# Beethoven in the Antarctic

If you’ve ever spent time learning to play a musical instrument, you’ve undoubtedly used a metronome—depending on your age, it may have looked something like this:

(For clarity, we’ll call that little trapezoid-shaped thingie the bob, while the bottom of the rod will be the pivot point.) The design of the mechanical metronome has not differed much since Johann Maelzel received this patent in 1815—more on this in a later post.

While today’s metronomes are often electronic devices, for centuries they were based on Galileo’s pendulum principle: the time taken by one full swing of a pendulum depends only on the bob’s distance from the pivot point (and on gravity). Crucially, the time is not dependent on the mass of the bob, or the width of the swing.* In fact, one early definition of the meter was the length of a pendulum that would swing from one end to the other in the space of two seconds.

In the end, though, this definition was rejected in favor of the so-called meridional definition: the distance along a meridian of the Earth from the Equator to the North Pole. Why the change? Well, it turns out the Earth isn’t a perfect sphere—it’s an oblate spheroid (that’s math-speak for “the spin of the Earth makes it bulge outward at the Equator”). So, the force of gravity is somewhat less strong at the poles than it is at the Equator.

Now back to the history of the metronome: musicians began to adopt the metronome in their compositions; Ludwig van Beethoven was notably one of the first to do so. By the 20th century, metronome notations (given in beats per minute) were included in nearly all musical works.

Given what we know about the Earth’s gravity, you may have already noticed that there’s a minor problem with metronomes—those at polar latitudes will click at a faster rate than those at equatorial latitudes. (Swiss Scientist & Mathematician Leonhard Euler gives a good summary of the issue in his 1738 work Von der Gestalt der Erden. See pages 4-5 of Langton’s translation, available here.)

Here’s the musical takeaway: if you are playing a piece that sets a tempo of 120 beats per minute, and are using a mechanical metronome to keep time, then you will play this piece more quickly at the South Pole than you would at the Equator. I do hope there are some musicians at the Amundsen-Scott Station who are enjoying the naturally-accelerated tempos of the region!

* I know what you’re thinking: it’s not actually this simple (it rarely is). There are some other factors in play, including the ever-menacing friction. But it’s close enough to the truth.