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"The bottom line is that the music played in inverted polarity sounds harsh and two dimensional . . ."
The OP is selling vaporware. Beware.
One of my DAC’s has a polarity switch. Yes, there’s a difference - and it’s minimal. In one phase, there’s slightly leaner sound that improves sound stage width & depth. In the other phase, there’s a slightly fuller sound that improves body. Nothing even close to harsh & 2D.
Take into account all of the equipment for the recording. Was each and every component and microphone in the same phase - including the sampled tracks from another recording? When the mixed tracks went to a different mastering house, were those components on the same phase? Highly unlikely.
Ironically perhaps Roger Skoff (please don’t scoff) - one of the XLO principals behind the XLO TEST CD - is not a big fan of a lot of the audiophile tweaks that have become semi popular over the years. Oh, well, you can’t please everybody. Dr. Keith Johnson is the voice you hear on the out-of-phase track.
I flipped the polarity on my system and listened to a few CDs. I think ishkabibil may have planted a seed in my head. I can't say for sure that I'm actually hearing anything different, but I like the idea that it might sound better, which is making me believe it does sound better. Makes me feel all warm and fuzzy inside knowing the polarity is inverted. So for now I'll leave it that way. Other users of my system have made no comment on the sound quality since I secretly made this change.