Fugal Science: Vol. 1, No. 3 - Four-Part Fugue for String Choir

EDIT: This is part 3 of 8. Here are the links to the entire series:

Index of Fugal Science, Volumes 1 and 2

Allright, I got the piece transposed. I find it wise to make what I call, "digital fair copies" after the development versions are done, as with all the cutting, copying, pasting, and other modifications, errors can accumulate to the point that the files become corrupted, and will crash the program. I was up to v3.4 with a couple of these, so it was time.

The point of this first volume is to reduce fugue to its irreducible essence, which is the two-part fugue for guitar, and build it up to the pluperfect arrangement, which is the five-part grand fugue. If I had had this information available to me when I first got interested in fugue, my progress would have been greatly accelerated. So I hope it is of benefit to anyone who undertakes this awesome journey of discovery and triumph.

Whereas in the two- and three-part fugues all voices resolved to the tonic at the seams between sections - ti-do, re-do, and sol-do - here in four voices we can now use fa-me (or fa-mi) to get a dyad at the resolution points. To keep this from increasing the possibilities exponentially, I will stick to the simplifying stratagem of having the thematic voices in the soprano and bass, while the accompanying voices will remain in the interior, with the exceptions of the exposition and recapitulation. This means I only have to decide which interior voice is the alto, and which is the tenor.

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

Four-Part Fugue for String Choir

I suggest you open the audio in a new tab, so you can follow the score while you listen.

We're now in the key of f#-minor, and the tempo has broadened to 72 BPM, down from 90 BPM for the guitar version, and 81 BPM for the string trio. I'll go back up to 81 BPM for the Grand Fugue so that the tempi loop into 90 BPM for the guitar version of Volume 2.

Other than the key, tempo, and instrumentation, the first three entries of the exposition are just like the version for string trio.

It is not until measure sixteen that we get our new elements, which are counter-answers two and three. No diad here - at least not including the mediant degree - due to the fresh thematic entry, so I use the interior voices to dramatically build up to that revelation. As you can see, the alto leaps up a fifth, and the tenor leaps up a fourth to tee this up. When your texture is primarily stepwise, leaps are dramatic. Likewise, when your texture is mostly leaps, the stepwise motions become dramatic.

At the seam into the first episode, then, we get our first dyad which includes the third degree. The arrangement of voices is quite plastic here, with several possibilities, so I auditioned them, of course. I arrived at this configuration by realizing that the bass is a hard part, the tenor adds profundity to it, the alto interacts with the tenor to get the major second in measure twenty-six, and the slow, soaring soprano is the only remaining choice here.

Note that the bass-tenor have a minor tenth - e#-g - moving into a major ninth - e-f# - in parallel motion, and that it is resolved first back to a minor tenth, and finally a major tenth. This is very beautiful.

For the first middle entries, we have the stretto of one measure of overlap that is also a perfect dovetail. But this time, I go back to the arrangement that I used for the guitar version, which has the subject entering first in the bass. While I liked the other arrangement in three voices, this works better in four parts because of the interaction between the tenor's e# and the bass. The first time the e# appears in measure thirty, it is over the g#-f# of the subject in the bass, giving a nice, dissonant effect for the introduction of the subject in the soprano. While the second time in measure thirty-four, the e# makes a consonant major tenth with the c# in the bass, which sets up the final resolution into the second episode better.

The second episode has the same arrangement as the first, but is a measure shorter due to the modulation to the dominant, as in the previous two versions, but the third voice makes possible the dramatic octave leap up of measure forty. This produces a particularly excellent effect.

Now the dyadic resolution into the dominant region is much more dramatic with the subject so high up in the sopranino register, and that note a in measure forty-two is also the highest note in the piece. We first heard it as the final answer entry in the exposition, and will hear it a third and final time when I next combine the subject with the episode. Note that the interior voices are in parallel sixths throughout this section, until they finally part company in measure forty-seven. This has a nice, suspenseful effect.

Here we have the subject on the dominant level combined with three of the voices of the episode, and you can now see why the soaring voice was there before: The subject replaces it, and we keep the rest of the voices in the previous arrangement. The dominant voice's tyrannical attempt to take over the piece is thwarted by the sudden and almost magical modulation to the relative major, which is enhanced again with the new, fourth voice.

Our relative major middle entries are in the same arrangement that they've always been - with the addition of a fourth voice now - because this is simply the best possible arrangement of the elements.

The fourth part adds greatly to the sonorities in this relative major stretto, as it does to the following shortest four-measure version of the episode that modulates us to the subdominant level.

So, the modulation scheme is, i, v, bIII, iv, i, which is fairly common for a fugue. This allows for the aspirations of the dominant level answers to be fulfilled with their own time in the sun on the dominant level, and then they're brought back down through the relative major and subdominant levels, and resolved back to the tonic minor with the recap canon.

The subdominant entry/remodulation to tonic is a hard part, as I've mentioned before, and the entry of the tonic is over a tied major second, which is super-excellent, and the reason I have the interior voices as I do; best possible arrangement. Note that, in measure seventy, we have a V7(m9) with the minor ninth between the soprano and alto. This is a dissonance climax, right at the point of the return to the tonic. One of the many things I learned from The Schillinger System is that every musical effect is a potential resource. All one has to do is employ the effects in a logical context as tactical devices in an overall stratagem for them to be effective.

Under the final episode we can now reveal that the subject works as the bass for this section. This is a marvelous level of integration of the elements, and even though this fugue is longer than the 1993/94 original, it is much less prolix due to the greatly reduced number of elements. Back then I was trying to cop Bach's late compositional style. Today I have my own style that is simpler, clearer, and more mechanically efficient (From an objectivist viewpoint). As a side note, my upcoming volume three of this series will be on this same subject, but with a stretto exposition and a freer number of elements.

The pedal point section is richer now in four parts, with the half cadence greatly enhanced.

In the original fugue, this recap canon had the bass entering last, with a A, T, S, B arrangement, but here the order of entry is as in the exposition. So both of those dominant level answers, and the three dominant key subjects - five thematic statements in all - are now resolved to the tonic. Note again that the canon is lengthened to six measures by having the trill figure appended. This doesn't work in the five-part version of the canon, but I came up with something even better there.

This order of entry produces a perfect cadence into the dual suspension, like it was for the guitar, whereas it was imperfect in the original and for the string trio.

And now, finally, the full hyper-stretto is revealed, in which three parts have thematic statements starting simultaneously: Rectus for the soprano, inversus for the tenor, and augmentationem for the bass. The alto has the lone free voice. So far as I'm aware, no other composer in all of music history has ever managed to pull this off. And far from sounding dry or academic, it is magnificent, containing many dramatic sonorities that add up to an overwhelming effect. This section is unchanged from when I first discovered it, all the way back in 1993.

We also get a vastly improved final series of cadences. Gone are the alternate trill figures in the lead from the guitar and trio versions. Instead we get a V(4/2)/IV into measure 103, and a V7(d5/m9)/V (Without root) in second inversion (The sonority the ancient theorists called a German Augmented Sixth, but which is clearly just an altered dominant function sonority with the minor ninth replacing the root) in 103, and then the Picardy Third at the end, which echoes the V/IV! I chose to use the so-called German chord because the original piece was a tribute to J.S. Bach, of course.

Now I'm ready to tackle the five-part grand fugue for orchestra. This may take a while, as I have to verify that the elements are deployed properly, and also the minor matter of orchestrating it.