Pseudo-Odo's Eccentric Theories of Species and Contour: Two Approaches to Pitch Relationships from Medieval Italy

John Snyder, University of Houston

Musicæ artis disciplina, a music-theoretical treatise originating in northern Italy ca. 1000 and sometimes attributed to one Odo, offers intriguing glimpses into a counter-current of musical-theoretical thought in the central Middle Ages. The treatise is at variance with auctoritas on several issues, including species theory, and offers a ground-breaking attempt to deal with the issue of contour. In both of these areas, Pseudo-Odo anticipates later theorists who would pursue these matters further.

His species theory is based on the location of the semitone in the interval, rather than on the location of the interval in the gamut, and is thus is strikingly bottom-up rather than top-down. It also results in an approach to pitch relationships that is akin to unordered sets, and includes a very limited recognition of inversional equivalence. Though Pseudo-Odo does not pursue the matter at great length, this line of thought was taken up (perhaps re-invented) over the next century and a half, first by the anonymous author of the Liber specierum and in the mid twelfth century by Theinred of Dover, who developed it extensively.

Pseudo-Odo's treatment of contour, though elementary, is notable in its attempt -- Centuries ahead of its time, conceptually -- to approach the topic systematically. He does not reach any sweeping generalizations (and lacked the mathematical means for doing so), but does succeed in cataloging the possible contours (with a few interesting omissions) for combinations of x notes comprising y discrete pitches, for several small values of x and y.