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this question is a bit is not possible to count them as there are more than thousand types of musics.the name of some are :
Fusion bhangra 
Fusion jazz 
Future jazz 
Electric blues 
Electric folk 
Dream pop 
Drill and bass 
Drone doom 
Classical Modern 
Classical Romantic 
and many more.........

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there are many types of music. classical music, pop, country music, electronic music, latin music, jazz, metal music, punk, rap, rock etc are some of them.
plz say thanks n mark it as best
music is endless