What is the connection between music, technology, and by extension, mathematics? Are there any? If so, how might they be connected? As I’ll describe, this topic holds a deep fascination for me; it has done so for quite a long time, dating back to my observations and experiences from a rather different segment of my life’s journey. It’s from an era that represents a formative, yet divergent path from the one on which I now find myself traveling. Yet, I couldn’t have arrived at this place of becoming a teacher on which I now find myself (joyfully so) without having gone off on a multi-decades long side trip.
First, I’ll note that the ancient Greeks considered music and mathematics to go hand in hand. Greeks such as Pythagoras, Plato and Aristotle initiated the development of the quadrivium (four ways) that was the foundation for the study of mathematics up through the middle ages. This structure divided mathematics into four sections: Number Theory, Geometry, Music, and Astronomy. Music did not become an area of independent study until the Renaissance and even then its affinity with mathematics has persisted (Papadopoulos, 2002). The connection continues to this day. Musical scales, measures, harmonics, tones, intervals, etc., all can be correlated to the much of the language, rules, and principles used in mathematics.
I want to note that the roots of these encounters with music and math go back to my childhood, though at the time, I don’t explicitly recall seeing a connection between the two. Rather, these were seeds planted during these times that enabled associations that would later arise. Bear with me as I first lay the groundwork of math and music on my own personal journey. It ultimately relates to the topic at hand.
Perhaps it was music that came first. I don’t recall quite what compelled me to request them, but for my sixth birthday I received a record player and three albums which I’d specifically requested (from my grandmother, who had no affinity with any of this). The Beatles’ A Hard Day’s Night, The Supreme’s Greatest Hits (a double album), and Petula Clark’s Downtown. For a six year old boy, these called to me musically (and Beethoven, Schubert, and Tchaikovsky did as well). About a year later, I began guitar lessons because I wanted to play the Beatles’ music.
Something got lost in the translation, because my mom signed me up for classical guitar, which obviously differs significantly from the rock and roll guitar playing. It was a serendipitous misstep, though, and I deeply appreciate the years spent practicing classical technique.
Then there was math. Math came rather easily to me. Perhaps it had something to do with my dad, who was an engineer and computer scientist. By the time I was in middle/high school, I happened to be enrolled at a school where, for certain groups, the high-school math path could be accelerated by a year. So, I took pre-Algebra in 7th grade. This was one year ahead of the typical middle to high school mathematics cycle then and was somewhat unusual (I’m not sure if this is common today). So, when we later moved and I switched to a new high school, I found myself a year ahead in math with respect to my 10th grade peers (having taken geometry and algebra as well by that time). So I was enrolled, instead, in an 11th grade Algebra II and Trigonometry class.
While I did quite well with math up through this point, my interests, academically, started to lead me in other directions. I became deeply drawn to the Humanities, particularly Homer’s Odyssey. And my abilities as a writer were just beginning to bud and bloom. I chose other lines of focus different from math as I finished high school and entered college.
College was a very conscious exploration for me. I wasn’t focused on a specific skill set or career, but set out to very deliberately pursue a full liberal arts education. I explored all the various schools of the university, tying my work together with the common thread that was Ancient Greek and Latin languages along with the history, archaeology, literature et al. that accompanies them.
Post college, it was this rounded, encompassing, humanistic line of study that prepared me for a return of a world that centered around mathematical concepts, implemented in practical ways: The world of the technology business.
These were the early days of the Macintosh computer and I was inspired by the vision of a device that was created as a tool for humans to pursue their work and passions, rather than a sandbox toy for technologists. This lead me to work for several startup companies. One of the early ones was a small company known as MacroMind (later to become MacroMedia). What is relevant to this discussion are the people who founded MacroMind and what they brought with them.
These founders where not traditional engineers. Rather, they were highly educated and trained musicians and artists. They witnessed the birth of personal computers and found a common desire and vision: they wanted to create music and art with these powerful new devices. Yet, when they tried, they were massively disappointed. Why? Because there were no adequate tools for creation on these machines. Rather than give up, they chose to create the tools themselves, realizing that no one else was going to do it anytime soon. It was at this point that I began to clearly see the connections between music and math (as I believe I think my colleagues had). They became software developers not out of a love of technology for its own sake, but because they had a vision to create music and art in new ways. The fact that both music and math are based on specific, measured languages built around relationships, proportionality, and scalability was not lost on me, nor on them. It followed naturally that these accomplished musicians would also make accomplished software developers, using programming languages to compose works just as they’d used musical theory and notation to play and create music. MIDI had meaning for me, not as a fashion skirt length, but as a tool for digital music creation (MIDI refers to Musical Instrument Digital Interface).
After MacroMind, I moved to work at NeXT Computer. The NeXT cube was an evolutionary leap (by a level of magnitude) after the Macintosh. Here I met and began working with a diverse and elite group of software and hardware engineers. Mathematics was the very foundation of everything that we created here; it was evident around every corner and in every office of the various engineering groups. In fact, one of the first roles I had was supporting software for our customers. One instance of which was the very first version of Steven Wolfram’s Mathematica which ran on NeXT computers.
The NeXT computer also included a dedicated digital signal processor (DSP) that was of particular interest to those interested in music as it could be used to specifically process complex musical signals with the speed necessary to perform complex, layered pieces. Indeed, at its introduction at Davies Symphony Hall in San Francisco in 1988, a NeXT computer played a duet with a violinist at the event’s closing (Schlender, 1988).
The number of musicians (professional or recreational) in the technology business has always been notable to me. Wherever I worked, there would typically be at least a few engineers who would play an instrument more than occasionally. Often their instruments would reside in their offices. I suspect that the act of playing music is, beyond its intrinsic value, a creative/thinking method that could help these individuals with their work, which naturally, as I’ve noted, is built on the foundation of mathematics. Additionally, at NeXT, we had at least one staff member from The Center for Computer Research in Music and Acoustics (CCRMA) at Stanford University who worked on applications for the DSP. Today, he is has returned to CCRMA full time and continues teaching and researching digital signal processing there.
In research this reflection, I came across a poem (below) aptly titled Music and Mathematics (Boucher, 2015). While Papadopoulos (2002) uses Pythagoras and Rameau to bridge the ancient and modern worlds and their connecting of music and math, Boucher’s poem does this in more lyrical language using Euclid and Beethoven. I find it an appropriate way to finish, as Geometry is amongst my favorite areas of mathematics; and, for me, Beethoven stands alone as a classical musician.
Music and Mathematics
Robert J. Boucher
Music and Math, their mystery unfurled
Exist outside our material world,
Without the sun, without the stars,
Without the earth, without mankind.
The “Ode to Joy” has forever been.
Beethoven, only the earth author
just one of many galactic men
recording what was revealed to him.
Euclid did not invent Geometry.
Euclid’s Geometry has forever been.
Euclid, one of many galactic
men recording what was revealed to him.
Did Euclid ever see the face of GOD?
Did Euclid ever hear HER voice?
Was it revealed in a geometric dream
as it was to the prophets of old?
We humans claim credit for so many things
that we will never, ever understand.
Note: This piece was originally published as part of my coursework at Pacific Oaks College in Pasadena, California. It's what we call an Academic Reflective Journal and originally was entitled Connections Between Music and Technology (vis a vis its mathematical foundations) (2019). How academic of me.
References
Boucher, R. (2015). Music and mathematics. Journal of Humanistic Mathematics, 5(2), 174. doi:10.5642/jhummath.201502.21
Papadopoulos, A. (2002). Mathematics and music theory: From Pythagoras to Rameau. The Mathematical Intelligencer, 24(1), 65-73. doi:10.1007/BF03025314
Schlender, B. R. (1988, October 13). Next project: Apple era behind him, Steve Jobs tries again, using a new system. The Wall Street Journal. Retrieved from https://tech-insider.org/unix/ research/1988/1013.html