I have fallen in love with this fugue. It's awesome!
And though it might seem easy, it's a bitch to play (as I'm sure Chris could attest to), especially if you care at all about emphasizing the proper bits, and using the proper ornaments. Gould plays some ornaments that aren't on this score, but I don't have Urtext so I don't know if they're originally marked ornaments, traditional ornaments, or if he just made them up - but the turns he uses on the downbeats of mms. 18 and 41, in the soprano, are perfect - (he inserts a sixteenth-note triplet for the duration of the first eighth note - for example, in measure 18, (A-G-F#)-G, with the G being played on the upbeat of beat one - which causes a sort of continuation of the countersubject theme that precedes it). I might be wrong, but I don't think that "tr" for "trill" is a baroque notation, but Gould plays those trills (found in the second quarter note at the end of the subject) less measured than other ornaments, and he uses this non-measured trill rather than the turns marked on this score in the soprano in mms. 9-11 - specifically, he plays all of them beginning
on the trilled note, and he ends all of them with a downward scoop. All of this works well in my ears for this piece.
I apologize if it's difficult to tell the difference between the red and orange - red is for subject fragments, orange for inverted fragments. The key is at the bottom of page one - as you can see, this fugue displays some awesome motivic unity:
For measure numbers, every 5th measure is numbered underneath the lower staff.
Basic fugue rules for those who don't know: the subject is introduced in one voice, and then is answered by the next entering voice in the dominant, which is followed by the next voice entry in the tonic again, and so on until every voice has been introduced. This fugue has three voices, so the exposition comes to an end technically with the last note of the subject with which the 3rd voice enters (downbeat of measure 8 ). If the answer in the dominant has been transposed exactly from the original, then it is said to be a "real" answer. If it has been altered in any way, it is said to be "tonal". This fugue has a real answer in the dominant, which means that it's not "truly" dominant, because it is minor (the dominant key is always supposed to be major - Bach obliges this need for a true dominant in measure 5, though he doesn't give us the root of the chord until the very last instant before the return to tonic on the downbeat of measure 6).
There is not always a countersubject in a fugue, and the countersubject is often not as independent as the subject (this one achieves independence in the sequential passages and in the cadential passages). A note on the subject material: everything in this fugue is constructed from subject or countersubject material, and one important figuration of the countersubject is blatantly borrowed from the subject itself. Therefore, there is a large amount of fluidity between the subject and the countersubject, and between the countersubject and the red subject fragments. The groups of 4 16ths in the countersubject that are marked with brown in addition to yellow are the bits that are blatantly borrowed from the subject. Measures 4-5 in the soprano are a good example of how fluidly that particular motive can flow into a bona fide subject fragment. Measures 11-12 in the bass exhibit the same technique, and Measures 32-33 in the soprano. So, Bach is working with a very small pool of motivic material, yet he manages to use these small ideas to create unique moment after unique moment throughout. All three of those I just mentioned are major pivotal moments for the harmony of the piece, and all three introduce a complete subject statement (non-inverted).
I have thought about moving the modulations. Is A minor established at measure 13? It still seems to be acting as a dominant there in some ways. Measure 17? Should the return to D minor be marked measure 25? There's a nice cadence there, but an immediate return to focusing on the dominant. Measure 28? That immediately leads into sequential material. Measure 34?
The confusion comes from the fact that this fugue manipulates modal shift throughout. The pinnacle of this technique is used in measures 17-20 in the dominant, which were so perfect that Bach transposed them exactly for measures 39-42 in the tonic.
Anyway, the subject enters in the bass in m.17, and the alto answers in stretto at the octave in m. 18. The entry of the bass begins as a real subject (meaning transposed exactly from the original subject), in A minor, but in the second measure, the bass switches to C# on the downbeat, which is the
major third of the A chord, and when the alto enters, it uses C# also. Meanwhile, the bass still uses the minor sixth, and the harmonic action remains concentrated on minor and diminished triads. Then, in measure 19, with the same 16th configuration that the bass used to switch to C# in the previous measure, the alto then uses to switch back to C natural. Though there is a clear cadence on A minor on the downbeat of measure 21, immediately the bass again begins the modal variation of the subject with the major third.
Also, there is a sense of retrograde in this fugue, though no strict retrograde technique was used that I am aware of (it is rather more difficult to detect than inversion, because it's counterintuitive to imagine music being played backwards, while inversions are rather more familiar, but I'm pretty sure that there is no strict retrograde technique used in this fugue).
The form is a sort of rounded binary with no repeats. The A section ends on the dominant (minor...sort of) and the B section ends back in tonic. The A section only has one inverted subject statement and two fragments of an inverted subject (one on either side of the complete inverted statement). The B section only has one real statement of the subject (in fact, this is the only perfectly real subject statement outside the exposition), and this is placed in stretto with two completed inverted subjects.
But the feeling of retrograde comes from this: just as soon as A minor is fully established in measure 21, the subject using the major third returns in the bass, and an inverted subject enters in stretto in measure 22 in the soprano, and when the modal subject in the bass completes, the bass continues with another inverted subject that enters in stretto with the second half of the inverted subject in the soprano, and this leads us back to D minor (sort of), which Bach had abandoned only shortly before, barely having established A minor. Also, the leading inverted subjects in the two It all gives the feeling of walking backwards over ground already covered.
Finally, there are some other unique bits I'd like to point out - I could go on forever about this fugue, but I'll try to limit it to these last few things:
The exact overlap of the stretto subjects is consistent throughout, and it creates an area of a measure where the first half of the subject accompanies the second half. This only happens in non-inverted fragments one in the entire piece, in measure 33. But measure 33 is a mirror in some major ways of measure 12. Both created a diminished harmony using a sustained tone against a subject fragment, while the other half of the subject fragment is played in the third voice, but invertible counterpoint is used here, so the eighth note fragment in measure 12 is inverted to achieve the same inward motion of the lines. Both measure 12 in the A section and measure 33 in the B section are followed by a modal statement of the subject, in the dominant for the A section, and in the tonic for the B section. Both of these modal subject statements are accompanied by the original countersubject. Both statements of the original countersubject motive are followed immediately by a subject fragment that leads into similar sequential passages. Oh, and both measures 12 and 33 are preceded by similar sequential passages, again using invertible counterpoint.
That's all for now - I had a huge written analysis written up but I ditched it and only touched on the more salient points.
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All I know is that it only vaguely resembles Bach in small places...
