11.3 The Art of Fugue and Musical Offering

Bach's "Art of Fugue" and "Musical Offering" showcase his mastery of counterpoint. These works demonstrate intricate compositional techniques, using a single theme to create complex, interwoven musical lines through various manipulations and developments.

Both pieces highlight Bach's genius in creating diverse, inventive works within strict contrapuntal forms. They explore fugal structures, canons, and other contrapuntal devices, showcasing Bach's unparalleled skill in manipulating musical ideas and themes.

The Art of Fugue

Concept of fugue

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• Contrapuntal compositional technique involving multiple voices or parts that enter successively, each imitating the principal theme (subject)
• Voices enter at different pitches, creating a complex polyphonic texture with intricate, interwoven musical lines (counterpoint)
• Demonstrates the composer's skill in manipulating and developing a musical idea, requiring a deep understanding of counterpoint and harmony
• Bach is considered a master of the fugue form, composing numerous fugues as standalone works (Well-Tempered Clavier) and movements within larger compositions (Mass in B minor)

Compositional techniques in Art of Fugue

• Consists of 14 fugues and 4 canons, all based on a single subject that is simple yet malleable, lending itself to extensive development
• Employs various contrapuntal techniques to develop the subject
  1. Augmentation lengthens the duration of the subject's notes
  2. Diminution shortens the duration of the subject's notes
  3. Inversion flips the subject's intervals upside down
  4. Retrograde plays the subject backwards
  5. Stretto overlaps entrances of the subject in close succession
• Explores different fugal structures and variations
  • Counter-fugues present multiple subjects simultaneously
  • Double and triple fugues feature two or three distinct subjects
  • Mirror fugues can be played upside down (inversion) or backwards (retrograde)

Musical Offering

Historical context of Musical Offering

• Composed in 1747 near the end of Bach's life during a visit to the court of Frederick the Great, King of Prussia, an accomplished flutist
• Frederick presented Bach with a musical theme (royal theme) and challenged him to improvise a fugue based on it
• Bach improvised a three-voice fugue on the spot and later developed the theme further, sending Frederick a set of compositions that became known as the Musical Offering
• Testament to Bach's skill in improvisation and ability to create complex works from a simple theme

Counterpoint and canon in Musical Offering

• Consists of 13 movements showcasing various contrapuntal techniques
  • Two ricercars (fugues) for three and six voices
  • Ten canons exploring different contrapuntal devices or variations (per augmentationem, per tonos, cancrizans)
  • Trio sonata for flute, violin, and continuo
• Canons demonstrate Bach's mastery of contrapuntal writing
  1. Canon per augmentationem has the follower voice play the leader's melody at double speed
  2. Canon per tonos has the follower voice enter a tone higher than the leader
  3. Crab canon (cancrizans) has the follower voice play the leader's melody backwards
• Trio sonata uses the royal theme as a cantus firmus in the continuo part with upper voices engaging in intricate counterpoint above the constant theme
• Showcases Bach's ability to create diverse, inventive works within strict contrapuntal forms