Oscillators for Singers
The interconnected nature of a true liberal arts education lets the disciplines inform one another—even physics and musical performance.
It's the first day of the course I teach on the physics of music. The students are mostly from my college's music conservatory; many of them have never set foot in our science building, except perhaps to take a shortcut from a dorm to the dining hall. A few slump in their seats. Others look around the room anxiously, as if trying to brace themselves for some strange physics equipment that they might be forced to use.
Before class began, I set up a small microphone which is connected to a computer. Now I open by welcoming them to the course and asking, "Who wants to sing a few notes into the microphone for us?" Some eyes light up in surprise and delight. Neighbours look at each other, seeing if the student next to them is up to it. One eager soul, a soprano, jumps up to the front of the room.
I ask the student to sing a single note at a comfortable pitch for a few seconds. The software that connects to the microphone does a quick analysis of the sound. The students smile and laugh with delight in the singer's obvious talent. I direct their focus to the projection screen, which shows a graph of amplitude, or size of the sound signal, versus frequency, the number of oscillations of air pressure the sound makes in a unit of time.
Then we discuss the science of sound. I point out that what appears to us to be one pitch is actually made up of several components. I ask the student to sing another note on a different pitch. We watch the changes on the screen, and the students describe the changes they observe. I ask for another volunteer and this time a male student volunteers. He sings a note and we compare again the similarities and differences in the components of sound. Another student volunteers to sing a note with quite a bit of vibrato. At this point the students are excitedly thinking about what types of sounds they can produce and predicting what changes might be seen on the screen.
For many of my students, this first day of class is the first time they have thought of their art as having a scientific basis. We spend the following class periods learning about oscillations: their descriptors of position, velocity, acceleration, time, amplitude, and frequency; how sound is a longitudinal pressure wave that oscillates in its direction of propagation; how instruments and the human body manipulate different variables to produce the wonderful variety of sounds that we hear. We measure the speed of sound by snapping our fingers at the end of a tube and measuring the time it takes for the sound to reflect back over a known distance. We learn about the history of tuning systems and how humans have devised a wide variety of temperaments, each one unique in how the notes differ in oscillation of air pressure.
As they build up the skills to quantitatively describe the oscillations that make up music, I sense their combination of amazement and frustration. They are thinking, where does all of this fit in with the joy that I have in music? How is it that a precisely known series of frequencies at different amplitudes can evoke emotional responses in listeners? If I know too much about all this, will it affect my ability to produce beautiful music?
These are weighty questions, but delving into them is the heart of the liberal arts mission of our college. No discipline is an island. Music especially is a wondrous example of the interconnectedness of the human experience. It is connected to science, as is our goal to explore in the course, as well as mathematics, anthropology, history, psychology—even religion and faith—and many other fields. The students are learning and experiencing that music is much more than notes on a musical staff. It is a high calling for our all-too-brief half-semester course.
It is (mostly) true that there is nothing new under the sun. These thoughts that my students are processing have been considered before and will be for generations to come. In 1863, Hermann Helmholtz, a man who oscillated between posts as professor of physics and professor of physiology, published his thoughts on the topic in On the Sensations of Tone as a Physiological Basis for the Theory of Music. He argued that the spatial and temporal reasoning in music evokes a sensory understanding of motion—and not just motion, but also emotion. Helmholtz considers music's origins in oscillations of variables in time and space and its extension to the rise and fall of notes, dynamics, and voices of a piece. He wrote, "It becomes possible for motion in music to imitate the peculiar characteristics of motive forces in space, that is, to form an image of the various impulses and forces which lie at the root of motion. And on this, as I believe, essentially depends the power of music to picture emotion."
Helmholtz later describes how the practice of learning the elements of music, both its theory and its physical basis, allow us to better understand the great works of others we experience. It enables us to see that "the artist is a man as we are, in whom work the same mental powers as in ourselves, only in their own peculiar direction, purer, brighter, steadier; and by the greater or less readiness and completeness with which we grasp the artist's language we measure our own share of those powers which produced the wonder." A careful study of music enhances our relationship to the art and its producers. We discover not only more about ourselves, but also more of what we are capable.
To my amazement, in a later class one student raises her hand and says that she has taught herself to sing two very different tones at one time as the Tuvan throat singers of Sibera do. She is somewhat hesitant to demonstrate her ability to the class, as the second, higher frequency at this point in her self-training is very faint. She holds the microphone and produces the sounds. The graph updates almost instantaneously and the class views it eagerly on the projection screen. There we see the quantification of the two sounds: the strong peak of the pedal note and the faint but measurable higher frequency note. The student smiles with great self-satisfaction; she and her classmates have connected with the skill, history, and culture of the Tuvan singers. And the science has quantified and enhanced how they understand the art.