Triangle wave

The triangle waveform looks similar to the sawtooth wave. But it is smoother. A triangle waveform can be obtained by integrating a square wave. Like a square wave, it contains only odd harmonics. However, the higher harmonics roll off faster than in a square wave, and so its sound is smoother than a square wave and and nearer to the sound of a sinewave. But a little more metallic.

You can approxiamate a triangle wave by additive synthesis, by adding odd harmonics of the fundamental, rolling them off with frequency faster than with a square wave. The infinite series will converge to a triangle wave.