Warmth - what is it? How do you get it? Nostalgia - it isn’t what it used to be (2)
Whatever their disadvantages though, we have to consider the fact that the sound of a well-designed valve circuit can be subjectively very acceptable, so what are the valves actually doing to accomplish that? The answer is in the nature of the distortion they produce. Valves have a habit of producing significant even-order harmonic distortion, due in part to the asymmetrical circuit design that has to be employed.
This means that for a single-frequency sine wave input, distortion frequencies will be generated which are twice, four times, six times, eight times, and so on, the input frequency. Our ears like it, but no-one really knows why. A waveform that is asymmetric between the positive and negative half cycles will contain even-order harmonics as well as odd, and yes it can provide subjective warmth. Oddly enough, you can get second order distortion from a transistor circuit too by biasing the transistor so that it clips on one half-cycle at a lower level than the other.
Why doesn't this sound so nice I wonder?
Circuit designers have traditionally strived to minimize distortion, and one obvious way to do this is to concentrate on making the design as symmetrical as possible with the result that even-order distortion cancels out, leaving only odd-order harmonics. As a point of comparison, a square wave consists of a fundamental and only odd-order harmonics. The sound of a clarinet approximates to this. For some reason, odd-order distortion is not held to be as desirable as even order, but it's harder to get rid of unfortunately. (Distortion, by the way, is often referred as 'non-linearity'.
A graph drawn of the relationship between input and output of a distortionless device would show a straight line. Any audio system that exhibits distortion would show a curve, hence 'non-linear' meaning 'not a straight line').
Although harmonic distortion can give rise to warmth, it can also give rise to undesirable harshness if the odd orders are allowed to prosper excessively. Harmonic distortion consists of whole number multiples of the frequencies contained in the input signal. This is similar to the sound of a string or wind instrument where whole-number multiples of the fundamental are intrinsic to the sound.
A drum on the other hand also has harmonics, but as well as whole-number harmonics there will be many which do not have such a simple relationship with the fundamental frequency. This is why the sound of a drum is more complex and less 'musical' than the sound of a string or wind instrument. Going back to distortion, harmonic distortion is not the only kind.
There is intermodulation distortion too where sum and difference frequencies are created which are not musically related to the input frequencies. The results may go beyond harshness into the realms of cacophony. The unfortunate thing is that where there is harmonic distortion, there will inevitably be intermodulation distortion too. It is up to the designer to ensure that intermodulation artifacts are kept to a minimum, even if they cannot be eliminated.