For example the first prelude, in C major, was originally an improvisation exercise on the given chord sequence, written for Bach's son Wilhelm Friedemann, and the version in the WTC is Bach's "solution manual" to the exercise. Some of the other pieces in Book I were original written specifically for educational purposes. The same may be true of the prelude and fugue in C sharp major, which arguably would be easier to read in D flat. That was before personal computers and notation software which could do the job with a couple of mouse clicks existed!) (When I first learned that prelude and fugue, as a teenager, my teacher gave me the task of writing out the music in the "opposite" keys by hand. In fact writing the prelude in D sharp and the fugue in E flat would have been "easier to read" if Bach had intended the music to be "easy to read". Because of the differing modulation schemes, the prelude contains some important chords of F flat major, while the fugue has some of E sharp major. The E flat minor prelude and D sharp minor fugue are a good example. The reason may be that, at least in the first book of the 48, Bach was deliberately pushing the notation of tonal music to its limits instead of taking the easier options.
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