The Quantitative/Measurement “Obsession”

The Quantitative/Measurement “Obsession”

Introduction

Another common complaint is that empirical researchers are obsessed with numbers and measurement. To many, this quantitative preoccupation seems contrary to the humanistic spirit.

Quantitative methods are important in empirical research for two reasons. The first reason is that counting can help us discover phenomena that might otherwise be invisible. The second (and more important) reasons is that counting helps make it clear when we are wrong. Counting and measuring are useful tools, like a magnifying glass or a stethoscope.

First, consider how numbers can aid in discovery: consider the story of radar imaging of the earth.

A Satellite Story

In the early years of the space program, NASA launched a simple satellite that used a radar beam to image the planet’s surface. The satellite produced very accurate readings of the height (elevation) for each point as it orbitted the earth thousands of times. The purpose of the satellite was to help geographers produce more accurate topographical maps of the earth.

About 3/4 of the earth’s surface is covered by water, so most of the data collected by the satellite was precise elevation measures of a given point on the ocean as the satellite passed overhead. Since the goal of project was to create accurate topographical maps of the landmass, the ocean data was considered useless. Moreover, each time the satellite passed over the same spot in the ocean, the water level was different (because of the effects of waves and tides).

Nevertheless, some bright scientist asked, “What would happen if, for a given point in the ocean, we averaged together all of the elevation measures?” Repeated measures would tend to erase the effects of the waves and tides. You might think that this would averaging procedure result in a smooth ocean surface. But when the researchers did this, they found that there were regions of the ocean where the average sea level was relatively high and other regions where the sea level was relatively low. This was how scientists discovered vertical currents.

We’re all familiar with horizontal currents — lateral movements of water, such as the “gulf stream” which moves water from the Gulf of Mexico to northern Europe. But there are also “vertical” currents: regions in the oceans where water is constantly welling-up from below, or being sucked-down from the surface. The radar data allowed researchers to see these vertical currents, and it was only possible to “see” these currents because of averaging large amounts of (highly variable) data. The averaging allowed the effects of waves and tides to be eliminated.

Melodic Arch

In music, the value of averaged measurements is apparent in the so-called melodic arch. Musicians have long observed an apparent tendency for melodic phrases to rise upward and then fall downward forming a sort of arch. Tunes like My Bonnie Lies Over the Ocean and Somewhere Over the Rainbow offer appropriate examples. In both songs, the phrases tend to ascend at the beginning and descend toward the cadence.

Of course, one can think of all kinds of exceptions. For example, both Joy to the World and the American national anthem begin with high initial pitches — dropping downward and then rising upward over the course of the phrase. So is there any merit to the notion of a melodic arch?

The figures shown below are from Huron (1996). The graphs pertain to samples of 7-, 8- and 9-note phrases. Almost twenty thousand musical phrases were averaged together in order to produce these three figures. Specifically, the first data points in each graph represent the average pitch height (measured in semitones from middle C) for the first notes in each phrase. The second data points represent the average pitch for the second notes, and so on.

Although we can identify plenty of individual exceptions, on average, the graphs are indeed consistent with the notion of a general melodic-arch tendency — at least in the case of some Western music.

Showing You Are Wrong

In my first year as an undergraduate student, I spent time reading some of the classic feminist writers — including works by Betty Friedan, Germaine Greer, Susan Brownmiller and Gloria Steinem. As a man, I frequently felt defensive when reading these works. From time-to-time I thought various claims were exaggerated or simply wrong. I recall reading one passage which discussed how men tend to dominate mixed conversations. My first response was skeptical. I’d grown up in a society where women were regularly portrayed as “chatterboxes” and “gossips.” I personally knew a couple of women whose monologues were perfectly capable of filling-in whatever air-time was available.

My skepticism led me to perform what may have been my first empirical study. One afternoon, I simply sat in a student lounge eavesdropping on different conversations around me. With pencil and notebook in hand, I watched the second-hand of a wall-clock, and recorded the amount of time men and women spoke in various groups. I also recorded the number of men and women participating in each conversation. After an hour or so, I tallied up the results. The numbers were sobering. In every mixed group that I monitored, men dominated the conversation by amounts that were disproportionate to their numbers. Despite the thousands of conversations I’d heard in my life to that point, somehow I’d failed to notice what was obvious to most women. The numbers in my notebook were not consistent with the “chatterbox” image of women. The numbers told me that I had been wrong. Ultimately, the numbers changed my attitude.

Research shows that it can be surprisingly hard to get people to change their views. Anecdotes can be easily dismissed as “one-off” exceptions to our beliefs. It takes constant battering with evidence, before people will finally acknowledge that their beliefs may be incorrect.

Although the essence of good research is to invite failure, we may be slow to recognize failure when we see it. Numbers provide a useful tool for defining failure. In research, the principal benefit of quantitative methods is that they can provide compelling evidence that you’re wrong.

Bean Counters

Empirical researchers typically don’t like being called “bean counters” for the same reason that anthropologist don’t like being called “travel writers.” It is true that anthropologists travel, and write about the cultures they encounter. It is also true that empirical musicologists count things. But in both cases the goal is understanding and discovery. Counting provides a useful way for discovering aspects about the world that might otherwise be invisible to intuition or informal observation.

More importantly, the humble act of counting is the clearest way to invite failure. Recall that we recognize failure by drawing a line in the sand. As noted earlier, drawing a line means that we must have some way of determining on which side of the line the observations lie. We count and measure things as a way of inviting failure. We count, not because of some quantitative obsession, but because counting helps us recognize when were are deceiving ourselves (Huron, 1999).

Counting the number of malaria parasites in a blood sample is not a symptom of obsessive-compulsive disorder. Nor does it arises from some dark allegiance to the mechanical. It arises from an understanding that intuition can often warp perception rather than inform it, and that quantitative methods are valuable checks against our own intellectual enthusiasms. A person who genuinely cares about human welfare may ultimately find that his or her commitment leads to acts such as counting the number of malaria parasites in a blood sample. People who genuinely care about understanding music may similarly find that their commitment leads them to acts such as measuring the spectral centroid in a sung vowel.

At first, counting seems to represent the very antithesis of the humanistic spirit. But the humble act of counting offers one of the very best ways of addressing some of the most important questions in music and culture in a way that reduces self-deception.

References:

David Huron (1996). The melodic arch in Western folksongs. Computing in Musicology, Vol. 10, pp. 3-23.

David Huron (1999). The 1999 Ernest Bloch Lectures. Lecture 3. Methodology: The New Empiricism: Systematic Musicology in a Postmodern Age.