A. Because he wanted to write pieces that would help people tune their pianos. = Dependent
Bach composed The Well Tempered Clavier. = Independent
B. Both Gould and Keith Jarrett have recorded Bach's Well Tempered Clavier = Independent
and both have played surprising versions of the music = Dependent
The basic info on the differences is as follows:
Independent Clause
An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence.
Jim studied in the Sweet Shop for his chemistry quiz.
Dependent Clause
A dependent clause is a group of words that contains a subject and verb but does not express a complete thought. A dependent clause cannot be a sentence. Often a dependent clause is marked by a dependent marker word.
When Jim studied in the Sweet Shop for his chemistry quiz . . . (What happened when he studied? The thought is incomplete.)
To help you better understand this for the future go to this web site. There is where I copied and pasted the info from above.
Hope this was helpful!
http://owl.english.purdue.edu/owl/resource/598/01/
It seems to be pretty helpful with this topic.