The Mathematics of Music and Art

Play an A at 440 Hz. Play the A above it at 880 Hz.

The second sound wave vibrates exactly twice as fast:

880 : 440 = 2 : 1

Our ears hear two different pitches—but also an unusually strong relationship between them. The octave isn’t alone. Simple numerical relationships appear throughout musical intervals.

Are you listening to music or listening to mathematics?

Meet Bella, a young visual artist who finds geometry hiding in the creative process.

ODD Times: Do you think about math when you draw?

Bella: I don’t usually think about arithmetic, but geometry overlaps with art. I start with basic shapes, then add details.

Proportion and perspective create depth, while a flowing line guides the viewer’s eyes.

Read the full interview →

A dancer pulls her arms inward and speeds up.

Why? Pulling mass closer to the axis of rotation decreases the dancer’s moment of inertia. Because angular momentum is conserved, her rotational speed increases.

Figure skaters use the same principle.

Which graph can you draw in one continuous stroke?

Rules

1. Don’t lift your pencil.
2. Don’t retrace any line.

In the 1700s, physicist Ernst Chladni scattered sand across a metal plate and made the plate vibrate. The grains jumped away from the vibrating areas and gathered along still regions- forming astonishing geometric patterns. Today they’re called Chladni figures.

Sound wasn’t just something you could hear. Suddenly, you could see it.