Hungarian folk music changed greatly beginning in the 19th century, evolving into a new style that had little in common with the music that came before it. Modern Hungarian music was characterized by an "arched melodic line, strict composition, long phrases and extended register", in contrast to the older styles which always utilize a "descending melodic line".
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https://en.wikipedia.org/wiki/Music_of_Hungary
http://www.hungarianhistory.com/lib/timeless/chapter03.htm
http://mek.oszk.hu/02700/02790/html/121.html
The oldest stratum of Hungarian folk music is characterized by the pentatonic scale and structure which repeats the melody a perfect fifth lower. If we take as our starting point the note “g”, the outline of the scale is as follows: g
1 – b
1 – c
2 – d
2 – f
2. The missing notes often occur as unaccented passing notes. Today this structure is rarely found in a pure and untouched form, but if the influences of later centuries are stripped away, numerous melodies may be uncovered which were thought to be new. The texts in this kind of folk music comprise four lines: the third and fourth being sung a perfect fifth lower than the first two.Although the pentatonic scale can be found in the music of practically every people, this melodic repetition at the interval of the perfect fifth is found mainly in areas of Hungary. Already a half century ago the idea emerged that this type of melody has its closest link with the melodies of the Mari (Cheremiss) people living in the Soviet Union. Often the similarity is so great that it is almost impossible to differentiate Hungarian and Cheremiss songs. This melodic form has also been found among the Chuvashes, where similarly it represents the oldest layer. Related forms occur even in Mongolia, so that this style can rightly be called Central Asian. We know what a great influence the Bulgaro-Turkish people, who spoke the language of the Chuvashes, exerted over the Hungarian language in the 7th to 8th centuries, and we have to suppose that musical connections also originate from this period.
The possibility also arose that the songs of mourning for the dead preserved Ob-Ugrian, or more precisely, Ostyak, connections. However {430.} the relationship is not that simple, because most likely this is a case of both having derived from the same source, the source from which the ancient Hungarian pentatonic world of melody, arising from North-Central Asia, could also have originated through appropriate transposition.