I became aware of harmonics and the sound of different shaped waveforms early in my electronics career (mid 1970’s) as I was an avid fan of [Emerson Lake and Palmer], [Pink Floyd], [Yes], and the list goes on. I knew every note of [Karn Evil 9] and could hear the sweeping filters and the fundamental wave shapes underneath it.
I remember coming to the understanding that a square wave, which is a collection of fundamental and (odd) harmonics frequencies, could then be used to give an indication of frequency response. If the high frequencies were missing the sharp edges of the square wave would round off. The opposite was then true, if the low frequencies were missing the square wave couldn’t “hold” its value and the top plateau would start to sag.
Using a copy of [SPICE] a free circuit simulation application, I have created several sine wave sources and summed them together. Seen here, the waves combine into a square wave with it looking squarer as I add more and more signals that are multiples of the main frequency called harmonics. When building a square wave only odd harmonics are used as even harmonics tend to cancel themselves out.
Knowing now that we can build a square wave from multiple signals it then stands to reason that we can take a waveform apart and display its constituent pieces or signals.
Enter the Spectrum Analyzer; In this case it’s some math that occurs in my Digital [Tektronix] scope in the form of a Fast Fourier Transform (FFT). For this demonstration I left the 102 pound [HP] RF Spectrum Analyzer in its nook below the bench.
Sure enough, the odd harmonics stand out right where they are supposed to be. I could lay a small ruler touching the tips of the waves and they form a straight line. This is possible as the display itself has already been converted to a logarithmic scale.
My inclination is to launch into a diatribe of how these frequencies, always higher than the fundamental, combine to create noise in the RF Spectrum and how the interaction of these waves also get caught up in transmission lines, ground planes, apertures and antennas. Instead I will go back to my roots and put the signals to a speaker so that they might be heard. It’s easy to hear a note from [ELP Lucky Man] and when listening carefully one can start to equate sine wave distortions with “spray” or the extra harmonics that give some depth to a note being played on a synth. Play around with this. Who knows, maybe you’ll end up getting the band back together?