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Blachly, Alexander

Mensuration and Tempo in 15th-Century Music: Cut Signatures in Theory and Practice

Ph.D. Columbia University, 1995

This thesis studies 15th-century music —- especially its notation —- with the aim of ascertaining the meaning(s) of cut signatures in musical practice from Du Fay to Josquin. Following an Introduction that illustrates the problems still awaiting a satisfactory solution and which, therefore, continue to bedevil both editions and performances of the target repertory, the thesis presents a detailed examination of notational developments in the 14th century (Chapter 1), an analysis of new notational features in music of the early 15th century, particularly the behavior of the earliest works to exhibit cut signatures (Chapter 2), a critical interpretation of the statements in the treatises of Johannes Tinctoris —- the most influential theorist of the 15th century —- pertaining to the relationship between mensuration and tempo (Chapter 3), a comprehensive survey of theoretical writings from c.1490 to 1550 that treat of the tactus (Chapter 4), a review of editorial practices in published modern editions of selected works from the repertory under investigation (Chapter 5), and a Conclusion (Chapter 6). The thesis ends with a collection of longer excerpts from treatises that discuss cut signatures or the tactus (Appendix A), a set of tables demonstrating a chronologically linked change in the size of the note receiving the dissonance in passages governed by cut signatures as the tables progress from mid 15th-century to early 16th-century sources (Appendix B), and complete transcriptions of 15 of the musical works discussed in the main text (Appendix C).

The author challenges the interpretation in most widespread use today, that of a “proportional” or mathematical understanding of the relationships between cut and uncut signatures, and illustrates how this interpretation, which finds virtually no support from contemporaneous evidence, frequently distorts the character of 15th-century music. A new understanding, based on a closer reading of the musical treatises and on a more analytical examination of the music itself, proposes a flexible interpretation of cut signatures dependent on context.

Since theorists from the 14th to the 16th centuries, despite their impressive number and frequently documented interaction with one another, rarely addressed the issue of tempo directly, the thesis deduces unstated principles of tempo by assuming that the pertinent statements in Tinctoris’s treatises reflect a coherent approach. These principles prove to be consistent with the views of the majority of Renaissance theorists who discuss cut signatures, but contradict the views of a handful of 16th-century German theorists in a peripheral tradition (who, however, subsequently came to dominate theory in all countries for several generations and whose views are responsible for the interpretations of 15th-century practice that prevail today).

By applying the deduced principles of usage to representative works from the beginning, middle, and end of the period in question, the thesis shows that the new understanding not only is consistently applicable but also provides a better explanation for the observed phenomena than previous interpretations. The thesis also demonstrates that for music of the mid 15th century the presence or absence of a stroke through a sign of mensuration has less significance than the duration of dissonances in the counterpoint, which explains why concordant sources transmitting both cut and uncut signatures for the same music do not reflect mutually contradictory performance traditions.

The author concludes with practical suggestions for interpretation that free the performer and editor from the constraints of the “proportionalist” tradition and encourage a more purely musical response to the repertory. Because these suggestions grow directly out of an analysis of both the theoretical and musical evidence, the author believes they will help future interpreters to a better understanding of the meaning of cut signatures in 15th-century music.