Someone reinterpreting a piece of classical music will go back to the score. They may be influenced by other interpretations, but they will not make significant changes to the piece, certainly not to the extent that a traditional folk singer might alter a song, possibly from one performance to the next.

The classical tradition is one of sequential historical development of Western Art Music wherein the aesthetics made possible by heavily notated composition lead from one era to the next beginning with Ars Nova and leading through the Renaissance, the Baroque, the Classical, the Romantic to the Modern & post-Modern. But no two performances of any piece from any era can ever be exactly alike; and there are traditional schools of interpretation in which the minutia of nuance in a single phrase carry as great, if not greater, significance than the innumerable variations of Child #2. In another sense, of course, John Cage's 4'33" remains of particular significance.

In improvised musics this is perhaps more evident, though with respect of such crucial works such as Stockhausen's Aus Den Sieben Tagen, the lines blur. The dynamic immediacy of an actual music is of greater significance than its ghost, however so recorded, but the context of playback and the effect in the listeners head is a crucial part of that process too, thus even records and musique concrete carry the same transformational potential.

Everything is change; everything else is just an illusion.