II. Counterpoint and Galant Schemas

High Baroque Fugal Exposition

Mark Gotham

Key Takeaways

  • The fugue is a contrapuntal genre popular since at least the eighteenth century.
  • This chapter sets out some key principles of the opening ‘exposition’ section.

We now move on from imitative practices common in the sixteenth century to the fugue which may be thought of as the eighteenth century equivalent and successor to this tradition. This chapter deals with the basics of writing a fugal exposition from a given subject according to the ‘high Baroque’ technique of Bach, Handel and their contemporaries. First let’s define some of the terms we’ll need:

Basic Definitions

  • Fugue: a surprisingly difficult term to define satisfactorily! Here we’ll deal with the idea of ‘fugue as process’, i.e. how to construct (the first part of) a fugue from first principles.
  • : a short tune which forms the melodic basis of a fugue, recurring throughout.
  • Answer: a transposition of the subject with is also sometimes slightly altered as discussed below.
  • Countersubject: a melodic line that is sounded with (and complement) the subject/answer.
  • : The first part of a fugue, during which each of the voices enter with the subject or answer. Note the similarities and differences between this use of the term ‘exposition’ and the equivalent in sonata form. Basically, they both refer to a first section setting out the main material. Otherwise they differ.
  • Voices: the separate contrapuntal lines; this term does not necessarily mean singers (though it can) and the number of voices is not necessarily given by the number of parts / musicians involved (though, again, it can). It is perfectly normal for a keyboard fugue (i.e. one player, no singers) to have 3, 4, 5, or 6 ‘voices’, and there are even some fugues for solo violin (which is quite a compositional feat!).
  • SATB: Notwithstanding the fact that we’re not necessarily dealing with voices in the sense of singers, it is customary to refer to a four-voice texture with ‘S’ (‘soprano’), ‘A’ (‘alto’), ‘T’ (‘tenor’), and ‘B’ (‘bass’) for those ‘voices’, working from highest to lowest. The ranges need not exactly match those of the vocal parts.

Structure / Voice Entries

Basically, the fugal exposition works as follows:

Voice 1 Subject Countersubject Free part
Voice 2 Answer Countersubject
Voice 3 Subject

One voice begins with the subject; then the next voices enters with the answer while the fist continues with a countersubject and so on.

Note that we’re numbering the voices here simply on the basis of their successive entries. While it is perfectly common for the voices to enter in order from highest to lowest or lowest to highest, this is not strictly necessary. What you will commonly find in the repertoire is an avoidance of inner parts entering last; specifically: at the moment of a new part entering, it should be the highest or lowest voice at that stage. That leaves us plenty of options. For instance the order of voice entries in a four voice fugue could be:

  • In register order from highest to lowest (SATB), or vice versa (BTAS);
  • Starting in the middle with the alto: ASTB, ATSB, ATBS,
  • Starting in the middle with the tenor: TBAS, TABS, TASB.

Any further subjects / answers entering (beyond the total number of voices) are described as ‘redundant’ entries.

Subject

When considering how to handle a subject, look at its structure and character.

The structure of a subject can often be thought of in three parts. As in many tonal contexts this charts a course from a distinctive opening to a generic cadence:

  • ‘Kopf’ (literally ‘head’) motif: an opening gesture;
  • ‘Fortspinung’: prolongation which may include sequence and/or motor rhythm;
  • Cadence

Types of character include the:

  • ‘Toccata’ style which has a moto perpetuo rhythmic feel, is often chromatic, and may have irregular rhythmic placing.
  • ‘Ricercar’: deriving from the plainsong / motet tradition, this is slow moving, has an antiquated feel, and makes extensive use of suspensions.

Answer

We distinguish between two types of answer: ‘Real’ for an exact transposition, and ‘tonal’ for one that has been altered further.

We need a tonal answer if the subject:

  • starts on scale degree 5 or otherwise uses it prominently at the outset. In this case, we must adjust the transposed version such that 5 is not transposed up to scale degree 2, but instead to scale degree 1.
  • includes any other V-I suggestion at start. Prominent dominant note in subject becomes tonic note in answer, so T → D progressions often become D → T and vice versa.
  • modulates. In this case, split subject into two phrases, one in each key, and adapt accordingly. If the subject modulates at its end to the dominant, the answer must modulate back to the tonic

In all cases, we seek to make minimal adjustment such that the subject and answer are still as alike as possible, and both make melodic sense.

Countersubject

Try working up a skeletal version of your countersubject first before. It’s frustrating to dash off a lovely tune and then realise that it doesn’t fit. Additionally, sketch the version that will go with the answer at the same time as the version that goes with the subject. It’s just as frustrating to write a countersubject that works beautifully with the subject, but which the answer makes harmonically nonsensical.

Hold on, harmony? Yes indeed! Countersubjects are melodies but they only work if they make sense harmonically as well. To that effect, remember that your countersubject will first appear in a two-voice passage so consider how best to outline clear, larger harmonies (triads and sevenths) with only two voices.

You may wish to set yourself the additional constraint of a countersubject which is invertible at the octave – basically, one which can appear above or below the subject and still work. In this case, again work on both versions as you go, and specifically make sure to:

  • avoid 5th because 5th invert to 4ths which have special rules in two-voice writing. Stick to unisons (/ octaves), thirds (/ sixths), and in the case of 7th chords, also 2nds (/ 7ths). The 5th is not a problem in the free part, so ‘reserve’ that note as the completion of the chord, and use it there.
  • similarly avoid 4-3 suspensions because the first note is not dissonant when inverted (5-6). Instead, use 7-6 and 2-3 suspensions (which invert to each other).

To create your skeletal countersubject, first look for skeletal patterns in the subject. Find the simple, un-embellished form of the subject and treat is as a kind of tonal cactus firms against which to write your counterpoint (skeletal countersubject) which you can then embellish into a more interesting musical line.

When it comes to embellishing, try to:

  • Be true to the character of the subject when composing the counter subject;
  • Establish complementary rhythmic motion such that one voices moves while the other is stationary;
  • Make changes to countersubject when moving between subjects and answers only and exactly where those changes appear in the subject/answer.

‘Free part’

Frankly, the idea of a ‘Free part’ is a bit of a misnomer, especially if you’re writing an invertible countersubject because the subject and countersubject will leave your options highly constrained. This part is ‘free’ in the sense that it doesn’t necessarily recur later on, so you might like to think of it as a ‘freer’ part, relative to the even less free subject and countersubject! Alternatively, you can embrace the extreme order, and replace the ‘free part’ with a second regular countersubject which does recur later.

Links

Your fugal exposition may include short interpolations between the subject/answer entries. We call these ‘links’. Links frequently make use of a melodic idea from the subject, for instance with sequential repetition of a short fragment. They may appear between any or all voice entries, and be of varying lengths.

There are many musical motivations for including one of more link. Links provide an opportunity to:

  • change harmony: the end of one subject/answer and the beginning of the next may not match up harmonically; in that case, you can use the link to get where you need to be:
  • change register: if you have a continually descending line, for instance, links can be a useful way of resetting the register so you don’t fall off the end of the instrument (or, indeed, audible!) range.
  • vary the phrase lengths: if you have a subject of exactly two measures, and just proceed through several voices entering successively, then you may well want to use a link to make the hypermetrical and phrase groupings a little more interesting. That said, the voices should always enter on metrically comparable positions. If your subject comes in on a strong beat, then so should all the subject/answer entries (at least in the exposition). If your subject is anacrustic (comes in on a pick-up) then again, make that consistent.
  • dovetail entries: apart from varying the phrase lengths, we can also vary the melodic context in which a voice enters. For instance, if a link develops the ‘Kopf’ motive sequentially, then you can bring in the next subject/answer in seamlessly as it begins with that motiv.

General Matters

Apart from the specific considerations of the fugue, naturally much of the general practice of writing (tonal) music applies here. Remember in particular to:

  • control rhythmic flow: if and when continuous use of a given metrical level has built up (e.g. quarter / eighth / sixteenth notes), consider carefully whether and when it is appropriate to discontinue that motion
  • graduate the relative strength of cadences, for instance by controlling the scale degrees in the top and bottom voices.
  • Write idiomatically for the instrumentation at hand. Remember to observe practical limitations of hand span, instrument range and the like. This also extends to stylistic matters, for instance, string fugues may be more extrovert and see the two upper parts operate closer together.

Example

For an example of all of this in action, let’s consider the C minor fugue from Book I of Bach’s Well Tempered Clavier (BWV 847).


Fugue exposition example (BWV 847) by FourScoreAndMore
Note that:

  • The exposition runs from from measures 1–8 (the extract here includes the start of the following ‘episode’).
  • All the subject and answer entries and highlights with blue noteheads.
  • There are two, regular countersubject (annotated as ‘CS1’ and ‘CS2’).
  • The answer is ‘tonal’.
  • The link between entries 2 and 3 (mm.5–6) and the episode which following the last voice to enter (mm.9ff.) and built on sequential handling of a motive from the subject as indicated with brackets.
Online Resources

Head to dezrann.net for a full version of this Bach fugue, complete with on-score annotations and an aligned audio recording of a real performance. You can even chose between this friendly version in modern notation with the fugal voices on separate staves, or to follow along with Bach’s manuscript.

Assignments
  1. In the Bach C-minor fugue shown above, the answer is ‘tonal’. Given what has been said about tonal answers in this chapter, try explaining how the subject and answer differ, and why.
  2. Pick another fugue, identify how many ‘voices’ there are, locate each voice’s entry and the end of the exposition.
  3. Trying writing your own answers and countersubjects. The template file below provides the subjects for all 48 fugues in both books of the Well-Tempered Clavier. An empty second stave is provided for your practice. (Note that the last note in many of the fugue subjects is given without a stem to indicate the pitch without the specifying the duration rhythm). If you know some of these fugues well, you may want to work on ones you’re less familiar with.
  4. Once you are feeling confident with writing answers and countersubjects, try writing up a full exposition. Again, you may wish to work on fugues you’re less familiar with.

For 3 and 4, you may wish to compare your solutions to Bach’s. Note that Bach’s solutions are not the only possible ones so don’t expect to come up with exactly the same music. Note too that not every fugue has a regular, invertible countersubject.

Here are direct downloads in: .mscz and .pdf formats, and here is the score online:


Well Tempered Clavier Fugue Subjects by FourScoreAndMore

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