No - at least not in the sense of some shared data structure that different music editors were all capable to work with, as was the case with fx MOD files.
C64 music is typically distributed as executables which contain both play routine and music data (cf. this question). Many different players and editors exist, some native, some for "cross composing". The music is played by the player software continuously changing the SID chip's parameters.
There is, however, a pretty standardized meta data header - PSID - that represents the information needed to play the music from emulating music players or for generic front ends on the C64 itself. All the tracks you find in collections such as the HVSC are wrapped in this header.