Visualizing Music
DJ Harrison · Journal of Music Theory · 2025
writing about music is hard, and if the writing is about compositional techniques and their analysis, then the difficulties are insurmountable for all but a few. Want proof? From the pen of an eminence (whom I spare from identifying in this space): The fifth horn part of [composer's] heckelphone concerto contains in m. 456 a subtle transformation of the viola line from m. 123. Specifically, the seventh thirty-second note in m. 123 is taken up five octaves, subject to the CSET(X,Y)-transform, and then hurled downward into the third line of the divisi string basses, where, after being inverted into the fourth piccolo, it is reharmonized by an augmented-sixth chord in G-sharp major, subjected to rhythmic diminution, and held by a fermata (example 789).I trust that you figured out—by the final, parenthesized punch line, at least—that it's a parody, written originally to show a bunch of callow graduate students how not to relate prose and visualization in music analysis.1 Even as parody, the writing is brilliant. Active verbs (“taken up,” “hurled downward”) have readers imagine an immense orchestral score, instruments divided from basses to piccolos, onto which they are plopped down in m. 123 and instructed to follow clues to m. 456, where a fermata marks the end of the trail. “Ah, there's a map!” exclaim first-time readers of the paragraph. But, alas, they must become second-time readers—now embarking on a tiresome trek up Mt. Tedium.Suitably toned up to make parody harder to detect, the description of the, er, heckelphone oboe concerto passage may be all too familiar to teachers who regularly read mediocre student writing. It certainly was to the original author, who was reading mine, along with those of several others. The teacher's recommendation was to invert the structure of the paragraph and make “example 789” the subject of the first sentence followed by an active verb like shows or (more daringly) reveals. Then came the predicate: the point of bothering with details to come.Even from the first sentence, it's clear that this far more effective approach requires example 789 to be completed in its essentials before any prose can be drafted about it. The rest of the teacher's “corrected” paragraph depended on it, as it was designed to keep readers involved with the example at every plot development, shuttling between prose and example, keeping place with their fingers. The example thus benefits from annotation, giving readers ways to reorient upon returning to it from the prose. Thus, Example 789 is a short-score arrangement of [composer's] heckelphone concerto, mm. 123 and 456, annotated for our purposes. The fifth horn part in m. 456 has a series of thirty-second notes, the seventh of which, labeled “x” in the example, is derived from the viola part in m. 123, labeled “y.” As shown by the solid arrow, y is taken up five octaves before being subjected to the CSET(X,Y)-transform. The dotted arrow shows how the resulting note, “z,” is hurled downwards into the third line of the divisi string basses, where a fermata marks the conclusion of the gesture.Despite such a thorough overhaul, reading this is still work, not play, and so strikingly at variance with the pleasures of music, with which it purports to be involved. Paragraphs upon paragraphs of this would be truly fatiguing for those not devoted to [the composer's] music. Acquaintances and the curious could very well be repelled—if not inspired to parody.Both versions, comic and earnest, are about an unseen example 789. In the comic version, it's imagined as an intimidating full orchestral score; in the revision, it seems to be a pared-down graphic mixing music notation with arrows and annotations. But no actual example is offered; the prose itself is sufficient to induce dread thoughts of the first kind of (parenthetical) example while stimulating good ideas about what should the second kind should look like.Writing about music is hard, but it's easier with good pictures. Eric Isaacson's Visualizing Music is all about this fundamental insight, useful for everyone who explains and teaches music, but pitched especially to the people who need it the most: regular readers of this journal. What Isaacson has done in the way of curating a wide-ranging show of music-related artwork is extraordinary, and most of this review respects that achievement by treating the book as an art-gallery exhibition catalog. This, I confess, is neither how the author has written it nor how Indiana University Press is marketing it. “Best practices of visual design for professional music theorists based on science!” is the reason you, dear reader of JMT, should consult if not run out and buy this book. Part 1, titled “Preliminaries” and nearly eighty pages long, discusses the best practices, and the final part, “Visualization in the Professional Realm,” starts off with a chapter full of sensible advice about making conference handouts.Even so, I recommend spending a lot of unstructured time looking at the artwork in the middle parts, devoted to visualizations of musical spaces, time, pitch, texture, timbre, form, and analysis, as well as consulting pieces in the offsite/online storage facility before getting down to the author's prose purposes.2 Approaching the main body of the book as a catalog of an imaginary gallery—laid out on an immense scale with dozens of distinct rooms, each containing thematically related yet contrasting works—unlocks the most consequential aspects of Isaacson's project for music theorists, those concerning the epistemologies of their various practices (as framed in Cook 2001), the history as well as the future of such practices, and the special problems of imagining them as multimodal discourses.3 None of these issues can be treated comprehensively in the space of this review; having raised them, however, I think readers coming to Visualizing Music after reading my admiring words about it will quickly form their own productive ideas about these and other issues, which will in turn inform their own efforts to become more effective communicators.It is eye-opening to be reminded that the catalog is not the collection itself. Everything in Visualizing Music is a reproduction, sometimes resized from original proportions and cropped from complete context. Just as a catalog might prompt a visit to the gallery for a more engaging experience, it can be very rewarding to look up the originals cited in Visualizing Music. For example, in the “Musical Spaces” wing is a small gallery, “The Overtone Series,” devoted to this phenomenon (chapter 21). Indulging my specialist tastes, I went there at once and found the familiar grand staff representation of the first sixteen partials from (cello) C2, whole notes for recognized pitches and filled noteheads for the “out of tune” ones. Reproduced at scale from Aldwell and Schachter's textbook, it represents an uncountable number of synonymous diagrams, which an internet search for “overtone series” will bring up only a few hundred. Nothing new to see here—though I'll return to the particularly disappointing design decisions that curator Isaacson points out.Next to this “old standard” is a (reproduction of a) handsome engraving from Ballière de Laisement1764 depicting the first sixty-four partials, rendered in French solfege syllables and ingeniously arranged in an upside-down pyramid to bring out octave equivalents of lower partials among the higher numbered ones. Drawn with the interests of acoustic scientists in mind rather than musicians, it beggars description in this space. (I invite you to consult the high-quality scan of the original page.4 The image in question is labeled fig. IV.) Reduced to half its original size for Isaacson's book and thus requiring a magnifying glass to make out its intricate detailing, the 12 × 5 inch original was pressed onto large format rag paper along with two other, smaller diagrams and, as typical for the practices of the day, bound into the volume at the end, folded up to fit the overall trim size. The author's drafting skills are outstanding (as are the engraver's), and his imaginative thinking with protractor, compass, and straightedge gives a subtle impression of a three-dimensional rendering. While it's far from clear how this feature clarifies the information Isaacson derives from it, it certainly enhances the image beyond its information content, inviting viewers to linger and discover what ideas of their own may be stimulated thereby.Which is to say, paraphrasing my earlier take, that while the purposes of Visualizing Music are practical, leading to near exclusive interest in and promotion of graphic content that's clear, efficient, thoughtful, contemporary, and aspires to professional standards of design, I urge readers to take interest and pleasure in considering such content as fine art rather than as illustration. Instead of coming upon an image primarily to extract its resources and then move on, please stay to find out what you could bring to it in return, going to an original if available, gazing instead of looking, wondering instead of confirming. Come for the information; stay for the pleasures of visual art!Sometimes, as with showing the overtone series on a grand staff, an object has entered mass production and may even be, like this one, a common, dusty tchotchke of the theory classroom and brass-instrument studio, occasionally reproduced live by the teacher. Many images included in Isaacson's book are like this and indeed truly lesser, with information that is indifferently implanted and thus difficult to extract. Western notation is often the culprit, as is the case with the overtone series. Consider this: Once “extended” from partial 7 through a typical stopping point at partial 16, the notational system can no longer accommodate pitches made by new prime numbers in that series as well as their octaves. Nearest neighbors have to be specially marked to represent these “out of tune” partials, ranging from vaguely, as in Aldwell and Schachter's sketch (Isaacson notes that it “doesn't specify the direction in which, much less the extent to which, the pitches are out of tune” [117]) to systematically, using some system of microtonal accidentals intended to move a notated pitch closer to an “out of tune” partial if not precisely onto it.In contrast, Ballière de Laisement's pyramid not only effectively treats the problem of having approximation mixed in with precise measurements, but also gives him an opportunity to invent a solfege name for partial 7, conventionally but inaccurately denoted in French as si♭; he dubs it za. Charming!—a theorist attracted to za as a way to explain the origins of seventh chords. Contrasting motives behind the drawings are very clear at this point: The staff representation is a good guide for brass players, arrangers, orchestrators, and “physics of music” teachers, while the inverted pyramid is a doctrinal statement about the generative properties of za.Another object in the same gallery can be seen in online figure 21.2, an at-scale reproduction of Robert Gauldin's staff representation of the overtone series, which Isaacson contrasts with Aldwell and Schachter's version. More informative about the placement of nonnotatable partials, it beams octave-related pitches, but, according to Isaacson, since “the beamed groups overlap . . . the effort required to see which notes are actually grouped significantly exceeds the value the beams add to the image” (118). While I sympathize with the point, my opinion is tempered by knowing the author's taste for line-dominated abstract art, as strikingly evident in cover choices for both editions of his Harmonic Practice in Tonal Music, with the first edition's use of Paul Klee's Ripe Harvest (1924) perhaps influencing the form of online figure 18.6. Does this knowledge invalidate Isaacson's criticism? No, but it does condition the way the object can be viewed, valued, and understood. Perhaps overbusy with the information conveying, it is yet pleasurably legible to appreciators of an art such as Klee's.I offer one more example of distinguishing between the catalog's representation and an object in situ. Online figure 18.6, an iconic image of “K and Kh complexes around set classes 6Z19 and 6Z44” from Forte 1973, is in color and thus more convenient to display on screen than to print on page.5 Iasaacson has cropped the image to its informational essentials and focuses on color choices: “Yellow does not stand out well against a white background, so a different color would have made those elements stand out more effectively, though the yellow + blue = green equation is a subtle indicator of what green means.” The equation may be subtle, but it is precisely the kind of valuable insight that can follow from taking time (out) actually to look for things in an image. The effectiveness of its color symbolism is somewhat at issue in the cropped image, an apparently at-scale scan of the original, but when looking at its cover-art context, sited beneath a bold green band exactly half its height, with title in white and author in yellow, the process coloration looks crisper and bolder on cardstock than the approximation on screen. (My copy has faded only slightly over time.)In the interests of advancing good design practices, Isaacson presents several visualizations that fall short of potential and offers improvements of either his own design or those of others. A particularly instructive case is the chord-group table from Hindemith 1937 (1942) reproduced on p. 203 in a chapter called “Schematic and Procedural Representations.” Hindemith's table is hampered by the use of music notation because it cites single elements of sets as examples of the whole category. While some small categories can be fully illustrated, others are immense and only a few samples can be shown. Kent Williams's rendition of the concept in flowchart form (204) is ingenious since it can sort any inputted chord into the relevant category with only a little effort, whereas using Hindemith's original as a lookup table for inputted chords can be slow and error prone. Proving the evocative powers of music notation to summon imaginary sounds, Hindemith's table, in Isaacson's view, has the advantage of providing at least a sample of representative types, whereas Williams's flowchart lacks objects to imagine, is therefore more abstract and thus in need of a supplementary visualization itself—perhaps, I would suggest, a couple of test chords to observe the sorting process. Isaacson concludes from this that “the emphasis on process over content makes flowcharts generally inferior to other representations” (202).A visualization of process and content, of flowchart and test-run results, moves toward a truly productive and multimodal interaction with the concepts at hand. Such interaction can be more fully realized with the addition of resulting sounds, with an interactive tool for inputting new test sonorities, and perhaps an illustration or two from Hindemith's works to support the general concepts. Another additional mode would be explanatory text, from as sparse as a symbol key to something as elaborate as several dozen words beginning with, say, “Figure 1(a) shows a flowchart of Hindemith's chord system as made by Kent Williams. Figures 1(b) through (f) show and document the process of inputting several test chords.”Current cultural drift is moving people away from verbal elaborations of this sort—at least as anything other than as a caption to some other nonverbal attraction. For if extended and permitted to dilate fully—even unto parody, as in the quotation in the opening paragraph of this review—the text section of multimodal discourse risks reader fatigue and stupefaction, especially if the other, more visually appealing modes are poorly done. Dora Hanninen recognizes if perhaps understates what's at issue: Verbal text can be an essential accompaniment for the effective use of visual images. Used strategically, it can complement and clarify, or duplicate and underline. Because words do not require the author to comment on, say, the spatial placement of nodes in a transformation graph, they can provide an opportunity to do so—to confirm or deny what, if any, iconic or propositional significance the given spatial placement might have. (Hanninen 2020: 728–29)Strategic rather than blanket use is surely to be recommended; it's the nature of any “comment” that's increasingly at issue. Time spent reading and thinking about the objects represented in Visualizing Music suggests that its author could very well be endorsing best practices in graphic design—which is to say, expertly conceived and executed—to take weight off the text mode as an “essential accompaniment” to the visual as well as to any others.Writing about music is hard; writing about its techniques is harder still; reading such prose without benefit of accompanying visualization and/or sound is unendurable. Isaacson's book testifies to the essential role that visualization plays, and has played, in communicating ideas about music theory and It at an time, as online of to the done visually sometimes with written for more of this is in and if content take the of Visualizing Music to intended by its author as well as those from its catalog of can be that ideas about music theory and can and more well into the