The Fifth Element
I enjoy it when a piece takes on a life of its own. It's genuine fun when that happens. Again, just after the previous post - in which the four elements were subject, countersubject, episode, and coda - I came up with the fifth element I was searching for, which ended up taking the form of a six measure interlude.
Fugal terminology can be fuzzy with respect to definitions, and at no place is this more evident than when trying to describe the material that comes between thematic statements. Here, I find it useful to have two broad - and yes, overlapping - categories: Episodes and Interludes. A typical episode will be short - one to four measures, usually - while an interlude can be quite long, so duration has a lot to do with the definition. Also, typical episodes will be based on tight, sequential material that is extracted from, or that is closely related to, the subject and/or countersubject, while an interlude can be composed of highly contrasting or even completely unrelated material. Obviously, there is usually a deft transition into these sections that makes them work, and they virtually always appear when they have to. One of the nice things about these little thumbnail fugues - I may end up calling them that - in the two-part invention format is that they provide clear examples for these definitions.
Here is the new AAC file: Imitation Study Number 3
Only a format change here: There are now four systems on this page. The elements remain the same: Subject on the top system, subject and countersubject on the second, a four measure episode on the third, and then the contrapuntal inversion of the subject and countersubject at the bottom.
Note how the episode springs organically out of the augmented version of the subject's head, and it is based on a sequential statement of a rising chromatic line. Since there are two complete descending chromatic tetrachords in the subject, this is an effective contrast. Also, the eighth-triplets are obviously from the tail of the subject. Very tight.
The contrapuntally inverted second episode statement on the top system is also unchanged. Now, at this point - the end of measure twenty-three - we have heard ALL of the elements so far presented in both of their orientations, or inversions, and so it is time for a new feature to appear.
As is so often the case, the most obvious solution worked out the best: Since the sequential episode is based on a partial chromatic tetrachord that rises, I made the interlude over a full descending chromatic tetrachord. You can see where the distinction between an episode and an interlude can be unclear: Both the episode and interlude are based on chromatic bass lines, and they are both sequential - and in this case the sequences even share the same rhythm - with the main distinction being one of greater length for the interlude.
I would call the listener's attention to another factor, though, and that is one of attitude: The episode sounds like a brief respite from the thematic material, and it seems anxious to get back to that material, while the interlude seems to be taking its sweet time with no particular urgency for a new thematic statement until the very end.
As for the structure of the interlude itself, I was able to get a lot of nice counterpoint into it. If we isolate the eighth-triplets and just look at them, the end of twenty-four into twenty-five reads, major sixth, minor seventh, octave, minor tenth - very conservative and conventional. The end of twenty-five into twenty-six reads, diminished fifth, minor sixth, diminished seventh, major sixth (plus octaves), which is much more interesting. Then, twenty-six into twenty-seven is, octave, major ninth, major tenth, minor tenth, which is conservative again. Twenty-seven into twenty-eight cements the alternating pattern with a major ninth, major tenth, perfect eleventh into another major tenth, which is quite delicious, and then I've set things up for the climactic penultimate measure. There, from twenty-eight into twenty nine, the counterpoint reads augmented fourth, augmented fifth, and augmented sixth - plus octaves - into the double octave on the dominant degree. This is just a killer little climax, and in a later version of this fugue I'll use this interlude to modulate to the dominant with this device. Oh, and sorry I had to cram all six measures onto one system, but it's a formatting issue: Didn't want to get into a fourth page for this post.
From thirty on then, things are unchanged from the previous version: This is the perfectly dovetailing stretto section with two measures of overlap (The only perfect dovetails I've been able to get to work out perviously had just a single measure of overlap).
The top system here is the sequential episode back in its original orientation, then the canonic stretto recapitulation followed by the concluding coda, which is the augmented subject head with modified tail over an ostinato, which is the full tail of the subject.
This piece is now complete in the octave fugue/two-part invention format. Next I'll turn this into a two-voice fugue with the answer at the fifth/twelfth, which will require at least a modulating version of the interlude, and probably a pedal section as well. I'll have to use a real answer with this subject because of all of the stepwise motion in the head and the chromaticism, but I have discovered a very humorous major key version of it, so that could end up in there too. Time will tell the tale.
I do think I'll snag that DVD next time I'm at Amazon. It's an old favorite I just never got around to picking up.