28.3 · Sound Itself

Rough or smooth

Tension and calm have physics underneath. Two waves whose frequencies agree lock together smoothly: consonance. Two waves that almost-but-don't agree fight, and you can hear the fight as a throbbing called beating: dissonance. Neither is good or bad: music moves between them.

From calm to rough

Six pairs, held long so your ear can settle in. Listen for the surface of each sound: glassy, shimmering, or throbbing.

same wave, no beating
2:1, every other overtone shared
3:2, overtones line up, no beating
5:4, a faint beat
no simple ratio, overtones clash
one semitone apart, a slow throb of beating

Where the throb comes from

Two close frequencies drift in and out of step: together they're loud, opposed they cancel, over and over. That wah-wah-wah is the gap between the notes, made audible. The closer the near-miss, the slower and deeper the throb.

Where harmony's tension comes from

The dominant 7th pushes because it carries a tritone. The suspension leans because the 4th sits a half step above the third it replaced. Every 'tension' in harmony is beating and roughness, organized. Hear both resolve:

Quiz

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Beating happens when…