motor driver on high resistance power source
As the Allegro A4988 uses PWM control to limit the current, anything affecting the effective current provokes regulation by changing PWM parameters. The PWM carrier modulates with the stepping pattern too. This gives a complex noise behavior, which may be audible under certain conditions. 

As the current reacts to even small disturbances like input voltage, motor temperature, recieved electromagnetic noise and more, it may change between different sounds, sometimes a dominant tone, sometimes white noise, and maybe even radio broadcasts. 

While for larger motors the actual driving currents expose audible tones, on smaller motors the noisy effects take over. 

There is nothing much to do about, experimenting suggests that some values of input voltage (smaller ones that raise the on times in PWM control I guess) gives  quieter operation, so it's all about try and error. Or chose another control IC or method.