The magic string

One string, one movable bridge. Cut the string into neat fractions and it sings in tune — the oldest music trick in the world.

slide the bridge · tap a piece of string to pluck it

bridge at 50% of the string

put the bridge at:

of the string

2 : 1

Octave

whole string: 220 Hz (A3) · left piece: 440 Hz (A4)

Half the string, double the wiggles

Slide the bridge to the middle. The short half sings exactly one octave higher — half the string, double the wiggles per second. Try 2/3 next: the piece sings a perfect fifth higher, the friendliest sound in music. Small, tidy fractions make notes that belong together. Messy in-between spots? Pluck and hear for yourself.

a 2,500-year-old discovery

The story goes that Pythagoras — the triangle man — heard blacksmiths' hammers ringing in tune and went looking for the reason. He found it on a single stretched string: divide it at 1/2, 2/3, or 3/4, and the pieces sing in harmony.

It was the first time anyone showed that music follows math. The instrument you just played is his: it's called a monochord — “one string.” Every guitar fret and every trombone slide position is this same idea, still working.

For the classroom

Learning goals

A fraction of a string's length maps to a musical interval: 1/2 → octave, 2/3 → fifth, 3/4 → fourth, 4/5 → major third.
Pitch and length are inversely proportional: shorter piece, higher note (f = f₀ ÷ fraction).
Simple whole-number ratios were the first recorded connection between mathematics and the physical world.

Try this

1.Ask students to predict: if 1/2 gives an octave, what will 1/4 of the string sound like? Drag the bridge to 3/4 and pluck the SHORT piece to test it (two octaves up).
2.Hunt for the ugliest spot: let students drag the bridge anywhere and vote on the crunchiest-sounding division — then check how far it is from a tidy fraction.