General:
* Improvisational music: This emphasizes the core element of jazz.
* Swing music: While not all jazz is swing, it is a significant subgenre and often associated with the term.
* Hot music: This term was used in the early days of jazz and evokes a sense of excitement and energy.
More specific:
* Bebop: A specific subgenre of jazz known for its fast tempos and complex harmonies.
* Dixieland: A style of jazz from the early 20th century characterized by its use of collective improvisation and New Orleans influences.
* Fusion: A blend of jazz with other genres like rock, funk, or Latin music.
The best synonym depends on the specific situation and the nuance you want to convey.