1. Matthias Röder Harvard University roeder@fas.harvard.edu
The Permutation Fugue and Johann Sebastian Bach's Compositional Development
The 14th Biennial International Conference on Baroque Music
Queens University Belfast, July 1, 2010
Matthias Röder
Harvard University
Matthias Röder |

2. Overview The Permutation Fugue Compositional Challenges
Permutation Fugues in the Early Cantatas
Implications for Chronology and Authenticity?
Matthias Röder |

3. { ….. The Permutation Fugue T D T D T D T D T The Five Principles1
Voices must enter successively
Voice entries alternating on tonic and dominant
Fixed sequence of subjects
Little or no free counterpoints
Multiple / invertible counterpoint
Fugue S { A T
….. B T D T D T D T D T
1 Walker1989
Matthias Röder |

4. { …? Compositional Challenges Central Question Harmonic Diversity
Fugue …? S { A T B T D T D T D T D T
Compositional Challenges
Harmonic Diversity
Large-Scale Development
Integration
Central Question
How does Bach address these challenges in the permutation fugues of his early cantatas?
Matthias Röder |

5. Permutation Fugues in Bach’s Early Cantatas
BWV
Cantata Title
Performance Date or Chronology
Movement or Section Title 71
Der Herr ist mein König
February 4, 1708
“Muß täglich von neuem”
“Dein Alter sei wie deine Jugend”
196
Der Herr denket an uns
Early, possibly in Mühlhausen on stylistic grounds1
“Er segnet das Haus Israel”
150
Nach dir, Herr, verlanget mich
Early, but authenticity and chronology debated2
“Denn er wird meinen Fuß“
208
Was mir behagt, ist nur die muntre Jagd!
February 27, 1713
“Lebe, Sonne dieser Erden”
182
Himmelskönig sei willkommen
March 25, 1714
“Himmelskönig sei willkommen”
“So lasset uns gehen in Salem der Freuden“ 21
Ich hatte viel Bekümmernis
June 17, 1714 (or earlier?)
“Daß er meines Angesichtes”
“Lob und Ehre und Preis und Gewalt” 63
Christen, ätzet diesen Tag
December 15, 1714
“Höchster schau in Gnaden an”
Basic use
Experimen-
tation
Full inte-
gration
1 Dürr Küster 1996 for a differing opinion.
2 Schering 1913 and Rifkin See also Glöckner 1988 and Dürr 1977.
Matthias Röder |

6. “Muß täglich von neuem” (BWV 71)tr
v I
v II
vla vc S A T B
Analytical Remarks
Picture book permutation fugue. Standard employment of the technique
Instruments fill-in when voices drop out. Later on, instruments double voice entries creating an impressive increase in sound
Fugue is contained in a multi-part movement, but thematically not connected to surrounding sections
Matthias Röder |
* Permutation scheme based on Neumann 1950

7. “Dein Alter sei wie deine Jugend” (BWV 71){ A T B
Analytical Remarks
First step towards incorporation of permutation subjects into the larger movement context
Fourth subject is fixed only rhythmically. Pitch content is variable
Used in combination with variations of the third fugue subject for the transition between the fugue expositions and for the ending
Matthias Röder |
* Permutation scheme based on Neumann 1950

8. Combination and Variation of Fugue Subjects for Transition
Source: NBA I/32.1
Matthias Röder |

9. “Er segnet das Haus Israel” (BWV 196)
v I
v II
vla vc S A T B
Analytical Remarks
Further refinement of instrumentation strategies as well as exploration of harmonic shifts
Irregularities in permutation scheme result from Bach’s idea to double voice entries with instruments in corresponding range
Real answer in Comes results in harmonic shift to subdominant
Matthias Röder |
* Permutation scheme based on Neumann 1950

10. Real Answer in Comes Results in Harmonic Shift to Subdominant
Tonic
Subdominant
Matthias Röder |

11. “Denn er wird meinen Fuß“ (BWV 150)
v I
v II
bsn S A T B
Analytical Remarks
Combination of permutation fugue with non-fugal violin solo. First step towards fusion of permutation principle with other techniques
Violin transition linking the fugue directly to preceding section. There is however, no thematic connection
Dux and Comes are overlapping
Matthias Röder |
* Permutation scheme based on Neumann 1950

12. Summary Pre-Weimar Fugues
All fugues have at least one complete exposition
If fugues are integrated into larger movements, there is no thematic connection
Four Compositional Strategies
Insertion of instrumental voices to fill gaps between vocal expositions
Instrumental doubling of voice parts to vary texture and increase sound
Increase harmonic diversity by employing the “wrong” Comes
Inclusion of non-fugal material
Matthias Röder |

13. “Lebe, Sonne dieser Erden” (BWV 208)
v I
v II
vla
Bsn + vc S A T B
b.c.
Analytical Remarks
First vocal exposition is not complete in order to pace movement
Incorporates Permutation Fugue into Da-Capo Form
Non-permutation-fugue sections contain fugue subjects as well, binding the fugue more closely into the movement at large
Matthias Röder |
* Permutation scheme based on Neumann 1950

14. Permutation Fugue Subject in Instrumental Interlude and B-Section
Source: NBA I/35
Matthias Röder |

15. “Himmelskönig sei willkommen” (BWV 182)fl
v I
vla I
vla II vc S A T B
Analytical Remarks
Da-Capo movement that contains a variety of fugal and canonic techniques
Permutation fugue is basis of entire movement, providing structurally important material
For example: uses permutation subject to signify arrival of new key in B-section of Da-Capo form
Matthias Röder |
* Permutation scheme based on Neumann 1950

16. Uses permutation subject to signify arrival of new key in B-section of da-capo form
Source: NBA I/8.2
Matthias Röder |

17. “So lasset uns gehen in Salem der Freuden“ (BWV 182)fl
v I
vla I, II, vc S A T B S
Analytical Remarks
Seamless integration of permutation fugue into Da-Capo movement. First instance in which permutation fugue subject is used for Ritornello
Furthermore: harmonic shift to subdominant widens harmonic space before launching into closing group.
Matthias Röder |
* Permutation scheme based on Neumann 1950

18. “Lob und Ehre und Preis und Gewalt” (BWV 21)
v I
v II
vla
bsn S A T B
Analytical Remarks
Combines the permutation principle with free fugal sections and a concertizing section between the solo, tutti, as well as instrumental choirs
Matthias Röder |
* Permutation scheme based on Neumann 1950

19. “Höchster schau in Gnaden an” (BWV 63)
Similarity to BWV 150:
Connection to preceding section
Overlapping of voice entries
Matthias Röder |

20. Overlapping of Dux and Comes
trp.
Comes . . . . .
Comes
Source: NBA I/2
Matthias Röder |

21. Comparison Pre-Weimar Weimar
All fugues have at least one complete exposition
Seldom integrated into larger context
If so, there is no thematic connection
Experimentation with use of free counterpoint within permutation fugue
First fugue exposition is often cut off
Always connected to larger context
Close thematic connection between sections
Free counterpoint used to connect permutation fugue with preceding or following section
Matthias Röder |

22. Some Implications? Chronology of BWV 196 Authenticity of BWV 150
Full exposition, use of instrumentation, harmonic experimentation all point to pre-Weimar practise
Authenticity of BWV 150
Overlapping of Dux and Comes (also in “Höchster schau in Gnaden an“)
Transition from free section to fugue (also in “Daß er meines Angesichtes“ and „Höchster schau in Gnaden an“)
Chronology of BWV 150
High degree of experimentation in permutation fugue excludes earliest composition
Lack of thematic integration does not point towards Weimar period, however
Matthias Röder |

23. References Matthias Röder | roeder@fas.harvard.edu
Carl Dahlhaus, “Zur Geschichte der Permutationsfuge,” Bach-Jahrbuch 46 (1959): 95–110.  
Alfred Dürr, Studien über die frühen Kantaten Johann Sebastian Bachs, 2nd ed. (Wiesbaden: Breitkopf & Härtel, 1977).
Andreas Glöckner, “Zur Echtheit und Datierung der Kantate BWV 150 'Nach dir, Herr, verlanget mich‘,” Bach- Jahrbuch 74 (1988): 195–203.
Konrad Küster, “Eine frühe Bach-Kantate und ihr Kontext,” Musik und Kirche 66 (1996): 84–96.
Werner Neumann, J. S. Bachs Chorfuge. Ein Beitrag zur Kompositionstechnik Bachs, 2nd ed., Bach-Studien 3 (Leipzig: Breitkopf & Härtel, 1950).  
Joshua Rifkin, “Bachs erste Kantate,” (presented at the Bach Colloquium, Cambridge, Mass, 2005).
Paul Walker, “Die Entstehung der Permutationsfuge,” Bach-Jahrbuch 75 (1989): 21–41.
Arnold Schering, “Die Kantate Nr "Nach dir, Herr, verlanget mich",” Bach-Jahrbuch (1913): 39–52.
NBA = Neue Bach-Ausgabe (Kassel: Bärenreiter)
Matthias Röder |
Slides are available from
Matthias Röder |