Fugal Science: Vol. 1, No. 4 - Five-Part Grand Fugue for Orchestra

EDIT: This is part 4 of 8. Here are the links to the entire series:

Index of Fugal Science, Volumes 1 and 2

Today we're going to look at the urtext version of the five-part fugue, both because I haven't finished the orchestration, and because it will be many less pages to deal with at this point. In fact, all of these have been urtext versions, as there are no performance indications, other than for the tempo. After finalizing the arrangements for the two-, three-, and four-part fugues, this one required heavy revisions to fit into the scheme of the treatise. The solution turned out to be having the fifth voice - which logically provides the fifth degree of the key of the moment - in the center with the violas, as they were the first to enter with the subject at the beginning. That is another simplification strategy that made the piece perfectly logical for this collection, but I did lose some nice effects with the earlier arrangement. But, that's the nature of these fugues as you progress from two to five voices: At each stage, something is gained, and something is lost. I will develop this theme more in the subsequent articles, which will become more and more detailed. These posts are little more than overviews.

Here is today's audio, which is, again, just a recording of the sound fonts I compose with. It's a CD quality AIFF file, so you'll need QuickTime activated in your browser.

Five-Part Grand Fugue.

Use a new tab to listen and follow the score.

The exposition begins with the same order it always has, with exception of the two-voice fugue for guitar, which has no tonal answer. Even there, though, the lower voice enters first, so the countersubject - or counter-answer in this case - is first heard in the bass.

Voice entries continue just as they did in the four-part version, with the only difference here being key and tempo.

Now we can see what the fifth voice does: It is just a slightly ornamented pedal point on the fifth degree of the key. Since I devised the subject to alternate between tonic and dominant, this is perfectly logical. However, since I use the bVI and vi chords, the pedal is sometimes the major seventh, or minor seventh, respectively. Note also that I am able to get a complete V7(m9) sonority at the very end of the exposition. This happens to create a simultaneous cross-relation between the f-natural in the viola part with the f-sharp of the first violins. This creates a momentary augmented octave, which is very nice in this context. In the former arrangement, there was an augmented unison at this point later in the piece, which is even cooler, but, alas, it had to go for this piece to fit into the schema of the treatise. Volume 3 will be art fugues on this same subject, so perhaps I'll be able to work it in there.

Previously, the second violin and cello parts were exchanged in the episode, but I had to do some irregular resolutions to make that happen, so this turned out to be the more logical and compelling arrangement. Since the exposition is a big double-canon between the first two subject entries and the two answers, I wanted to make sure I didn't break that inexorable logic until I absolutely had to.

With this arrangement, we get a diminished octave between the f-natural and f-sharp at the end of the episode.

Technically, the soprano and contrabass could be exchanged in the first middle entry stretto/perfect dovetail here, like I did in the three-part version, but the effect is simply less good in more than three parts, so that will remain a unique feature of the string trio fugue.

There's a super-hot dissonance progression during the last two beats of this middle entry, where we get a minor ninth followed by a major seventh between the soprano and tenor, and it's seasoned quite spicily with the diminished octave with the contrabass on the final beat. This is a minor dissonance climax, which leads to an even more gnarly one later. Note also that I use a cambiata figure in the tenor part.

We're then into the second episode, which is as before for the first four measures.

Then the fifth measure modulates us to the dominant, and there's an augmented sixth at the very last second between the bass and contrabass.

In the four-part fugue, we had parallel sixths in the inside voices at this point, but in this opened up version, those are now parallel tenths (Plus an octave).

Sorry for the missing half-note f-sharp in the bass in measure 53, but that's the problem with doing these digital fair copies: transcription errors abound afterwards. I've fixed it since I uploaded these images. Then, the f-natural in the contrabass in 57 is supposed to be an f-sharp, which I've also repaired. Way back in the guitar fugue, that was an f-natural, as we didn't have the ascending voice with f-sharp to worry about.

The third episode then has the episode supporting the subject, which is one of the major revelations of the piece, and it modulates suddenly and smoothly to the relative major at the end, to great effect.

Our relative major middle entries - a canon at two measures of delay/three measures of overlap - sounds magnificent in five voices. There is a complete V7(M9) in first inversion on the last quarter note, which sounds amazing going into the next episode.

This shortest version of the episode modulates from the relative major to the subdominant minor, as before, but I have rearranged the parts - a very wonderful feature of this scientific fugue technique I've developed - to set up the next section, which is the one measure overlap stretto that remodulates us back to the tonic. That will also lead to the main dissonance climax of the piece on the next page.

While the soprano and contrabass are in the same arrangement as previously - and the tenor keeps the fifth degree - I now have the original countersubject 3 in the alto, to get the subject entry over the tied second, which is just way too good not to use (It was like this in the previous two fugues). In fact, the following dissonance climax would not be nearly as effective without it.

So here is the dissonance climax of the piece. The degrees of the dominant harmony, from bottom to top, are, M3, m7, R, R, and m9. It's the minor ninth in the lead, with the root underneath that puts the sizzle in the sonority, but now this is enhanced with a second root in the tenor, which has appeared earlier, and so is tied, making a beautiful effect because of the well wrought context. Nobody from Bach's era would have done this, of course.

Then we get the third and final episode on the tonic, in which the subject proves it is an effective bass under the episode materials, now quite awesome with the subject in the contrabass octave.

Note that the tenor gets some nice licks in near the final half cadence, and that I built this wonderful climax using almost nothing but diatonic material in the interior voices. The subtitle of this volume is, The Diatonic Subject, after all, and the aim is to be as simple and transparent as possible, so students of fugue have elements that are easy to grasp at first. That's why the chromatic lines are used so sparingly.

First things to notice in the five-voice version of the recapitulation canon are that I can't use the raised sixth degree anymore - due to the clash with the natural sixth in the subject - and that the solution I came up with causes parallel perfect fourths alternating with parallel perfect fifths; a clear violation of the laws of contrapuntal motion. However, the parallel movement is not stepwise, but by leap, and the effect is just wonderful, with the final leap in the soprano making the false ending sound awesome. I may or may not keep this, but for now, I've decided to give myself license for the exception.

The final hyper-stretto is unchanged from the four-part fugue - and almost unchanged from what I composed way back in 1993, the triplet figure in the lead being the only modification - with the bass doubled by the contrabass now. In the orchestration, this will be the only tutti section of the piece, with nothing but the string choir all the way until the recap canon, at which point the winds will enter for the first time. Here, the brass and percussion will enter. In the finale for the second volume, the winds will enter from the beginning.

Next step is to do the analysis versions, but first, I'll do the digital fair copies for the second volume and present overviews of them.