All music played during the party is from Earth-That-Was composers. This piece plays during the introduction of the party and then again in the scene that begins with Kaylee holding the strawberry.
String Quartet in D Major Op. 76 No. 5. I. Allegretto
This music plays in the scene when Atherton makes his offer and Kaylee arrives at the party. We hear it again later when Kaylee is in her quarter lost in reverie.
String Quartet in D Major Op. 64 No. 5, I. Allegro moderato
This music begins when Malcolm asks if he may have Inara for a dance. The two actors had to practice their dance scene with the music playing to get the timing right. In fact, neither could remember their lines without the music according to the DVD commentary.