How Does a Fugue Work? One Tune Chasing Itself

A fugue opens with the subject stated by one voice alone and unaccompanied, which is the most useful fact about the form because it means the listener is handed the material at the start with nothing competing. A second voice then enters with the same melody transposed, usually a fifth higher or a fourth lower, while the first continues with a countersubject or free material against it. A third voice enters with the subject again, then a fourth if there is one, until every voice has stated it. That opening section is the exposition, and by the end of it the listener has heard the subject several times at different pitches and in different voices, which is exactly what makes it recognisable later.

The rest of the piece transforms the material in defined ways:

• •Transposition, stating it beginning on a different note
• •Inversion, turning every interval upside down so a rise becomes a fall
• •Augmentation, stating it in longer note values so it moves more slowly
• •Diminution, stating it faster
• •Stretto, overlapping entries so a new one begins before the last has finished
• •Fragmentation, developing a characteristic phrase from within the subject rather than the whole

Listening to a fugue is a skill and the entry point is specific. Listen to the opening statement deliberately, since it is alone and will not be again, and fix the shape of its first few notes rather than the whole thing. Then track where it returns, which is what the ear can actually do, noticing which voice has it and whether it is higher or lower than before. Between entries there are episodes built from fragments, which supply contrast and modulate to new keys, and recognising that nothing new is being introduced there is half the battle. Towards the end, entries frequently pile up in stretto and the texture thickens, and a final statement in the home key over a sustained bass note is a common close.

Imitative entry is not confined to fugues and recognising it elsewhere is useful. A canon is stricter, with one voice following another exactly throughout rather than only at entries, and a round is a canon anybody can sing. Fugal passages appear inside larger works, in symphonies, masses and operas, where a composer wants the density and seriousness the texture supplies without writing a whole fugue. Fugato is the term for such a passage. Choral writing uses imitative entries constantly for practical reasons, since voices entering in turn are easier to hear than voices entering together. And the procedure appears in jazz and in film scoring where a composer wants the same effect, which is generally recognisable immediately to anybody who knows what to listen for.

Fugue was already regarded as learned and somewhat archaic in Bach's lifetime, and it never went away, which needs explaining. It is the most complete demonstration of contrapuntal skill available, so it functions as a test piece and a display, which is why composers write one to prove something and why examinations demand them. It generates a large structure from minimal material, which is attractive whenever economy is valued. It can be written in any harmonic language, so composers in the nineteenth and twentieth centuries wrote fugues with entirely different pitch materials while retaining the procedure. And it carries an association with seriousness and with the past that composers have used deliberately, placing a fugue at the climax of a work to invoke exactly that.

The subject is stated alone at the start, which hands the listener the material before anything competes with it, and other voices enter with the same melody transposed. Inversion, augmentation and overlapping entries transform it afterwards. Following one means fixing the opening shape and tracking its returns, since the episodes between introduce nothing new.