Underlying the concept of harmony is the idea of the difference tone.
You are probably accustomed to hearing a beat rate when two tones whose fundamentals are close in frequency are sounded together. The beat rate is caused by the interference effect which occurs as the waveform of one tone gradually shifts in phase relative to the other tone. The beat rate is useful in determining the consonance of notes; if the beat rate is high, then the we know the tones are distant; if we retune one we know we are getting close to unison as the beat rate slows down.
It happens that the beat rate is exactly equal to the difference in the two frequencies so if we retune in the other direction, shifting the relative frequencies apart, the beat rate will speed up and when it reaches the audible range at approximately 30hz it becomes a difference tone.
Difference tones play a big part in harmony. The perfect fifth for example, comprises two tones in the ratio 2/3, producing a difference tone an octave below the lower of the two tones and the modulation of the combination tone gives the fifth its stridency. The perfect fourth on the other hand has a difference tone a fifth below the lower tone and two octaves below the higher one, producing a different modulation.
