Time and Space from Beethoven to 1913

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(Variation V m. 30 from the second movement of Beethoven’s Piano Sonata no. 32 in C minor, op. 111.)

In 1913, an art exhibit was mounted at the 69th Regiment Armory on Lexington Avenue in New York City (around the corner from where Hunter College is now located). This exhibit, which came to be known as the Armory Show, was the first introduction to American audiences of Modernist art. One of the most notorious and vilified paintings in the show was Marcel Duchamp’s Nude Descending a Staircase.


The artist spreads out every moment of a motion that takes place over time —  a woman walking down stairs — on one plane.

The artist Man Ray did something similar a few years later with his painting The Rope Dancer Accompanies Herself With Her Shadows.


The painting shows every moment of a dance, flattened out on one canvas, all at once.

It has been theorized that the perception of time changed with the birth of Modernism. Certainly technology had something to do with this: the invention of the automobile and innovations in railroads made it possible for distances to be breached more quickly than anyone would have imagined even a few years earlier. 1913 was also the year that Stravinsky’s ballet The Rite of Spring had its premiere:

What does Stravinsky do with the concept of time in this ballet?

Do you think that Henry Ford’s assembly line, also rolled out in 1913, contributed to the changed idea of time? How?

Einstein published his Theory of General Relativity three years later, in 1916, in which he declared that gravitation is a principle of space and time, or spacetime. 

Nevertheless, let us think back to the year 1822, when Beethoven wrote his last piano sonata, no. 32 in C minor (op. 111). In it, Beethoven (who was by then profoundly deaf) begins to experiment with space and time, predating Einstein’s theory by decades. In a sense, it’s not even a sonata, but rather a searching meditation on time itself.

If you look at the second movement (out of only two!) in your course packet — which Beethoven calls an “Arietta” — you will see that it starts with a sixteen-bar theme in 9/16 time. Why do you think Beethoven used such an unusual time signature?

The movement takes the form of a theme and variations. Notice that, as the variations succeed one another, Beethoven is further subdividing the beat and the time signature. Notice, for instance, that by variation III, the pianist is playing 64th notes against 32nd notes. And notice that Beethoven takes the meter from 9/16 to 6/16 to 12/32 and back. 12/32! Why does he do this?

Note that tiny note values does NOT mean fast playing. What does it mean?

And it’s not just time Beethoven is playing with: it’s also space. Space on the page, and distance on the keyboard. By the time we get to variation V, there are only eight measures per page, which is necessary because of the infinitesimal divisions of the beat. And notice that in variation V, m. 30, the pianist is asked to play virtually as high as possible on the keyboard, while in variation VI, m. 8-10 the right and left hands are outlining an enormous space across the piano from high to low.

Beethoven is expanding and compressing time and space in this late work in a way that foreshadows Einstein. Why? What do you think he means?