The Well-Tempered Clavier,
Preludes and Fugues
through all the tones and semitones
both as regards the tertia major or Ut Re Mi
and as concerns the tertia minor or Re Mi Fa.
For the Use and Profit of the Musical Youth Desirous of Learning
as well as for the Pastime of those Already Skilled in this Study
drawn up and written by Johann Sebastian Bach.
You must see Bach for what he was. He was a pioneer in seeing what could be done. He got to the point where he was a master in counter-point and he wanted to see how far he could take it. These pieces were an exploration in what the art of fugue sounded like in all the different keys, this was his treatise into how keyboard players should determine a ...
There are a few leading factors which have a bearing:
pedagogical / theoretical
convenience / historiography
The first is well covered by other answers: that there was a didactic element to Book I of Das Wohltemperirte Clavier. By having this key, the most remote of the minor keys from the non-accidental A minor, represented by two ...
Bach was simply completing his task of writing a movement in every key. It would be unlike Bach to leave any out.
Bach's new keyboard tuning/temperament allowed him for the first time to move through all of the keys pleasingly. The most accurate recreation of this tuning is the Lehman Tuning. Here is a demonstration
. Each ...
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.
The E flat minor prelude and D sharp minor fugue are a good example. Because of the differing modulation schemes, the prelude contains some important chords of F flat major, while the ...
Why didn't he just name both E♭ or both D♯?
Why not both in D# major seems clear to me as D# major would need 9 sharps. Eb minor has 6 flats like D# minor has 6 sharps. As usual Bach’s pieces are extending to the dominant and subdominant what would imply additional sharps for the secondary dominants: e.g. F7 in measure 9 would be a E#7, the major 3rd of V/...
There is a lot that is special about the work of Bach but the fact that some of it is called Invention has nothing to do with it.
Invention comes from latin and originally means 'discovery'. All the way through the Middle Ages, that was what it meant. Today still, the technical legal term for acquiring ownership of a lost treasure is 'invention'.
Inventions is a title that Bach uses in his foreword to the collection of this work. It is adapted from the theory of rhetoric. The inventions used by Bach means clearly that he first shows an invented motif and develops of this simple figure an entire (but short) composition:
"Straightforward Instruction, in which amateurs of the keyboard, and especially ...
According to Honegger-Massenkeil reference the first musical piece called invention was by Claude Janequin and dates from 1555. This weakens the strong Bach connection.
There the title already described a piece not restricted by a specific scheme or formalism. From this kind of originality it is not far to the phrase that each piece is invented.
When you listen to this music you don't only hear chords. He plays a melody with passing tones (like chromatic approaches, passing notes and turnarounds):
Your chords are correct as far:
F#m A D# .... - but the E# is surely not (F)!
This E# in the first motif la do fi si la do is the 7th (E# = si the leading tone of F#m) and just a passing tone which ...