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Thesis Format



Doctor of Philosophy




Grier, James N


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.

Summary for Lay Audience

Every musical composition (or part of a composition) has a characteristic mood that results from its mode. For the last few centuries, most Western music has used only two modes: major and minor. These two modes may use the same notes (for instance all the white keys on a piano) but treat a different note as the origin point of the musical scale (in this example, C for major and A for minor). It is also possible to start the scale from other notes, creating other modes that have been used in other historical contexts and are still used, in a somewhat different manner, in folk music, jazz, and some forms of popular music.

However, the concept of mode, which goes back to ancient Greece, has been defined in many different ways throughout history and was understood very differently in the Middle Ages. Around the beginning of the ninth century, musicians adapted mode to the classification of ecclesiastical chant according to a set of recognizable musical characteristics, to facilitate the joining together of chants with similar characteristics. From that time onward, although the modal system continued to develop, a degree of continuity in the modal concept was maintained right down to the present, making the ninth-century essentially the origin point of the current system of modes. The Alia musica is one the very few treatises from this period that provides technical details about them, describing them according to a set of mathematical ratios that correspond to favoured musical spans. These details are completely unlike any other known description, and this aspect of the treatise has not been well explained in previous studies. This dissertation analyzes the description of the modes in the Alia musica to clarify the meaning of its unusual definitions and increase our knowledge of the earliest stages of the current Western modal system.

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Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.