The Pythagorean theory of a harmony found in music and manifested throughout the cosmos is one of the richest ideas in western thought. What seems strange about the theory is that it rests in part on erroneous observations. In particular, the results of the experimental tradition which supposedly support Pythagoras's discovery of the harmony or tuning were not challenged when they were quite easily tested. For, while the Pythagorean numbers produce the required results when applied to the relative lengths of strings and air columns, they do not in other physical experiments associated with this tradition. To be specific, they do not work as represented, for example, in the weight of hammers hitting an anvil, the size of bells, the amount of water in vessels, or in the weights suspended from strings. Focusing on the account of the empirical tradition found in Franchino Gaffurio's Theorica musicae (Milan, 1492), this paper will grapple with the issues underlying the acceptance and transmission of erroneous information.
Cathy Ann Elias (DePaul University): Recipes Produce Good Food Not Music
Jan Herlinger (Louisana State University): What Is the Compendium musicale of Nicolas de Capua?
In 1864 La Fage published the _Compendium musicale_ of Nicolaus de Capua (_Diphthérographie musicale_, 309-38), conflating the text from two fragmentary Roman manuscripts. The final 2-1/2 pages of La Fage's text deal with counterpoint, and have been identified as a treatise elsewhere attributed to Philipoctus de Caserta. But it appears unlikely that the balance of the text constitutes a single work: letters, syllables, clefs, properties, hexachords, intervals, and mutations are twice defined or identified, before and after the words _Dimissa teorica parte, nunc de practica habendum est_.
Fortunately, the _Compendium_ appears also in a Venetian manuscript that La Fage did not take into account. Examination of the appropriate texts in the three manuscripts reveals the following. Nicolaus' _Compendium_ survives in two versions. The Roman version?shorter, perhaps truncated?occupies only the first 4-1/2 pages of La Fage's text. The next 22 pages of that text must now be regarded as an anonymous treatise or, more probably, a series of anonymous treatises that the compiler of one of the Roman manuscripts regarded as a unit. The Venetian version of the _Compendium_, which has never been published, is about ten times longer than the Roman and includes an important, and evidently unique, treatment of musica ficta, as well as the assertion that secular songs observe the melodic modes.
Lester A. Castellana (Independent Scholar): In Defense of the Medieval Imagination: A Study of Registration and Voice-Crossing in the Songs of Machaut