This is dynamic issue, not a response to the static sinewave (or a few). I give you an example with piano. Sound has three stages:
1. Hammer hit set of strings (3 maximum). Each string is divided in two non-equal parts, each one produce sound of two different and distant frequences with their own harmonics which is not controled by design, as this stage lasts very short time. We are aware of a completely wrong, distorted sound, but perceive it as a pleasant colouration to the sound that comes after.
2. Hammer bounces back and each string start to resonate at a full lenght, but deformation cause that pitch is higher than piano was tuned for. There is also a dissonance between different strings as they were hit with not equal force. A pitch is changing constantly alligning to the base frequency of each string.
3. During a second stage of a decay observed in previous stage, tone of all strings start to synchronise together (sound becomes tuned to a single base frequency), but it is a complex process, going through the multiple transformations. Resonation from a body comes to the effect and if pedal is pressed, it is observed interaction with all other strings.
I hear all these stages on my Audio GD R2R-11. DS converters tend to expand first two stages, maintaining dissonant sound over longer time. It is how DS converter alter the sound, I call it producing false harmonics, it may be a better term. This type of alternation to the sound cause fatigue after couple minutes. On the Topping D30 (which is extreme case) dissonant sound lasts to the end, stage three is not observed.