The purpose of copyright is to make the public domain larger, so that there will be more tunes that people can take false credit for, (heh, heh!).

Seriously, the purpose of copright is, indeed, to enlarge the public domain. In my thinking, whether one explicitly acknowledges one's sources depends on circumstances, but in most cases it's better to acknowledge the source than not to.

I think (I'm partly guessing here though--don't take my word for it) that there was a period, circa 1955-1965, when performers were pressured into claiming authorship as a way of covering the record labels' butts against lawsuits for breach of the right of first publication, as happened in the case of George v. Victor Talking Machine Company back in the 1930s.

However that may be, I think that one can usually find a place in the sheet music to put a little note in fine print saying that, say, "the bass line is based on Old Hundredth" or something like that. In the case of "Old Hundredth" it might not be necessary, since many would recognize the allusion or derivation anyhow, but I don't see any harm in being explicit.

As I understand the matter (but I am not a lawyer, this is not legal advice, etc. etc.), in the case of parody, in the U.S., some (not necessarily all) parodies are considered "fair use" and can be made without permission or payment, but a writer might be wise to consult a lawyer on the point before committing to writing a parody.

T.