I might suggest a compromise -- Ideally, you could implement a fixed-position element that includes all of the music playing functionality. That way, the user can manipulate the music from any location on the website, from the tab of the website, and the player remains consolidated with the remainder of the display.
Having an external player, particularly a pop-up one, forces the user to interact with it more than they need to (dragging it to a useful position, out of the way, out from behind windows). Even if it's made into a tab, it still constitutes a new separate element than the user needs to worry about, and consciously bring back up when needing to change the music.
With the inclusion of downloading functionality, having an external window may cause even more problems. Downloads initiated from the separate window will appear in that window only. The user may close the window and expect the download to be completed by the browser, but it will not.
DatPiff features an external music player, which becomes a nuisance when multiple tabs (and perhaps other applications) are open in the first place.