<p>A semiminim is typically defined as a note value worth half a minim, usually drawn as a flagged or colored minim. That definition is one according to which generations of scholars have constructed chronologies and provenances for fourteenth- and fifteenth-century music and the people who created it. `Semiminims' that do not match this definition are often portrayed in modern scholarship as anomalous, or early prototypes, or evidence of poor education, or as peculiarities of individual preference. My intensive survey of the extant theoretical literature from the earliest days of the Ars Nova through c. 1440 reveals how the conceptualization and codification of notation occurred in different places according to different fundamental principles, resulting not in one semiminim but a plethora of related small note values. These phenomena were dynamic and unstable, and a close study of them helps to clarify a range of historical issues. Localized traditions have often been strictly bounded in scholarly literature; references to French, Italian, and English notation are commonplace. I explain notational preferences in Italy, England, central Europe, and the rest of western Europe with regard to these small note values but demonstrate that theorists educated in each of these places routinely incorporated portions of other traditions. This process began long before the `ars subtilior,' dating at least to the time of Franco of Cologne. Rarely were regional traditions truly isolated; the various aspects of semiminim-family note values were debated and adapted for decades across these cultural and geographical boundaries. The central theme of my research is to show how and why the theoretical conceptualization of these myriad small note values is key to understanding the continual merging of these local preferences into a more amalgamated style of notation by the mid-fifteenth century.</p> / Dissertation