Rhythm in the polyphonic conductus : a computational model and its implications

Includes abstract and vita.The two-part conductus in thirteenth-century manuscript sources employs notation in which the rhythm and alignment of the parts is often unclear. Modern atttempts to root the rhythmic interpretation of this notation in in poetic meter have been largely unsuccessful. Recent research indicates that the musical culture that created this music was largely oral and relied extensively on memory. Rather than being a primitive notational system, the rhythmically ambiguous notation may have been an efficient "shorthand" that relied on the unwritten, implicit knowledge shared by the musicians in the culture. This study demonstrates not only that this implicit knowledge existed, but also that is is at least partially recoverable 800 years later. Using a body of the repertory where the rhythm is clear alongside musical concepts that would have been familiar to a thirteenth-century musician, a machine learning algorithm (Bayesian network) is employed to learn implicit musical relationships through experience--much the same way a medieval musician would have. The resulting model indicates that the melodic contour of the voices communicates a large amount of implicit information about rhythm while, surprisingly, harmony does not. A reexamination of a previous study that relates harmony to rhythm in this same repertory confirms these results. Moreover, the structure of the learned model is in many ways analagous to the human way of dealing with the notation. The model is then applied to a piece of music where the notation is rhythmically ambiguous but in which we know the correct rhythms by other means. The model is successfully able to recover many of the correct rhythms in this piece, thus demonstrating that it was able to learn implicit musical relationships from the repertory much the same way a period musician would have