Approximating a square wave by 
  
    
      
        sin
        ⁡
        (
        t
        )
        +
        sin
        ⁡
        (
        3
        t
        )
        
          /
        
        3
        +
        sin
        ⁡
        (
        5
        t
        )
        
          /
        
        5
      
    
    {\displaystyle \sin(t)+\sin(3t)/3+\sin(5t)/5}
Approximating a square wave by

A harmonic spectrum is a spectrum containing only frequency components whose frequencies are whole number multiples of the fundamental frequency; such frequencies are known as harmonics. "The individual partials are not heard separately but are blended together by the ear into a single tone."[1]

In other words, if is the fundamental frequency, then a harmonic spectrum has the form

A standard result of Fourier analysis is that a function has a harmonic spectrum if and only if it is periodic.

See also

References

  1. ^ Benward, Bruce and Saker, Marilyn (1997/2003). Music: In Theory and Practice, Vol. I, p.xiii. Seventh edition. McGraw-Hill. ISBN 978-0-07-294262-0.