W. A. Mathieu is the author of The Listening Book, Harmonic Experience and The Musical Life. He has recorded solo piano music for Windham Hill and other labels. He lives in Sebastopol, California, where he writes and teaches.

Editor's Preface

Introduction
Part 1: Harmonic Purity: Feeling the Numbers

1 Seeing Air and Touching Sound
2 Singing Unison with a Drone
3 Singing Octaves
4 Singing Perfect Fifths
5 Singing Major Thirds
6 A Map of Harmonic Relationships
7 The Perfect Fifth Below: Hello Mother
8 The Major Third Below
9 The Central Section of the Map Completed
10 The Five-limit Lattice of Twelve Notes
11 Available Modes: Lydian Through Phrygian
12 Mixed Modes
13 Internalizing the Lattice
14 Numbers and Mysteries
15 Chomatic Pairs
16 Beyond Twelve Notes: The Extended Five-Limit Lattice
17 The Seventh Partial and Beyond
18 The Practice of Pure Harmony

Part 2: The Selective Use of Equal Temperament
19 Leaping from Paradise
20 Six Unambiguous Chords
21 Twelve Unambiguous Chords: Tonal Harmony within the Lattice of Twelve

Notes

22 Unambiguous Triadic Harmony in the Extended Lattice
23 Dronality in Equal Temperament: Mixed Modes
24 Dronality in Equal Temperament: Mixed Modes
25 Chromatic Pairs and the Magic Mode
26 Pushing the Magic Mode Envelope

Part 3: The Function Commas of Equal-Tempered Tonal Harmony
27 Comma Phenomena
28 Didymic Pairs of Tones
29 Didymic Pairs of Triads
30 The Great Diesis: The Beauty of the Beast
31 The Tonal Array of the Great Diesis
32 The Diaschisma
33 Quasi-functional and Nonfunctional Commas
34 The Shape of Tonality

Part 4: Harmonic Practice, Analysis, and Review of the Theory
35 Practical Matters
36 A Small Syllabus of Diatonic Sequences
37 Cadential Practices: Parallel Borrowing
38 The Long Cadence: A Comprehensive View of Cadential Energy
39 Tonicization and Modulation
40 Modal Modulation
41 A Syllabus of Cyclic Sequences
42 Symmetrical Harmony and the Dissolution of Tonality
43 The Notation of Positional Analysis
44 Review of the Theory

Afterword

Glossary of Terms

Glossary of Singable Tones in Just Intonation

Sources

Acknowledgments

General Index

Index of Ratios

Index of Most-Referenced Examples, Figures, and Tables