Tonality : an owner's manual /

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Includes bibliographical references (pages 583-598) and index.Implicit musical knowledge. Gesualdo's trick ; The quadruple hierarchy ; Philosophy ; Statistics ; Schema ; Outline -- Prelude : Transposition along a collection -- Rock logic. A melodic principle ; A harmonic princlipel ; A first loop family ; Two more families ; Sheptard-tone passacaglias ; Minor triads and other trichords ; A fourth family ; Other modalities ; Function and retrofucntion ; Continuity or reinvention? -- Prelude : The Tinctoris transform -- Line and configuration. The imperfect system ; Voice exchanges ; Other intervals ; The circle of diatonic triads ; Voice exchanges and multiple chord types ; Four-voice triadic counterpoint ; Thinking within the chord ; Seventh chords ; Harmony and counterpoint -- Prelude : Sequence and function -- Repetition. Repetition reimagined ; Repeating contrapuntal patterns ; The geometry of two-voice sequences ; Three voices and the circle of triads ; Three voices arranged 2+1 ; Four voices ; Contrary-motion sequences ; Melodic sequences and near sequences ; Near sequences ; Sequences as reductional targets -- Prelude : Three varieties of analytical reduction -- Nonharmonic tones. The first practice and the SNAP system ; Schoenberg's critique ; Monteverdi's "Ohimè" ; The standardized second practice ; A loophole ; After nonharmonicity -- Prelude : Functional and scale-degree analysis -- The origins of functional harmony. The logical structure of protofunctionality ; Similarities and differences ; Origin and meaning ; Harmony and polyphony ; The Pope Marcellus Kyrie ; A broader perspective ; "I cannot follow" -- Prelude : Could the Martians understand our music? -- Functional progressions. A theory of harmonic cycles ; A more principled view ; Rameau and Bach ; Functional melody, functional harmony ; Fauxbourdon and linear idioms ; Sequences ; Bach the dualist -- Prelude : Chromatic or diatonic? -- Modulation. Two models of key distance ; Enharmonicism and loops in scale space ; Minor keys ; Modulatory schemas ; Up and down the ladder ; Modal homogenization and scalar voice leading ; Generalized set theory -- Prelude : Hearing and hearing-as -- Heterogenous hierarchy. Strategy and reduction ; Two models of the phrase ; Chopin and the prime directive ; An expanded vocabulary of reductional targets ; Simple harmonic hierarchy ; The four-part phrase ; Grouping, melody, harmony ; Beyond the phrase : hierarchy at the level of the piece -- Prelude : Why Beethoven? -- Beethoven theorist. Meet the Ludwig ; From the schema to flow ; The Tempest ; The Fifth symphony ; The "Pastorale" sonata, op. 28 ; Schubert's Quartettsatz ; The prelude to Lohengrin -- Conclusion -- Appendices. Fundamentals ; Deriving the spiral diagrams ; Sequence and transformation ; Corpus analysis, statistics, and grammar."This encyclopaedic book proposes a sweeping reformulation of the basic concepts of Western music theory, revealing simple structures underlying a wide range of practices from the Renaissance to contemporary pop. Its core innovation is a collection of simple geometrical models describing the implicit knowledge governing a broad range of music-making, much as the theory of grammar describes principles that tacitly guide our speaking and writing. Each of its central chapters re-examines a basic music-theoretical concept such as voice leading, repetition, nonharmonic tones, the origins of tonal harmony, the grammar of tonal harmony, modulation, and melody. These are flanked by two largely analytical chapters on rock harmony and Beethoven. Wide-ranging in scope, and with almost 700 musical examples from the middle ages to the present day, it weaves philosophy, mathematics, statistics, and computational analysis into a new and truly twenty-first century theory of music"--