TL;DR: Wave shaping is just function composition. I don't know why a new term is needed, but if you can visualize function composition for simple functions li

TL;DR: Wave shaping is just function composition. I don't know why a new term is needed, but if you can visualize function composition for simple functions like floor, min, max, you can visualize wave shaping. If the input signal is f(x), you obtain clipped signal g(x) like this: g(_) = min(1, _) ○ max(-1, _) ○ (a * _) ○ f(_) This can also be written as g(x) = min(1, max(-1, a * f(x))) In the example in the article, T(x) = min(1, max(-1, ax)) is called a transfer function. I find it easier to understand function composition by breaking the functions down into simple parts, though. The sonic effects of this are completely unexplained in the article. Other comments here discuss the effects on harmonics; mathematically, the TL;DR is that the Fourier series of g = t ○ f are more interesting (the intuition why can be obtained by looking at the Fourier series for a square wave). Without getting into math: a clipped signal retains some of the input, and adds more of square wave characteristics. A square wave is the buzz you get by flipping + and - very rapidly, which will force the speaker cone to go all the way in/out very rapidly. The reason why math above doesn't fully represent the effect is that an actual speaker cone won't be able to teleport to min/max positions instantaneously; and the unfaithfulness of the speaker cabinet creates pleasing tonal characteristics.