Why does more resistance mean a higher sound frequency...?

I have googled 'hee-haw siren' and have found several different circuits, all of which contain several resistors. So to give a proper answer to your question, we need to know which circuit you are using, and which resistor in it you are varying. However, I will say this:-

All of the circuits I have seen (some of which use 555 timers, others use discrete components) are based on a class of circuit known as a relaxation oscillator. In the siren one oscillator runs at about 1Hz and controls the periodic change in pitch, while a second oscillator produces the actual sound output. This second oscillator has its frequency of oscillation (and therefore the pitch of the resulting sound) controlled by the output of the first oscillator. The pitch of the sound therefore varies between high and low at a rate of about 1 Hz

Relaxation oscillators operate in this way: a capacitor C charges through a resistor R from a voltage source V, and the voltage on the cap (Vc) rises progressively as the cap charges. When Vc reaches a certain critical value, the surrounding circuit changes state, and V is made to fall abruptly to a lower value. The cap then discharges, and when Vc falls to a lower critical value, the circuit changes state again so that V abruptly rises to its original value. The process repeats indefinately. The periodic changes of state of the circuit (or alternating high-low values of V) produce the output of the circuit which is essentially a square wave of definite period or frequency (f). The rate at which C charges or discharges depends on the product R*C. The larger this product is, the more slowly the voltage on the cap rises or falls. This means that we normally expect that the frequency of oscillation will be higher when R is smaller; but this is the opposite to what you describe ("As resistance rose, pitch also rose").

Clearly, if what you say is correct, you are not referring to the resistor (R) which controls the charge/discharge cycle of the cap, as described above, but to some other resistor in the circuit. To comment on your observation intelligently, we must know what circuit you are using, and which resistor you are changing.

Hee Haw Siren