Your combined charge and discharge time sets the frequency. The smaller the capacitance, the higher the frequency. The duty cycle is the ratio between the on and off time. Increase the resistance in the inner leg and decrease the resistance in the outer leg to improve that separation. With a narrower on time and a wider off time but the total time = 2.4KHz you can approach the desired 3.7%. The stock 555 has a frequency limit near 1Mhz (1uS total time) if IIRC - I need to look it up - but that is well faster than your required range. A 15.2μS on time and a 402.9μS off time should give you ~3.7% @ 2390Hz
Cheers,
Cheers,
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