Earlier quoted context omitted.
A slider is just a UI element as is a knob, the underlying resolution does not have to correlate 1:1 with the exact number of pixels something takes up on a screen. The resolution could be effectively infinite depending on the implementation of the controls.
Sure but if you need to resort to tricks to make it work are they really the right UI element for the job? Their being 1:1 is what makes these work. If you fill your UI with 20 pixel sliders which all cover .2khz to 20khz and use shift clicking or the like to make it work, it is going to get irritating rather quickly. 20 pixel knob will not be much better with such a wide range but has the advantage of being able to…
And 20 pixels wide on a modern screen is so tiny you would have trouble seeing it, so the whole premise of a "20 px knob" is blown. A slider with 100 pixels width would also be pretty small. The smallest I'd make it to work on a modern screen is at least 250 pixels wide. And that's plenty of resolution for most things. If a slider is more important, make it bigger, and you get more resolution.
Arguing about a 20 pixel knob or slider is kind of stupid considering how small that actually is in screen real estate. If the knob or slider is 20 pixels in any direction then you have other UX problems.