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State of Flow: Analysis of a Bach Fugue : BWV 952::journal

Analysis of a Bach Fugue : BWV 952

Lance Walton - Friday October 14, 2011

Fugue is a process, not a form. So what is the gross structure of a fugue? What does it look like from a distance?

Having been an amateur and infrequent composer of mostly baroque music for the last 28 years, I think it’s about time I learned how to do it properly. Over the years I have read numerous books on harmony, counterpoint, form, etc. but I have never put in the hard work of doing the exercises presented in the book, and have always been content with reading the analyses of works presented.

Dissatisfied with continuing to be a musikant, I have started doing the exercises and performing some of my own analyses.

At the risk of encouraging some young, aspiring composer to be satisfied with reading rather than doing, I would like to present a part of one of my analyses here. I’m not going to present the majority of the detail because that would be too long, would reflect several areas in which I know I am weak, and thus would most likely be uninteresting to almost everybody else. Instead I will content myself with a brief discussion about the subject followed by an equally brief discourse on the overall structure.

The piece I have chosen is BWV 952, a 3-part keyboard fugue in C major. Here is a midi-rendition:

There are numerous recordings available on the web too.

For the purposes of analysis, I have produced a score with the parts separated out onto three staves. I have added various notes to this score to assist with my analysis.

The Subject

The subject of the fugue is one and a half bars long and consists of continuous semi-quaver movement.


This subject can be segmented into a number of motifs, which Bach makes use of later:

Motif A

Motif B

Motif C

Motif C clearly extends motif B. This causes me some consternation, since it suggests that we could exclude the motif B fragment (the first four notes) from motif C, leaving us with a smaller, third motif. The remaining four notes certainly could be used as counterpoint against the subject, and it would also make good episodic material. That Bach does not use it in either of those ways is interesting, and I believe I have an explanation.

Directing our attention to the notes falling only on the quaver parts of the beat, we see the following in the first and second instances of motif C (both occurring at the end of the subject, or course):

When motif B is presented first, there is a clear end due to the ascending leap of a fourth from E to A. When motif B appears as the first four notes of motif C, it is followed by stepwise motion upwards, and then a continuation of the general scalar motion downwards. Even in the original decorated form in which it is presented, my ear locks onto the strong scalar movement, smoothing over the ‘join’ between the first part represented by motif B and the second part.

On a point of unity, this descending fourth outlined by motif C is an inverted and augmented version of the ascending fourth constituting motif A. This simplified form (of motif C) is used intensively throughout the fugue. Sometimes it is in the inverted form shown here, sometimes uninverted. Sometimes it is extended, and sometimes elided.

If this fugue is ‘about’ anything (apart from the subject itself, of course), it is about filled in, rising and descending fourths.

Overall Structure

One of the aspects of composition I struggle with is musical structures larger than a single phrase. In order to cast some light on this, I have prepared a schematic that you can see at the bottom of the page. The purpose of this schematic is to show a great deal of structural information in a single diagram.

The schematic is divided vertically into 6 sections. In each section, there are four thick horizontal bars.

The top three thick bars each have a thinner bar underneath. The thick bars categorises activity in each of the three voices (see the legend). The thin bars underneath each voice show when the voice is using some motivic material from the subject. Darker versions of the motif colours in the legend indicate a modified form of the motif (augmentation, inversion, etc.)

The fourth, thick bar at the bottom of each section indicates my estimation of the current tonal centre, relative to the home key. Upper case roman numerals indicate major keys and lower case roman numerals represent minor keys.

The schematic clearly shows the structure of entries (including two expositions), and episodes. Episodes are often made out of sequences using motivic material.

Of particular interest is the series of keys. There is a fairly firm, systematic movement to the dominant side of the home key.

The sequence of keys that the piece moves through is I V (I) ii vi iii IV I. The increasing tension that result from this is clearly felt when listening to the piece. Once the most extreme key of iii is reached, the next modulation is to IV, a close relative to the home key, but this time on the subdominant side. This dissipates a lot of the tension, and the subsequent return to the home key in the middle of the re-exposition gets us back onto firm ground.

  1. Mum    Sunday October 16, 2011

    Wonderful stuff. Both Bach’s work and your analysis, I don’t know how you find the time.