If you regard ornamentation as an inseparable element of the tune, as I do, then I don't think much else is needed to make the music complete in itself. Having said that, I do like a good band and I wouldn't be without all my Planxty, De Dannan and Bothy albums (to name but a few). Bands generally play arrangements, which (in the ones I've played in anyway) is not something that's to the fore in sessions. But good "pure drop" playing can be in another dimension altogether.

If you listen to the set of six unaccompanied Bach cello suites, in which double-stopping is either sparse or absent, harmonies not explicitly played by the cellist happen inside your head. It's magic, and it's a good way to listen to music. I know what Robin is getting at.