when studying the show-art of the 19-20th century we can not ignore one of the most significant techinical innovation, the sound recording. first it was used for office/business purposes, but soon it was clear that it can be used for entertainment purposes aswell. in 1903 for the first time they recorded almost an entire opera (Verdi: Ernani), and till 1906 we had a record from almost every opera singer. the first whole symphony was recorded in 1913 (Beethoven: 5th Symphony by Artur Nikisch)

as part of an important world power Hungary was a world leading country of sound recording. major international recording companies opened offices in Budapest )The Gramophone Company, Columbia Records, Pathé, Favorite, Dacapo etc.). they introduced the coneless gramophon (Eufon) in 1907 as a hungarian invention, and thanks the First Hungarian Sounddiscfactory - established in 1908 - we have sound recordings of the greatest hungarian artists from the first years of the 20th century. where to find these original recordings and are they any good to listen to? my google was not strong enough sry.

main trends were romanticism and impressionism, and no doubt some of the major attractions/artists were:

Huszka Jenő's opera Prince Bob

Winesong from Prince Bob on youtube

Bob's Entry from Prince Bob on youtube

Bartók Béla was a famous Hungarian composer and pianist, and many of his works were composed in the 10's.

Kodály Zoltán was the other famous Hungarian composer, googling up any of his works might help you further.

Kodály Zoltán - The Peacock P1 on youtube

Lehár Ferenc another composer, and his Baron of Luxemburg from 1909

Polka from Baron of Luxemburg on youtube

Bartók Béla: Bluebeard's Castle (1911) one of the many Bluebeard's Castle on youtube

besides these classicals, gipsy-music was also very popular in saloons and coffeehouses, a nice compilation from youtube.

another interesting aticle, maybe you find something useful in it