In recent years we have come a long way in appreciating the complexities of rhythm in tonal music. This development is in part an outgrowth of our enhanced understanding of the complexities of tonal music itself: for example, our awareness of hierarchical structure as postulated in the theories of Heinrich Schenker. Tonal structure and rhythmic structure are closely intertwined. In a loose, informal sense, one may even say that tonal structure implies rhythmic structure, for such tonal entities as motives, linear progressions, phrases, and so forth carry with them a durational component at any given level.

In studying the rhythmic aspect of tonal music, fugues and related genres pose a special challenge. One of the main reasons for this is that tonal structure in fugal genres—even at a foreground level—is extremely complex. For example, fugal writing demands motivically and thematically independent parts; the rhythmic implications of this independence (which can sometimes be far-reaching) appear not to have been yet systematically studied.

A frequently encountered “symptom” of rhythmic complexity in fugal genres is rhythmic displacement, where corresponding thematic statements do not correspond in terms of notated metric position. Broadly speaking, one may distinguish between two main categories of rhythmic displacement in fugal genres. The first category consists of half-measure displacements in common time. In the 1760 Anhang to his Handbuch bey dem Generalbasse und der Composition, Marpurg addresses the issue of half-measure displacement with reference to the three fugal excerpts given here as example 8.1. Evoking a prevalent eighteenth-century conception of common time, Marpurg states that the measure consists of two equally “good” parts, and therefore there is no essential difference between its first and third beats. It should be noted that half-measure displacements occur frequently in eighteenth-century music notated in common time, whether in fugal or non-fugal genres.

The second category of rhythmic displacement is a more specifically fugal one. In this category the non-correspondence in notated metric position between corresponding thematic statements is considerably more acute than is the case with half-measure displacement in common time. For example, thematic statements may occur on successive beats in some given meter, as is typically the case in fugal strettos. Marpurg uses the locution “per arsin et thesin” to refer to this type of rhythmic displacement.