The harmonic series is an ordered set of frequencies which are integer multiples of a fundamental frequency.

A visualization of the harmonic series

The first harmonic is the fundamental frequency and the second harmonic is the first multiple of it (the first overtone) and so on.

For instance, if we take the note A (440 Hz) above middle C on a piano, the following are the first eight harmonics:

  • First harmonic: 440 X 1 = 440 Hz
  • Second harmonic: 440 x 2 = 880 Hz
  • Third harmonic: 440 x 3 = 1,320 Hz
  • Fourth harmonic: 440 x 4 = 1,7600 Hz
  • Fifth harmonic: 440 x 5 = 2,220 Hz
  • Sixth harmonic: 440 x 6 = 2,640 Hz
  • Seventh harmonic: 440 x 7 = 3,080 Hz
  • Eighth harmonic: 440 x 8 = 3,520 Hz

NOTE: The term harmonics is used to describe both the fundamental AND the series of overtones.

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