Linear-Derived Harmony, by Arthur Komar

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Linear-Derived Harmony, by Arthur Komar. Cincinnati: Ovenbird Press, 1992. x +285 pp. ISBN 9781886464032.

Arthur Komar had a long and productive career as a scholar, teacher, music theorist, author of pedagogical materials, and as a former Editor of the College Music SYMPOSIUM. Most recently he served as Head of the Division of Music Theory and History at the College-Conservatory of Music at the University of Cincinnati (1982-89). Two especially valued and influential books are his Theory of Suspensions and his edition of Schumann's Dichterliebe in the Norton Critical Scores series.

Komar's Linear-Derived Harmony is a recent textbook for the teaching of common-practice period harmony—the result of over thirty years of thinking about the deficiencies of vertically bound conventional theory pedagogy for this topic. There is no doubt in my mind that the book has immense value and offers an original and fresh approach to the understanding of tonal harmony. But it is difficult, at first, to picture exactly how to take maximum advantage of its many benefits. Where would it fit in the curriculum, for example?

This text presents a strange combination of the most elementary topics (e.g.,"what is a passing tone?") alongside some very sophisticated ideas involving subtle distinctions of chord function and the meaning of individual pitches in particular situations. In defense of the approach, the distinctions are almost always useful and given to make valid musical points, not just for the sake of nit-picking. Because of the highly ambitious goals of understanding implied by such abundant and demanding content, the book could be intimidating for beginners, unless guidance from the most masterful teaching is provided, yet many of the topics are presented for a naive audience as if starting from scratch (although knowledge of fundamentals is assumed). It would be somewhat challenging to make such advanced and nuanced inquiry into the structural weight of musical events while at the same time learning to spell accurately the most basic chord vocabulary.

In spite of these contradictions, perhaps the best way to utilize such a book is as a supplement to a more standard text—as a kind of foil against which to test concepts and practices or as a way to extend discussion into deeper levels. In this regard, I can imagine that advanced undergraduate sections of freshman/sophomore theory would most profit from contact with these ideas. Other more likely uses might involve graduate analysis courses in advanced harmony and especially graduate theory pedagogy classes where instructors would want to compare approaches to teaching undergraduate harmony. This book certainly offers some stimulating alternatives to traditional methodology. At the least, the text is a tremendous teaching resource and even inspiration—a treasure trove of musical illustrations and advice for understanding dozens of subjects and situations.

The strong pedagogical bent is supported by a generous final section (almost 100 pages) of very useful and detailed classroom applications: (a) assignments; (b) part-writing and analysis exercises; (c) study questions (for review and classroom discussion); (d) summaries of pedagogical principles; and (e) definitions of terms. The study questions are especially useful. A minor inconvenience is that many of the analysis projects refer to specific passages from the standard repertoire by measure number only, so the task of searching out the music itself is left to the teacher. There is also a glossary and index (of music, but not topics).

The tacit assumption driving the content, organization, and pedagogical foundation of this text can be stated simply: Context is All. Every new chord studied is introduced as part of a 3- or 4-chord grouping so that, in addition to gathering important information about individual chords, the larger surroundings have to be continuously evaluated too. According to this view, harmony is the result of lines; the only truly vertical event in music is the tonic triad itself. Such a thoroughly linear philosophy places this book in the tradition of other undergraduate texts such as Leo Kraft, Gradus (Norton, 1987-90); Aldwell/Schachter, Harmony and Voice Leading (Harcourt Brace Jovanovich, 1989), and Joel Lester, Harmony in Tonal Music (Knopf, 1982). All of these texts, including Komar's, could be described as Schenker-oriented, although instead of instructing students how to do Schenkerian analysis, they prepare for such studies at a later time by tuning the mind to horizontal forces.

Regardless of whether someone would use the Komar book as preliminary work for another subject or to prepare for further study, the material does have merit in its own right. At the heart of Komar's linear approach, which is not, by the way, merely a rehash of what has appeared in other books, is a focus on the subtle interplay of dissonance and consonance and particularly a focus on tendency tones (e.g., on the urgency of scale degrees vol33id185, vol33id185, and vol33id185, under most conditions, to move toward their more stable "partner" pitches in the tonic triad—vol33id185, vol33id185, and vol33id185 respectively in this case). Of course, anyone who has ever learned about resolving V7 chords knows these facts. What makes Komar's approach distinctive is that he features these proclivities and scale-degree patterns (rather than just the more typical Roman-numeral analysis) in every situation, not just in the expected environments, to explain how and why one event leads to another.

It is this thorough and systematic—almost relentless—way (always relating pitches to the prevailing key through scale-degree function and not to the immediate chord as root, 3rd, 5th, etc.) that gives his teaching approach a special intensity and wholeness. The generative power of harmony is thus revealed to be the relationship of global forces of pitch centricity to local-level voice-leading maneuvers rather than just the voice-leading moves themselves. Said differently, the true topic of harmony is not chords, but tonality. Such a view is reminiscent of the concept of tonal framework first favored by the Belgian theorist, Francois-Joseph Fétis, in the 19th century—the view that tonality is the sum of all attractions between pitches (tugs, pulls, aversions) that singles out one of them for special focus. (Komar does not mention Fétis, but he does mention Godfrey Winham, a former colleague at Princeton, as a particularly strong influence.) Komar's approach is potent because he stresses what so many other more traditional approaches ignore: the bird's-eye view of the forest rather than the lumberjack's.

The master plan of the book is well constructed. Simply put, it evolves from a discussion of diatonic 3-chord patterns to elaborated 3-chord patterns to simple 4-chord patterns to chromatic 3- and 4-chord patterns to larger syntactic relations. This last section involves the relationship of the smaller chord groupings to one another, which in turn leads to the study of musical form. A chord grouping, according to Komar, is itself a tiny formal unit whose principles of structure also form the basis for the connections and inner workings of phrases, sections, and whole movements.

The simple 3-chord groupings (chapters 1-6) are nothing more complicated than a "I - V - I" pattern ("tonic - dominant - tonic" functions) and its endless permutations. Stated bluntly, the psychological foundation of this pattern (stability - tension - stability) can be summarized by the witticism, "All art includes a beginning, a muddle, and an end." The "dominant" function is described as a linear chord since it always contains at least one linear note (a scale degree other than the stable vol33id185, vol33id185, and vol33id185 of the tonic triad, especially vol33id185). Various configurations of neighbor and passing tones provide the necessary motion between or toward tonic-triad tones. The simultaneous and combined movement of scale steps other than vol33id185, vol33id185, or vol33id185 (i.e., linear tones) is the source of chords other than tonic.

Out-of-alignment possibilities (appoggiaturas, suspensions, anticipations), and then transformations of registral placement, are introduced eventually as desirable complications, variational techniques, or expansions of the simpler groups. It should be stressed that a 3-chord grouping does not necessarily mean that three attack points will be heard. Because of inversions, chunking by similar function, ornamentation, etc., more than three conventional Roman numerals may be required in analysis to represent all the "events" of a more basic 3-chord unit (e.g., I - I6 - Ivol33id185 - V - V7 - I). On the other hand, one could just as well argue that the truer (more meaningful) analysis here is the simpler, more foundational 3-chord pattern—proof of the principle "less is more"—and this is the way that Komar would want us to think.

Chapters 7-9 expand the range of options to include a 4-chord grouping ("I - IV - V- I") by adding various dominant-preparation chords (diatonic first, then chromatic: IV, ii, V/V, Aug6 chords, N6, etc.). Naturally the combinational possibilities here become endless, and representative samples are explored. Some of this recalls material found in Clough/Conley, Basic Harmonic Progressions (Norton, 1984) and, of course, dates back much further to Riemann. Excellent final chapters on melody harmonization, tonicization, and full-blown modulation (chapters 11-13) introduce the larger aspects of form briefly alluded to above.

Small touches that I especially appreciated include: (a) the treatment of the N6 chord, which is defined—correctly, in my opinion—not as a first-inversion major triad built on the flattened supertonic, but rather as an altered form of the minor subdominant ("iv")—almost no textbooks seem to get this right; (b) excellent distinctions among various kinds of enharmonicism (chapter 10); and (c) the treatment of "nesting" (a lower-level group of functional meanings embedded inside a larger functional unit, which could, in turn, be part of an even larger function)—all of this beautifully illustrating the concept of hierarchy. The nesting is sometimes represented by what I call "line technique" (e.g., ii - V - I, all over V). This idea is especially handy for situations midway between a simpler and briefer secondary dominant and more fully realized modulation. Mediant common-tone relationships are crisply characterized as just "MCT" without the messy fussing of Roman numerals that so many books get sidetracked with. Some of the melody harmonization solutions are especially well worked out too (numerous Bach chorales and the famous Brahms theme from the fourth movement of the first Symphony), as are ways of representing the functional similarities of chords that normally have very different kinds of labels (e.g., the "[V]o7" for the fully diminished seventh chord built on the leading tone).

Minor quibbles might include mention of a number of production errors. There are misprints and a lack of polished editing from time to time. For instance, not all page number references or example numbers are correct, and formatting choices are not always consistent. This is probably a by-product of what appears to be hasty production and desk-top publishing procedures with computer generated camera-ready copy. The book is published with a soft cover and spiral binding in 8 1/2" by 11" size without the glossy professional appearance associated with more commercial ventures, but it is thoroughly readable and the musical examples are large and clear.

Occasionally I felt that Komar made topics unnecessarily complicated. For example, his generally fine treatment of dominant-preparation chords was somewhat marred by getting bogged down in details of the many very slightly different variations. The larger point that these chords almost always include the combination of scale degrees vol33id185 and vol33id185 (or vol33id185 and/or vol33id185), although correctly made, became buried among all the examples. I would have liked to have seen it more highlighted. On the other hand, to the book's credit, it is the only text I have ever seen that defines the dominant-preparation category in such a sensible way—as a confluence of these particular scale degrees. In several other cases the same problem exists: lack of sufficient differentiation between the core and the periphery. This, of course, is where an experienced teacher would be required to operate as a tour guide through the thicket.

Ultimately what you value in a book of this standard, however, is not just the information conveyed, but the quality of mind of the author—and this is where Komar's book excels. This text is not just a collection of facts but is clearly the result of a lifetime of accumulated wisdom about how and why music works. To simultaneously celebrate both the richness and simplicity of tonal music, which this book so admirably achieves, is a remarkable accomplishment. Komar has been successful at helping us to understand why each note is present in the examples he discusses and why some notes give meaning while others take meaning. The musical lessons go beyond harmony in a book like this because the habits instilled by such a musical approach become activated over and over outside the classroom setting, whether those other situations are performance, composition, or listening. This is what all fine music books (and teaching) aspire to—to reverberate in the mind and ears of the recipient past initial acquaintance.

A related book (not seen by this reviewer) should be mentioned at this point. Publication of Workbook in Tonal Analysis (Ovenbird Press, 1994), also by Arthur Komar, has just been announced. The book is a collection of analyzed works from the traditional repertoire (Bach, Handel, Mozart, Beethoven, Chopin, Brahms, etc.) and according to the publisher, "it is designed as a supplement to classroom discussions, homework assignments, student examinations, and independent projects. A coordinated set of questions and answers is featured for each assigned selection. . . . The goal of the Workbook is to encourage students to notice as much as possible about any music they choose to study. In addition to covering the gamut of traditional analytical subjects—form, harmony (local and large-scale), motivic continuity, etc.—the Workbook places heavy emphasis on features which are specific or possibly unique with respect to each individual piece of music." I am guessing that the book would provide a worthwhile complement to the harmony text reviewed above, not only for the wealth of insights about individual pieces discussed but as a model for analyzing any tonal composition.

Except for the time-honored treatises of past eras, the only other modern harmony books I know of even remotely similar to Komar's are the well-known Richard Franko Goldman, Harmony in Western Music (Norton, 1965) and the little-known Leland Smith, Handbook of Harmonic Analysis (Stanford University Department of Music, 1979), each totally different from Komar's book in approach and content but all three alike in having a unique flavor (the stamp of specialness) and strength of temperament—and so unlike the generic retreads we see so often under the guise of educational materials.

All serious music libraries and all serious theory teachers should keep a copy of Linear-Derived Harmony on the bookshelf for ready reference at all times.

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Last modified on Monday, 22/10/2018

Michael R. Rogers

Michael R. Rogers, Founding Editor of the Journal of Music Theory Pedagogy, is the author of Teaching Approaches in Music Theory (2004) and co-author of the multi-volume, Tonality and Design in Music Theory (2005), as well as numerous journal articles on pedagogy and analysis.  His teaching appointments have included the University of Maryland, University of Arizona, Michigan State University, Australian National University, and the University of Oklahoma, where he was the Kenneth and Bernadine Russell Endowed Professor of Music Theory (now retired).  His current appointment is as Visiting Professor at the University of Oregon, where he teaches part time and continues his research on the role of intuition in musical performance.

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