I can tell chord qualities fine. But I'd never be as good as someone with good relative pitch. For example, music majors have classes in sight singing: this is where the professor plays a note, say, a C, and tells everyone it's a C, then proceeds to play a sequence of chords and people learn to write down the chords based on relative position. But I and another student with perfect pitch would ace the class by just writing down the chords based on what they actually were. This went on until he started playing, say, a C and then telling everyone it's an F#. Then he'd play a sequence of chords relative to C and everybody would write them down relative to F#. Everyone except for us two, who were totally hosed.

When I went to my parent's church, the organist would spot me and then immediately transpose the organ down a half step. Nobody noticed in the entire room except for me -- I couldn't sing any hymns because the notes didn't match what was on the sheet. It was his private prank just between us two, and he knew that I was the only other person in the room who knew what he had done to me.

Thanks for the video link! Very cool. The poor singing combined with the on-the-fly guitar tuning gave the piece a grungy punk-like feel, at least to my ears. I rather enjoyed it.

A cute (translated) comment from the video: “To sing with this guitarist is easy! Just praise the Lord and he does the rest!”

I'm really impressed by the guitarist making her sound better and her pitch was all over the place

Jazz. Jazz is all about transposition.