IRREGULAR WAVES

Not all waves are sine waves. Some nonsinusoidal waves are simple but are seen rarely in nature. Some of these waves have abrupt transitions; unlike the smooth sinusoid, they jump or jerk back and forth. If you’ve used a laboratory oscilloscope, you’re familiar with waves like this. The simplest nonsinusoids are the square wave, the ramp wave, the sawtooth wave, and the triangular wave. These can be generated with an electronic music synthesizer, and they have a certain mathematical perfection, but you’ll never see them on the sea. Irregular waves come in myriad shapes, like fingerprints or snowflakes. The sea is filled with these. In the world of waves, simplicity is scarce, and chaos is common.
 

Most musical instruments produce irregular waves, like the chop on the surface of a lake. These are complex combinations of sine waves. Any waveform can be broken down into sinusoid components, although the mathematics that define this can become complicated. Cycles superimpose themselves on longer cycles, which in turn superimpose themselves on still longer cycles, ad infinitum. Even square, ramp, sawtooth, and triangular waves, with their straight edges and sharp corners, are composites of smooth sinusoids that exist in precise proportions. Waves of this sort are easier on the ear than sine waves. They are also easier to generate. Try setting a music synthesizer or signal generator to produce square, ramp, sawtooth, triangular, and irregular waves, and listen to the differences in the way they sound. They all have the same pitch, but the timbre, or tone, of the sound is different.