The Art of Fugue

I speak for the whole of the music community when I say that fugues are daunting things. They feature multiple melodic lines, take a lot of time to perfect, and, let’s be honest, they’re really confusing.

Fortunately, I have some good news. There is a secret to learning (and understanding!) fugues. That secret is structure and analysis. If you know the structure of a fugue and how to analyze it, it will be much easier to play.

Today, I want to discuss the structure of a fugue and then I’m going to delve into an actual fugue that I’m working on at the moment. It serves as a healthy analysis project for me and an edifying post for you. I’ll try to make it as clear as possible. Even if analysis isn’t your thing, I hope you’ll derive some pleasure from the beautiful color coding I did.

Okay, let’s just dig into it, shall we?


The Structure of a Fugue

Fugues differ from typical piano pieces in several ways. Firstly, fugues are comprised of what we call counterpoint. That is, multiple voices, each with an independent melody, working together to create a rich texture. That texture is called polyphony (“many voices”). In fugues, you find a minimum of two voices and up to six. I’d say your average fugue has three to four voices – the fugue we’ll be discussing today has only three, which is relatively manageable.

Fugues tend to be extremely compact. And by “compact”, I don’t mean short in length, I mean that fugues are comprised of very little. To write a fugue, you take a minimal amount of music to start with and rework it in a variety of ways so you hear the same basic music but in different registers, turned upside down, or in fragments. That way, you use very few notes to create a lot of music. Fugues are fascinating to listen to for precisely that reason – even if you don’t consciously understand what’s going on, you can hear that connectedness. That’s because almost every single bit of the fugue is based on music that has already appeared.

One characteristic of the fugue is that it usually begins with only one voice, which states a theme or subject. This subject is the basis for the entire work. (In our 44-measure fugue, the subject enters 31 times.) Next, another voice comes in, repeating the theme after the first voice. While the second voice is reciting the subject, the first voice continues into what we call the countersubject – it’s just extra material layered against the subject. In our three-part fugue, the third and last voice also enters by stating the subject, while the second voice continues into the countersubject and the first voice starts to take bits of the theme and alter them.

The truly amazing thing about fugues is that they are tremendously rich in texture while being the most minimalistic kind of music out there. In our fugue that I’ll be dissecting in a bit, there is roughly one measure of music which I can’t connect to the subject or countersubject. The rest of the fugue is based completely on the subject or countersubject. Please bear in mind that the subject and countersubject combined can be as little as three measures, while the fugue can go on for pages. The ability to take that little bit of music and transform it into a piece that develops and fluctuates really is an art – the art of fugue.


Analysis

Now we can get to my fugue. It’s in D minor, No. 6, from Bach’s Well-Tempered Clavier Book I. I did a little simplifying when it came to trills and other ornaments so we could see just the bare bones.

You can see below that I’ve color coded each voice. (I don’t know why, but it brings me so much joy to see the voices color coded! It’s almost like the fugue’s natural state of being.) As I mentioned before, you can see that voice #1 comes in first. (I’ll soon show you where the subject and countersubject are.) Next, voice #2 enters with the same theme. Finally, in measure 6, the third voice enters with the theme.

Example I-1

If you want to see the whole thing, you can download it here. If you’d like to see the voices written out separately, go here.

Now, that’s pretty cool, but wait for my next example. In this one, I’ve used only two colors. The pink is the subject and purple is the countersubject. Any material that is derived from the subject or countersubject is color coded accordingly. Material that is not connected to either the subject or countersubject is colored black.

Example II-1

To see the rest of the fugue in this example, click here

Can we just take a minute to look at that? That’s all derived from the theme and countersubject. And it’s beautiful music. (I have a video of it at the end of this post.)

Now, let’s go on to my third example and get into what’s actually going on and how each bit is related to the subject and countersubject. I’ll only show voice #1, but I’ve analyzed all three voices and you can see them right here.

For this example, I have a whole new set of colors involved because there are a couple different relationships to the subject that a bit of music can have (these do not apply to the countersubject):

⦁ Firstly, we have fragments: pieces of the theme. Oftentimes, composers will take a fragment of the theme and put it into an episodic progression, repeating the fragment and moving it down or up with each repetition. (We’ve got some episodic sections which I’ll point out.)

⦁ Then there’s the inverted theme. We didn’t talk about inversions, but they’re pretty simple. Imagine taking a simple tune like happy birthday and turning it upside down; instead of going up and then down when singing “birth-day”, you would go down and then back up. You’re inverting the melody by going up when you should go down and vice versa.

A few other notes: I’ve slurred an important motif which appears in the theme and is reused as a sort of building block throughout the piece. I’ve also numbered the spots where the theme comes in so you can see all 31 entries for yourself. (It should be noted that only 16 of them are complete subjects. The rest are merely fragments or change the end of the subject slightly..)

Example III-1.png


After all that analysis, it’s about time we actually heard the piece. Try to hear the theme when it comes in at different times! For a well-executed and well-voiced interpretation, try Glenn Gould.

For a more sedate and smooth version, listen to Richter.

Here’s a helpful discussion on fugues if you’re interested in learning more about them.


A couple last notes: 

The Chamber Music Society is starting to stream more lectures, masterclasses, and concerts. The next livestream is on October 18th – you can view the schedule here.

Lastly, Cammi and I have decided to undertake a composition challenge and would like to publicly commit to it here. I think I’m going to try for a fugue and Cammi is going to write a work for violin and piano. Depending on how the pieces turn out, we might upload them to La Musica. (I’ll be honest, though, that’s being a bit optimistic. I expect my fugue to be a complete mess. ;)) Wish us luck!

~ Maggie

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3 thoughts on “The Art of Fugue

  1. Well ladies, I’m confident you’ll both have beautiful compositions given the talents you both have shown to date. We’ve had the privilege of hearing Cammi play her violin at a few public events this Fall, and she plays beautifully! Our past memories of you (Maggie) playing the piano are equally impressive and dearly memorable.
    Go to it ladies…can’t wait!
    Love you.💞
    Gramps

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