The Harmonic Series
Every note you have ever heard is a stack of notes. A string does not only vibrate along its whole length; it also vibrates in halves, thirds and quarters at the same time, and those extra vibrations are why an instrument sounds like itself and why some intervals sound sweet.
- 1 note = many
- whole number ratios
- the source of harmony
Where you run into this
- Every acoustic instrument
- Synthesis
- Tuning
- Mixing
In short
A vibrating string moves in several ways at once. The whole length gives the fundamental, the pitch you name. The halves give a tone an octave above, the thirds a twelfth above, and so on up a fixed series of whole-number multiples. Each one is quieter than the last. Change the recipe of loudness across that series and you change the instrument without changing the note.
Adding harmonics one by one is the fastest way to understand why a flute sounds hollow and a trumpet sharp. Nothing about the pitch moves and the character changes completely, which makes obvious how much of what we call sound is actually the harmonics.
How it works
The first few harmonics are an octave, a fifth, another octave, a major third. That is a major chord, present inside every single note. It explains why those intervals sound consonant: playing them adds nothing your ear was not already receiving.
Where you run into this
- The bright edge of a trumpet, which is upper harmonics
- The hollowness of a clarinet, which is missing even-numbered ones
- A guitar harmonic, where you silence the fundamental and leave one member of the series
Our own examples
Three demos from our own synthesis: the fundamental alone, the first nine harmonics added one at a time, and the same nine with the fundamental removed so you can hear how much of a note survives without its root. Each one is a slider you move yourself, with a bar per partial so you see what you hear.