recording - Is it asur to listen to a parrot which is a perfect mimic of a woman singing?

I know listening to a woman sing when she is married or a niddah in person is for sure asur. I know Rabbi Moshe Feinstein says (O.C. vol 1, S 26) that in a theoretical case where she is unmarried and not a niddah it not asur (except of course for sensuous songs). I also know most contemporary opinions say that listening to a recording of a woman who is asur to listen to (the married or niddah woman) is also asur if the listener knows what she looks like (and some opinions also say that it is asur even if the listener doesn't know what she looks like, but I am not asking about those).

However, I am confused about why it would be asur in the last case. The sound waves themselves aren't asur, because the same woman could sing the same song whether or not she is the theoretical unmarried non-niddah and produce the same spectrum sample when put through a digital audio converter or etched into a recording. (Or the memory of a parrot.)

So, consider the fairly absurd example of my question of the parrot. An African Gray can mimic a voice with amazing precision. It could imitate a woman singing. Is it asur to listen to a parrot that is imitating a forbidden woman singing? Are there any actual opinions one way or the other about such a case?

So is it asur to listen to something that can simply be associated with a forbidden woman? If so, then it should be asur to listen to the parrot and it should be asur to listen to a recording. If not and if it's only asur to hear what is directly coming out of the mouth of a forbidden woman, how could an MP3 player, which itself is certainly not a married niddah woman, be forbidden to listen to? If it's mutar to listen to the parrot and asur to listen to the MP3, what is the distinction if both cases are nothing more than disembodied reproductions of another's voice?