The Alia musica and the Carolingian Conception of Mode
Abstract
The Alia musica is perhaps the most idiosyncratic of the early treatises on the ecclesiastical modes. It is a composite made up of at least three independent treatises and additional commentary, and the majority of the scholarly attention that it has thus far received has been devoted to questions of dating and authorship, as well as to the place of the Alia musica in the development of the octave species paradigm of modality. However, the majority of the treatise is dedicated to the explanation of a complex harmonic numerology that applies the fundamental relation 12:9:8:6 (which generate the intervals of an octave, a fifth, and a fourth) in a unique way to each of the eight ecclesiastical modes to define a set of intervals thought to be particularly characteristic of the chants in each mode.
This dissertation reviews the previous studies about the Alia musica, as well as the manuscript sources, examines the theoretical context within which the treatise was written, and analyzes the numerological system both from the evidence of the text of the Alia itself and from an analysis of the chants that the Alia cites as exemplifying the numerical relations proposed for each mode. The intervals represented by these numbers show only partial consistency and can generally be explained as being constructed from the simplest, or perhaps the most numerologically meaningful, multiples of the four base numbers from 12:9:8:6 that successfully filter out the intervals that are not considered to characterize a particular mode.