Fugal Science, Volume 2: Introduction, Part 1

I first used the term Fugal Science here on MMM to describe my method of doing the Sergi Taneiev Convertible Counterpoint treatment, but for the free style, and mechanically instead of using his formulas. The process of elimination, essentially. Once I got the idea for this series - a summation of the possibilities of the two five-measure subjects I've devised that make five-part canons at the octave - I decided Fugal Science would be the perfect title for it.

Bach, in Musical Offering and Art of Fugue, wrote many fugues, canons, and ricercares on the two subjects he worked with therein, but I've decided on a much more modest format of two, three, four, and five-voice fugues on the two subjects I've created. Whereas Bach's unlimited fecundity lead to massive summations of impenetrable depth, I'm only interested in what, to my lights, are the best possible arrangements in two, three, four, and five parts. I also hope that this format will be more accessible to others who wish to learn this most noble of all arts, which has been tragically neglected for the past century (Taneiev died in June, 1915, just over a hundred years ago, and he was the end of it). I analyzed Contrapunctus 1 of Art of Fugue for months - every intervallic relationship between every voice pair down to the resolution of a sixteenth note - to make the final push to understanding Bach's fugal style, so I know this will be much simpler for disciples to grasp.

The initial inspiration for the two-voice fugues, both of which are completed, was a project to get all of my fugue subjects in two-part arrangements for solo guitar, so those are the versions I will present. The three, four, and five-voice fugues will be for string trio, string quartet, and string choir or symphony orchestra, in the case of the five-voice versions. It is the orchestral versions I'll present here. Now that I have Logic Pro X on my Mac Pro, I'm able to simultaneously play the Encore file and record it, so for the first time you'll be able to hear exactly what I do when I compose these pieces, even though the timbres are just soundfonts. The MIDI to MP3 program introduced a lot of vagueness and artifacts, so this will be a significant improvement. I am starting with Volume 2 of the series because the two and five-part versions are completed - so there's a fantastic juxtaposition to present here - and because this is my later, more mechanically efficient style, whereas the earlier subject is more Bachian, and therefore more ambitious and busy. I like to describe my current style as ascetic because of the minimalist approach, and acerbic because of how I treat dissonances.

On with the show.

Here is the AIFF file of the audio for the two-part fugue for solo guitar.

For some reason, there is a lot of empty time at the end, and I thought I'd scrubbed the tail, but oh well. You'll need to have QuickTime activated in your browser, since it's a CD-quality AIFF file, and I suggest opening another tab so you can listen and follow the score at the same time.

The guitar version has to be in A minor because of range and fingering considerations - it literally won't work for guitar in any other key - and the finale for orchestra is also in A minor (Figuring on basses that stop at E, instead of going down to C), so this works out perfectly. The string trio and string quartet versions will be in the deep, dark key of F minor.

The subject enters in the bass, and the answer is at the octave at measure six. Bach called these two-part inventions, but for two-voice fugues, the most natural answer is at the octave. Answers at the fifth beg for another subject statement in the tonic, so this is really the most normative arrangement for a two-voice fugue.

Note that, starting in the bass at measure eight, the countersubject is the head of the subject in augmentation. This will lead to the dovetails - I call them Musical Escher Morphs - in the three, four, and five-voice versions.

At measure eleven is the episode, and I mean, the episode, as there is only this one in it's two contrapuntal inversions. On the bottom system is the contrapuntal inversion of the subject/countersubject combination presented in the exposition.

That leads naturally and organically - inevitably, even - to the contrapuntal inversion of the episode at measure twenty. At the end of the second statement of the episode, we get the interlude, which is also, the interlude, for this entire series of fugues. My definition for episodes are that they are one to four measures in length, and I define interludes as five measures or longer. This, combined with the interlude appearing after every two episodes, is a feature of the very conservative and minimalist architectural style I've developed over the years. It makes the drama easier to follow than Bach's style, which was driven by his monumental improvisatory abilities. A beautiful thing, to be sure, but I strive for clarity and efficiency. This is driven by the fact that I'm a guitarist, and so I'm used to dealing with a much more restrictive idiom than the keyboard (This piece is impressive on the guitar, but would be trivial for keyboard).

At thirty the strettos start, and the first one is at three measures of delay/two measures of overlap. A single measure overlap is, of course, possible, but it does not create the perfect dovetail you see here: The first three measures of the countersubject are smoothly interrupted by the stretto statement, and the leading subject in the bass goes seamlessly into the augmented version of the subject's head. I love the purity of these kinds of musical structures. They also sound quite compelling and beautiful.

And so, that perfect dovetail stretto leads inexorably to the episode again, in the original contrapuntal arrangement. Immediately following, we get the second and final stretto - for this two-part version - at one measure of delay/four measures of overlap. That allows the leading voice to go into the augmented form of the head, which is allowed to run its course this time, with the modified tail that will become part of the Musical Escher Morphs of the following fugues, and the final ricercare. Note how the tail of the subject is used as an ostinato, which is a beautiful way to wind this little fifty-four measure fugue down. The day I noticed that would work was a good one! Note, finally, that the piece never modulates. I love that! Even the final ricercare only alternates between tonic and dominant, whereas the fugues on the earlier five-measure subject visit all of the allowable keys for a fugue (Tonic, relative, and those a sharp or flat away).

Next post will be the five-voice Ricercare for Orchestra, but it's a twenty-nine page score (!), so it will be a while before I get to it.