Harmonic Experience

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." Pete Seeger, folksinger

"This book goes beyond what most textbooks offer, and its highly original pedagogy deserves the attention of every teacher of harmony.  Above all, this is a book for anyone who would like to acquire harmony as a lived experience rather than as mere memorization of unyielding rules on paper." 

Chien-Chang Yang, Quarterly Journal of the MLA

"Mathieu is consistently proving himself to be one of the best in musical theory." 

John Coltrane in Downbeat Magazine

"This volume offers experiential keys to help unlock the mystery of how music works its deep affect upon us.  Harmonic Experience extends any reader's understanding of music and is a user-friendly, elegant and graceful work. It is a technical treatise about the inner workings of music."

Daniel Atesh Sonneborn, Smithsonian Institution

MUSIC

“Harmonic Experience opens the door to a genuine renewal of music’s fundamental structure. At once an experience of discipline and freedom, it makes the ear aware of the finest subtleties of tuning at the core of harmony and does this in a way that clarifies the perception of our culture’s music while inviting the crossing of cultural boundaries.”
--Ben Johnston, composer

“Harmonic Experience is the Rosetta stone of music. It turns harmonic theory into a web of ah hah’s! What has been a tangle of inexplicable concepts is transformed into a repertory of generative experiences. Mathieu puts together what no one has put together before.”
--Will Johnson, professor of music, Sonoma State University

“This book is an epic investigation into the hierarchy of musical tendencies of just intonation and how these make equal temperament function the way it does. Everybody has been shaking their heads about the relationship between the two systems, but Harmonic Experience clears up the confusion and shows how to apply the central energies of harmony toward music of your own making.”
--Terry Riley

“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.”
--Pete Seeger

“Mathieu is consistently proving himself to be one of the best in musical theory.”
--John Coltrane, in 1962

Harmonic Experience offers a comprehensive view of music that reconciles the ancient harmonic system of just intonation with the modern system of twelve-tone equal temperament. Saying that “the rules of music were not formed in our brains but in the resonance chambers of our bodies,” W. A. Mathieu recognizes the pronounced need for an experiential kind of teaching that reconnects the way we think music with the way we do music. Mathieu provides over one thousand musical examples and diagrams to illustrate the ideas he presents, allowing readers to reach a deeper level of response, to hear existing musical compositions more clearly, and to become thoroughly engaged in their own musical creativity.

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.