Dedication

pp v-vi

Contents

pp vii-viii

Acknowledgments

pp ix-x

Note to the Reader

pp xi-xii

Introduction

pp 1-8

Part I - The Ancient Greek Tradition in Practice and Theory

pp 9-10

1 - The Ancient Harmoniai

pp 11-23

2 - The Tonoi

pp 24-41

3 - Alypian Notation

pp 42-50

Part II - Mathematical Foundations

pp 51-52

4 - Pythagorean Harmonic Ratios from the Octave to the Comma by Continuous Subtraction

pp 53-55

5 - Boethius's Error in the De institutione musica, 4.6

pp 56-59

6 - Aristoxenus's Proof That the Perfect Fourth Is the Sum of Two Tones and a Semitone

pp 60-62

7 - Aristoxenus's Anticipation of the Logarithmic Logic of Musical Cognition

pp 63-67

8 - The Three Mathematical Means in the Theories of Euclid, Boethius, Glarean, and Zarlino

pp 68-76

9 - Guido and the Monochord

pp 77-82

Part III - Emerging Theories of the Ecclesiastical Modes

pp 83-84

10 - Transposition and the Doctrine of Modal Affinity

pp 85-91

11 - The Misunderstood Confinalis

pp 92-110

12 - Reading the First Quidam of the Alia musica

pp 111-130

13 - The Prologus in tonarium of Bern of Reichenau: A Translation

pp 131-148

14 - Reading Hermannus

pp 149-161

15 - Idealist and Empirical Perspectives in Theories of the Ecclesiastical Modes

pp 162-170

Glossary of Terms

pp 171-176

Notes

pp 177-212

Bibliography

pp 213-218

Index

pp 219-225