In music, the name of a composition wherein the parts do not all begin at once, but follow or pursue one another at certain distances; hence the name Fuga, a flight or chase, each part successively taking up the subject or melody. Any voice may begin the fugue, but the others follow according to fixed rules. The subject is generally a few bars of melody, which is given out in the principal key by the voice which begins. The subject of a fugue should always be short, three or four bars, so that it impresses itself upon the memory, and can be followed and distinguished in the course of the composition. Also, it must never be constructed periodically. After the subject (dux) has been announced, the second voice repeats it a fifth above or a fourth below. It is then called the answer (comes). The first voice meanwhile proceeds with a counterpoint, as does every successive voice upon the completion of the fugue theme. This counterpoint is constructed so as to afford the composer opportunities for ingenious contrapuntal combinations in the further development of the fugue. The third voice follows with the subject again in the principal key, but an octave higher or lower than the first voice, and is answered by the fourth voice in the same manner as the second voice answers the first. When the subject and answer have been introduced in all the parts, the first section or first development of the fugue is said to be completed; an episode of a few bars then follows, sometimes in its form like part of the subject, and with a modulation into a nearly related key. The subject and answer are again brought forward, but following in a different order from the first section; while at the same time all the parts are continued, and in some of them the original counterpoint appears either simply or inverted, the subject and answer forming the predominating idea throughout the whole composition.

This is the second development, and is again followed by an episode. The greater the number of voices that are employed in a fugue, the greater will be the number of development sections. A four part fugue admits of no less than 24 possible development sections; while in a five-part fugue the composer may use any number of developments out of a possible 120. In extended fugues the composer must exercise all his ingenuity on the episodes, otherwise the frequent repetitions of the development section will tire the hearer. Beginning with the third or fourth development, the answer is often given in another interval than the fifth, so as to avoid monotony. Even transposition into other keys is permissible. Masters of the fugue sometimes give the answer in inversion, augmentation, or diminution. The last development is generally an exhibition of all the composer's contrapuntal art. Bach generally closes with a stretto, where the subject and answer are crowded together, so that the latter begins before the former is completed. Often the stretto is elaborated over an organ point. When the subject does not extend in compass beyond the half of an octave, the answer is invariably made in the other half, and to avoid modulation out of the key, the progression of a fifth is answered by a fourth. A Fugue consisting of one subject with a counter-point throughout is called a strict fugue.

When a second subject is introduced in the middle of the composition and afterwards worked up with the first subject, it is then called a fugue on two subjects.

A double fugue begins at once with two subjects in different parts, both of which are strictly treated throughout.

There are also fugues with three subjects (triple fugue); a famous example is that in the finale of Mozart's C Major (Jupiter) Symphony. A free fugue is that in which the subject and counterpoint are not strictly treated throughout, but mixed up with episodes and ideas not connected with the subject. The fugue is not, as has been erroneously believed, a production of German genius. This form was gradually developed from the canonic tricks of the Dutch masters by the great Italian masters of the sixteenth and seventeenth centuries__Merulo, Frescobaldi, Pasquini. It reached its highest development in the eighteenth century, in the works of Bach (instrumental) and Handel (vocal). Bach's fugues have never been equaled, and are, in fact, musical problems of great depth. He devoted a special work to the subject, Die Kunst der Fuge (1749). His Invention and Das wohltemperirte Klavier (1722) are necessary to every pianist, and his Musikalisches Opfer, elaborated on a theme given to him by Opfer, elaborated on a theme given to him by Frederick the Great in 1747, are among his best examples. Handel ranks next to Bach. Celebrated treatises on fugues are by Mattheson, Marpurg, Fux, Albrechtsberger, Andre, Marx, Lobe, Jadassohn, Cherubini, and Fetis.