That which wolfishmusings says notational systems did not exist in Dovid’s time is not accurate, in fact there are musical notes preserved from ancient Greece from just about that time.
I may need to stand corrected on this. Some basic research indicates that there were musical notation systems at least in the latter days of the Bayis Sheini. (However, that they actually existed in the Bais HaMikdash is NOT a given.)
That being said, however, the fact remains that we don’t have the “sheet music” of the day. So, even if it existed in the BhM (not a given) and even if it existed to this day (which is doesn’t) and even if it could be deciphered (also not a given), there’s STILL no guarantee that it wouldn’t drift. Once again, I point you to the example of laining. Even though we all use the same symbols, my darga may not be the same as someone else’s darga. My gairshayim is not the same as another’s gairshayim. Yes, they’re similar in the here and now, but they aren’t the same — and that makes them liable to drift over the centuries — much like the pronunciation of words can (and does) drift over the centuries.
According to Rav Schwab ztl the tune of “ledovid boruch” sung in Breuer’s on motzai shabbos dates back to the beis hamikdash.
WADR to Rav Schwab, I don’t know how he could possibly know that. He might be able to credibly claim that the present tune has its *origins* in a tune that came from the BhM (still quite a claim given the geographic, temporal and cultural differences), but to say that it is the tune they sung? I don’t know how he could possibly say that definitively.
The Wolf