This article is intended for students who need to add one or two contrapuntal parts to a given melody in the tonal style of the Baroque, as is often required for Tonal Counterpoint papers in undergraduate music degrees. It is hoped that it will also be of some use to anyone who wishes to gain some understanding of the processes involved in completing a tonal contrapuntal texture in the style of J. S. Bach’s Two- and Three-Part Inventions.
Typically, the examination question for Tonal Counterpoint papers asks students to complete a given opening for a total of between 12-25 bars in either two- or three-parts. For this article we will be using the following question:
Complete the given opening in the style of J. S. Bach’s three-part inventions. It should be between 15-25 bars in length and be scored for keyboard.
Because most contrapuntal works are constructed from only a few motivic features it is important to extract all of the harmonic and melodic information contained in the given theme, this will give us the necessary elements we can use to continue, and complete, the work.
The key of our example is D minor. We must, therefore, include at least one modulation to a related key. The possible destinations for our modulations are listed below.
A minor-key invention will typically include an initial modulation to either the dominant, which in our example would be A minor, or to the relative major, in our example, F major. Other modulations may not be necessary, or possible, given the restriction in length, however, a modulation to the subdominant, G minor, may be included after the initial modulation.
The melodic outline of our theme is based on an embellished stepwise descent across five quarter-note beats from the dominant to the tonic (5-1) in D minor.
A short descent to the tonic is also found across the first three quarter-note beats.
The theme may also begin on the tonic and descend to the dominant (8-5).
This also contains a short descent to the dominant across the first two quarter-note beats.
The 5-1 and 8-5 thematic statements may also be inverted, beginning on the tonic,
or the dominant.
The various thematic statements can also be transposed and used in different keys. By cataloguing the various thematic possibilities of the given opening prior to beginning our invention we can easily insert them when and where they are required.
Within the given theme there is also a number of rhythmic motifs which should also be included in our continuation.
Of course, these can be altered through augmentation, diminution and modification of the note values as needed.
Now that we have a better understanding of the harmonic and melodic potential of our given opening let us proceed with introducing the second and third parts.
One possibility for the initial point of imitation is to alternate the 5-1 and 8-5 themes.
This connects the final note of the first part (bar 1) with the first note of the second, and the final note of the second part (bar 2) with the first note of the third, in this way the opening resembles a fugal exposition. By sketching in the theme in each part we have a melodic, and harmonic, foundation from which we can construct the other parts. To write an effective counterpoint to an existing part we must establish a potential harmonic basis for the relevant bar/s. A possible sketch for bar 2 is shown below
Now that we have the underlying harmonic framework for bar 2 we can begin to sketch in the continuation of our first part.
After reaching the tonic note in bar 2, the first part leaps through various chord notes of the underlying harmony to create a line which takes the first part back into the higher register. This creates a registral contrast with the second part in bar 2 and also gives the necessary ‘height’ for the right hand to accommodate both the first and second parts once the third part enters in bar 3. Remember: you are writing for a keyboard instrument so you always need to be thinking about the playability of your contrapuntal parts by two hands.
In bar 2, the rhythms of the given opening have already been modified in part one’s melodic line, however, the origins of each motif can still be seen, and heard.
Let us now sketch in a possible harmonic basis for bar 3,
with a possible solution for parts one and two.
Here, part one includes an augmentation of the dotted eighth note-sixteenth note rhythm introduced in bar 2.
The addition of the initial sixteenth-note in part three (D) establishes root position harmony rather than the second inversion harmony suggested by the use of the 5-1 theme in the lowest part. In bar 3 parts one and two can comfortably be played by the right hand on a keyboard instrument while still possessing some melodic and rhythmic interest.
In bar 4 the theme is used in stretto in the second and third parts.
Stretto should be included if the given theme allows such treatment. Here, the initial sixteenth-note rest has been replaced with notes in both thematic statements. As with the entry of the third part in bar 3, discussed previously, replacing rests with notes is frequently used once the theme has been established.
Let us now sketch in bars 5-7.
In bar 5 the inverted theme (beginning on the tonic note) is introduced in the third part, third beat; this entry is incomplete. The inverted entry beginning in bar 6, again in the third part, presents a complete statement and is used in stretto with a further incomplete statement of the inverted theme in the second part, bar 7. Bar 7 also begins a modulation to the dominant, A minor, which is effected through the use of a pivot chord. The D minor chord on the second eighth-note beat of beat 3, bar 7, is chord i in D minor and chord iv in A minor. This leads to a thematic entry in A minor in bar 8
This A minor entry resembles the 5-1 theme in D minor but with the necessary modifications needed for the new key, however, the theme now outlines a descending 8-5 in A minor. The upper parts in bar 8 use essentially the same rhythms as the upper parts which accompany the third part’s initial entry in bar 3. Using melodic and/or rhythmic features at comparable sections of a work creates cohesion, while also reducing the need for new material to be written.
Bars 9-12 establish the dominant.
In the third part, bar 9, the inverted ascending theme beginning on D is modified and leads to a full ascending theme in A minor, second part, beginning on the tonic, bar 10. This theme is used in stretto with a descending 8-5 theme in A minor in the third part, bars 10-11. In bar 11, a 5-1 theme in A minor is used in the second part, which combines in stretto with a further 8-5 theme in part one, bar 12. Frequent use of the theme, in all of its variations, is a characteristic of the invention style.
Bars 13-16 modulate into the subdominant, G minor.
This modulation is effected through the use of a Neapolitan 6th in A minor, bar 13 beat one, which is then left as chord III in G minor.
Again, incomplete and complete statements of the theme are found across these four bars. Also, many of the rhythmic motifs which were introduced in the first 12 bars continue to be used in the new key.
From the first beat of bar 16, the melodic material is taken from halfway through bar 5, but is now transposed to G minor. Like bars 5-6, this passage, which continues into bar 17, see below, is also modulatory and leads the work back to the tonic, D minor.
Bars 17-21, modulate back to D minor through the use of the pivot chord on the third beat of bar 17: this chord, chord i in the key of G minor is left as chord iv in D minor.
Bars 18-20 restate the thematic material from bars 1-3, with accompanying counterpoint in the other parts. The work ends with a Picardy third in bar 21.
We now have a complete work.