David Damschroder's Thinking About Harmony focuses on the history of harmonic theory and its practical applications for analysis in music from the first half of the nineteenth century. The book presents a kaleidoscopic view of the varied conceptions of harmony and harmonic analysis in a broad and comprehensive survey, centred primarily on nineteenth-century France and Germany, but temporally spanning the eighteenth through the early twentieth centuries and geographically spanning the British Isles to Bohemia. The theories and analyses presented therein are illustrated with many examples from primary sources, lavishly annotated and clearly explained.

The canonical early harmonic theorists, Jean-Philippe Rameau, Georg Joseph Vogler and Gottfried Weber are best represented, followed by Johann Christian Lobe, Simon Sechter and a core group of about four dozen other writers on music whose ideas reappear throughout the book. An appealing feature is that the works of many lesser-known theorists are considered, including a few of the 400 or so that were excluded for reasons of space from Damschroder and Williams’ extensive history-of-theory bibliography,Footnote 1 such as Jean-Baptiste Rey, José Joaquín Virués y Spínola, Johann Anton André, Daniel Jelensperger and François Durutte. Also given their due here are the harmonic theories of Johann Gottlieb Portmann, who is included in Damschroder and Williams’ bibliography but not in The Cambridge History of Western Music Theory,Footnote 2 and is better known for his writings on sonata form than those on harmony. Brief biographies of the theorists discussed are provided at the end of the book.

The preface borrows the words of Augustus Kollmann, written just over two centuries earlier, explaining that the work is ‘calculated for the use of those who wish to study musical composition, to teach music with propriety, or to judge of the music they hear, practise, and encourage’ (p. vii). Damschroder describes his hoped-for audience as all performers and scholars of music, but admits that a more realistic view of his potential readership comprises graduate students and professionals in the fields of music theory and musicology. Certainly Thinking About Harmony would serve as an excellent text for a history of theory course or a supplement to enrich a tonal harmony course at the graduate or advanced undergraduate level, as well as a valuable resource for music scholars and analysts concerned with issues of harmony. The biographical appendix of theorists is a potentially useful quick reference tool.

The chapters are organized by topic, and each surveys various perspectives on its subject and a core of surrounding issues, as expressed by a constellation of writers on music from the common-practice era. In each chapter, the theoretical discussions are followed by practical analytical demonstrations. The chapters end with these analyses, lacking more conventional conclusions, and thus readers are left to summarize and assimilate the materials for themselves. Sections within the chapters are preceded by shaded boxes of text whose function is not explicitly explained; although in form they strongly resemble textbook-style chapter or section summaries, their contents serve as introductions or transitions to new subtopics.

The analyses in the book are a mixture of excerpts from primary sources and new interpretations proffered by the author. Many of these are compelling, and Damschroder has drawn some fascinating connections between passages of music and abstract models in more or less contemporaneous treatises. His explanatory commentaries translate the theoretical ideas into modern terminology while for the most part avoiding modern analytical biases. He cautions readers that treatises should be understood as prescriptive rather than descriptive, and that they better reflect the music in currency at the time than the small percentage of those works enshrined in the modern canon (p. 86). These are important points which would be better placed in the introduction than a third of the way into the text.

Another important point reinforced throughout the book is that there was – and still is – no unified and universal analytical practice. The author critically assesses the explanatory power of various analyses, but for the most part avoids privileging any particular view as singularly correct. One exception to this multiplicity of perspectives is the author's comment regarding a dominant chain in C major presented in the third volume of Weber's Versuch: ‘Analysis in A major and D major [as opposed to Weber's more diatonic interpretation of A minor and D minor] would more accurately reflect what actually occurs’ (p. 66). This statement is at odds with Damschroder's prevailing and very welcome analytical heterodoxy, expressed later in his text by the comment that ‘ultimately every analysis is a conjecture’ (p. 155). Further, his assertion is disputable on purely analytical grounds: the chord qualities mark their status as dominants rather than tonics. One could easily imagine an analytical gloss on this passage that interpolates diatonic minor chords between each dominant-seventh chord, providing temporary tonic resolutions. In other words, Weber's analysis of the progression E7–A7–D7–G7 as a series of dominant sevenths in A minor, D minor, G major, and C major respectively, can be imagined as an elision of dominant–tonic progressions in those keys: E7–Am–A7–Dm–D7–G–G7–(C). Another encroachment of modern bias is Damschroder's description of omnibus progressions in Beethoven (p. 135) and Schubert (pp. 239–40) as ‘deformed’. Even if this term is used here in Hepokoski and Darcy's sense of departure from a norm,Footnote 3 without any negative connotations, it suggests that the composers consciously altered a standard or idealized version of the progression, which in light of the numerous differing variants of it in contemporaneous musical practice seems inappropriate and unlikely.

The chapters are arranged in increasing complexity of harmonic and tonal structures, not unlike the conventional ordering of topics in an undergraduate theory sequence: from chords to progressions to modulations, and from diatonicism to chromaticism. The topics addressed are chord identification and representation (Ch. 1), hierarchies of notes and of chords (Chs. 2 and 5), progressions (Chs. 3 and 4), modulation (Ch. 6), and chromatic chords (Chs. 7 and 8). Many of the issues considered remain subjects of debate today. The identification of chord roots, and in particular two well-known problematic examples, diminished-seventh chords versus dominant minor ninths with omitted roots and first-inversion seventh chords versus added-sixth chords, are treated in detail in the first chapter but recur in analyses later in the book. The problem of distinguishing chord tones from nonchord tones, and functionally independent harmonies from passing and neighbouring chords, is part of a broader consideration of vertical versus linear conceptions of harmony. The most famous debate along these lines, which is still a significant concern in the teaching of undergraduate theory, is whether six-four chords represent consonant second-inversion triads or dissonant double suspensions. Damschroder describes another perspective on these chords, which is to the best of my knowledge not offered in any typical harmony textbook: Koch's view that they are not suspensions but dissonant elevenths and thirteenths (pp. 43–5).

The last three chapters of the book are concerned with the topic of chromaticism. Chapter 6 on modulation investigates the distinction between temporary chromatic alterations of notes and chords versus tonicizations and modulations, Vogler's conception of Mehrdeutigkeit as multiple meanings of chords, and Weber's expansion of this idea to encompass our perceptions of chords and even keys, which might change upon repeated hearings of a work (p. 156). The derivations and enharmonic potential of diminished-seventh chords and augmented-sixth chords are surveyed in Chapter 7, and those of Neapolitan-sixth chords in Chapter 8. Teachers of undergraduate harmony will likely find it counterintuitive that augmented sixths were analytically parsed sooner and more readily (albeit variously) than Neapolitan sixths, which were interpreted by some theorists as chromatic alterations of scale-degree 1 rather than scale-degree 2 (pp. 198ff).

A valuable underlying thread in the analyses is the author's consideration of the relationships between theory, analysis, and composition, along with some small explorations of hermeneutic issues scattered throughout. In the epilogue (pp. 238–43), and very briefly earlier in the text (pp. 35–6), the relationship of analysis to performance is touched upon. Although its title makes no such claims, the book would have been enriched and would appeal to a broader swath of Damschroder's hoped-for audience of performers and scholars if performance considerations were more consistently addressed. The subtitle ‘Historical Perspectives on Analysis’ suggests a broader temporal scope than is found within the book. ‘Perspectives from the Eighteenth and Nineteenth Centuries’, which seems to have been the original subtitle as listed on the author's University of Minnesota faculty web page, would be more appropriate.

Its focus on harmonic theory makes the book an excellent companion to Ian Bent's Music Analysis in the Nineteenth Century.Footnote 4 Both works are collections of excerpts from primary analytical sources, provided with explanatory comments and interspersed with new analytical glosses. Bent's two volumes are organized around theorists rather than topics, encompass a broader range of issues, and contain only a handful of analyses that are concerned with harmony.

Overall, Thinking About Harmony provides a complete view of harmonic theory and the fledgling discipline of harmonic analysis in the nineteenth century, with no significant omissions and only a few minor ones. There is no separate chapter on cadences, which are treated in Chapter 4 along with other harmonic progressions, harmonic function theory (Funktionstheorie), and scale-degree theory (Stufentheorie). In the opening chapter on chord identification, André's system of geometric symbols for chord labelling is described (pp. 22–3), but unfortunately no visual example is provided. A strange omission from the bibliography is Damschroder's own earlier and more detailed version of the last section of Chapter 3, ‘Schubert, Chromaticism, and the Ascending 5-6 Sequence’.Footnote 5 The use of dashes versus hyphens to distinguish between horizontal and vertical collections of notes is too visually subtle, especially since much of the commentary regarding examples from primary sources is set in small type. Moreover, the beginning of Chapter 1, which immediately follows the explanation of symbols, uses three vertically stacked small capital letters to represent harmonic triads, which is both inconsistent and awkward on the page.

As noted, however, the above caveats are fairly trivial. Thinking About Harmony is a useful resource that provides a clear understanding of the origins of many of the theoretical systems and analytical conventions now taken for granted. In addition, through the breadth of writers and perspectives it represents, the book demonstrates that our current systems of harmonic analysis are not necessary or essential, but represent only a few of multiple possible viewpoints. Damschroder has continued this project with similar studies focused on the music of particular composers: Harmony in Schubert (Cambridge University Press, 2010), Harmony in Haydn and Mozart (in preparation), and promised future volumes on Beethoven, Chopin, Schumann and Brahms and Liszt and Wagner. Teachers and scholars of analysis and the history of theory will surely find these to be likewise helpful and worthwhile contributions to the field.