This puzzle consists of excerpts of 20 fugues from Bach's Well Tempered Clavier (Das Wohltemperierte Klavier) as alluded to by the title. Each excerpt begins at the start of the piece and ends at the end of the first entry of the (first) subject. The first thing that one notices when comparing the excerpts to a score (available from IMSLP) of the Well Tempered Clavier (WTC) is that the excerpts do not match up with the fugues in either book with the same number (in the same key). Indeed, they are transposed. The next logical step is to work out the actual keys of the fugues and by how many semitones they have been transposed.
From Book I we have
The 10 excerpts correspond to the 10 distinct notes which occur in the Inhalt (contents, from German) line before the double bar, taking enharmonic notes to be equivalent. Assigning to each note the number corresponding to the number of semitones in the interval which the excerpt was transposed up gives
From Book II we have
The 10 excerpts also correspond to the 10 distinct notes which occur in the Inhalt (contents) line before the double bar, again taking enharmonic notes to be equivalent. Assigning to each note the number corresponding to the number of semitones in the interval which the excerpt was transposed down and adding together the values assigned to the pairs of notes joined by slurs gives
Now the fact that the Book I excerpts have all been transposed upwards and the Book I excerpts have all been transposed downwards implies subtraction. More specifically, subtracting the Book II sequence from the Book I sequence termwise gives
Stem directions were ignored throughout the excerpts to be consistent with the clef being ignored in FUGA XXII (1) as this would otherwise call for an absurd amount of ledger lines.
The fugue in C sharp minor from Book II was swapped out for the fugue in C sharp major to avoid the subject being transposed beneath the lowest note which appears in the WTC. However, the C sharp major fugue comes with its own problems---it opens with a stretto. In hindsight it would have been simpler to just use the C sharp minor fugue.
|The answer is: partition|