Greek and Latin Music Theory: Principles and Challenges

Long recognized as a foundation of musical composition, criticism, pedagogy, and appreciation, the literature of ancient and medieval music theory has maintained its strong position in the academic curriculum up to the present day. Now blessed with fine English translations of many of the ancient and medieval authors, modern students of music theory have advantages that their predecessors lacked just a few generations ago. Yet the ancient writings by themselves do not yield to easy comprehension. They need expository help. In this collection of fifteen topical essays, the author offers a contribution to that educational goal. Covering a dense theoretical literature from the classical period of ancient Greece to the sixteenth century of the Common Era, these essays present a detailed examination of subjects of concern not only to specialists in the history of theory, but to scholars of the general history ofancient Greek music and the liturgical plainchant of the medieval West. More than just a collection of specialized studies or a syllabus of obligatory learning, these essays present a persistent reflection on the timelessness of theoretical questions that engaged our musical forebears and that still engage us today. The author's approach is perennialist. It teaches us things about our musical heritage that never go away. Table of Contents Introduction Part I: The Ancient Greek Tradition in Practice and Theory The Ancient Harmoniai The Tonoi Alypian Notation Part II: Mathematical Foundations Pythagorean Harmonic Ratios from the Octave to the Comma by Continuous Subtraction Boethius's Error in the De institutione musica 4.6 Aristoxenus's Proof That the Perfect Fourth Is the Sum of Two Tones and a Semitone Aristoxenus's Anticipation of the Logarithmic Logic of Musical Cognition The Three Mathematical Means in the Theories of Euclid, Boethius, Glarean, and Zarlino Guido and the Monochord Part III: Emerging Theories of the Ecclesiastical Modes Transposition and the Doctrine of Modal Affinity The Misunderstood Confinalis Reading the First Quidam of the Alia musica The Prologus in tonarium of Bern of Reichenau: A Translation Reading Hermannus Idealist and Empirical Perspectives in Theories of the Ecclesiastical Modes Glossary of Terms Notes Bibliography