I’ve always loved puzzles—the more complicated, the better. But my obsession didn’t seem to have an obvious relationship to my musical ability for many years. My musical trajectory was typical: I started piano lessons in elementary school and did the usual competitions and associated music theory workbooks, which I thought were pretty boring. Perhaps relatedly, I hated Bach (J.S., of course, I didn’t know there were others) until late high school, when my piano teacher, Caryl Smith, showed me how to analyze motivic relationships in imitative polyphony—a puzzle I enjoyed untangling. I didn’t make the connection between my interest in this sort of analysis and a future career in music theory until much later.
When I began college, I knew I wanted to continue playing piano, so I planned to double-major in music and a STEM discipline. I started with chemistry, but found that my favorite part of any class was deriving equations—so I found my home as a math major. As befitted my puzzle-solving interests, I planned to become a cryptographer. But at the same time, I loved my piano lessons, I enjoyed the puzzles of counterpoint and model composition, and I liked learning about obscure musical genres in music history. Still, I thought music theory wasn’t something that was for me—I was starting to consider changing my career path, but I wanted to pursue piano professionally.
Fortunately, I had a wonderful music theory professor, Youyoung Kang, my first year at Scripps College, a women’s college that takes as its motto the charge to help women become confident, creative, and hopeful. Professor Kang was a role model in a place I didn’t know to look: a fellow woman who had dual interests in music and mathematics, someone who didn’t underplay her love for the “geeky” parts of music. She recognized something in me that I didn’t: my excitement over analysis, over the especially “mathy” portions of our classes together (I loved set theory). Professor Kang inspired me to pursue music theory at the graduate level.
In graduate school, I thought I’d continue integrating math and music theory directly: I intended to study transformation theory or some sort of music psychology. But my musical interests and my graduate training led me elsewhere. In an early graduate seminar with Steven Rings, I was introduced to David Lewin’s writing on multiple hearings and experiences of music as wide-ranging as Schubert and Stockhausen. We read T.J. Clarke’s art history monograph, The Sight of Death, in which he re-analyzes the same painting, finding new details, day after day. I thought that this approach to analysis was freeing and fascinating, and I found myself less and less interested in studying a single analytical methodology. Instead, I found myself drawn to a type of music in which I had multiple, different experiences. The music that captivated me was one of Stravinsky’s early neoclassical works, his Concerto for Piano and Wind Instruments. I realized I wasn’t alone in my varied experiences of the work—and that this kind of neoclassicism has struck many people in a variety of different ways.
Although I wasn’t conscious of it, my mathematical interests gradually crept into my research: I wanted to catalogue historical experiences of neoclassicism, to understand whether these experiences matched my own, and to use these responses to understand, analytically, how Stravinsky modified expected tonal structures to strategic effect. I was fortunate to receive grants from my department and the university to do archival research that further strengthened my interest in the language the people used to describe these experiences. My preliminary, handwritten attempts to analyze all the adjectives people use to describe this music at different points in time became increasingly mathematical, so Seth Brodsky suggested that I look into text mining and the digital humanities. And, then, it all clicked: the right way to approach the mass of responses I had accumulated was through combining statistical analysis with closer reading of specific responses. I found that my results suggested that relationships between expectation and alteration were quite important to listeners, so I began to look into ways to represent these ideas in music analysis. Ultimately, I found that a combination of recomposition, schemata, and topic theory helped to reflect and reanimate those experiences.
In my teaching, however, I find that many of my students are reticent to explore music theory, in large part because they find its mathematical qualities disinteresting or intimidating. This response seems to come disproportionately from my female students. If we want to encourage more women to pursue music theory, one thing that may help is to consider the possibility that many of our students are afraid, that they have been taught that they are not good at math, that they have been told they have no aptitude for this kind of thinking, and that this predisposes them to dislike music theory and its mathematical trappings. Articles come out frequently about relative lack of confidence in STEM classrooms, indicating that women often underestimate their aptitude and skill in the classroom. Thus, encouraging confidence and creativity in our classrooms ought to be an important focus. Many of my students tell me they simply can’t think this way—and I take this as a challenge to show them that they can.
There are many ways, of course, to encourage students to overcome their anxieties, to enjoy and participate in music theory and analysis, but I want to suggest some that have been especially helpful for me:
- I emphasize that at its core, music theory and analysis is a humanistic discipline, not a scientific one. There are multiple ways to interpret a chord, a non-chord tone, or a form, and each interpretation adds richness to our musical understanding. It’s okay, preferred even, to experience the same piece differently on a different day!
- I work to demystify the myriad ways that music theorists use numbers to represent musical and music-theoretical ideas (c.f. Megan Lavengood’s “There are too many numbers in music theory”).
- I don’t shy away from the psychological and mathematical ties to our discipline. I lean into algorithmic thinking, emphasizing my own excitement at musical puzzles and mathematical ideas, but I also work to help students find ways to interpret these ideas creatively. One common exercise that I find helps with the overwhelming numbers in music fundamentals, for example, is to ask students to draw their understanding of relationships between parallel and relative keys—the results are often surprising and fascinating, and it allows them to encode many numbers in a way that makes more sense to them.
- I frequently ask students to bring in musical examples from their lessons, ensembles, or daily listening practices so that we can analyze them together and ground these abstract, sometimes mathematical ideas in music that they find compelling. Sometimes this may mean stretching the boundaries of what might seem acceptable, like analyzing sets in the music of Lana del Rey, but students end up less overwhelmed and more engaged.
Sarah Iker is Assistant Professor of Music at the University of Tampa. She holds a Ph.D. in Music History and Theory from the University of Chicago, and a B.A. in Music and Mathematics from Scripps College. Her research focuses on analyzing historical experiences of neoclassicism, digital humanities, schemata, and musical theater, and has recently presented research at the annual meetings of several regional music theory societies. She is a pianist, handbell player, and swing dancer.