One of the simpler observations that has been made about fugal subjects over the centuries is that you're going to have an easier time of things if your subject, generally, does not exceed the range of an octave.
In traditional tonal music a subject based on a rising fourth will often be thought of as having the second interval being the tonic. But ... with a modal subject that's not necessarily how things work, and there are linear ways to offset a rising perfect fourth as being defined only as an implicit or explicit V-I linear/harmonic move.
I mention that because that's exactly what Brouwer avoids doing with this fugue subject. He is using a natural minor scale but uses sequence in measure 2 to have his fourth-leap go from F natural to B flat before dropping down to A natural. One of the things that makes his use of sequence so effective is that he gets to the F natural by way of C natural. Chains of ascending fourths might seem bad for vocal contrapuntal writing but for the guitar, come on, for the guitar chains of ascending fourths are just a few open-string level gestures.
Now measure 3 and 4 are simple oscillations between the fourth and fifth degree. If you're watching along in the video because you don't have your own copy o fthe score we're not looking at accidentals. Those are left hand indications about which fingers on the left hand are advised for playing the notes. We'll be getting to accidentals in system two, as you'll see, but we're not there yet in the first few measures of the subject, the first 14 seconds of this performance.
The subject appears at the dominant like we'd expect it to at 0:14 in a lower voice. There isn't exactly a countersubject in this fugue but the treble material introduces a dorian element that offsets or plays against the natural minor mode of the subject.
Almost straight out the gate on this answer we'll have to address a point that pedantic approaches to counterpoint will highlight. Doesn't Brouwer almost immediately have parallel fifths in beat two of the FIRST MEASURE in which his subject gets an answer. Well, yet. This is on the first half of beat two but in metrical terms beat two is a weak or often unaccented beat and, further, the parallel fifth is a function lf retaining the melodic contour of the subject which, as we can hear and see, drops very quickly down to B flat. In other words, the parallel fifth does happen but it's excusable by way of happening on a weak beat and by being skipped past quickly in favor of a sixth. Parallel fifths are bad in counterpoint if you keep landing on them on strong, accented beats but if you're landing on them as you're passing through unaccented beats you have wiggle room. Brouwer obviously knew this and with a bit of help from a video-score we can talk about that.
There's clearly been plenty of good contrapuntal music for solo guitar and not nearly enough discusion of how it works, whether it's 19th or 20th or 21st century counterpoint for guitar. We can try to fix that.
The third voice, in the treble strins and the soprano to the alto and tenor that respectively initiated this exposition, arrives at 0:28. The dorian modality that took over in the answer is retained in this new entry of the subject. While the dorian mode doesn't have a lot of "forward motion" as traditionally understood to inhere in major keys on account of the activetones of the leading tone and the fourth, it has an advantage for a guitar fugue, namely that the dorian mode is a symmetrical scale. The intervallic relationships are the same going up or down and if you try to invert the scale the interval relationships don't chnage.
D E F G A B C D (all natural)
That's the archetypal dorian mode on the piano or the guitar.
Given how demanding counterpoint in three voices for solo guitar is always going to be having a dorian mode cast to the subject in its third presentation shows that Brouwer is willing to adjust the subject modally as playability requires. It also just sounds more fun than being stringent about what mode the subject is supposed to be.
By 0:40 the exposition is over and we're at the section of the score marked "piu mosso" In this case the tempo picks up and the music becomes very agitated. Brouwer hammers away in the two upper voices with a harmonic major second (G and A natural) above the lowermost E natural (open string 6). This, sure enough, sets up a presentation of the subject in E dorian as the beginning of the episodes/middle entries realm of the fugue.
Something George Oldroyd and others have pointed out is that just because you have three voices in a fugue doesn't mean those three voices have to constantly be identifiably variant. In other words, you can have two voices in a dependent relationship in musical textural terms while one of the three voices takes all of the spotlight. For a guitar this point is all the more crucial because it's better to subordinate two voices as support or ornament for your actual hook (i.e. often your subject) than trying to going for the most complex texture you think you can play at the expense of the polyphonic aspect of polyphony. Your polyphony is about having good tunes first, and secondarily about having those voices generally being independent. You won't hear total independence of the three voices in Bach's Fugue in C minor from WTC Book 1, will you?
So Brouwer races along with the subject starting on E and it rises as expected to A but as the subject rushes along it is turned into a running bass line that loses its association with the subject while the seconds pulsating in the trebles become pulsating thirds. We're briefly in, if you will, E minor but this turns out to have been an episode and not a middle entry (i.e. a complete presentation of the subject. By 0:49 we have the subject appearing in the bass strings but, once again, it's just the first half and it dissolves into a flurry of rising scale runs that lead to a measure of 12/16 where, finally, we start getting some transformation of the second half of the subject as episodic material.
We're going to see that Brouwer consistently blurs the lines between what could be called a middle entry or an episode. At 1:03 we get a presentation of the first part of the first half of the subject but it leads abruptly into a curtailed form of the second half of the subject. The subject rises with its signature fourth leap but it's only here that it has the "expected" fifth-to-tonic implication we would expect it to have in a tonal fugue. Here the dorian element of the subject is really audible. Like I was writing earlier, making the subject a minor key tune that could be shifted at will from natural minor to dorian was a very good move on Brouwer's part, it's one of the things that makes him a great composer for the guitar.
This new first half of the first half and first half of the second half of the subject is sequenced at about 1:07 where the counterpoint is "flipped" and the subject appears in the upper voice whereas previously the pulsating pedal tone was in the upper voice above the subject. At 1:10 we get another motoric iteration of the second half of the subject but here we get a nice rippling, cascading call-and-response texture. Obviously when you're playing scale-work this fast on the guitar you thin the textures out to two rather than three voices. Even Bach didn't keep all the voices introduced in an exposition in constant motion throughout a fugue. If there's a grave misunderstanding guitarists can have about counterpoint in general and counterpoint for their own instrument in particular it would be this, mistakenly thinking that once you have your third voice in a piece you have to keep all the voices active and never let one or two voices drop out.
So, where was I? Right, the call-and-response runs based on the second half of the subject at 1:10. At this point fully homophonic/harmonic writing is in play. Brouwer starts to slow down and vamps on minor third gestures in widely spaced triads. He's clearly winding down and laying back on the counterpoint because he's building up to something ambitious. If you have heard this piece or read along with the score you can already see what he has in mind. He's going to go for a grand stretto.
At 1:19 the grand stretto arrives. It is, of course, only on the first half of the subject but it's a pretty grand stretto! Remember what I wrote earlier about how chains of ascending fourths is a gloriously idiomatic thing to compose for the guitar? THAT is what Brouwer employs for this grand stretto. He knew that his subject could be taken on open strings in a grand stretto passage so that there's technically no voice crossing. The stretto also allows him to strategiclaly stagger the entries in the stretto so that as each new voice enters the other voices are taking up material that can be assigned to open strings in a modal texture so that the voices that are no longer actively carrying the subject can get lines that can be subordinated to the newest entry of the subject. This can be done in terms of walking-bass lines and open strings as you can see in the score via video.
At 1:28 Brouwer has another stretto on the first half of the subject. This time the alto and tenor enter at G and C respectively and at beats 1 and 2. It's a blink-and-you-missed it moment but as contrapuntal writing for solo guitar goes it's one of the more glorious passages in the literature I've seen so far.
Then Brouwer chokes up, on purpose. He begins to stagger and interrupt the flow of the fugue. After a full measure pause the subject appears in the trebles with the material in the answer from the exposition (1:40), which is presented as the could-have-been countersubject that it functionally wasn't in the fugue up to this point. The subject isn't presented in its entirety but is instead sequenced against the countersubject line. At this point the first half of the subject has been run through enough stretto sections that Brouwer is winding down for the fugue but prepares to wind up for a rambunctious finish. By the time you reach the coda of a fugue you have an option to cast off polyphonic constraints and go for a bravura toccata style texture.
Any guesses what Brouwer does? I admittedly gave it away.
1:50ish we get some ornate toccata textures in sixteenth notes, full of agitation, soaring over a series of low E pedal points. You should be able to hear and see how even thse riffs are all derived from embellishing the second half of the subject. Brouwer has set aside the first half of the subject because he developed it extensively and is using free-form derivations of the second half of his subject as the foundation for the coda that will complete this fugue. He even uses that second half of the subject material as the basis for a short quasi-grand stretto section for that material at 2:09. By now the pounding away on the E pedal point suggests that our closing cadence is going to be A rather than D and so we do have a final cadence on A ratehr than D.
A more pedantic approach to a fugue would insist that we have to end on the key in which we started. That's what I prefer to do at a personal level. Leo Brouwer is Leo Brouwer and he shows that there are other ways to get a fugue for solo guitar to work. The closing A cadence is effective.
Now some of you may have noticed that I have not described any episodes that would be understood as episodes in traditional pedagogy. I have also not described there being any middle entries in the fugue either. There aren't any. Brouwer only completes his presentations of the subject in the exposition. So some of you may understandably ask, "Well, if Leo Brouwer doesn't have any middle entries for his subject and doesn't have anything but a series of episodes using parts of his subject then how is this a fugue?"
That's a good question. Depending on how you answer we could say that Fuga No. 1 is either not a "real" fugue and must be a fughetta or some fugue-like textural study. Or we can propose that it IS a fugue but then go back to observations made by Manfred Bukofzer and others about how in the 19th century there really was no such thing as a fugal form and that everything about any given fugue depended on the exigencies of the fugal material on the one hand and what was idiomatically reasonable to execute for the musical forces specified for the material on the other. In that broader and more "old school" and less doctrinaire approach to defining what a fugue is, Brouwer's Fuga No. 1 is a fantastic fugue, fantastic for the level of development he gives to his subject and also fantastic for the way in which he does so working with the idiomatic strengths and weaknesses of the six-string guitar.
If there were a book about counterpoint for solo guitar I would say this is a work that has to be in such a book.
Even though the fugue is just barely more than two minutes I've managed to write at least 2,300 words about it. That's how fugues tend to be as literary subjects. You can write thousands of words simply describing what happens even if you're not trying to mine the depths of the emotional content that this or that writer might here in the work. Since I love fugues, love writing them, and enjoy writing about them Brouwer's Fuga No. 1 was on my list of thing I wanted to blog about for a while but I didn't get to it until today. I am going to try to get back to Koshkin's cycle, of course, but you'll understand how hugely demanding that project is. I hope you listened to the fugue and read along with the score (either because you watched the video or, even better, own a copy of the score yourself!) and enjoyed the work.