Bach-WTC Prelude in C minor

[hazypurple21]

There's something that confuses me about the prelude in Book 1 in c minor. I know Bach didn't write tempo indications in his music, so what are the marks of "presto" and "adagio" based on? In another words, how did one come up with these tempo markings if Bach didn't write them in?

[mlsmithz]

I have the Alfred edition of WTC Book I (edited by Willard Palmer), and, as anyone here who also owns that book knows, Palmer is very fastidious when it comes to distinguishing between original and editoral performance prescriptions.  While Bach didn't often include tempo prescriptions in his work, there are a few important exceptions, and the aforementioned Presto and Adagio are two such exceptions - Bach did actually include those himself.  He also specifically indicated tempo prescriptions for the B minor prelude and fugue from the same book (meaning, I suppose, that he originally intended for it to take nearly twice as long as any other prelude and fugue in the book to perform).  However, there is certainly not much agreement on exactly how fast "Presto" and "Adagio" should imply - just that they should be, respectively, faster and slower than the first section.