Why does my square to sine converter sound fine at low notes but rough up high?

Two stages of passive RC only knocks the harmonics down so much, and how much depends on how far the note sits from the filter corner. Down low you're miles away so it looks clean. Up high the third and fifth harmonics of the square move closer to the corner, so they leak thru and you get that lumpy triangle look. That part is normal, not the 555 being ragged.

The fizz is a seprate issue and it's usually supply junk. A 555 pulls big current spikes every time it flips state, and without decoupling right at the chip that noise shows up on your output. Stick a 100n ceramic straight across pins 8 and 1, as close as the socket allows, plus a bigger electrolytic nearby. Also scope pin 3 and check the square stays roughly 50/50 across the range. If the trimmer lets the duty cycle drift uneven you get even harmonics that two RC stages barely touch, and that reads as fuzz in the audio. On chaining stages, yes it works, but passive stages load each other. The second one drags the corner of the first one around, wich is exactly why bigger caps make everything quiet and dull. Put a buffer between them, even a single transistor stage or half an op-amp, and each filter starts doing its job properly. With buffering, three stages will give you a genuinely decent sine without the volume sag.

The level wobble as you sweep is just what a fixed RC filter does. Output amplitude follows the filter curve, so as pitch moves toward and away from the corner the level rises and falls. It's baked into the passive approach. An active two-pole filter with a bit of feedback flattens the top of that curve, which is why most people end up there eventually. One gotcha on the trimmer while you're at the layout stage. If it can turn to a position that shorts the rail through pin 7, put a series resistor in so it can't. I learned that one the expensive way.

The point about putting a buffer between the filter stages makes a ton of sense. When I set up my own sequential filtering, I ran a single common emitter transistor stage between the first and second RC filters. That made a noticeable difference in the signal quality. It relly stabilized the output and stopped the overall sound from getting that thin or loose feeling. I also found that I had to dial in a bit more series resistance in the first stage to help manage the transients before the buffer could handle them.

I wonder if you also need to consider the attack time of your square to sine conversion, because sometimes the perceived lumpiness isn't just a harmonic issue but how fast the signal settles into the filter's peak. If the time constant of your initial RC stage is excessively high, you’ll get a slight transient ripple as the signal transitions between states, which can manifest as textural artifacts even if the steady state is technically smooth. This whould require careful tuning of the resistor value in relation to the cap to properly dampen those initial switching spikes.

I ran into similar fuzz issues trying to use a cheap power supply right on my bench. The noise was awful, way worse than the harmonic issues. I fixed it by putting the whole thing on a totally isolated regulated rail. The simple power regulator I used made a massive difference. It sounds like you are dealing with power rail noise coupling into the analog stage, not just component noise from the 555. Try isolating the voltage feeding your filter stages completly from whatever is running your clock or digital gear.

Update: sorted it. Took the buffer advice and stuck a single transistor stage between the two filters, and the fizz up high basically vanished. The lumpy shape is gone too, the sines look clean across the whole range now. Level still wobbles a touch when I sweep, but way less than before. Good enugh to etch the board, thanks for the pointer.