 6, 5]
Ponte Answer/Process/Transition [5, 7, 2] [5] S W S [5, 7, 7]
Fenaroli Pre-Cadential [4, 3, 7, 1] [7, 1, 2, 3] S W S W [6, 5, 6, 6]
Indugio Pre-Cadential [2, 4, 6, 1, 7] [4, 4, 4, ‘4#’, 5] S W S W S [‘6,5’, ‘6,5’, ‘6,5’, ‘6,5’, 5]
Deceptive Cadence Pre-Cadential [1, 2, 2, 1] [3, 4, 5, 6] W S W S [6, ‘6,5’, 5, 5]
Evaded Cadence Pre-Cadential [1, 2, 2, 1] [3, 4, 5, 5, 1] W S W S [6, ‘6,5’, 5, 6]
Passo Indietro Pre-Cadential [7, 1] [4, 3] S W S W S [‘6,4,2’, 6]
Cadenza Semplice Cadence [1, 2, 2, 1] [3, 4, 5, 1] W S W S [6, ‘6,5’, 5, 5]
Cadenza Composta Cadence [1, 2, 3, 2, 1] [3, 4, 5, 5, 1] W S () S W S [6, ‘6,5’, ‘6,4’, 7, 5]
Cadenza Doppia Cadence [4, 3, 2, 1] [5, 1] S W S W S [5, ‘6,4’, 4, 3, 5]
Comma Cadence [4, 3] [7, 1] W S [‘6,5’, 5]
Converging Cadence Cadence [3, 2, 1, 7] [‘3’, ‘4’, ‘#4’, ‘5’] W S [6, ‘6,5’, ‘6,5’, 5]
Quiescenza Post-Cadential [‘b7’, ‘6’, ‘7’, ‘1’] [1] W S W S [‘b7’, ‘6,4’, ‘7,4,2’, 5]

Schema Scores: Templates for pieces based on combinations of schemas

As reflected in the above grid, one key element of these schemas is their order.

This section provides some combinations of schemas which can be thought of as prototype pieces, both to illustrate how they work, and as a template for scaffolding student exercises in pastiche composition.

N.B. To be abundantly clear, these prototype pieces are not intended as ‘real music’! It takes a lot of fleshing out to get from these to anything worthwhile: that’s the exercise. Use these templates but bury them beneath layers of musical character and embellishment.

Some tips for getting started:

  • Rhythm: Try picking a single, characteristic rhythm to serve as the basis for your piece and use it often (but not exactly: see how many different ways you can adapt it);
  • Melody: Introduce embellishments, decorating some stepwise motions with turns, for instance, and filling in some large leaps;
  • Accompaniment: introduce one or more characteristic pattern for chordal accompaniments like the ‘Alberti Bass’;
  • Texture: particularly for longer piece, vary the number of voices present, and the way they relate.**

… and finally … Buried Treasure for the Budding Theorist

On symmetry in the ROTO

The upper, melodic lines in the Rule of the Octave are intended to harmonise a symmetrical bass line (rising scale, falling scale), but they also exhibit a certain degree of symmetry themselves both overall and within each half. That property may seem obvious, given the symmetry of the bass, and the fact that they are deliberately static, conjunct lines, but tonal harmony is rather asymmetric by nature: think of the fundamental difference between I-V and V-I, for instance.

What we might call the ‘overall palindrome’ emerges more strongly than any other kinds of comparison among this set such as the possible internal palindrome in the ascending or descending lines, or the parallel (rotational symmetry) between those two halves.

These are the four distinct forms to be considered from comparing ascending and descending versions with each other and with retrograde versions of themselves: there are six permutations in total, of which two pairs which are duplicates by definition:

  • AscFwd/AscBwd: Palindrome over the first half (ascending scale)
  • AscFwd/DescFwd: Second part repeats the first (a kind of ‘rotational’ symmetry)
  • AscFwd/DescBwd: Palindrome overall
  • (AscBwd/DescFwd = same as AscFwd/DescBwd)
  • (AscBwd/DescBwd = same as AscFwd/DescFwd)
  • DescFwd/DescBwd: Palindrome over the latter half (descending scale)

Those four distinct comparisons are reported in the table below for each of the three lines, in the format ‘same : different’ (adding up to 8 notes in total):

Melodic Line AscFwd/AscBwd AscFwd/DescFwd AscFwd/DescBwd DescFwd/DescBwd
Upper Voice 1 4 : 4 5 : 3 7 : 1 6 : 2
Upper Voice 2 6 : 2 5 : 3 6 : 2 4 : 4
Upper Voice 3 4 : 4 5 : 3 7 : 1 6 : 2