Untersuchungen zur Rationalität der Musik in Mittelalter und Früher Neuzeit, vol. i: Das platonische Paradigma: Untersuchungen zur Rationalität der Musik vom 12. bis zum 16.Jahrhundert (review)

This book is the first in a projected three-volume set, published both as part of the Freiburger Beiträge zur Musikwissenschaft and in Rombach Buchverlag's series Voces. The second volume will reportedly cover concepts of rationality and reason in musical thought of the seventeenth century, and the third will engage with the early eighteenth century—in Bayreuther's words, 'das galante Paradigma' ('the galant paradigm'). The present volume is a highly ambitious work, both in scope and purpose. Its author wishes to consider, among other matters 'welche Merkmale und welcher Begriff von Rationalität formte die Musik vom Mittelalter bis in die Frühe Neuzeit. Und umgekehrt: Welche Merkmale und welcher Begriff von Musik formte die Vorgänge des Rationalisierens?' ('which attributes and what concept of rationality shaped music from the Middle Ages up to the early modern period—and, conversely, which attributes and what concept of music shaped the process of rationalization?').

The definition of ratio through which Bayreuther interprets his historical texts is, to judge from the analytical discussion, one rooted in the lowest possible deducible basis for a phenomenon, that which cannot be further reduced to epistemological subcategories and which is therefore accepted as normative for the nature of all speculation. This places the focus on indications of latent rationality in musical practice as much as on external rationalization. Naturally, other connotations of the word (regarding measurement, proportions, etc.) need to be examined as well, as arguments and analytical corollaries unfold.

The book is structured as three independent case studies, each containing its own introduction and concluding remarks. An introduction, conclusion, and general index for the entire volume would have made it considerably easier to delineate its content, but it appears that it would be difficult to summarize the general tendencies in the scholarly material covered. Moreover, one would be hard pressed to identify one general thesis comprising the three essays. On this account Bayreuther should be commended—far too many studies in the history of ideas take too broad a view in the interpretation of how widely disseminated sources of general theories really affected narrower particular theories (in this case music theory).

Bayreuther's discussion concerning the overriding role of arithmetic in medieval scholarly thought supersedes, on some points, positions commonly taken in historiography today. Music was, all things considered, the ars that consisted of numerical relationships without itself depending on calculation by numbers, and it was the only scientia with its own graphemic system. This is, one supposes, the main reason why notation is the prime empirical material under study in the first two sections of the book: 'Zahlteoretische Rationalit—t der Modalnotation im 13. Jahrhundert' ('The rationality of number theory of rhythmic modal notation in the thirteenth century') and 'Rationale Struktur der Zusammensetzung in der Ligaturen der mehrstimmigen Saint-Martial-Musik des 12. Jahrhunderts' ('Rational structure in the configuration of ligatures in Saint-Martial polyphony of the twelfth century') respectively.

The first case study offers a penetrating discussion of modal rhythm and the philosophical-cum-graphical matter of thirteenth- and fourteenth-century notation. Taking as one of the starting points the conceptual trichotomy figura, denotatum, and tempus, Bayreuther elucidates the different semiotic and logical implications in notation as discussed by Johannes de Garlandia and Johannes de Muris.

The second case study scrutinizes the consequences of a Neoplatonic ontology of music, with special emphasis on the reception of Proclus Diadochus in the twelfth century and the hierarchy of 'Being' concepts as applied to music in the same period. The Liber de causis, before the time of Aquinas and probably also afterwards in some scholarly contexts, was generally regarded as an Aristotelian source. Since it was commented on by Aquinas, Albertus Magnus, Meister Eckhart...