Analog Avenue: Frequency Components of Square vs Triangle Wave

The frequency components of the square wave are greater than the frequency components of the triangle wave.   The square wave components vary as 1/n times the fundamental while the triangle wave components vary as 1/n^2 times the fundamental component.  This means the triangle wave has less frequency content and can be transmitted over a limited bandwidth medium with better resolution than a square wave.

To illustrate, the included diagram shows the reconstruction of both a square and triangle wave with the same number of harmonics, n=11.  The original triangle wave is shown at the top of the diagram and the reconstructed waves are shown below that.

We can see that the triangle wave looks very much like the original, while the square wave clearly has very visible distortion near the peaks.