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Johann Sebastian Bach's "Contrapunctus I" and "Contrapunctus III" are part of "The Art of Fugue" (BWV 1080), a monumental and unfinished work. Here are some interesting facts about these pieces:

1. "The Art of Fugue": Bach composed "The Art of Fugue" in the last decade of his life. It's a collection of contrapuntal pieces exploring various types of fugues and canons.

2. Contrapunctus I: This is a straightforward fugue, showcasing a single theme. It serves as the opening piece, establishing the groundwork for the entire collection.

3. Contrapunctus III: This fugue is notable for its use of inversion, where the original theme is played upside down. Bach demonstrates his mastery of counterpoint, creating a rich and intricate texture.

4. Unfinished Work: Bach did not specify the instrumentation for "The Art of Fugue." It was likely intended for keyboard instruments, but interpretations and arrangements for various instruments, including string quartets and orchestras, have been made.

5. Theological Significance: Some scholars believe that "The Art of Fugue" may have a hidden symbolic or theological significance, given Bach's deep religious convictions. The unfinished nature of the work has led to various theories about its intended purpose.

6. Mysteries Surrounding the Composition: The reasons for Bach's composition of "The Art of Fugue" and its exact purpose remain mysterious. Some suggest it was a theoretical exploration of counterpoint, while others believe it held a more profound, symbolic meaning for the composer.

These facts highlight the complexity and depth of Bach's "Contrapunctus I" and "Contrapunctus III" within the context of "The Art of Fugue."