I have been intrigued by fugues for a long time. The one that most people have heard is from Bach’s Toccata and Fugue in D Minor, a Halloween staple and the opener in Disney’s original Fantasia movie.
But what is a fugue exactly? It is a piece of music where different voices echo one another, but with a very specific formulation. A voice means a melody line, which may be represented by a human voice, an instrument, or one of the melodies played simultaneously on a piano.
The opening passage, the theme of the piece, is called the subject. For it to be an “official” fugue, the subject must be stated by each voice participating in the fugue. Typically, the first restatement of the subject (in a different voice), called the answer, is an interval of a fifth higher. The subject may be followed by a countersubject, a new passage that works well with the subject and will help in building the fugue.
The section where the subject, answer, and any countersubject are stated is called the exposition. The way in which the voices play off one another is called counterpoint. Typically, the key will change (sometimes multiple times), which keeps things interesting.
After the exposition, there is a development section. The subject and countersubject may be restated, probably numerous times, but they don’t have to repeat themselves in the same way each time—otherwise it would be a round or canon (like “Row, row, row your boat”). Changes will be made to reveal nuances in the musical passage (which sounds fancier than “to play around with it”), or to accommodate harmony in the interweaving of voices (so you don’t get unpleasant clashing of notes).
Finally, the whole fugue may wrap up with a coda or codetta that brings the fugue back to its initial key, but it’s not a necessary component.
Ok, so how do you do it?
Answer: not easily.
To start out, it helps to write a plain, vanilla passage for your subject (and countersubject), because once you start bouncing notes off one another, chaos will ensue if you pick weird intervals.
Chaos, like handing an 8-year-old an alarm clock and a screwdriver. Bits will be left over; parts may disappear; things will not fit together right. And it may never work.
That being said, it can be done, and done brilliantly. Bach makes it look effortless. His Well-Tempered Clavier presents preludes and fugues in every key, and his Art of Fugue is mind-boggling. Here is a sample, Contrapunctus 11, with the themes indicated by different shapes. Beethoven’s Grosse Fuge is a monument (although it was not initially well received). Brahms caps off his Variations and Fugue on a Theme of G. F. Handel (Op.24) with a wonderful fugue (measure-by-measure analysis here). And in the 20th century, Paul Hindemith used a fugue in the last movement of his third piano sonata and achieved a thoroughly modern sound.
The fugue is alive and well, though you probably won’t hear it on a top-40 radio station. That being said, YouTube yields facetious fugues written on themes by Adele and Lady Gaga and more (the Nokia ringtone?!).
But the fugue that tickled me the most was this one by none other than Glenn Gould, titled So You Want To Write a Fugue. The link is to a performance; you can find a performance with a visual presentation of the words and music here.
See the references for sites where you can find out more about the fugue.
Anatomy of a Fugue, a television program about the fugue and its history by Glenn Gould (really, a whole television program about the fugue) https://youtu.be/5_y6q4m0vew
Anatomy of a Fugue, a detailed written description unrelated to the television program above, from Northern Arizona University http://www2.nau.edu/tas3/fugueanatomy.html
How to Analyze a Fugue http://www2.nau.edu/tas3/analyzefugue.html
Yale University lecture on the Fugue: Bach, Bizet, and Bernstein https://youtu.be/nn1Xfr4cAU8
What is a Fugue? https://youtu.be/3tU1PDS9kyI
Composing a Fugue from Earlham College http://legacy.earlham.edu/~tobeyfo/musictheory/Book2/FFH2_CH8/8C_FugueComposition.html
Image attribution: Schickele, Peter, The Definitive Biography of P.D.Q.Bach. New York: Random House, 1976, p 149. Original caption: “An unfinished keyboard piece employing invertible counterpoint.”