If I Were a Rich Man
Chagall's Jew at Prayer
DIGGUH-DIGGUH-DEEDLE-DAIDLE-DUM
This song contains something very similar to a nigun, but with more varied syllables it's a little more glitz and glamour-- what is expected from a Broadway show. It is still repetitive, and the syllables don't mean anything, and so it has the spirit of a nigun but also the spirit of someone making up a song as he goes, which is what Tevye is supposedly doing.
Fun Fact! This is based on Sholem Aleichem's monologue "Ven ikh bin Rothshild" ("If I'd been Rothschild", a wealthy Jewish family. However, he concludes that, in essence, money isn't everything. Somewhat different to Tevye! Listen to him recite it here!
Important Takeaways
This is one of the most famous songs from the musical, and a lot of people have covered it through the years. But it is one of the most important moments in Fiddler on the Roof, in terms of broader social impact, because it takes an extremely common antisemitic stereotype (of a money hungry jew) and complete turns it on its head. Instead of planning to just enjoy Luxury in his fantasy of a world with more money, he imagines that, in addition to the luxury, he'd be more observant, with the freetime from not having to work so hard all the time.
In Tevye's ideal world, he gets to go to the synagogue more. He gets to help others. The cornerstone to his plea to God is that he wants the ability to more easily fulfill mitzvot he currently struggles with: to study at synagogue, and participate in daily prayer. Beyond being wealthier, Tevye cannot see a way to add anything more to his day, even if he feels regretful and wishful about it.
More about the history of Jewish people and Finance can be found here.