W. A. Mathieu is the author of The Listening Book and The Musical Life. His compositions and solo piano music have been extensively recorded. He lives in Sebastopol, California, where he writes, composes, and teaches.

"Mathieu's books are worth reading for anyone in any field of music--jazz, classical, gospel, or any other. He's found the words to tell the power of music."

• 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

W. A. Mathieu is the author of The Listening Book and The Musical Life. His compositions and solo piano music have been extensively recorded. He lives in Sebastopol, California, where he writes, composes, and teaches.

"Mathieu's books are worth reading for anyone in any field of music--jazz, classical, gospel, or any other. He's found the words to tell the power of music."

• 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