Friday, October 21, 2016

Fugal Science: Vol. 2, No. 1 - Two-Part Fugue for Solo Guitar

EDIT: This is part 5 of 8. Here are the links to the entire series:

Index of Fugal Science, Volumes 1 and 2

Whereas the first volume had a diatonic subject that took a tonal answer, and could appear in either the major or minor mode, this second volume has a chromatic subject that requires a real answer, and it only works in minor. Both volume's subjects are five measures in length, and make five-part canons at the octave and one measure of delay, so that in the fifth measure all five measures of the subjects are heard simultaneously, but this one lends itself to some truly astonishing contrapuntal devices.

Since this subject is more restrictive, the two-part fugue here does not need to be very long to get everything said that can be said in two voices: a mere fifty-four measures. Also, a wide ranging modulation scheme is neither required nor desirable here, so tonic and dominant are the only regions used in all four of the fugues. There is not, however, any way to combine this subject with an all-purpose episode, as in volume one, so here I required a third element: an interlude. When both an episode and an interlude are present, the difference is a matter of length as much as character; our episode here is four measures, while the interlude is six. The episode is built around a rising chromatic line, while the interlude's device is a descending chromatic line. After every two appearances of the episode, an interlude is required to define the form and avoid monotony. This fugue is so short, the interlude only appears once.

Finally, this volume has fully evolved artistic fugues, not greatly simplified ones like in volume one, though the style is very elemental still. While volume three will be art fugues on the diatonic subject, no fourth volume will be required on this subject: these are the art fugues.

Here is the recording for today's fugue: Two-Voice Fugue for Solo Guitar

It's an AIFF file, so you'll need to have QuickTime activated, and another tab will allow you to listen and follow the score.

As for the traits of the subject, it is five measures of 4/4 time, it has 21 attacks, the range is a minor ninth, and it contains eleven of the twelve pitch classes. The missing note is the minor second, or Phrygian, degree.

Note that the countersubject has, after the first two measures, the head of the subject in augmentation as the accompaniment. This is massively portentous vis-à-vis the implications for the rest of this volume.

Our episode appears at measure eleven, and it has the chromatic line in the bass. At fifteen, we get a counter-exposition with the subject and countersubject inverted...

... which leads to the inverted form of the episode. When there aren't a lot of possibilities, as here in this two-voice fugue, presenting a counter-exposition in inversion is a very common solution. Getting an inverted episode is less common, however.

It does lead perfectly to our six-measure interlude, however, which is why the exposition has the entering voice in the bass.

The first middle entries at thirty present a perfect dovetail stretto with three measures of delay, and two measures of overlap. Though a single measure of overlap is possible, it had no features to recommend it in this context.

Now it is time for the episode again, and this time it returns in its original configuration - with the chromatic line in the bass - and that leads to the only logical presentation left, which is the recapitulation canonic stretto at a single measure of delay, and four measures of overlap. Here - and in the rest of the fugues - the top voice enters first, as that is necessary to get the ostinato in the bass.

So there you have it. A super-tight fifty-four measures of perfection.

I already have the urtext for the three-part fugue for string trio done, so that should be ready in a couple of days. It is exactly twice as long as this little gem, at 108 measures.


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