In the most correct sense of the word, a distortion effect is any process that acts directly upon the shape of a wave. This includes clipping, tape saturation and any designer-type distortion imaginable. Within this realm, multitudinous distinctions can be easily made between the characteristic sounds produced by different permutations of equipment. Mostly, these stem from barbaric uses and abuses of amplification. Other factors such as harmonic distortion and pre-filtering can be involved also, and we will go into those later on, but for the time being, let's concentrate on two important types or methods of distortion: firstly wave shaping synthesis, and secondly clipping.
Wave Shaping Synthesis.
The official name for this process does not allude at all to its major field of usefulness. What is more surprising is the fact that it does not actually synthesize anything. It can only work if it is given an input wave, and might therefore be better referred to as a wave shaping process. In this article, we discuss only the form developed by Risset, but other forms are discussed in the article, Synthesis Methods: An attempt at an Outline.
It can be used - with a degree of care - to produce effects other than distortion, but in the vast majority of cases, especially where the input wave is complex and changing, the result is much what you would expect from an overdriven amplifier.
In a digital format, the algorithm generates either a lookup table or preferably a set of functions to provide rules for changes in the values of samples. Sample values are then fed in and altered one by one. In many cases, a block of samples may be moved to a position very different from those on either the leading or following sides. When this occurs, a sheer cliff appears in the wave: a moment of very high frequency content. All on its own it would simply sound as an annoying click. As this occurs every time the wave passes through this decibel range, and perhaps (depending on the parameters used by the algorithm) in other ranges too, these club together to transmogrify the wave. What may have been a gently sounding, musical input source might now be rather wild, raucous noise. Obviously, effects like this are more frequent with complex input signals than with simple or steady-state waves. A highly complex wave will tend to be rendered full of treble inharmonics, and may bears only a small resemblance to the original. A simpler wave processed the same way may turn out with a pleasant and musically useful quality.
The other form of amplitudinal barbarism is the far more commonly understood, and far more traditional, clipping. If you take a wave and amplify it to a point that the circuit can no longer carry its whole amplitude then the greatest peaks and troughs of the wave are snipped off. A very slight clip, especially on a wave whose contour is close to horizontal at the clipping-point results in a sound not unlike tape saturation. But where the clip meets a more vertical contour, the sound is far more noticeable as it holds a great deal more treble. But you already knew that. There, however, are some variations within this simple paradigm.
The first in importance is whether the negative and positive sides of the wave are affected equally. In 60's style fuzz effects, it is an essential characteristic that either one side or the other is allowed to pass undisturbed while the other is given a significant chop. This creates that half-clean, half-distorted sound. The second is the angle of the clip. Yes, it seems odd, but this has been done: the classic Fuzz Face pedal was just such an animal. It created a one-sided, angular clip whose leading edge was clipped less than the following edge.
Now we may speak of either valves or tubes, depending on from which side of the Atlantic Ocean our dialect draws. Here is a general principle behind the sound of a tube driven amplifier. When the signal passing through a tube increases in amplitude, the octal harmonics within it are amplified a little bit more than all the others. In jargon, these are the first order harmonics. They clip all on their own and so are accompanied by their own arrays of treble enharmonics. The arrangement of octaves is nice and smooth, and is pleasing to the ear, if less faithful to the original sound. In this sort of system, one might inquire about second and third order harmonics. But inquire not! These are half octaves and third octaves. They are nasty little gremlins that make horrible sounds. You need to keep them at bay because too much is very bad all within the one sound. It works like playing notes that are close together on a distorted guitar, because that these are all harmonising with a number of quite different fundamental notes.
To implement this in a digital form there is only one possible way I can think of, but it would take a damn lot of programming and a damn lot of know-how to make it work. First, you must use a Fourier or wavelet method to detect the presence and the amplitude of the octal harmonics. Then create files of sine waves of these frequencies at the same relative amplitudes. The next step would be to estimate how much amplification and clipping is required according to the distortion required, and mix the clipped sines at an appropriate volume back into the original.
Certain kinds of filtering placed before a distortion routine can bring about a dramatic change in the character of the sound. Again, let us refer to guitar equipment. The wah-wah pedal provides an active band-pass filter with a very sharp cut-off and so is able to greatly affect the sound, particularly when used pre-distortion. It is somewhat deceptive, however, in that the remaining clean bits of the wave are also thus affected, but this is simply inescapable.
The passing or emphasis of upper midrange and lower treble makes for a jagged wave, one whose contours are, by and large, more vertically posed. Do you remember how when a clip meets a near-vertical contour then more treble components are created? That is why a sharp sound can be more noticeably distorted. In addition, harmonics with an odd relationship to the fundamental frequency in a sound (that is, high-order harmonics) are to be found in great plenty in the higher frequencies. That is the reason for the nastiness of treble distortion.
In this article, we have touched briefly only a few areas of what is truly a fascinating subject. Distortion could be said to have the potential for lots of permutations and lots of very different results, without becoming in any way difficult to recognise as distortion. Contemporary western musical traditions virtually demand that it be used everywhere that an energetic or striking sound is required. It can be used in small measures simply to add brightness or warmth to a sound, or to add extra interest to a mix. Old, old amplifiers and valve-driven gear have a special appeal purely because they don't make 'em like they used to. And this is quite literally correct: the smallest characteristics of a circuit design and the specific nature of the components, and the way they have changed through aging and use, through the nature of what the effect does physically, can have a striking effect on the resulting sound.
Risset, Jean-Claude, 1969.
Catalog of Computer Synthesized Sound, Murray Hill, Bell Telephone Laboratories.