Today we have yet another Imitation Study - as J.M. pointed out in comments, I should write real studies instead of just imitation studies (lol) - which are what Bach called two-part inventions, and this is the fourth in the series. This is also one of my all-time favorite fugue subjects, as it is a twelve-tone row, albeit one that is easily interpretable as tonal. I came up with this for a graduate level Twentieth Century Counterpoint class when I was a doctoral candidate at UNT, and it became the final project for that class, which was a wind trio. You can see and hear that piece here.
To get this subject onto the guitar in two-part form has been a serious challenge and an amazing learning experience. I first tried it out as a fugue with an answer at the fifth/twelfth, but that lead me to noting but frustration. Then, I did complete a previous octave-answer version back in 2010, but it ended up in B minor, and the material was all drawn from the wind trio, so it really wasn't a very good guitar piece.
There turned out to be three missing elements: I needed a constant quarter-note countersubject to fit into my spartan, objectivist guitar fugue style, I needed an interlude, and I really needed the piece to be in A minor instead of B minor. You'll see why as we go through the piece.
Once I got the interlude, the new countersubject happened almost immediately, and in a single session, the piece was 90% done, with just a few minor tweaks here and there left to do. After struggling with this for years, it was so easy to write that it was almost anticlimactic.
Here is the AAC audio file then: Imitation Study Number 4
This also happens to be only the second fugue subject I've written in 3/4 time, but since you need twelve attacks to get the twelve pitch classes presented, it was a natural thing. The opening interval is also a tritone, which you would never find in a traditional subject.
The breakthrough constant-quarter countersubject is in the bass of the second system, and it outlines the harmonies that the subject implies: i, V/V, V, V/IV, IV, iv, i(6/4), iv, IV, v, V. The second note of measures one and two imply the root, and the final notes imply the seventh, so I got the chromatic notes into the head with secondary dominants. The final measure - the tail - is a chromaticized IV, V, and I was able to get a diminished triad under that in the countersubject.
It should be obvious that a subject that is serial - super serial! - would require chromatic episodes too, and so that's what I created there at the bottom: Both augmented sixths and diminished tenths are in there, but it doesn't modulate.
The first middle entry has a different countersubject over the subject, and it allows the subject to enter under a tied fourth (A re-attacked fourth in this case), which is the traditional slick way to do it. Since I didn't compose this subject as a canon, as I did with the previous three, I don't have a bunch of stretti to work through, so varied accompaniment is the ticket.
The second episode starting in sixteen is a modulating version of the first one, and that takes us to the dominant for another statement with the original countersubject. The third episode needs to be different, of course, and it returns us to the tonic for the next statement.
For the third middle entry, there is a fully developed version of the second countersubject in constant eighth notes over the subject, and then the interlude appears. It is so much easier for me to come up with these homophonic interludes that I usually avoid them until I can use all contrapuntal material for the sections between thematic statements, but this piece really, really called out for a relaxing chordal section. In later versions of these studies - versions that are actual fugues with answers at the fifth/twelfth - I'll introduce some homophonic sections into the previous three as well.
At thirty-six we finally get the contrapuntally inverted version of the original combination, and that leads back to the exact same episode that modulated us to the dominant previously. Obviously, this subject does not yield a major key version, so the relative is out of the question.
One stretto does work, and it's a doozy: One measure of delay/three measures of overlap, and at the twelfth above or eleventh below. Because the subject is completely chromatic, this sounds fantastical in the sense that it is perfectly clear counterpoint, but very, very outside of the diatonic system: Two tone-rows a fifth apart in stretto. Pretty bad ass, IMO, and it sounds awesome.
The lower subject does something else verboten in fugues, and that is it tonicizes the, "dominant of the dominant" that fugue books warn you against. In this case, that's a B minor statement in an A minor fugue. It works fabulously well though, and for a tone-row subject with the opening interval of a tritone, why not?
In the lead voice we also get two consecutive statements of the subject (!) on the dominant, which ameliorates the distant region just touched upon, and it also sets up the return to the tonic. Note how a sequence of the tail makes a nice new countersubject, and hints strongly that, "the end is near."
In forty-nine is the figure I had to transpose up an octave to keep the piece in A minor. There is no doubt but that it sounds better connected to the previous sequences - of which it is an inversion (!) - but the piece won't work in B minor now because of the homophonic interlude. That simple move was actually the toughest nut to crack for this piece to fit on the guitar properly.
At fifty-one is the final episode - filled to the brim with augmented sixths - and then the final statement, which has yet more new material as a countersubject.
I have at least four more subjects I could turn into studies like this, so we'll see where things go from here.
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