The Music in the Data: Corpus Analysis, Music Analysis, and Tonal Traditions

computerized corpus studies, the new kid on the music theory block, is here to stay. Corpus studies, both analog and digital, have long been met with a mixture of suspicion and awe: Some have embraced them with enthusiasm, but many have rejected their legitimacy as research tools in the humanities offhand. Nevertheless, in the past decade they have become standard features in music theory conferences, special journal issues, and books. As Christopher White points out in his new book, The Music in the Data: Corpus Analysis, Music Analysis, and Tonal Traditions, tentative attempts at music informatics date back at least to the 1950s,1 and yet its first instances were sporadic relative to the recent explosion of corpus-based research. The recent explosion of interest is the culmination not only of advances in information theory, but also of an increase in resources, with the availability of both printed and recorded music expanding dramatically over the past century. For instance, while Donald Frances Tovey could complain in the 1930s of the lack of access to the majority of Haydn's scores, by mid-century Haydn's complete works, as well as those of many lesser-known composers, were widely available. The advent of online libraries and digital formats in recent decades has further revolutionized access. This increased availability, combined with modern data-crunching tools and a computer-savvy generation of scholars, has facilitated large-scale musical corpus studies, enabling inquiries of a scope that until recently sounded like science fiction. The past decade has also seen the crystallization of several corpora for scholarly use. Some of these, such as the Cantus Database, the Troubadour Melodies Database, the OpenScore Lieder Corpus, or the McGill Billboard Project, focus on the digital representation of scores in a manner that allows computerized analysis.2 Others include manual analytical markup that accompanies scores, annotating entities such as cadences, harmonic verticalities, or schemata.3These two types of corpora correspond to two methodological approaches. The first, to which my own work belongs, relies on human analysis of the scores and uses computers to analyze the data. The other, of which Christopher White's The Music in the Data is representative, relies on computers to analyze both the musical corpus and the data gleaned from it. The distinction between these two methodologies is not merely technical—whether the markup of the data is performed by humans or computers affects the questions asked. For practical purposes, humans are quite unable to accurately analyze millions of chords in tens of thousands of works, whereas computers can do so in considerably less time than it takes us to make an espresso. Manual markup, on the other hand, enables us to ask more complex questions, investigating phenomena such as expressive schemata, hypermeter, cadences, and varied repetition that can only partly be explored through entirely computerized means. In both cases, however, we are required to work with categorizable data, restricting the kinds of questions that can be asked regardless of whether the analysis is manual or computerized.White's book is a welcome, thoughtful, and, importantly, reader-friendly contribution (at least to novices like myself) to the literature on computerized corpus analysis. After an introductory chapter dedicated to an overview of the state of the field and the book's methodology, White tackles a different fundamental concept of music theory in every chapter, showing how corpus studies may productively engage with them: style, harmony, function, meter, and key. Each of these chapters is composed in a literary genre of its own, a choice that White explains as designed “to highlight the creative, playful and interpretive stance” of the book (36). Thus, the chapters are modeled as an essay, an epistolary, a conversation, and a diatribe. The logic behind the choice of literary genre isn't always evident, but the variety in style makes for a constantly fresh reading experience and contributes to ameliorating the daunting aura that data studies hold for many in the music theory community.In the introductory first chapter, White presents his basic model for interpreting corpus data called the Meaningful Corpus Model. He maintains that corpora should be approached as a form of metascores, “as texts to be read, digested, and creatively analyzed” (294). He enumerates six strengths afforded by corpus statistics: The ability to make independently verifiable claimsContextualization of musical eventsClear and thorough argumentation, due to the necessity of clarifying assumptions for the sake of computationThe ability to build bridges between music analysis and cognitionA “bird's-eye view” (my term) that allows observations unachievable through traditional analysisThe ability to let go of preconceptions and biasesAlthough I thoroughly agree with White's list, I believe some qualification of points 1, 3, 5, and 6 is in order. We can indeed make independently verifiable claims, but this does not necessarily make them unbiased or less subjective: Just as a public opinion poll can manipulate questions so as to receive “the right” answer, so can the categories we define influence the outcome.Similarly, the opportunity to “lay bare assumptions” (20) is a mixed blessing. Corpus analysis and statistics require crisp categories, yet so much of everyday experience, not least of music, cannot be easily categorized. Anyone who has worked with musical corpora will have experienced the sense that they are doing violence to the data by forcing it into pigeonholes. When the problematic cases are few and far between, we can tolerate them due to the overall gain. But even in these cases, it is important to remember that the categories we use are a heuristic convenience, not a reality. And even more importantly, in corpus analysis, there are many questions that we simply cannot ask. Likewise, objective results are only an advantage if they are based on reliable information. Otherwise (returning to White's image of corpus studies as a score to be read), we are akin to an analyst interpreting incorrect details in a corrupt score. I will return to these points in more detail below.Chapter 2 investigates the manifestation of musical style in the Yale-Classical Archives Corpus (YCAC), which constitutes the main (but not sole) referential corpus throughout the book. The YCAC is parsed into what White calls “salami slices,” which are “the pitch content of each moment that a note is added or subtracted from the texture” (257), and this chapter demonstrates how statistical properties of 3-grams (three consecutive salami slices) over the corpus reflect musical style. Chapters 3 and 4 tackle harmony and function, respectively. It is in these chapters that White's methodology is at its most creative. Chapter 3 invites us to imagine a Martian who encounters several corpora of earthly music, including the YCAC. The Martian then tries to derive harmonic entities from the corpus based on statistical properties, and succeeds in doing so by using a series of reasonable logical steps, reducing the huge variety of vertical “chords” by subsuming rare ones within the common chords they are most similar to (i.e., slices with the closest pitch content), or within slices that behave similarly (i.e., that tend to move to or arrive from similar salami-slice classes). The framework story of the Martian, as well as White's clear, step-by-step reasoning, suggests an a-priori, no-assumptions approach, arriving at chord classes solely from the corpus properties. This, however, is an illusion: The process is teleological, driven with an eye to arriving at a foregone conclusion. White's Martian is no tabula rasa, but is instead thoroughly versed in music theory. His task is not to derive a harmonic system with no prior assumptions, but rather to check if existing theories are supported by the data. Although this defeats the purpose of having summoned the Martian in the first place, the chapter, like its successor on function, is both illuminating and entertaining, and provides some excellent insights on the stylistic differences between corpora. Chapter 4, in the form of an epistolary exchange between the author and an enthusiastic yet critical reader, continues probing chords, this time showing how the data reflects chordal functions.In chapter 5, White tackles meter, showing (largely on the basis of preexisting scholarship) how we can fathom meter in Western music using autocorrelation on a variety of parameters, yet without our being able to map the meter onto the corpus's patterns (i.e., to determine where the strong beat is). Importantly, the mapping between surface patterns and metric organization behaves very differently across different repertoires, problematizing meter detection even further. Chapter 6 inquires into key, surveying in turn various approaches to key finding, and demonstrating how these approaches work differently on different repertoires.Much of the scholarship within these chapters is not new, and the book does not provide a comprehensive guide to the literature on each topic. But it is very well-presented and, due to White's clear prose and excellent pedagogical skills, provides easy access to what could otherwise be a daunting field. In addition to the topics covered, White also offers excellent explanations of most of the central techniques he uses for corpus analysis, including entropy and cross entropy, clustering, correlation, and autocorrelation. These, as well as the connections he forges with information theory, language, and cognition, make this book a valuable asset to teachers (I have already enjoyed reading chapter 3 with an undergrad analysis class), as well as to scholars interested in making their first steps in computerized corpus analysis.Inasmuch as White's book constitutes an enlightening account of what we can do using corpus analysis, it is less enlightening about what we should avoid doing—the pitfalls present in this kind of research. Here, I wish to refer to four types of problems: misuse of statistics, reliance on noisy data, contentious inferences from the data, and a lack of awareness of the limitations of the methodology.Statistics is the bread and butter of corpus studies, our primary tool for creating the metascore that White encourages us to read. And yet, the study of statistics has still not found its way into the core studies of humanities, and many enterprising scholars must thus rely on their own, often unsystematic, forays into the field. The most common errors made are misinterpretation of (or disregard for) statistical significance, incorrect inference of causality from correlation, and mistaken handling of conditional probability. Although some of the statistical work in The Music in the Data is impressive, the book nevertheless loses its footing occasionally on some familiar stumbling blocks. It is with an eye to increasing awareness about these stumbling blocks that I point them out here.Chapter 1 introduces a hypothetical case of copyright infringement, invoking corpus data to weigh in on whether an identical sequence of notes in two songs is likely to be coincidental or not. White calculates how likely that sequence was to appear and uses that (low) probability to infer the likelihood of infringement (“34 times less probable than average random melody”; 8). Although this approach sounds intuitive, it is erroneous. If we assume that most similar songs are likely to end up in court, the judge should be asking not how likely a particular sequence is to appear, but rather how likely it is that pieces including any two identical sequences—not necessarily the sequence in question—will exist. This ends up being several orders of magnitude (a factor of nearly one hundred thousand) higher than White's calculation, and the likelihood ends up being very high, not very low. A slightly different, and simpler version of this error, known as the Birthday Problem, asks how likely it is for two members in a group of n people to share a birthday. Although the probability of someone else having my birthday is n/365 (hence we would need 183 or more people for a higher than 50 percent likelihood of someone sharing my birthday cake), the probability of two people having any birthday is much higher: A group of 23 people is more likely than not to include at least two people sharing a birthday.4As part of White's approach to the corpus as “a text to be read,” he advocates “the act of quickly manipulating a few lines of code to explore a corpus,” which is similar to “flipping through a score” (34). I doubt that any serious analyst would base their scholarship on flipping through a score, but where statistics are involved, White's advocacy of exploratory research because “running prior exploratory tests shouldn't diminish the actual probability that results are believable” (43) is particularly problematic. Running prior tests and selecting those that render results certainly diminishes the credibility of the results. The multiple-comparisons problem in statistics states that the larger the number of inferences made, the more likely we are to receive erroneous inferences. Thus, running multiple exploratory tests necessitates a more rigorous degree of significance. The primacy of statistical significance as the sole yardstick for quality of results has been challenged in recent years, yet by speaking of “the actual probability that results are believable,” White himself is inviting statistical significance in through the back door. Furthermore, in other cases, White is happy to summon statistical significance in the service of credibility: Figure 6.8a, for instance, presents some very similar data from corpora in different styles, yet White invites us to understand the barely perceptible differences between the stylistic trends (it would have been helpful if Routledge had included a larger version of the figure!) by invoking statistical significance. On the other hand, in chapter 5, no data on significance is provided regarding the slight and erratic advantage of pitch-class change over other parameters in identifying meter, yet White still offers an explanation for this advantage. Considering that when measuring any four features, one feature must be greater than the rest, the point of statistical significance would be to demonstrate that this means anything, or whether it should be interpreted.5A case could be made that in musical corpus studies, musical intuition or common sense can stand in for a prior hypothesis. In other words, if, flipping through the data, we come across something that also makes musical sense, we should adopt it with greater readiness than otherwise and insist less on rigorous statistics. 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Nevertheless, White does corpus studies a service by this of research not as a field but rather as a or where with new tools can be both enlightening and