It's long been argued that the polarity of an audio signal doesn't make any difference to the sound, or it does. In essence I'm talking about swapping the + & − wires going to your speakers (or your turntable cartridge, or microphone wiring *, or the 180 button on your mixing desk, or whether your amplifier inverts it's input/output polarity).
* I mean the overall polarity, not the combination of one mike's polarity in a group of mikes. That will definitely make a difference to how they combine together.
In the all years I've been working with sound, I'm going to say “no” it does not sound any different to me. All my ears hear is the frequency and pattern of air pressure changes, not the direction of them. The quality of something, or its timbre, is the same, either way.
However, I can notice some difference with a particular pair of my loudspeakers, though probably not for the reasons people claim. While rewiring my stereo, I did an experiment of listening to them with the speakers wired normally, and both speakers wired backwards (a simple test that involved no changes in the electronics of the signal path). Again, I can't hear a difference in sound quality, but there was a very slight difference in sound level. Which is probably down to some non-linearity in the speakers themselves (being harder to push than pull, perhaps).
My speakers are mounted on the wall above the window, at at certain levels I can hear the glass buzz along with the audio. If I reduce the volume to the point where it just happened occasionally, it didn't happen at all when the speakers were wired the other way around.
So, yes, a slight difference. And a completely unimportant one. I can have the exact same affect by a slight nudge to my volume control (which can be said about an awful lot of different audiophool claims, such as $5 cables versus $5000 speaker ones). But whatever instrument is being listened to sounds exactly the same one way or the other.
I've spent well over three decades working in audio–visual production, and I'm a musician. I'm used to listening to music reproduction, and tweaking things to be just the way I want. I have nothing but contempt for the crazy claims by audiophools and bullshit written by Hi-Fi reviewers (many of which sounds like someone with mental problems just keep crapping on meaningly gibberish about sound stages and how a veil was lifted).