Traditional, classical, and early jazz began in New Orleans, Louisiana. There are many subgenera of jazz: bebop, free jazz, cool jazz, jazz fusion, and modal jazz.

BeBop Jazz is a style of jazz developed in the early to mid-1940s in the United States. The songs are characterized by a fast tempo, complex chord progressions with rapid chord changes and numerous changes of key, and improvisation. Improvisation is the process of spontaneously creating fresh melodies over the continuously repeating cycle of chord changes of a tune.

Free Jazz emerged during the late 1950s, reached its height in the ’60s, and remained a major development in jazz thereafter. The main characteristic of free jazz is that there are no rules. Musicians do not adhere to a fixed structure. There is a lot of improvisation in free jazz artists will modulate or change keys at their own will.

Cool jazz is a style of modern jazz music that arose in the United States after World War II. It is characterized by relaxed tempos and lighter tone, in contrast to the fast and complex bebop style. Cool jazz often employs formal arrangements and incorporates elements of classical music.

Jazz Fusion is a music genre that developed in the late 1960s when musicians combined jazz harmony and improvisation with rock music, funk, and rhythm and blues. 

Modal jazz is jazz that makes use of musical modes often modulating between them instead of relying on one tonal center. Modal jazz was most popular in the 1950s and 1960s, as evidenced by the success of Miles Davis and John Coltrane, both of which were directly inspired by composer George Russell.