It sounds like this“A sound has a single frequency, the pitch you hear, so a note on a violin is just one wave at one speed.”
Thinking a sound has one frequency
Why it feels right
We name notes by one number: concert A is 440 Hz. Tuners show one number and school diagrams draw one smooth sine wave labelled with its frequency. It is easy to take from this that every sound is a single wave, and that a note is that wave.
Why it’s wrong
A real note is a stack of pure tones: the fundamental you hear as the pitch, plus whole-number multiples called harmonics. A violin and a flute playing 220 Hz share the pitch but differ in how much of each harmonic they contain, and that mix is what you hear as the tone.
A worked example
A pure sine wave is a very particular sound, like a tuning fork or a test tone. It has exactly one frequency and sounds thin. Almost nothing in nature makes one.
When a violin string vibrates at 220 Hz, it also vibrates in halves, thirds and quarters, at 440, 660 and 880 Hz, each more faintly. These are the harmonics, at whole-number multiples of the fundamental. Your ear hears the whole mix as one note at 220 Hz, with the character of the violin. A flute playing the same note has far less of the higher harmonics, which is why it sounds smoother. The picture of the wave itself looks different for each, even though the pitch is the same.
Seen this way, a wave shape is a recipe: how much of each frequency. A square wave of height 1, for example, is the sum of sines at 1, 3, 5, 7 times the base frequency, with strengths 4/pi, 4/(3 pi), 4/(5 pi) and so on. Fourier's insight was that this recipe exists for almost any wave.
How to catch yourself
- You say a note 'is' one frequency.
- You think two instruments playing the same note make the same wave.
- You picture sound only as the single smooth wave in a diagram.
What to hold instead
A real sound is a sum of pure sine waves: a fundamental, which sets the pitch, plus harmonics at whole-number multiples. The recipe of strengths gives each instrument its tone.
Where you’ll meet it
- Wondering why a violin and a flute sound different on the same note.
- Reading a spectrum display on an audio program.
- Understanding what a synthesizer does.
Questions people ask
- What are harmonics?
- Pure tones at whole-number multiples of a note's fundamental frequency, such as 440, 660 and 880 Hz for a 220 Hz note. Their relative strengths give an instrument its timbre.
- Why do instruments sound different on the same note?
- Because they have the same fundamental frequency but different amounts of each harmonic. The wave shape, and so the sound, is different even though the pitch is the same.