Note that the timer divisor is very short - only 16 bits - and that the input frequency is very low. So even if the total range is 45Hz to 10kHz, there will be very specific jumps between the different frequencies that may be generated.

Because the division value doesn't contain any fractional part, the jump in resulting frequency will be higher for higher output frequencies. This is similar to a baudrate generator, where just about any crystal can be used for 300 baud, but att high baud speeds, you need a specific crystal frequency to keep down the error.