The notes in the Bjork tune are D, D flat, and C. Half steps, in other words. Cool sounding tune, BTW.
Microtones in western pop music are extremely rare. Or maybe that should read intentional microtonal melodies are extremely rare. Most of the time, it's simply people who can't really sing or play their instruments in tune, or like you say, there's just some push/pull going on that stretches the tuning, sometimes in a pleasing way. Also there are different tuning systems, as you probably are aware, so that the equal tempered major 3rd is 14 cents* sharp of the major 3rd in just intonation. (Check out Miles' solo on Freddie Freeloader: his minor seventh on the four chord is quite a bit flat from the piano's minor seventh. But it's still "in tune", because he's playing the seventh partial of the overtone series, whereas the piano is playing the equal tempered minor seventh. Sorry if that went over anyone's head. )
(this is where 7/4 says, there he goes again... nevertheless... )
From the book Harmonic Experience:
... for example, the quarter tone that sits right in-between E and E flat.
Some jazz musicians have delved into quartertonal and microtonal music, like Brad Shepik (in his Balkan jazz ensembles), and I heard one Tribal Tech record where Scott Kinsey played a solo using microtones programmed into his keyboard. W.A. Mathieu recommends Easley Blackwood's CD Microtonal Compositions as an example of the potential of equal temperments from thirteen to twenty-four tones per octave.
I'm not sure if Harmolodics belongs in this discussion. Actually, I'm not even sure what Harmolodics is! (I've heard the term, but who among us can explain it???)
*cent: a unit of measurement that equals 1/100th of a semitone, and 1/1200th of an octave, in equal temperment only.