Fundamental Frequencies and Harmonic Series

Hey all,

I'm Andres, Film and Media Studies major and Mass Communications minor, looking to graduate next fall. I have a pretty sound/music intensive project I'm currently working on and I'm looking forward to this class as it will probably be of great help.

A friend of mine that is music inclined once explained to me the harmonic series, I just didn't realize it was what we were talking about in class. But to get there I should first discuss what I've found on fundamental frequency. In plainest terms, the fundamental frequency is the lowest frequency at which an object vibrates freely. This is one of the definitions I found, but mostly applies to just physics. In music however, this is incomplete. A fundamental frequency is the lowest frequency of a periodic waveform. If I'm correct, periodic waveforms in sound are sustained sounds without varying pitch, although their frequency may be low enough that you can hear the variations in wavelength. Because the wave is periodic, meaning it repeats exactly the same, one period alone of the wave serves to describe the entire wave. This period is thus known as the fundamental period, and the lowest frequency for which this smooth repetition remains true is the fundamental frequency. The fundamental frequency is also the first harmonic.

The harmonic series then is the series of sounds produced when the frequency is increased by adding the initial frequency repeatedly. For example if the frequency of the fundamental is 50 Hz, the second harmonic would be 100 Hz, the third 150 Hz, etc. The harmonic series is related by whole number ratios, and like stated before, have periodic waveforms. When these are played in conjunction to each other, they sound very smooth and pleasant, whereas other notes whose frequency does not fall in the harmonic frequency, have irregular and/or non-repeating wavelengths, and thus don't sound nearly as pleasant. This is because all the tones on a harmonic series are related by whole number ratios; same wave with increased frequency by two times, three times, four times, etc.

I have heard this being played in a piano, going up a harmonic series from C to C to G... etc, and with dissonant keys not from the series thrown in to clarify the point.

On another note I found this video on YouTube about an iPod application that may help on the understanding of periodic waves.