Tonality: An Owner's Manual

dmitri tymoczko'sTonality: An Owner's Manual (hereafter TOM) is an impressive achievement that no doubt will inspire and challenge innumerable theorists for years to come. Tymoczko once again takes on the central big questions that have exercised generations of theorists, as he did in his previous book A Geometry of Music (hereafter GOM [Tymoczko 2011]): What is tonality?, How and why did functional harmony develop?, What are the basic building blocks of tonal harmony and how can we model them?, What is the purpose of music analysis?, to name a few. His answers in TOM build off and reiterate those in GOM, and yet his theory has at the same time taken great strides forward. Voice-leading geometry remains central to his thinking but has receded much more into the background. Given the many ideas and the hundreds of analyses each of which could be the subject of an entire article by itself, a review of TOM is necessarily selective and not comprehensive. I therefore offer here instead a review essay that focuses on places where I see TOM pointing in especially promising directions for future research, giving special attention to critiques of a few of Tymoczko's ideas and conclusions that I think could be productive. I will address three main topics: the concepts of abstract voice, enharmonicism, and harmonic function.The organization of TOM can be interpreted, like that of GOM, as the time-honored format of theory followed by applications, although Tymoczko maps it somewhat differently (33). Chapter 1 is essentially introductory, setting the methodological stage and taking an abbreviated run-through of the theory of chapters 2–4. Chapters 2–4 present what I would characterize as the core of the theoretical basis of the book: spiral diagrams, the concept of transposition along a scale, chord-scale hierarchies, and a generalization of sequential repetition. Chapter 5 could also be technically characterized as theoretical, but the theoretical content consists largely of textbook non-harmonic-tone theory, with the interest primarily being in the refutations of alternatives, some statistics showing historical development of NHT usage, and the identification of specialized “Renaissance seventh” idiom that problematizes an otherwise simple reductional approach to NHTs. The remaining five chapters apply these tools to corpus analysis and the historical development of functional harmony (chapters 6–7), scale theory and larger-scale modulatory schemas (chapter 8), applications of chord-scale hierarchy (chapter 9), and, the longest chapter of the book, a study of Beethoven's distinctive approach to harmony and counterpoint, ending with five extended analyses of complete pieces, three from middle-period Beethoven and one each from Schubert and Wagner (chapter 10).The theory in chapters 2–4 builds off Tymoczko's previous work on voice-leading geometries. What sets TOM apart from GOM is that the theory in TOM abstracts away from most of the geometry of the earlier theory. The most explicitly geometric tool that Tymoczko develops in TOM is the spiral diagram, which reduces each n-dimensional chord space for n-voice chords down to one dimension by projecting onto the line of transposition, which is cyclic at the interval of 8ve/n. These diagrams serve as a foundational tool throughout the book, which as a whole illustrates the strikingly many ways this one type of construction explains deep-seated features of harmony. 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