Wednesday, September 01, 2010

Imitation Study Number 4 in A Minor

This is an interesting piece. It's a fugue with the answer on the subdominant and in inversion, and the initial statement of the subject has an accompaniment line. This was necessary because the subject begins on the third degree of the mode, which may very well be unique. I've never encountered another subject like this, anyway.

Interestingly - to me - this is actually the very first fugue subject I ever came up with back in 1986 or 1987. I got the idea while studying through Joseph Schillinger's System of Musical Composition. Historically, fugue subjects have begun on the tonic or dominant degrees - or with approach notes to those degrees - and I wondered why not the mediant, since it is a degree of the tonic triad? So, I came up with this wedge shaped theme with the idea of writing a two-part invention for guitar with it. That idea fizzled because I just had no idea how to proceed.

Later, when I was working on my masters degree, I wrote a three-part invention for string trio with the subject, which I really, really like. In that piece, I came up with the chromatic countersubjects and the solution of having the answer on the subdominant degree and in melodic inversion.

So, here we are 23 years later and I've come full circle back to the idea of writing a two-voice solo guitar piece on the subject; only now I have the compositional technique to make it work.

Here's today's MIDI to M4A conversion:

Imitation Study Number 4 in A Minor



Despite the subject's unusual feature of starting on the mediant degree of the minor mode and having a diverging pair of melodic trajectories, it's actually fairly Bachian (Since Bach was my inspiration here). However, you'll notice the G-sharp a the beginning of measure two is followed by a G-natural one beat later: This is strange, and it sets up a tension that I really like a lot. Furthermore, on the last eighth note of measure two, there is a diminished octave - equalling a major seventh in sound - between the C-sharp in the bass and the C-natural in the subject, and the final sixteenth is a diminished seventh (Which equals a major sixth in sound, of course). These bold cross-relations give the piece the dark feel of a lament: Something is just not right with the universe, and so there is quite a bit of expressive sadness to the piece.

This is only reenforced by the true counter-answer in measure three, which is an ascending chromatic line at the beginning, and a descending chromatic line at the end. Pathos. On the last eighth of measure four, we have a diminished fourth (plus an octave) and then a diminished tenth (Which is the inversion of an augmented sixth). This is another highly unusual feature of the exposition.

As I mentioned in the previous post, many times two voice fugues work out better with a thrid statement of the thematic unit, so that two subjects appear and you can reveal the true countersubject: That's the case here. Just as the answer is inverted from the subject, the counter-answer is inverted for the countersubject. IMO, this is very, very cool.



Most of the time I use tail figures for the episodes in my fugues, but in this case the head works better. Since there are losts of wide leaps, this also allows for range adjustments that keep the elements within an executable range on the guitar. I made that adjustment in measure eight, which set up the upcoming middle entries, which are in the relative major.

The major mode version of the subject and answer worked out better starting off on the tonic degree of the triad, and the countersubject and counter-answer therefore ended up diatonic instead of chromatic. this provides a happy sounding contrast to the dark sounding exposition.

The second episode that starts at fourteen required another range adjustment in fifteen, whereas the string trio version allowed the violin to continue into the stratosphere.



The second middle entries are all about displaying the contrapuntal inversions of the previously revealed material. the original orientation of answer and counter-answer are first stated, only in the dominant level minor of E, and then the countersubject over subject appears starting in nineteen.

Episode three at twenty-one takes the piece to the subdominant minor region, where I present the answer over counter-answer orientation. At the end of this, we get an augmented sixth, of course. Both of these inverted orientations sound very dark. Darker than one might expect just judging from an intervallic analysis. I've never really been able to figure out why this is - even the consonances sound dissonant - but I really like the effect (Even if it was a happy - or sad, I guess - accident).



The final page gets us to the concluding stretto section - also the first stretto I ever composed - and there is no episode needed to get here because the subject to the previous answer is back in A minor. Is that cool, or what?

The first 1.5 beat overlap appears in measure twenty-seven, and then the 2.5 beat dovetail starts in twenty-eight. To get everything back in sync vis-a-vis the bar line, I relax that back to 1.5 beats in the first half of thirty, and then just the head appears in the second half, which sets up the conclusion.


Obviously, it's bedtime.

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