Possible Clues:

• Dance from Burma
• That's an odd class of a degree from South America
• Spirited Spanish to a certain degree
• Odd start and finish to ballerina's dance
• Odd kind of degree in dance
• That's an odd sort of a degree at the ball
• Odd degree in dance music
• Graduate had drink before dance
• Latin lilt
• Drink barrels brought to a dance