This is all very intriguing! Yes, pitch can get shifted by the A2DP bluetooth codec - I have heard it, as have others. But it wavers the pitch up and down, just like a bad cassette player.
I can’t imagine a real time pitch shift persisting across the spectrum, other than that obvious ‘undersea’ conversion effect used by studios, because surely any shift would cause a voice to go on after the speaker has stopped, or anticipate their conclusion! 

You’re ignoring this member’s posts.
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