Natural tone
Fundamental frequency of a vibrating body.
What it means
The natural tone (German Eigenton) is the pitch at which a body vibrates of its own accord when it is excited. Every body has such preferred vibrations — a string, a column of air, a drumhead, a bell, a room. Which ones these are depends on dimensions, material, and tension. With a string, length, mass, and tension determine the fundamental frequency; with the air column of a wind instrument, the length and the form of construction.
Musical use
The concept explains several phenomena that are met directly in music-making. A body vibrates not only at its fundamental frequency but at the same time in partial vibrations; their relation determines the tone colour and yields the harmonic series. If a body is excited from outside at its natural frequency, it begins to vibrate in sympathy — that is why related strings ring along on the piano with the pedal down, why an open string responds when the corresponding note is fingered on another string, and why resonance boards and instrument bodies react with differing strength to different pitches.
For instrument making this is the central subject: a well-built instrument reinforces the vibration of the string or air column evenly over the whole compass. Where individual natural vibrations of the body stand out particularly, unevenly responding notes arise — a well-known problem with string instruments. Rooms too have natural frequencies, which explains why certain pitches in a hall seem conspicuously louder than others.
Every body that can vibrate has one or more natural tones; with a string or air column these are the fundamental and its overtones, whereas with bells, plates, and membranes they are mostly inharmonic frequencies. With instruments a natural tone of the body can stand out disturbingly; with violins and cellos one then speaks of the wolf tone. In room acoustics, natural frequencies of a room lead to booming at certain low notes.
Performance practice
Use sympathetic vibrations in intonation: if an open string clearly rings along, your fingered note lies right. On the piano the effect can be heard by silently pressing down a key and striking a related note strongly. And adapt to the room — a note that stands out excessively in a hall needs less force there, not more.