It is something of a truism that the ideas that make up the body of Riemannian theoretical thinking did not spring up in a historical vacuum. Riemannians and neo-Riemannians have long been familiar with certain figures from nineteenth-century music theory, and indeed have raised many a figure out of historical obscurity. It would perhaps be overstating the case to say that theorists such as Ottokar Hostinsky, Carl Weitzmann, and Arthur von Oettingen are now household names, but they are doubtless much better known now, in the context of neo-Riemannian theories, than they would have been only a few years ago. And yet, these names are merely dots in the rich intellectual landscape that was central European music theory in the nineteenth and twentieth centuries. In examining the cultural and historical contexts that inspired and shaped Riemann's ideas, this section also aims to expand the circle of ideas and names associated with Riemannian theories so as to present a fuller and richer picture of that landscape.
Ludwig Holtmeier leads the exploration by tracing the reception of Riemann's ideas and examining their gradual transformations in the hands of his contemporaries and successors. By placing Riemann's legacy in the wider context of music-theoretical traditions, Holtmeier shows that, contrary to common belief, there was in fact a middle ground between Viennese scale-degree theory and Riemannian function theory, between voice-leading approaches and Klang-based approaches. (p. 2) Names such as Georg Capellen, Rudolf Louis, and Johannes Schreyer are seldom encountered even in the history of music theory, but Holtmeier shows how this generation of theorists, epitomized in Louis's “Munich school,” is the missing link between the two great music-theoretical centers, Vienna and Leipzig.
Benjamin Steege presents an introduction and translation of Riemann's “The Nature of Harmony,” Riemann's 1882 account of his intellectual and theoretical and forebears. Steege's translation makes readily accessible an important document in Riemann's own theoretical evolution—written at a moment when an incipient psychological perspective was beginning to supplant Riemann's earlier acoustical and physiological perspective. Just as Riemann tries to place his own theoretical program within (or at the logical conclusion of) a historical trajectory, Steege's introduction locates the work within the broader historical and intellectual discourse of nineteenth-century physics, physiology, and psychology, underscoring the implicit and explicit polemics with Helmholtz and others that course through its pages.
Brian Hyer takes another look at a concept that appears to be sufficiently familiar, perhaps even overly so: tonal function. In particular, Hyer examines the mathematical and philosophical understandings of function, most notably in the writings of Gottlob Frege. By taking this concept out of its usual sphere of influence, into the fields of epistemology and mathematics, which are its natural habitat, Hyer points out the strengths and limitations of this important Riemannian idea.
Finally, Matthew Gelbart and Alexander Rehding turn to an aspect of Riemann's theoretical writings that has rarely been explored: his late “theory of folk musical tonality,” with which he sets out to cover pretonal and nontonal repertoires. With this “universal” theory, Riemann ventures into areas as diverse as Greek tetrachordal theory, Chinese pentatonicism, and Scottish folk song—areas that are traditionally the domain of comparative musicology, the precursor of ethnomusicology. Among Riemann's many theoretical systems, this sketch is distinguished by proposing a model based on melodic structure, not on harmony. Yet, as Gelbart and Rehding show, a certain number of Riemann's fundamental convictions also make their way into this new area of inquiry.