I was playing 'If I were a rich man'. I noticed how it makes use of alot of notes outside its scale even though it's in C major. and I was wondering what the term is for what is it doing. Is it borrowing, modulating, using some kind of mode, or doing something else. In the main verse, I think it's getting the notes from its parallel minor scale as it sounds minor sometimes, and then at 0:40 I think it modulates to its parallel minor. But maybe I'm missing something..
It's 'In C major' the same way Beethoven's 5th Symphony is 'In C Minor' or Wagner's Ring cycle is 'In Eb'. C major is home, but it goes plenty of other places too!
Yes, there's a consistent harmonic feature of contrasting C major and C minor, and in the 'middle 8' doing the same with F minor and F major. Quite a few touches of the bII note, characteristic of Jewish music too, though it never quite goes full-blown Klezmer!
(Incidentally, the show score and original cast recording are in Db, though in the movie, a somewhat older Topol takes it down to C. Quite a shock when you've been used to the 'songbook' version and someone throws you the vocal score to play!)
No word is besserwisser safe, but I would say that it modulates between C major and C minor. https://en.wikipedia.org/wiki/Modulation_(music)