Greek and Latin music theory principles and challenges - Nowacki, Edward 1945- (University of Rochester Press, 2020)
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