Blue Ortolan, organ player, and leader of the Max Rebo Band, Max Rebo was often known to think with his stomach rather than his head. When signing a contract with Jabba the Hutt, he agreed to a deal that paid the band very little in exchange for unlimited access to Jabba's kitchens. While this infuriated other member of the band (especially Sy Snootles) Rebo was ecstatic about the deal and refused to renegotiate.
All things considered, Rebo was an excellent organ player and was probably one of the only really talented members of the band. He accompanied Jabba everywhere including the sail barge and visits to his penthouse in Mos Espa.
It is also known that he was kind to Jabba's slave girls who he saw as unhealthily thin and would often sneak them food that he was able to procure with his unlimited access. Shortly after Leia is captured, Rebo brings her some food while Jabba sleeps much to her gratitude.
Rebo was a dedicated musician through and through, hence why he was willing to play in a place as dangerous as Jabba's Palace. When he threw himself into a song there wasn't much that could break him out of it. While the entire court was watching Oola's final performance he barely looked up from his key board. Even as Sy Snootles and Joh Yowza, the band's singers, were shouting at Oola not to defy Jabba, Max's concentration wasn't phased in the least. It took Oola's blood curdling scream as she fell through the trapdoor to knock him off beat. He looked up and was puzzled why everyone else had stopped playing and the court was gathered around the middle of the room. It took him a few seconds to figure out what had happened, when he did he felt only a mild annoyance at the Twi'lek for interrupting such a perfect song.
BousshHe had expected to dive back into another song once the crowd had settled down the singer had a chance to reset. He was frustrated by the arrival of a bounty hunter escorting the captured Chewbacca. Max waited, impatiently, for Jabba to conclude his business so that he could get back playing. Frustration gave way to terror when the bounty hunter threatened Jabba with an explosive device. All the Ortolan could do was cover his eyes and wait for the blast but it never came.
He never thought he would be so happy to hear anyone call for a song as he was when the Wookiee was lead out of the throne room and Jabba demanded music. To Max's surprise he looked around but could not see Sy, Roy or any of the back up singers in the chamber, leaving him and Droopy to play for Jabba.