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I recently wrote my first canon. Specifically it was a round. My round involved three parts. First began the soprano part. Then two measures later alto, and then two more measures later tenor. But the point is all of them started at the beginning of a fresh measure, not in the middle of one.

When I asked myself "how does one write a fugue?", I said "maybe a good way to introduce fugue themes is to always place them at the beginning of a fresh measure, just like in my round." But I have been studying Bach's fugue BWV 578 and, for several of the theme introductions, they begin halfway (exactly) through the measure.

So I attempted to do this. But when I tried, somehow I couldn't quite get the rhythms right between the already present parts and the newly introduced theme. Specifically, I always end up "playing off" the newly introduced theme rather than continuing them as distinct voices.

Does anyone have any suggestions for how to introduce fugue themes mid measure?

  • en.wikipedia.org/wiki/Stretto – Dom Jan 3 '15 at 1:28
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    Stretto is certainly one very common way that you can address the title question in fugues, but the more detailed question uses the example of the "Little Fugue" by Bach, which doesn't involve stretti at all. – Caleb Hines Jan 3 '15 at 1:56
  • @CalebHines if not stretto, does it use a different technique? Or is there no name for what Bach does in BWV 578? – Stan Shunpike Jan 3 '15 at 2:09
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In the example that you posted (the "Little Fugue"), what you have is the rhythm getting a half-bar "out of phase" with itself. This is something you actually see quite frequently in classical music (or at least Baroque music) that's written in common meter (4/4). It's by no means unique to fugues. I'm not sure I've ever heard anyone directly discuss the technique, but I've seen it quite often. If there's a more specific name, I'd love to know what it's called.

Essentially, what happens is that, in common meter, beats one and three are heavily accented, while beats two and four are lightly accented. In theory, one is supposed to be more heavily accented than three, but what happens in practice, at least in some pieces, is that they get roughly equally accented. If you wanted to, you could analyze the piece in 2/4 instead of 4/4. I think of these two-beat units as "half-bars" (I'm not sure this is a proper music theory term). In order to strengthen this effect, you need to use a melodic figure that only lasts a half bar, and you need to change harmony at least that frequently.

What happens then, is that you have a phrase of music that takes up an odd number of half-bars, and from that point on, all the music becomes out of sync with the barlines. In your example, (using the youtube video that I edited into your question) this occurs after the first two voices have entered. There's a 3 half-bar sequence, ending with the dominant D chord in the first half of the measure (indicated by the F♯ and D in the alto voice), which sets up nicely for the return of the tonic (Gm) on beat 3, where the enters.

Nevertheless, with fugues, voices often overlap, so while the alto voice is cadencing in the middle of that bar (where the tenor voice is entering), the soprano voice doesn't reach its cadence until half a bar later (at the next bar line), at which point the alto voice is re-entering.


EDIT: To demonstrate that this "out of sync with the barlines" rhythm is not a technique unique to fugues or to Bach, I just searched youtube for Vivaldi violin concerti with scores, and the first result I came across (an A minor violin concerto) has a great example. Fortunately, the bars are numbered so I can refer to them (note, the video only contains the violin solo part). The main motive for this piece is a repeating series of four (actually five) eighth-notes, which you hear in the first half of the opening measure (after the pick-up beat). However, in the third through sixth measures, this motive has already been shifted to the second half of the measure (fun exercise: Try chopping out the second half of the first bar, and see what you think).

But in case that's not enough for you, when the main theme is restated later, in measure 35, it enters in the middle of the measure, so the entire thing is shifted.

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Dom's article on stretto applies in many cases, but not this one. At the start of BWV 578, Bach is using a real (not tonal) answer. That means that the answer is an exact transposition of the subject a fifth up. Consequently he is obliged to write a small bridge episode of 1-1/2 bars to prepare for the entry of the subject on the tonic in the tenor.

It comes in on the half measure partly because the episode has been kept short and sweet (this kind of episode is not unusual in the middle of an exposition), and partly because Baroque rhythm doesn't really differentiate between 1st and 3rd beats in quite the same way as music in, for instance, the High Classical period would. The 4-bar phrase was by no means set in stone. Notice, for instance, that the subject of BWV 578 is 5 bars long. Charles Rosen's The Classical Style: Haydn, Mozart, Beethoven goes into some detail about what changed in the transition between High Baroque and High Classical music - well worth reading even just for its insights into Baroque music.

When writing a fugue yourself, go with points of entry that work for you. Use Bach as a model to the extent you can while you're learning, but bear in mind that your sense of rhythm is probably different: our vernacular has had 4-bar phrases and a hierarchy of beats within those phrases for well nigh two and a half centuries now.

  • Hmm. Thanks for posting. I will check on that book too. Your analysis is real nice. I hope I can eventually dissect his pieces as well as that. Actually, surprisingly most of my fugue themes have had an odd number of measures. I've written five or six themes. The one I'm working on most is 5 bars long. I am what you might call an instinctive imitator, so I tend to find myself mimicking unconsciously whoever I am listening too. prior to writing fugue themes, I had never consistently written themes with odd number of measures. Perhaps I picked this piece unintentionally because it is similar. – Stan Shunpike Jan 4 '15 at 6:40
  • I revisited Shostakovich's fugues and I can see your point. One could hardly say fugues died out given how masterfully his are. I gather they were based on Bach or something, but to me they sound nothing like his. – Stan Shunpike Jan 4 '15 at 6:41
  • Well, Shostakovich was surely not an 18th-century Thuringian German, eh? Neither was Hindemith, for that matter. Fugue is mainly a procedure, and, to a great extent, you need to adapt it to your needs. Bach's harmony was driven by harmonic sequence, and you can see that informing a great number of his episodes. I found that, for instance, my own harmonic motion works through rhythmic preparation (in some ways similar to High Classical music), so, if I tried using that sort of episode to anywhere near the same extent, the music would end up treading water. – user16935 Jan 4 '15 at 8:12

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