The Fugue and The Sonata: Reconciling the Two Worlds

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Foreword: This article requires some background knowledge of the various forms discussed. For reasons of length (and time) I must leave detailed explanations out when the point can be made without them. But, never the less, it is something that is of importance regardless of the details discussed and therefore I can recommend at least giving it a look even if you are unfamiliar with some of the terminology and so on used.


In the course of western music history, we can identify a fundamental composition problem which many have tried to solve or somehow come to terms with. This problem is the clash between the polyphonic ideal that each voice is independent and counterpoint and horizontal thinking accounts for everything and the idea of vertical thinking where chords are formed and they dictate what happens.

The representative in this case of the polyphonic tradition, as many composers have interpreted it, is the fugue. At its heart is the concept that each voice is independent from each other and indeed through this independence a texture of sound is created through careful control of interval relationships. Fugues have been throughout music history, specially J.S. Bach's, thought as the highest expression of this tradition or at the very least the way in which the characteristic elements of the time are best represented.

In the other corner, we have the sonata. The sonata is a staple of the post-baroque period, an offshoot of the influence exerted by the Galante style and the tendencies of the late baroque composers such as C.P.E. Bach. Here, what defines the music and the relationship between each notes as well as the harmony is the idea of chords. This so called vertical thinking is what sets it apart from the predecessors and gives raise to an emphasis in harmonic thinking. The sonata form is dependent on this principle, as its anatomy depends on pivotal harmonies and chord sequences which are elaborated from the point of view of form rather than as a mere consequence of melodies interacting with one another as in the polyphonic tradition.

This shift from one to the other is plagued with problems and a great deal of composers have wrestled with understanding the problem and trying to find ways to reconcile these two types of thinking. Let's look at this more in depth and get this show on the road, shall we?

Let there be Mozart

It's very likely that the first major composer of historical importance that dealt with this problem in a rather consequent and extreme manner is Mozart. Unlike the attempts of C.P.E. Bach, Mozart specifically tackled this problem in a way which would later prove to be one of great foresight. But before we proceed with the example in question, it's first important to understand the context in which this piece is to be understood.

Mozart was familiar with the baroque forms and had displayed great interest towards J.S. Bach as well as being influenced enormously by his son C.P.E. Bach. However, when one addresses Mozart as a composer, it's not usually to talk about how great a fugue-writer he was. Instead it's to look at his string quartet compositions, his conception of form, the operas and so on. However, there's a great deal more to him than is shown by his more popular works.

Indeed, by the time Mozart was alive and writing music, the fugue itself had all but vanished from popular interest. Nobody cared to write them anymore and the influence from the Galante style was felt strong as an anti-thesis to the complexity of the polyphonic schools. Within this context, it's understandable why few composers bothered to continue the tradition.

But one must only observe with more care to notice that Mozart was very much interested in fugue writing, though the reasons for this are far different than one would expect. Though Mozart displays the knowledge and handwork necessary to craft rather good style copies of his predecessors' fugues (such as Fugue in G min KV401-375e), it's not these that we'll be looking at.

Instead, let's turn our attention to the fugue in C minor for string quartet, KV 546.

(The score can be obtained at completely, from the open Mozart edition online 100% legally, for those who care about that. A recording of it can be heard here )

Though I will not analyze the entire fugue here, I will point out the relevant aspects of it and why I have chosen it to represent the struggle mentioned previously in the opening section.

Just from hearing it, the first thing to notice is the strong dissonance with which Mozart works here. And, those with a good knowledge of Bach's work will recognize the fugue's subject to be the same type of subject Bach used in the musical offering. Both are in C minor, both contain the same famous diminished 7th jump (known as Saltus Duriusculus in the baroque affect context) and both contain sequences within the theme.

Understanding the anatomy of the subject is of crucial importance. This subject also contains chromatic movement and a rhythm contrast. From these elements alone, we can get an idea where the fugue will go. First, we have to make clear what these elements imply, specifically the point that the fugue contains in its subject a sequence.

If we take Bach's fugues as examples, there will always be a clear distinction between episodes and expositions of the theme. Even by fugues which contain sequences (such as the one in B-minor in WTC book 1, or the musical offering theme), Bach maintained a clear relationship between these two important parts of a fugue's form. The biggest problem with a subject that contains a sequence, is that due to the fact that episodes also contain sequences, it's easy for the subject to become "lost" in between the episodes' sequencing so that one simply doesn't hear the subject at all as such.

What we'll see here is this being taken to an absolute extreme, where by the end it's practically impossible to recognize the elements of the fugue as such. Mozart destroys the audible difference between exposition and episode in such a way that all that is heard is a constant chaotic organization of pieces from the subject, counter-subject and the constant sequencing of them.

The fugue begins as anyone would expect, with a tonal answer at the 5th. The counter-subject in this case is a very well-known baroque model based on note repetition (measure 5.) The exposition follows through through all voices including an extra exposition in the cello in measure 14, as is also typical by Bach. But something is strange right at the beginning. If we look carefully in measure 4, there is a suspension. The B in the cello resolves to C, however there is a sharp dissonance produced by this as the viola begins the theme in C. This is extremely atypical, and right here it is clear that this is not a style copy but something else.

Let's jump to measure 25. Here is where we first see the phenomenon described above happening first hand. The subject is introduced in the second violin, yet the first thing to notice is what is happening in the other instruments. The subject is "drowned out" by the constant sequencing of the chromatic portion of the subject, so that by this point it's very difficult to tell that it IS indeed the actual subject without looking at the score. Harmonically, beyond all the sequencing that's going on the subject here is in the relatively close key of G minor, which follows in accord with the tendency that pieces must modulate to the dominant after the start. Important to notice that the counter-subject, the repetition motive, is also missing here.

In measure 30 we can see in the cello only the start from the subject being introduced, alongside the counter-subject once again in measure 31. However, here we witness something which very uncharacteristic of Bach and the baroque period in general.

We encounter motive-thematic development, rather than simple sequencing. Indeed, what Beethoven is known for and is the staple of the romantic period appears here. The sequencing of fragments of the subject, counter-subject are much like the sequencing and fragmentation that happens to sonata themes. By this point it should be clear just how far away from the polyphonic tradition, Bach's style and so on, is what is happening here.

We not only encounter this in this particular measure (31) but also previously in measure 25 and indeed all over the fugue. It only becomes bluntly evident here (31), when the theme itself is fragmented and sequenced. It tricks the listener into thinking that an exposition will take place, when in reality it's another sequence and no theme appears yet in its entirety.

And here also comes something which is not found by Bach, which is inversion and an stretto so early in the fugue. First, it must be made clear that by Bach, if the stretto technique is used at all it only comes in the later half of the fugue and never so early. Likewise, the usage of diminution, augmentation, inversion and retrograde by Bach, unlike what is thought popularly, rather sparse. In the entire first book of the WTC there are only a couple of occasions where any of these techniques appear, for instance.

Mozart here introduces both almost simultaneously in measures 35-36 between the first violin and the viola. This model of stretto is based on the "pair imitation" known in the pre-baroque music (specifically in chants, a verse would be sung and in imitation a second verse would be sung while the first was not yet finished), a form so old that even by Palestrina it was antiquated. This model is seen here clearly, when we see again a stretto but again in a pair, now between the second violin and the cello in measure 39.

It must be noted that this mixture of extremely old form elements and quasi-futuristic ideas is what characterizes the bulk of Mozart's late work. It can be interpreted to be a struggle with trying to fit in his appreciation for the polyphonic tradition with the new tendencies of his time, as is the case here quite clearly.

What is most interesting by this fugue is that the harmonic constellation of it remains fairly simple. With the exception of the Neapolitan key appearing in measure 44, the fugue is for most part based on the primary triads from C minor, such as subdominant, dominant and so on. However, this is not to mean the fugue is harmonically still; instead, it means that the constant sequencing and development are very much trying to modulate the entire time, but are anchored down in order to keep consistency.

However even that starts to fade near the end of the piece. By measure 73, we get something extremely uncharacteristic which is the introduction of a subject, and alongside it its own inversion. Even more puzzling is by measure 103 where the subject is fragmented to the point that it's combined with the counter-subject in a single voice. Indeed, by this point in the it's impossible to make out the different portions of it and break it down into sections like one is used to by Bach or other baroque composers.

This fragmenting and chaotic arrangement of combination and sequencing gets more and more extreme as the fugue goes on. It leads us, eventually, to what is probably the single most puzzling aspect of the entire fugue: its ending.

From 106 onwards, if we look at what we have in the first and second violin it will become apparent that this is an accompaniment figure. Indeed, the entire ending is built by throwing aside the very principle of fugue writing, the independence of voices and counterpoint relationship.

Also the ending is extremely dissonant and by the registers and spacing used it is the loudest and thickest portion of the entire piece. In what is probably the only example out of Mozart's entire literature, the ending is riddled with dissonance. Every element we would expect to find by him is gone, such as dominant/tonic pendula, pedals, and so on. Instead we have this thick chord sequences riddled with dissonance and something very peculiar.

In measure 118. The chord here is diminished 7th+9th chord in the dominant, but something is wrong with the suspension in the viola and cello. It's something that, were anyone to write this in a theory lesson today, it would be labeled as "wrong." That is, by suspensions the resolution of the note being suspended should never sound at the same time as the note being suspended.

A simple example:

In C major, a D 4-3 suspension will look usually like so: G D C G, where the C moves to B. However, here we have, if we follow this example, G D B C G. The note C is supposed to resolve to is played along with the suspension. This is something that Beethoven was pretty fond of, we can see it used a whole lot in the early Bagatelles for piano, which is practically teeming with this sort of suspension.

It makes the suspension that much more dissonant and here we can clearly state with certainty that Mozart did not do this out of following any traditional norms or ideas. This was something he picked on his own - it was his decision.

In conclusion to the analysis here, it must be pointed out that while not very in depth, it should be clear that this fugue is no ordinary fugue. In fact, one may as well said it is not even a "real" fugue, but why must we use Bach as the measure every time? Mozart did not pick the name "fugue" for this particular piece on a whim, he had a specific purpose for it.

This purpose was to experiment with the elements from both worlds which at his time were colliding. It was not by chance, but by sheer need to resolve and deal with these issues that he ventured into this territory. I chose to examine this work because of its importance to the later composers and because it demonstrates very cleanly the struggle with this problem of uniting both types of thinking and composing.

From Beethoven to Hindemith and beyond

Mozart was far from the only one to experiment and try to solve this problem or at least find a way to resolve this. Beethoven also explored the topic of fugues within the context of the sonata form, vertical thinking. His late pieces are riddled with fugues and they exhibit the same qualities as Mozart's fugue analyzed above. Beethoven tried to approach fugues a little differently, trying to figure their place in the sonata form altogether both in the string quartets and the piano sonatas.

By the 20th century, turn of the century composers such as Luis Vierne or Erik Satie also struggled with the problems associated with counterpoint and fugue writing. By Shostakovitch, Hindemith, Duruflé and Stravinsky we find the problematic still alive and kicking, but this time facing different issues such as new techniques and ideas. The composition language of the 20th century opened up many more ways in which this classic issue could be tackled.

But despite the combined efforts of all these composers, we cannot say the problem has gone away. Instead, it remains as interesting as ever. It's something that perhaps will never become "old" so long as the attempts yield such interesting results as we see by Mozart, Beethoven or Hindemith.

One must not restrict the term "fugue" to simply copying Bach, or any such archetype. There are some that believe that Mozart or Beethoven couldn't write fugues, that fugues that do not adhere to X or Y criteria are simply not fugues. However, hopefully I have shown that this is simply not the case and things are not as simple as they seem.


Much like we can see Mozart trying to come to terms with the transition of the practices of his period, other composers have similarly tried to combine the tendencies of their time with fugues. It's up to us, composers in the 21st century, an era of rather dubious overall qualification and categorization, to see where we stand in relation to these timeless composition problems and perhaps attempt to give them a go.

Who knows, maybe someone WILL figure out how to bridge all the gaps someday. Until then, I'd say most of the fun is in trying so have at it.