Intervals

Story · Guided tour

How did one finding
open the next?

Start with one stretched string. Seven pages each add one finding and one sound experiment.

Discovery 7 of 7
1636 to 1863 CE

The reason underneath

Every note is a chord already.

In 1636 CE Marin Mersenne listened closely to one plucked string and heard quiet extra tones ringing above it. In 1701 CE Joseph Sauveur measured them: a string vibrates whole, in halves, in thirds and onward, all at the same time.

This museum calls each pure component a partial, numbered from 1 at the fundamental. Sauveur named the whole-number multiples harmonics and coined the word acoustics. An older name, overtone, skips the fundamental, so overtone 1 is partial 2.

This explained the ancient pattern. Two notes an octave or a fifth apart share many of these partials, so they fuse. A rough pair sets neighbouring partials beating against each other, a mechanism Hermann von Helmholtz worked out in 1863 CE.

Even the major triad was waiting inside the string: partials 4, 5 and 6 of any deep note spell it out. The small-number ratios the Greeks measured on the monochord match the spacings between one string's partials.

Play the deep string, climb partials 1 through 6, then hear partials 4, 5 and 6 as a triad. Listen for the staircase to rise while the last three tones fuse into one chord. A string vibrates in whole-number sections at once, creating these partials. Their shared pattern connects the ancient ratios to the physical structure inside every periodic musical tone.

Three partials of the same 110 Hz string, written as a chord: A4, C♯5 and E5.
Build a tone from its partials in Harmonics
You have completed the seven discoveries.

From the lobby, visit any exhibit room to hear its discovery more closely.

Phonology · The vibrating string

This is a monochord.

One string is stretched over a sounding box between two fixed ends. The rule beneath it measures the string, and the movable bridge stops it wherever you set it. Musicians and early students of nature both worked with this instrument, because it turns a length you can measure into a pitch you can hear. Set the equal parts, watch the bridge slide, then pluck. The shorter the sounding length, the higher the pitch.

One string over a sounding box, a rule that measures it, and a bridge that stops it. Musicians and early students of nature both used this instrument to turn a measured length into a pitch. Set the equal parts, watch the bridge slide, then pluck. The shorter the sounding length, the higher the pitch.

Move the bridgewhole string · 110 Hz
Sounding length1