>In the beginning of this book, I see the phrase translated as The Song of
>Songs. Does the prefix apply a definite article to the whole phrase or just
>to the 'songs'? Could it be read as A song of the songs? - i.e. implying
>there were other songs in the cited group.
The definite article on the second word does not necessarily mean that
the whole phrase is definite. Rather, the Hebrew construction is, in
general, ambiguous.
In this case, however, the meaning is almost certainly an idiomatic
superlative.