Introductory Seminars for First-Year Students

Harmonic Convergence: Music’s Intersections with Science, Mathematics, History, and Literature


How does music relate to neuroscience and the study of the human brain? In what ways are music and mathematics related? What are some connections between music and literature, and can novels be written in musical form? How has the relationship between music and politics changed the course of music history?

These are some of the topics we will explore in MUSIC 11N, Harmonic Convergence, an interdisciplinary course with music as its central focus. Through readings, recordings, videos, and creative projects, we will learn about scientific studies involving music and the brain by Oliver Sacks and other researchers. Through a hands-on approach to the topic of intonation, students will use a monochord to demonstrate minute differences in tuning between the Pythagorean, meantone, and equal temperament systems. They will also learn how the Fibonacci series, π, various forms of symmetry, and other mathematical properties have been employed in music composition.

Another topic will involve the intriguing connections between Beethoven’s “Kreutzer” Sonata for violin and piano, Leo Tolstoy’s The Kreutzer Sonata, and Leos Janacek’s Kreutzer Sonata (String Quartet No. 1), and the sociological and philosophical issues raised by Tolstoy’s novella. We will examine how the British composer-novelist Anthony Burgess spent much of his career exploring the interconnections between music and literature, especially in his most famous novel, A Clockwork Orange, which is written in a musical structure.

In the USSR during the 20th century, inescapable political realities compelled composers such as Dmitri Shostakovich to find the delicate balance between satisfying their creative needs and serving the requirements of the Soviet government. To explore this issue, we will examine Shostakovich’s opera Lady Macbeth, his Symphony No. 5 and String Quartet No. 8. 

Music by Bach, Mozart, Debussy, Stravinsky, and Bartok (among others) will also be studied, yet the ability to read music is not required for this course. Students with musical backgrounds may have the opportunity to perform works in class. The course meets twice a week, with 2-3 class meetings devoted to each topic, occasional student presentations, and class discussion in every class meeting. Each student will write two papers during the quarter, and there will be a final exam in the course. There will probably also be one class trip to hear a live musical performance (possibly at San Francisco Opera).

Meet the Instructor(s)

Paul Phillips

"I am a conductor, composer, and pianist who holds appointments at Stanford as Associate Professor of Music and Director of Orchestral Studies. I first taught Harmonic Convergence at Stanford in 2018 during my first year here, having created it a decade earlier while on the faculty at Brown University, where I taught it annually beginning in 2009. The concept for the course arose from research for my book, A Clockwork Counterpoint: The Music and Literature of Anthony Burgess (2010),and my longstanding interest in music’s relationships with science, mathematics, and history. Students in Harmonic Convergence have represented a wide range of interests and majors. Some of the top students in this course have not known how to read music and never played an instrument, while others have had extensive musical backgrounds. Some students credit Harmonic Convergence with having led them in new academic directions, including graduate study in music cognition."