History of fugue theory 1: from Zarlino to Fux

From the origins to the sixteenth century

In the Middle Ages the term fuga indicates any composition in which one voice follows another by imitating it, including what we now call a canon. The first theoretical use is found in the Speculum musicae of Jacobus of Liège (c. 1330). In the Renaissance imitation becomes the basic technique of the motet and the mass: each phrase of the text receives a motif, the voices imitate it, then a cadence closes the point of imitation.

Gioseffo Zarlino

Zarlino (1517–1590), maestro di cappella at St. Mark's in Venice and a pupil of Adrian Willaert, published Le istitutioni harmoniche (1558). The third part is devoted to counterpoint; the fourth to the modes. Main contributions:

• He distinguishes the fuga legata (bound fugue), in which the second voice imitates the first in its entirety (our canon), from the fuga sciolta (free fugue), in which the imitation concerns only the beginning.
• He calls fuga the exact imitation at perfect intervals (unison, fourth, fifth, octave) and imitation the one at other intervals or not exact; he also describes imitation by contrary motion.
• He explains the prohibition of consecutive fifths and octaves in terms of variety and the independence of the voices, and studies the cross-relation.
• He bases harmony on the triad and on the senario (ratios from 1 to 6): it is the beginning of modern harmonic theory.
• In the Dimostrationi harmoniche (1571) he renumbers the twelve modes starting from C.

The method of the species already exists in embryonic form: Lanfranco (1533) and Zarlino describe the exercises by stages; Diruta (Il Transilvano, 1610) and Zacconi (Prattica di musica, 1619) present them more systematically.

From the seventeenth century to Fux

In the seventeenth century the fugue becomes an instrumental genre (ricercare, canzona, capriccio, fantasia) with Frescobaldi, Sweelinck, Froberger, then Buxtehude and Pachelbel. Theory distinguishes the old style (vocal polyphony) from the modern style (monody, basso continuo); the treatises of Bernhard and Berardi describe the figures and the different styles.

Johann Joseph Fux

The Gradus ad Parnassum (Vienna, 1725) codifies the five species and then devotes a part to fugue:

• Fugue in the modes: subject and answer exchange the fifth and fourth of the modal octave.
• Fugues in two, three and four voices with short subjects in long values.
• Double counterpoint at the octave, the tenth and the twelfth, as an instrument of the fugue.
• Ecclesiastical style a cappella and mixed style.

His view is conservative (the model is Palestrina), but the clarity of his teaching made the book the foundation of European instruction for over a century. Alfred Mann translated and commented on its part on fugue in The Study of Fugue (1958), together with the texts of Marpurg, Albrechtsberger and Martini.

Lines of continuity

Typical mistakes in historical reading

• Confusing the Renaissance fugue (imitation) with the Baroque tonal fugue.
• Attributing to Fux the invention of the species: Fux systematized them, he did not invent them.
• Thinking that the Gradus describes Bach's style: it describes the old vocal style, and its part on fugue is modal.

Modern application

• Film composition in the old style: knowing the difference between Renaissance imitation and Baroque fugue lets you choose the right style for a setting (an imitative motet for the sixteenth century, a tonal fugue for the eighteenth).
• Teaching: following the historical sequence (imitation, canon, modal fugue, tonal fugue) is an effective course of study even today.
• Choirs: the imitative Renaissance repertoire is the best training for a choir that wants to tackle a Baroque fugue.

Related topics

Fux's Gradus ad Parnassum, fugue in the modes, imitation, types of canon, history of fugue theory 2.