On the poverty of digital sound synthesis

This is an electric generator that I assembled when I was a child. It can generate a sinusoidal and a rectangular signal. I used it to debug radio equipment. But I also just played on it, because it is essentially the simplest synthesizer, and an analog synthesizer at that. There is only one way to play it, namely by turning the frequency control knob.

Then I moved from amateur radio to programming and made a digital analogue of the same generator, i.e. the simplest digital synthesizer.

Comparing both generators, analog and digital, I found that if the generators are not touched, they sound the same. But if the frequency of the generator is changed, a difference in sound occurs: the digital generator, compared to the analog one, sounds uninteresting. Therefore - the difference appears with external influence.

(I did a similar experiment with 2nd order analog and digital filters. The result is the same as with generators: while the filter cutoff frequency does not change, there is no difference in the sound, when the frequency changes, the difference is noticeable and it is not in favor of the digital filter.)

Without external influence, the generator is in a certain state of equilibrium. External influence takes the generator out of the equilibrium and starts transient processes. After the completion of the transient processes, the generator comes to a new state of equilibrium. Therefore, the difference in sound is due to transient processes.

Transient processes of the analog generator can be not only heard, but also seen - on the oscilloscope screen. When the "frequency" knob is rotated, not only does the signal frequency change, but its amplitude also fluctuates.

But the transient processes of a digital generator cannot be heard or seen - when the "frequency" knob is rotated, the signal simply changes frequency instantly, without fluctuating amplitude.

Then we can say that a digital generator DG is an analog generator AG, but without transient processes TP:

DG = AG - TP

AG = DG + TP

Therefore, in order to enrich the sound of a digital generator, it is necessary to add transient processes to it. Judging by the sound of music made on digital synthesizers, this turns out badly. I believe that the reason is the lack of a good mathematical model of transient processes.

Why do most people not notice the poverty sound of digital synthesizers?

Based on the above, we can write:

analog_synthesizer  = AG = DG + TP
digital_synthesizer      = DG + imitation_of_TP

Therefore, the poverty of digital sound can only be felt by those who can perceive the difference between transient processes and their imitation.

Using the terminology and model from the article "Analysis of information", we can imagine transient processes and their imitation as information flows. Since transient processes occur according to the laws of physics, i.e. nature, and the imitation of transient processes is a creation of man and man cannot act as subtly as nature, it is quite natural that transient processes are a more rich information flow than the imitation of transient processes. To perceive a more rich information flow, a more developed nervous system is needed. Therefore, the aesthetic advantages of analog synthesis cannot be evaluated by most people. But they can evaluated the practical advantages of digital synthesis, which are undeniable: the cost of equipment, ease of use, and space savings in the studio. This is why analog synthesizers have been replaced almost everywhere by digital ones.