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Introduction | |
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About the Companion Web Site | |
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Mapping the Triadic Universe | |
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Three Ways to Calculate Triadic Distance | |
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Triads in Chromatic Space | |
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Remarks on Syntax and Maps | |
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Hexatonic Cycles | |
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A Minimal-Work Model of the Triadic Universe | |
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The Hexatonic Trance | |
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Contrary Motion and Balance | |
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Hexatonic Progressions, Tonnetz Representations, and Triadic Transformations | |
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Near Evenness, Minimal Voice Leading, and the Central Role of Augmented Triads | |
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Remarks on Dualism | |
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Triadic Structure Generates Pan-Triadic Syntax | |
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Triads Are Homophonous Diamorphs | |
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Reciprocity | |
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The Historical Emergence of Augmented Triads | |
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Consonance/Dissonance Reciprocity | |
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Two Early-Century Examples: Beethoven and Schubert | |
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Three Late-Century Examples: Liszt, Rimsky-Korsakov, Faur� | |
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Reciprocity in Weitzmann's Der Uberm�ssige Dreiklang | |
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Weitzmann Regions | |
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The Structure of a Weitzmann Region | |
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Weitzmann Transformations and N/R Cycles | |
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Remarks on the Tonnetz | |
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Historical Origins of Weitzmann Regions | |
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The Double-Agent Complex | |
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Expanded N/R Chains | |
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Weitzmann Regions without Sequences: Wagner and Strauss | |
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A Unified Model of Triadic Voice-Leading Space | |
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How Hexatonic and Weitzmann Regions Interact | |
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Chromatic Sequences | |
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Transformational Substitutions | |
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Voice-Leading Zones | |
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Remarks on Disjunction and Entropy | |
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Navigating the Triadic Universe: Three Compositional Scripts | |
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Neighborhoods and Pitch Retention Loops | |
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Departure → Return Scripts | |
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Continuous Upshifts | |
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Dissonance | |
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Four Eighteenth-Century Approaches to Dissonance | |
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Reduction to a Triadic Subset | |
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Hexatonic Poles in Parsifal | |
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Vie Tristan Genus as Nearly Even Tetrachord | |
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Circumnavigating the Tristan-Genus Universe | |
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Scriabin's Mystic Species and Generalized Weitzmann Regions | |
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Syntactic Interaction and the Convertible Tonnetz | |
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Some Previous Proposals | |
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The Diatonic Tonnetz | |
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Horizontal Extensions | |
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Vertical Extensions | |
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The Convertible Tonnetz | |
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Two Analytical Vignettes: Wagner and Brahms | |
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Double Syntax and the Soft Revolution | |
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A Summary Example from Schubert | |
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Double Syntax and Its Skeptics | |
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Code Switching and Double Determination | |
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Cognitive Opacity | |
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The Soft Revolution | |
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On Musical Overdetermination | |
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Glossary | |
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Bibliography | |
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Index | |