It’s kind of apples to oranges. Smoothness or variance is noticeable above discrete human ‘limits’. For a variety of reasons.

With music you have multiple types of feedback.

Maybe it helps to know that it can’t perfectly capture your voice. It can get close enough no human can tell the difference, but it’s still not perfect. First of all it has a sampling rate. To make this more understandable let’s think of a sample rate of 1 sample per second. Think of two speakers playing at the same time. One is playing your favorite song, the other is playing the exact note of that some for one second each and only changing notes every second. It’s going to somewhat mimic your song, but it’s going to be terrible. Now imagine that second speaker makes 4 samples every second, now it’s playing your song a quarter of a second at a time. Sounds a lot more like your song, but in the same way stop motion looks a lot like movement but isn’t right. Note up that sample rate to 100s or thousands of samples a second, now you’re getting to the point you can’t tell the difference, but it still can’t be perfect, because it’s still based on a sample rate.

If you can grok pictures from pixels, you can picture the same thing. If you averaged a picture out to one giant pixel, it’s unrecognizable, 4,8,16 pixels, maybe a simple icon starts to approximate into something recognizable. That little icon in your browser tab is usually 32 x 32 pixels. 1024 pixels total, and we barely consider that an image. It’s all about pixel count (sample rate). When you zoom in, you find that it’s not perfect, you always get to the point of individual pixels, unlike optical zoom where you can zoom almost indefinitely as long as you can collect enough light.

It’s doesn’t get your exact voice. Your speech gets compressed into digital “steps” that closely mimic the continuous “analog” output of your voice.

Everything about the exact timbre of your voice is captured in the waveform that represents it. To the extent that the sampling rate and bit depth are good enough to mimic your actual voice without introducing digital artefacts (something analogous to a pixelated image) that’s all it takes to reproduce any sound with arbitrary precision.

Timbre is the result of having a specific set of frequencies playing simultaneously, that is characteristic of the specific shape and material properties of the object vibrating (be it a guitar string, drum skin, or vocal chords).

As for how multiple frequencies can “exist” simultaneously at a single instant in time, you might want to read up on Fourier’s theorem and watch 3Blue1Brown’s brilliant series on differential equations that explores Fourier series https://www.youtube.com/watch?v=spUNpyF58BY