Let's start with a video, one which I find totally delightful (although you may want skip ahead, for reasons I'll explain in a moment):
Ba Ta Clan, Opera mobile from Jonathan Kaell on Vimeo.
This is Ba Ta Clan, a one-act operetta by Jacques Offenbach. Offenbach was a wildly successful operetta composer in 1850s, '60s and '70s France. He was also wildly popular in London and Vienna, where he had a big impact on later operetta creators like Johann Strauss and Gilbert and Sullivan, and through that influence, on the direction of musical theater in general.

This may be seem surprising. But the explanation is simple: Jacques Offenbach was a cantor's son. Offenbach the older was a cantor in the German city of Cologne, and Jacques is said to have used some of his father's melodies, along with other German-Jewish cantorial melodies, in his compositions. The tune here may be one of these: it is remarkably like the melody of a Reader's Kaddish found in a nineteenth-century collection. (As far as I know, this similarity was first pointed out by musicologist Eric Werner.)
Offenbach seems to have been alone among major cantor's-son-composers in bringing cantorial melodies to the compositional table. This may be less notable than it seems, however; in nineteenth-century Western Europe, cantorial music was becoming less and less recognizably Jewish anyway, and more and more similar to other European liturgical styles. Perhaps this even made the transition from cantor's son to composer a little easier.
In any case, you could say that choosing to be a cantor's son was a very clever move for Offenbach, because being a cantor's son seems to have been one of the two main paths open to aspiring nineteenth-century Jewish composers. The other choice was perhaps even cleverer: it consisted solely of being born into a wealthy family.
It's true. Examples of rich-kid-Jewish-nineteenth-century-composers abound. Scions and scionesses of assimilated and affluent families, these kids studied music, especially piano, as part of a broad, cosmopolitan, European education. Showing remarkable aptitude for the instrument, and rubbing shoulders at the same time with elite cultural figures among their parents' social circles, they were launched into artistic careers.
This description fits a number of composers to a tee, but none better than Felix Mendelssohn, who was perhaps the greatest musical prodigy of all time. Mendelssohn began piano study at the advanced age of six, made his public debut at nine, and in 1822, at the age of only thirteen, wrote this:
Mendelssohn's family background was extraordinary: his grandfather was the philosopher Moses Mendelssohn; his father and paternal uncle, bankers. On his mother's side, Mendelssohn's great-grandfather was Court Jew to two Prussian kings and the head of Berlin's Jewish community; as such, he was responsible for the removal of many restrictions on Jews in Prussia. One of Mendelssohn's great aunts on the maternal side was a pianist who studied with one of Bach's sons, Wilhelm Friedemann Bach; another great aunt was a patron of Mozart in Vienna. A great-uncle by marriage, another banker, translated the Hebrew prayer-book into German, and founded a Jewish free school. An uncle was Prussia's Consul-General in Rome and an art patron, to whom is attributed a revival of fresco painting by German artists.
So … you can sort of see how he might have ended up with a little bit of talent, culture and ambition …
Following the lead of some older relatives, including his parents, Mendelssohn was eventually baptized as a Christian. This is something else he had common with most of the other rich kid composers.
Meanwhile, orbiting Felix in Germany's musical firmament were others with similar backgrounds: first, his sister Fanny, who according to some visitors to the Mendelssohn home was as great a prodigy as Felix, and who, although her composition career was not enthusiastically encouraged, did write a large number of works including this vocal duet:
… and also, Ignaz Moscheles. Moscheles, a virtuoso who was one of Felix and Fanny's piano teachers, himself came from a German-Jewish merchant family of Prague, and married the daughter of a German-Jewish banker who was related to the poet Heinrich Heine. Here's an etude by Moscheles:
… and also, Felix's close friend Ferdinand Hiller, the son of a Frankfurt textile merchant. Hiller's spectacular playing and kindly disposition inspired both Chopin and Schumann to dedicate compositions to him. He is also said to have introduced to his non-Jewish composition pupil Max Bruch the Kol Nidrei, with results that are still heard every autumn. Here's a composition of Hiller's, the Piano Concerto in F sharp minor:
But the other big star among these rich kids, who was not in Mendelssohn's orbit at all, but had one of his own, was Giacomo Meyerbeer. Meyerbeer, though you don't hear his music a lot today, was the most frequently-performed opera composer in the whole nineteenth century. Meyerbeer was actually related, distantly, to Felix and Fanny. He grew up in Berlin just like they did, only about fifteen years earlier, and made his piano-playing debut at age nine, with a Mozart piano concerto.
Meyerbeer was the son of a financier who gave his children an unbeatable education. (The father also kept a private synagogue, and Meyerbeer, unlike these others, remained Jewish all his life.) One of the composer's brothers, Michael Beer, was a poet and co-founder of the Association for Culture and Science of the Jews. Another brother was Wilhelm Beer, who worked as a banker and was also a passionate astronomer, collaborating on the first maps of the Moon and of Mars, and in his spare time, helping to establish the Prussian railway system, and later, getting elected to the Prussian parliament.
Brother Giacomo (he picked up the name in Italy) ended up in Paris, where he ruled the operatic roost for over thirty years, from the 1830s to the 1860s, writing super-deluxe operas like Robert le diable. As it looks like I've run out of time again for those other poor cantors' sons, let's finish up with a clip from that once insanely popular opera: