**Harmonic Series**

A
harmonic series is a set of vibrations whose frequencies are all integral
multiples of one fundamental frequency.
If F_{1} is the fundamental frequency then members of the
harmonic series may be found by F_{n} = n*F_{1}, where n = 1,
2, 3, etc.

**Periodic Complex Waves**

Any
set of sine waves whose frequencies belong to a ** harmonic series** will
combine to make

Any
periodic waveform of period P may be built from a set of sine waves whose
frequencies are from a harmonic series with a fundamental frequency equal to
1/P. Each sine wave must have just the
right amplitude and relative phase. These values can be determined from the
shape of the complex waveform.

**Nonperiodic Complex Waves**

Any
set of sine waves whose frequencies do ** not** belong to a harmonic series will
combine to make a complex wave that is not periodic, and will generally sound
impure or unsteady in one way or another.

Any
nonperiodic waveform may be built from a set of sine waves, but their
frequencies will ** not** belong to a harmonic series. Each component must have the right amplitude
and relative phase, which can be determined from the shape of the complex
waveform.