Electronic – arduino – LDR circuit does not change sound frequency

I think you are approaching this the wrong way. You shouldn't be placing the resistor in parallel, rather you should be placing it in series. If you place them in parallel, you will only ever read a fixed 5v on one side or 0v on the other. You will then use the ADC on the Arduino to measure the voltage between the temperature sensors and the resistor.

What you are doing is creating a voltage-divider where the resistance of the temperature sensor is changing.

The equation become non-linear, so if you would like to make it simpler you can combine series and parallel as explained in this answer.

There are, I think, a number of issues. Try this:

Reduce C2 to .01 uF, and increase R47 to 10k. You don't list your pot value, but I'm assuming 1k. Increase this to 100k, and put a 1k in series with it. As you've got it now, the pot value gets way too low for the circuit to operate properly.

Then, you need to do a major change on your transistor output. Try something like

^{simulate this circuit – Schematic created using CircuitLab}

Note that there are 2 LED outputs. Divide your LEDs into 2 equal groups and drive each group with one output. This will keep the PNP current levels within spec (3906s are only rated for 100 mA).

Alternatively, get rid of the transistor and R48/49 completely. The output current for a 555 is rated at 200 mA, that's about what your LEDs will draw. R48 and R49 are so low that you're drawing near that anyways.

Finally, I'd suggest reducing your base resistors (R17 - R32) to about 1k to 2k, just to make sure the transistors are driven hard on.