The Musical OfferingBWV 1079 (1747)
This work is dedicated to Frederick the Great of Prussia. It consists of 13 compositions:
All are based on a theme by Frederick on which Bach had improvised while visiting him in 1747. (Bach's son, C.P.E., was the court harpsichordist for Frederick.) Upon returning to Leipzig, Bach revised and wrote out his improvisations.
- a 3-voice ricercar
- a 6-voice ricercar (a wonderful example of Bach's mastery of the "stile antico")
- 10 canons
- a trio sonata for flute (Frederick's instrument), violin, and continuo; one of very few written by Bach (an example of Bach's command of an "up-to-date" idiom)
The proper order of the pieces is uncertain (as is the instrumentation, except for the trio sonata), although some believe the trio sonata served as the middle portion of the whole.
The work is noted for its intense look at the form and procedures of the canon. The types of canons found in the "Offering" are:
- "enigma" canon - the material is given for the realization of the canon, which is to be done by the players themselves; it is not written out in complete score form
- "spiral" canon - the melodic line of the canon ends in a different key from which it began. It should be repeated until the tonic key is reached again
- "retrograde" canon - a "crab" canon in which the melodic line played backwards accompanies the melody in its original form
Art of FugueBWV 1080 (1745-1750)(See also Bach's Fugue)
The printed edition of this work contains 14 pieces (referred to as "contrapuncti"), all based on the same theme. It is a systematic, didactic demonstration of all types of fugal writing, arranged in a general order of increasing complexity (some controversy exists as to the correct order). The intended medium of performance is uncertain. Bach had it engraved in open score without instrument designations. It was unfinished at his death.
The work explores:
- "perpetual" canon - the end leads to the beginning allowing multiple repetitions
- double fugue
- triple fugue
- quadruple fugue
A concluding chorale prelude, "Wenn wir is höchsten Noten sein" (BWV 668), was added to the work by its editors to "compensate" for incomplete and missing material.
- 4 canons
- 2 "mirror" fugues arranged for 2 keyboards
- Numbers 12 and 13 are invertible, thus creating 2 versions each
- 1 quadruple fugue (left unfinished)