I think your best bet is to use a CMOS 555 such as LMC555 or TLC555 and use @hacktastical's suggestion of feedback from the output. The bipolar 555 output does not swing symmetrically to the rails and it is getting pretty pokey (the propagation delays start to matter) when you get into the tens of kHz). It also adds much bigger spikes to the power supply.

The 555 is not that stable anyway- the pot element can capacitors will also have temperature coefficients etc.

In simulation I get 22.78kHz at 12%, 22.67kHz at 50% and 22.76kHz at 88%, corresponding to pot at positions 0.1/0.5/0.9. An NP0 or film capacitor is recommended for the timing cap.

I think your best bet is to use a CMOS 555 such as LMC555 or TLC555 and use @hacktastical's suggestion of feedback from the output. The bipolar 555 output does not swing symmetrically to the rails and it is getting pretty pokey (the propagation delays start to matter) when you get into the tens of kHz). It also adds much bigger spikes to the power supply.

The 555 is not that stable anyway- the pot element and capacitors will also have their own temperature coefficients etc.

In simulation I get 22.78kHz at 12%, 22.67kHz at 50% and 22.76kHz at 88%, corresponding to pot at positions 0.1/0.5/0.9. An NP0 or film capacitor is recommended for the timing cap.