Contrapunctus X from the Art of the Fugue
What is a double or triple fugue?
A double fugue is based on two subjects. A triple fugue is based on three subjects. The subjects can be presented at the exposition or they can appear separately before being combined later as in this fugue.
Contrapunctus X from the Art of the Fugue (Kunst der fuge BWV 1080) is a double fugue based on two subjects:
The second subject is a variation by inversion of the main subject of the Art of the Fugue:
The First Subject
The first subject is presented by the alto. The notes on the second measure (descending second - ascending fourth) are the notes from the first measure transformed by contrary motion or inversion:
This subject is rhythmically similar to Contrapunctus XI's subject:
Contrapunctus XI's subject is a variation of the subject of the Art of the Fugue, we show the notes from the original subject in the previous example. This may leads us to think that the first subject of the fugue we are analyzing may also be related. In fact, the first 3 notes of this subject are the first 3 notes of Contrapunctus XI subject transformed by retrograde motion:
The answer, presented by the tenor, is a real answer:
The answer takes us to the subdominant key (G minor) instead of the traditional dominant key. It starts on the fourth beat instead of on the second beat as the subject.
The bass presents the subject for the second time in measure 7 transformed by inversion. The first three notes of the subject presented by the bass are the same notes as notes 4 to 6 of the alto subject (blue square) and notes 4 to 6 of the bass subject are the same notes as the first notes of the alto subject (red square):
Finally the soprano ends the fugue exposition presenting the inverted answer in measure 8. The final answer enters in stretto:
Another interesting aspect of this peculiar exposition is the fact that each voice starts on different notes:
During the exposition we have visited three different keys:
|subject (alto)||d minor|
|answer (tenor)||g minor|
|subject (bass)||d minor|
|answer (soprano)||a minor|
Here is the complete exposition: