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Harmonic Experience
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Table of Contents


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

About the Author

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.

Reviews

"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 *
"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 *

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