Wednesday, March 15, 2006

Phase Shifting

No, I'm not talking about the analog-cum-digital effect which has to do with out of kilter upper harmonics, but rather I am referring to the phase shifting which results in a change of primary focus in one's life. This is obviously related to the previous post on procrastination/prioritization.

It seems that I have now entered a "guitar phase" from my previous "composition phase" which was sparked by a "theory phase" which grew out of a yet earlier "guitar pedagogy phase." Pure guitar phases are rare and delicious for me, because I usually view practicing as a chore. Hell, I even view performing as a chore a lot of the time. I'm not sure how to handle this from a blogging perspective: Daily updates on my latest fingering and articulation solutions for pieces I've written over the last year seems like just about the most boring possible blogging material extant. This is bound to be compounded by the fact that - though rare - my "guitar phases" tend to be of very long durations. I mean, the last one of these guitar phases of mine lasted over eighteen months, and I haven't even been blogging for a year yet. You can see the dilemma.

I do not want to put off this decision or procrastinate, nor do I want to be redundant and repeat myself... over and over again... time after time after time... seemingly, without end... however, I really don't know what I'm going to do with the blog for a while. So, I'm going to do a post on an old fugue I wrote about ten years ago to fill some space... and put off this decision until I can come up with some sort of a solution: A direction for the blog for the next eighteen months while I'm in the woodshed practicing.


There have been several times over the past ten months when I have thought about creating an entry about this fugue, but one thing or another always re-directed me away from the idea. I have read various accounts by great composers over the years in which they have singled out certain pieces as being particularly significant to them. For Beethoven, it was his third symphony: Some critics claim that it was the greatest single compositional stride ever made by any composer in all of music history. I'm not sure if I agree with that or not, but Beethoven always had a special place in his heart for the Erioca, and he even intimated that he attributed supernatural origins to it. This fugue is no Eroica Symphony, nor is it among the greatest compositional strides ever made by a composer, but it was at the time I wrote it an unprecedented piece for me, and I have no doubt but that it has magical - even overtly spiritual - qualities to it. As you will see if you have any familiarity with the intricacies attending the creation of appropriate fugue subjects, this subject has to be one of the top ten fugue subjects of all time.


The first time I ever encountered Bach's Die Kunst Der Fuge, BWV 1080, was when I was attending Berklee College of Music. A drummer friend of mine (Who would later be my roommate in NYC, and later yet one of the founders of Digidesign) had a string quartet recording of it, and he whipped it out one evening just because he thought it was excellent, exotic, and cool. The experience I had when I listened to it was as though I was divorced from time, and the lineal continuum we usually experience was a free path I could look ahead or behind upon. What I mean by that is that I was totally absorbed in trying to be a hot rod burning contemporary guitarist at the time - and I knew that wasn't going to suddenly change - but I could both see ahead to a time when fugue would be my life, and back to my earliest musical memory, which was the sonata/fugue that is the scherzo to Beethoven's Ninth (The theme music for the Huntley/Brinckley Report when I was a baby). I got those chills like we sometimes get listening to great music, but also a bitter-sweet feeling that my "career" was not going to go as I planned... regardless of whatever efforts I might put into it.


Fast forward five years and Don and I were roommates, I was becoming disillusioned with being a contemporary guitarist, I was writing a bunch of contrapuntal solo classical guitar pieces, and I recognized that fugue in general and Die Kunst Der Fuge in particular were the pinnacles of contrapuntal artistic expression. His recording of The Art of Fugue became a kind of talisman for me: I could never get it out of my mind, and it seemed to be with me always... an albatross hanging around my neck, as it were.

I decided then that I understood exactly what Bach was doing, and that I ought to try to add to what he did. It took me seven years and a bunch of fugues of various qualities from profoundly lame, to half-assed, to not too bad, to good, and even excellent... but I finally did it.

Schillinger's Theory of Melody (As well as others among the books of his System) and Hugo Norden's The Technique of Canon (Which he STOLE from Taneiev with out crediting him!!!) were keys to this breakthrough fugue, because no fugue can ever be any better than it's subject is: This fugue is the ULTIMATE stretto fugue.


Instead of starting at the beginning of the fugue, we need to preview the recapitulation first, because this is what I composed first: The subject as a four-voice canon at the octave.

As you can see, the five measure subject was written as a six measure canon. The final measure with the written-out trill is an addition which I used as a thematic element in the fugue (i.e. The Subject is five measures in length).

I used both the ascending perfect fifth of the Kunst Der Fuge motto theme and the descending diminished seventh of the Musicalisches Opfer "royal theme" (Which was certainly composed by C.P.E. Bach in collusion with Frederick the Great in an effort to embarrass "old Bach"). By using a measure of tonic and then introducing the minor sixth, the subject has a deceptive rsolution built into it. This feature plays a huge role in the fugue, and is one of the main features which makes this subject objectively far superior to that of J.S. Bach in The Art of Fugue.

To be fair, Bach wrote the Motto Theme as a four-part compound fugue subject, one part of which is the BACH (B, A, C, B-flat) musical anagram, so he had a higher agenda for Art of Fugue - and I've never (yet) attempted a compound fugue - but in terms of pure stretto possiblilties, my subject is objectively and demonstrably superior. That was my only goal from the beginning.


The fugue is in F minor. The subject is five measures in length (Odd is better than even, and fractional is better than whole: This subject is odd and whole). There is no countersubject; the counter-voices are freely composed, but they use fractally realted elements to achieve unity.

In measure ten the "thematic trill" makes it's first appearance. The origin of this rhythm is interesting: MIDI couldn't interpret a trill back in those days (1995), so I had to write it out. Not being familiar with the details of trills, I asked a few profs about how they were actually played. Well, I was entirely unimpressed with all of the answers I got, so I decided that the most logical solution for this fugue would be to take the trill out of the hands of the performer, and make it a specific rhythmic feature of the work. This was a very good idea.

Note that in the exposition there is a stretto of one measure of overlap for all thematic statements except for the first one. This sets up the entire fugue.

Formally, the exposition takes eighteen measures due to the stretto overlaps. The first episode is non-modulatory and is based on the thematic trill figure.

The first middle entries begin in measure twenty-three, and are based on the original canon's stretto possibility for overlap at three measures of delay. Four measures of delay appeared in the exposition, and so this is another step in tightening up the stretto delay: The entire fugue is based on this ever-decreasing interval of appearance of the subject against itself in stretto.

Through measure thirty the stretto of 3m delay in the tonic minor key is worked out, and then the second episode begins. This episode is based on the tail figure of the fugue subject - an excerpt of which appears in the cello part in measures twenty-nine and thirty - and it modulates to the dominant tonic region. This kind of geometrically precise modulatory episode is something apart from the style of Bach. He was an improviser who wrote all of these sublimely introspective passages linking his thematic statements: I wanted a more mechanically effecient way that was more direct, had better musical punctuation, and yet still gave a satisfying impact to the process. I frickin' love this episode: It does all of that.

Though the chromatic decending line in the bass is never interrupted, I still managed to get the thematic trill into the end of the episode, and so the next section of stretto at two measures of delay can begin.

Since there are not particular countersubjects in this fugue, I used instead the thematic trill figure linked to the suspended figure to get a fractal relationship background. The more you look at the thematic statements in this fugue, the more of that you'll find.

Note how I worked a form of the subject in diminution into the third episode over a chromatically decending bass line. I avoided the can of worms that this opens up, but I realized that I could write an entire "Art of Fugue" series on this subject when I reached this point: This subject is that good.

Using only this suspended tied figure and the subsequent thematic trill means that no matter how close the immitation gets, those elements will always work as counterpoint! This realization almost gave me fart-hailure when it hit me.

Since the one measure delay stretto will be in the recap's concluding canon, and that will be in the tonic minor, I gave the one measure delay stretto here in the body of the fugue to the major mode. This is effective on too many levels to list: It really is absolutely fracking amazing. In ten years I've never ceased to get chills at this point in the piece.

The melodic peak also occurs during this closest stretto, and it is at almost exactly the 67% point, naturally.

After this major mode one measure delay stretto, the next episode is again based on the thematic trill figure, and it moves the piece to the subdominant minor region.

The fourth middle entries that start in measure fifty-five are set up as a false recapitulation. They unfold as the original exposition - which is the closest thing to a recurring countersubject set that you'll ever find in this fugue - but they are in the "wrong" key. Most listeners won't perceive this.

Instead of the expected answer however, the inverted form of the subject appears in measure fifty-nine.

After the inverted subject tips off the listener that this is not really the recap, the fifth episode returns to the tonic level over an ascending chromatic bass line (As opposed to the earlier decending chromatic bass lines). The geometry of this episode is also perfectly calculated, and its mechanical effeciency is far beyond the episodes of Bach. Whether you find it as compelling as the episodes Bach wrote is a matter of taste: To me superior logic is more compelling (If not always as "pretty").

This elongated version of the thematic trill into the half cadence leading to the real recap was the last thing I came up with for this fugue. In fact, I had completely finished it so far as I was concerned almost two months before I thought of this section. There is no doubt but that this completes the piece though.

Now, we are back to the canon I wrote to start off the fugue.

At the end of the canon/recap is the real killer: A three voice hyper-stretto. You may have never even heard of a hyper-stretto before. It is the technique of having two different versions of a subject start at exactly the same time. Traditioanlly, this has been done with the rectus and inversus forms of the subject, or with the rectus and augmentationem versions of the subject. Here, I combine both by having the rectus, inversus, and augmentationem forms all starting at the same time.

If you'll notice, the ascending chromatic line in the lead which starts in measure eighty-seven is exactly the same as the modulating bass line from the episode which sarted back in measure sixty-four. There are a lot of relationships like this which I have not pointed out, but you can see them for yourselves.

I wrote this fugue for a doctoral level Invertible Counterpoint and Fugue class at UNT back in 1995. I turned it in five weeks into the semester. Dr. Dworak said it was the best fugue he'd ever heard that was written by a living composer, he gave me an A for the course, and he also gave me the rest of the semester off. This is one of those pieces I'll never forget composing. When I wrote this, I realized I could do anything I wanted with fugue.

Bach's Art of Fugue and Beethoven's Gross Fugue are not safe from me. If I live long enough, I'll do better.

UPDATE: MP3 and PDF files of this fugue are here.

Man, I had a great gig tonight. Bunches of tourists, tons of tips, and one chick who looked exactly like this.


Anonymous Anonymous said...

Hurry up and complete the Art of Fugue! We want a definitive ending!!

5:29 PM  
Blogger Hucbald said...


Davitt Moroney has written what I believe to be the definitive ending for the unfinished fugue, making it a quadruple fugue by using the motto theme and signing off with the BACH theme in the upper voice for the last statement. You can hear it on his excellent two CD set of Art of Fugue. he uses reproduction baroque harpsichords and well-tempered tunings too, and the result is outstanding.



5:40 PM  

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