Vibration

What it means

A vibration is a regularly recurring movement around a position of rest — the string swinging back and forth, the air column in a tube, the head of a drum, the vocal folds. How often this process repeats in a second is called frequency and is given in hertz; it determines the pitch. The size of the excursion determines the volume.

Musical use

The relation of frequency and pitch is not linear but proportional: a doubling of the frequency always gives the octave, regardless of where in the tonal space. This is why intervals rest on ratios — fifth 3:2, fourth 4:3, major third 5:4 — and not on differences.

A vibrating body, moreover, never moves only as a whole: it vibrates simultaneously in parts and thereby produces the partials, from whose composition the tone colour arises. If a body is excited from outside at its own frequency, it is set into sympathetic vibration — this explains why, on the piano with the pedal pressed, related strings ring along, and why a soundboard reinforces the sound of the string.

Practically important, finally, is the beat: if two notes of slightly different frequency sound, their vibrations overlay into an audible pulsing that becomes slower the closer the notes lie to each other. This phenomenon is the most reliable means for exact tuning.

Vibrations are described by frequency, amplitude, and shape. The frequency determines the pitch, the amplitude the volume, and the shape, that is, the ratio of the partials, the tone colour. In instruments, strings, air columns, membranes, or solid bodies vibrate. The vibration is transmitted to the surrounding air and spreads as a sound wave.

Performance practice

Tune by beats: when the pulsing disappears, the interval is pure — this is more exact than any display. Check octaves and fifths first, thirds afterward. And bear in mind that temperature and humidity change the vibration ratios: tune only once the instrument has taken on room temperature, and check again after some playing time.