Intervals: where physics becomes music

Discovery 2 of 7

4th century BCE

Consonance counted

Small numbers sound calm.

Sound both notes of a 2:1 pair together and they melt into one. 3:2 keeps a little shimmer, 4:3 a little more. Move to 9:8, two notes a single step apart, and the blend turns to grinding.

The Pythagoreans measured all of this with fractions and noticed that calm arrived with the smallest numbers. Nobody could yet say why.

Lacking a cause, Greek thinkers promoted the pattern into cosmology and tuned the planets themselves to the same fractions, a music of the spheres said to surround us unheard.

The physical cause went unmeasured for another two thousand years. It appears on the last page of this story.

Play the five pairs in order, from octave to semitone. Listen for the octave to fuse, the fifth and fourth to shimmer, and the close pairs to grow rough. Small-number ratios repeat their joint wave pattern sooner; larger ratios take longer to meet again. The sequence turns an old numerical ranking into a change you can hear.

Measure every distance in Intervals ↗

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.

How did one findingopen the next?

Small numbers sound calm.

How did one finding
open the next?