I know this is a little subjective in regards to what roughness is. So, imagine the sound of a sine wave, you could say this is the purest, or cleanest sound there is.
Now contrast that to a sawtooth wave, it's quite rough, though if you add in some AM or/and FM, then the roughness of a sawtooth wave (or any wave), will increase.
Now, what's interesting is that a sawtooth wave has more harmonics then the sine wave, this is obvious, however, consider that it's rougher than a square wave also, and when you trasition from a sine to a square to a saw, you add in more harmonics, and the overall roughness increases. Indeed, FM introduce an unholy amount of sidebands, and roughness seems to increase rapidly.
However, now consider the sounds of white noise, which is an equal distribution of frequencies low to high. This isn't rough at all, and so this shows that the frequency distribution of a sound is only correlated with roughness, but is by no means a direct cause.
What is, however, the direct cause of the roughness of a sound? What is the one factor from which roughness arises from?