- Prosdocimo de' Beldomandi's Plana musica and Musica speculativa
Prosdocimo de' Beldomandi (d. 1428) was a professor of arts and medicine at the University of Padua who wrote treatises on all of the subjects in the traditional [End Page 1336] quadrivium. His eight writings on music cover both practical and speculative aspects of the field. The two works in the present edition deal with different topics, but both are responses to the influential Lucidarium of Marchetto of Padua (1317-18), which covers plainchant from a combination of practical and speculative points of view. Prosdocimo objects to the inclusion of both of these perspectives in a single work. His Plana musica, which has not been published previously, discusses the medieval pitch system and the theory of mode. His Musica speculativa, which was previously available only in an obscure journal of 1913, considers the definition of intervals in both qualitative and quantitative terms, the mathematical operations by which interval ratios are determined, and the problems that Prosdocimo finds with Marchetto's treatment of these subjects. Prosdocimo approves of Marchetto's views on practical issues, but objects strongly to his approach to the quantitative definition of musical intervals.
The issue at stake in Prosdocimo's quarrel with Marchetto is one with deep historical roots and long future resonance. Ancient Greek music theorists took two contrasting approaches to the definition and measurement of musical intervals: the Pythagorean, which equates intervals with numerical ratios based on string measurements, and the Aristoxenian, which defines intervals in qualitative terms and rejects the view that they should be identified with ratios. The Pythagorean tradition, which was transmitted to musicians principally through Boethius, was the only one known to medieval music theorists. It had profound philosophical implications in that it provides the foundation for the musical cosmologies of Plato, Ptolemy, and their followers. Marchetto, whom Prosdocimo dismisses contemptuously as a "simple performer" (159), defied this tradition by dividing the whole tone into five equal parts, probably for the purpose of discussing subtle shades of intonation in performance. His approach was Aristoxenian in character, though he had no knowledge of the writings of Aristoxenus. Prosdocimo, following the Pythagorean-Boethian tradition, asserts that it is impossible to divide the whole tone (9:8) into any number of equal parts and insists on its traditional division into major and minor semitones (ratios of 2187:2048 and 256:243, respectively). This view is correct if one accepts the premise that intervals must be defined as ratios of integers (equal divisions can be quantified only with irrational numbers), though there is no obstacle to producing any division of an interval through qualitative judgments based on aural perception. Marchetto further provoked Prosdocimo's ire by applying traditional terms such as enharmonic, chromatic, and diatonic in unconventional ways to his newly defined intervals. Prosdocimo was distressed to find that Marchetto's views were widely accepted, because in his opinion they undermined the entire scientific edifice on which the theory of music was based. The same philosophical issue reappears in different forms in music-theoretical controversies throughout the fifteenth and sixteenth centuries.
This edition and translation by Jan Herlinger, who has previously edited and translated Marchetto's Lucidarium and three of Prosdocimo's other treatises —Contrapunctus, Brevis summula proportionum quantum ad musicam pertinet, and Parvus tractatulus de modo monacordum dividendi —is ideally suited to the needs [End Page 1337] of modern scholars. Latin and English texts appear on facing pages. Minor textual variants from different sources are recorded in footnotes, and significantly revised passages are provided in full-size print between the main text and the footnotes. The introduction summarizes the content of the treatises, places them in historical context, and describes the manuscripts in which they are found. Footnotes to the translations discuss issues relating to the interpretation of specific words and sentences and provide further information about the relationship of Prosdocimo's ideas to those of his...