Saturday, October 01, 2016

Fugal Science: Vol. 1, No. 2 - Three-Part Fugue for String Trio

EDIT: This is part 2 of 8. Here are the links to the entire series:

Index of Fugal Science, Volumes 1 and 2

Well, I've gotten to the critical mass point on this project, so I have another post already. While the first post was about a two-part fugue for solo guitar, this one is in three parts, and it's for string trio. It is also in g-minor, whereas the first one was in a-minor.

Our subject and countersubject are the same, but now we also have a tonal answer, a counter-answer, a second countersubject, and a second counter-answer. Note also that the two-part fugue was in a continuous two-voice texture, and this one is in a continuous three-voice texture. This is not how fugue writing has ever been taught, but it is the simplest way to exploit our elements, as you'll see.

I continue this for the four- and five-voice fugues as well, so if it says five-part, it means five parts for the entire time that all voices can be active.

There is still only the one episode, and it continues to appear in six, five, four, and nine measure variants.

Without further ado, here is the recording, which is just the sound fonts I compose with recorded into Garageband (I still use Garageband if I only have a single stereo track to capture, and no MIDI tracks). It's a CD quality AIFF file, so you'll need to have Quicktime activated in your browser.

Three-Part Fugue for String Trio

I suggest opening the audio in a new tab so you can listen and follow the score.

The subject remains the same, but now we get the tonal answer beginning at measure nine, and it has a counter-answer that is as much like the countersubject as it can possibly be. Though I composed the initial version of this fugue back in 2012, this was the last element that came to me, just within the past few months. A glorious revelation that came to me on the toilet.

When the second subject statement comes at measure eleven, we have the original countersubject now joined by countersubject two, which is an accompaniment voice, as simple as it could be, yet it has enough character to be a subject in its own right.

Then our first episode begins at measure sixteen, and there is a new voice here too, of course. Again, note that all three voices converge on the tonic: ti-do, re-do, and sol-do. This is pretty much 180˚ contra the way three-part counterpoint is traditionally taught - you are supposedly required to get diads or triads when possible - but this method allows for the freest interchangeability of the materials.

This is not a hard part, per se, but after much experimentation, this ended up being objectively the best arrangement, though the alto and soprano could technically be switched out.

The first middle entries that begin at measure eleven are the same soprano and bass as in the guitar version, but now joined by a third accompaniment voice in the alto. Also, the entry order is reversed, with the soprano entering first this time. I really love the effect of this arrangement in three-voices, but not in two or four (Not sure about five-parts yet). It is the only place that this arrangement can exist, as the modulating version near the end has the tonal answer head in it, which cannot appear in the bass.

Note also that the third accompaniment voice always appears in the middle, and this is the case with the four- and five-part fugues as well. This decision saves a lot of headaches, as you can find out by rearranging the elements yourself, if you want.

Episode two is one measure shorter than before, as it was in the solo guitar fugue, and it also modulates to the dominant level, as before.

These dominant entries are also a hard part, considering the objective decision to have the accompaniment voices in the interior of the texture. Otherwise, the soprano and bass are the same as in the fugue for guitar.

You may have noticed a slight change in the lead voice of the first episode from the guitar version. There, the first three sequences were diatonically identical, but now the third sequence's penultimate note leaps down a perfect fifth. This was necessary to allow that voice to work accompanying the subject. What I call the dissonance flow is much ameliorated by the third voice, as you can hear. The modulation to the relative is also even more sublime.

Mozart did much of his writing with three essential voices, and said that the interior voice should allow the soprano to soar, and add profundity to the bass. Look at the trajectory of the accompaniment voice in this relative major stretto: It accomplishes both feats with great aplomb. Just a joyous respite from the minor key heaviness.

The four measure version of the following episode is also more dynamic with three voices, with the modulation to the subdominant nicely enhanced. It gets even better with four and five parts.

Now we've arrived at our false recapitulation/remodulation to the tonic. As I mentioned previously, this is a hard part that can only be arranged in this manner.

Once returned to the tonic, we get the third and final version of the episode on the tonic, which is again extended by the pedal point section. Now, however, we have the subject in the bass, revealing yet another contrapuntal combination, and this time the tail figure is not modified for a modulation. Very gnarly. The half-cadence is also improved by the third voice, and the wisdom of not having the lead voice hand off to the subject in the lead is again proven by having the order - alto, soprano, bass - echoing the exposition. Again, this is the most perfect possible arrangement of the available elements. Much work and experimentation went into arriving at this form.

The third voice improves the hyper-stretto coda as well, with the piquant minor-ninth ameliorated by having the fifth of the harmony - a V7(m9) - in the middle voice. The harmonic logic perfectly justifies the minor-ninth in two voices, but probably only the guitar could make it sound right. The piano is far too strident and harsh for counterpoint.

And so two posts in two days! I have to transpose the four-part fugue for string choir from g-minor to f#-minor, so no post tomorrow; that will take a few days.

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