Mensuration and Proportion Signs: Origins and Evolution.

Mensural practice in the music of the fourteenth to the sixteenth centuries holds the same considerable interest for music historians and performers today as it evidently did for musicians then. The attraction is to a subject that is complex, highly technical, and fraught with ambiguity and contradiction, a state of affairs due to the variety of agents who helped develop the mensural system (if we may safely speak of it in the singular at all). Mensural practice was prescribed and described by theorists, some of whom were also composers; composers followed traditions, adhered to the prescriptions of influential theorists, or experimented with personal innovations, some of which might become authoritative conventions for the next generation; and scribes and publishers manipulated signs, too, thereby correcting or confusing the situation as they found it.

Musicologists, for their part, have sought in the first place to find the proper resolution in transcription for the meaning of mensural signs and proportions as found in musical sources. As a distinct undertaking, they also seek the correct logic or rationale to explain them. And having a fully realized, contrapuntally correct solution in score, they must still address basic questions concerning absolute and relative tempos in performance. The attendant music theory claims attention, moreover, in its own right. Thus mensural practice has generated a considerable body of scholarship, a literature so often in conflict that it generated a strong call by the late Arthur Mendel for a more 'orderly method of gathering and sorting evidence from both the theorists and . . . the music itself' ('Some Ambiguities of the Mensural System', Studies in Music History: Essays for Oliver Strunk, ed. Harold S. Powers, 1968, p. 153).

Anna Maria Busse Berger's new book derives its evidence principally from theorists, not musical sources. To an important degree it fulfils Mendel's desire for an orderly and comprehensive approach, while dwelling mainly on the problems that Mendel identified. Though she casts her gaze over music theory from c.1320 to c.1560, the focus of her study is on theorists writing in Italy between 1460 and 1560, their contemporaries in German-speaking lands, and the relevance of all of these to the behaviour of music from Dufay to Josquin. It is in this later period that she is most comfortable and comprehensive. Occasional overblown statements such as 'most theorists favored equality of the breve' (p.3), unqualified as to where or when, indicate the frequently unconscious or unacknowledged narrowness of her focus, since she can only be referring to a specific Italian tradition of the fifteenth and early sixteenth centuries, and to no other. Thus the title needs qualification (as do the exaggerated claims made for the book in its dust-jacket blurb and the publisher's advertising). More precise, if longer, would be something like this: 'Mensuration and Proportion Signs according to Italian and German Music Theorists of the Fifteenth and Sixteenth Centuries: the Origins and Development of Certain Aspects of the Renaissance Notariohal System'. In her introduction. it should be mentioned, the author explicitly and appropriately delimits the scope of her study; one of its greatest strengths is her concentration on a fixed and well-defined body of material.

Berger here assembles a programme of work that has been unfolding over the last decade. In four core chapters (3-6) she adopts the same general methodology and layout, involving the careful definition of a performance problem and the systematic examination of theoretical evidence concerning it. Of these core chapters, three derive from articles published in journals between 1985 and 1990 and here lightly modified. Berger's approach and principal conclusions will thus already be familiar to those close to the field. These chapters make for dense reading - they are exhaustively argued and enriched with much useful observation and detail. For the reader in a hurry', or having trouble distinguishing the wood from the trees, the Introduction and especially the Conclusion provide useful, succinct overviews.

Chapters 3 and 4 analyse how geometric signs are related to each other in fifteenth-century practice, tackling some of the most commonly encountered and problematic relationships found in the music. In Chapter 3, 'Perfect and Imperfect Time' (an expanded version of 'The Relationship of Perfect and Imperfect Time in Italian Theory of the Renaissance', Early Music History, v (1986), 1-28), Berger demonstrates a fifteenth-century Italian theoretical tradition of breve equality under all four mensurations. She draws special attention to imperfect and perfect time under minor prolation, where breve equality establishes a sesquialtera relationship (2:3) on the semibreve level between C and O. Her demonstration of a widespread Italian theoretical tradition for breve equivalence is very significant. It shakes to its very roots the assumption that the minim equivalence of the French Ars Nova theory of Jehan des Murs and Philippe de Vitry (later defended by Tinctoris and Gaffurius) is universally applicable in the fifteenth century, and it offers a powerful new rationale for familiar solutions to tempo relationships in Renaissance music that have been argued for frequently by other means.

Such difficult material is often subject to alternative explanations, and one can nitpick at many of Berger's …