What is a Fugue: Bach Toccata in E minor

Piano Lessons / music theory / What is a Fugue: Bach Toccata in E minor

Welcome to LivingPianos.com, I’m Robert Estrin. Today’s subject is about the ultimate musical form: The fugue. Even if you don’t know what a fugue is, you’ve heard them many times, from Beethoven’s Ninth Symphony to Handel’s Messiah. The fugue is actually a technical type of form that can be utilized within compositions. There are also whole movements that are fugal. The master of writing counterpoint and fugues is Johann Sebastian Bach. He could craft such unbelievable compositions of counterpoint, of interweaving lines, that it’s a mathematical wonder that he could create such intricate music. But it’s the joy of the music and the emotional content that is most important!

What is the structure of a fugue?

A fugue is an amazing type of composition that is based upon counterpoint, the interweaving of separate lines. Rather than just having melody and harmony, imagine having more than one melody at the same time. Is this possible? Well, we all are familiar with a round. A fugue is a bit more complex than a simple round or canon. First let’s talk about a simpler form than a fugue, which is called an invention. Then you’ll understand and appreciate what goes into writing a fugue. An invention is simply two different lines or voices. One line played by one instrument and another line played with another instrument. One isn’t melody, one isn’t harmony. They’re both melodies that interweave with one another.

Bach wrote a whole bunch of inventions for the keyboard. To understand what an invention is and what counterpoint is about, listen to the beginning of Bach’s 1st Invention in C major. It starts off with what’s called the subject, which provides the seed for the whole composition! It starts off rather simply. Then the subject is repeated an octave lower, while the other hand plays the countersubject. The entire composition is built upon both the subject and the countersubject. Even though they’re independent lines that could be sung by different people or played on different instruments (or in the context of the keyboard, played with different hands), the way they intersect creates harmonies that are lush and beautiful.

Bach lived from 1685 to 1750, or dates around that. (Nobody is 100% sure.) He wrote Preludes and Fugues in every one of the major and minor keys. But that wasn’t enough for Bach! He wrote two complete books. So, you have all 12 major keys, all 12 minor keys – times two, for 48 preludes and fugues! It’s one of the milestones of musical literature.

What kind of things can be done with the subject and the countersubject of a fugue?

There is so much that can be done! Naturally, the subject and countersubject can be transposed. They can also be played slower or faster. This is referred to as augmentation and diminution. They can also be played backwards. This is called, retrograde. They can be played upside down as well which is called inversion. These can be combined, for example, retrograde/inversion. For a demonstration of this, listen to Bach’s fugue in C-sharp minor from book one. This is an example of a five-voice fugue. This means there are 5 separate lines of music interweaving with one another. Can you believe this? There are at least three voices in a fugue. The initial statements of the subject and countersubject are called the exposition which is followed by the development where the subject and countersubject are presented in many ways.

For example there is Bach’s fugue from his Prelude and Fugue in C-sharp Minor from Book I. The subject of this fugue is incredibly simple. It has only 4 notes! As in all fugues, it is restated a fifth higher. This is the way fugues work. As in inventions, you have a counter subject. And once again, it can be altered in many ways. It can be played backwards, upside down, faster, slower, or it can be altered in combinations of techniques. But the entire work is built upon the seeds of the subject and countersubject. Listen to the first section of this fugue to get a feel for what a fugue sounds like. And listen for how this simple subject keeps coming back again and again along with the countersubject. It’s remarkable how 5 voices keep interweaving with one another! There are five separate lines going on. The writing requires mastery in order for a piece of music constructed this way to hold together.

Fugues are rarely pieces all by themselves.

Fugues are usually just parts of pieces. Even Bach wrote preludes and fugues which are two movement works. The only way to really appreciate a fugue is in context. Just like if you really wanted to appreciate a great motion picture, you wouldn’t watch just one or two scenes of it. You’d watch the whole movie! Because the whole is greater than the sum of the parts.

So what I’m going to do for you is play a complete work of Bach that ends with an absolutely stupendous fugue. I’m going to perform on my grand piano so you can really get the full experience. Bach wrote several toccatas and they’re emotionally charged works. And his E Minor Toccata is one of my favorites. I’m going to play you the whole toccata. It’s not that long, and it ends with a brilliant fugue. Be sure to listen to the fugue subject. This is a three voice fugue, meaning there are three separate lines going on at the same time. The emotional content and how this affects you is unbelievable.

I’m a firm believer in listening to music to really understand it.

I could go deep into the weeds and show you the subject, countersubject and all of the permutations. At a certain point later on in fugues, there is often a section called a stretto, where the statement of the subject is interrupted before it can finish again and again. It creates a chaotic madness of emotional tension. We could go through and analyze it very methodically. But I learned a lot from my father, Morton Estrin. I’ve talked about him so much because he was my piano teacher, my theory teacher, my harmony teacher, sight-singing, everything! Aside from his private piano teaching, he gave many classes. He was a professor at Hofstra University. He also gave classes in our home where he had a big studio. One of the things I used to love was attending his classes. Whenever he would have a class about music, he would play recordings of music, and people coming from other teachers would ask, “What should I listen for?” If you go to a music conservatory, you understand where this question comes from. I remember in music conservatory, whenever we had any kind of theory, harmony or dictation, if we would listen to music it would be to listen for specific techniques, such as where the development starts or where the stretto is. We were told to listen for this, listen for that. But if somebody asked my father what to listen for he always said, “You listen to enjoy!” Because you will understand in an intuitive way what makes a fugue great by listening to a masterfully composed composition. So I hope you enjoy the performance of Bach’s Toccata in E Minor which accompanies this article.

So, that is just one example of how a fugue at the end of a toccata can build such tremendous emotion. It’s not all just about mathematics. You have to have a certain awe that someone could craft a composition that has such intricacy. These lines all coming together and forming this magnificent piece of music out of all these separate voices that somehow weave in and out of one another in ways that you can’t even imagine. It’s hard to believe what’s actually going on!

I hope this has enlightened you enough that you’ll take an active interest in listening to more fugues! Beethoven, Brahms and other composers also wrote magnificent fugues. If you are interested in part two where I get really deep into analyzing a fugue, telling you all the statements of the subject and countersubject, the retrograde, inversion, diminution, augmentation, and how it’s all crafted, I’m happy to do that for you. Just let me know in the comments or send me an email. I’m Robert Estrin here at LivingPianos.com, Your Online Piano Resource.

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