The meaning and grammatical role of 'set to the words'

The passage below comes from a webpage as follows:
http://anecdotesofmusicians.blogspot.kr/

But the pianist had his revenge. The next night, on his appearance at a concert, when he sat down at the instrument be began to improvise on a theme from Mozart's “Figaro," and immediately the audience broke into laughter and applause. The theme he had chosen was in the opera, set to the words“Will the Count venture on a little dance?”

I don't think I had a complete understanding of the last sentence.
Here's my line of thought.

Without modifiers the sentence can be made brief as follows:
The theme was set to the words “Will the Count venture on a little dance?”
Am I right?

Then, we can rewrite it as follows:
Bülow set the theme to the words “Will the Count venture on a little dance?”

Does the rewritten sentence mean that he set the words “Will the Count venture on a little dance?” to the theme?
Am I right? (I don't think I am right, though.)

If I am wrong, what is the last sentence trying to say? And what made the audience burst to laughter?

Regards.