Greek and Latin Music Theory – Principles and Challenges: Eastman Studies in Music

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 Index