A lesson from J.S. Bach: 'The Art of Fugue' as a teaching and learning tool. |
By: Roger Hansford |
To teach within a single work the fundamental techniques of simple and advanced fugal writing is no easy task, yet - as my analysis of Contrapuncti 4, 7, 9, 11, 12 and 14 will show - this is what The Art of Fugue by J. S. Bach (1685-1750) achieves. It is the work’s careful presentation and layout that best enabled it to instruct within its own time; how useful its lessons are to today’s students depends on our definition of the ‘student’ and their learning objectives.
In order to understand what The Art of Fugue teaches we should first examine the work’s teaching methods, not least that the contrapuntal arrangement was fully notated. This set the work against the tradition whereby musicians treated knowledge of contrapuntal techniques like alchemical metals, hoarding them so that ‘the secrets of music [would not] become common’ to the masses.[1] One account from around 1729 describes how the teacher Buttstedt ‘forced his student to pay twelve Thalers - six up front - to see a treatise on double counterpoint’.[2] Even as late as Easter 1752, Friederich Wilhelm Marpurg could write: ‘A particular merit of this work [The Art of Fugue] is the fact that everything contained in it is set in score’ [3], a statement seeming humorously fatuous to the modern reader. The full notation of the work enabled it to teach, as Stephen Daw suggests, ‘by immediate example’, providing a clear template for Bach’s many copyists.[4]
The Art of Fugue also teaches by virtue of its musical characteristics. It is based throughout in the key of D minor, a feature enabling cross-reference between the fugues within a relatively accidental-free tonal area, chromaticism [5] notwithstanding. Another unifying aspect which constitutes a teaching method is that the single theme from which all fugues are derived is handled with increasing complexity as the work progresses.[6] Therefore, despite ‘anomalies’ [7], there is progression from the known to the related unknown; the student meets the harder contrapuntal techniques only as their familiarity with the theme grows. Despite assertions by commentators from C. P. E. Bach [8] to David Schulenberg [9] that The Art of Fugue was a keyboard work, its actual arrangement in open score [10] made its lessons accessible to music students of all instrumental disciplines.[11]
So paramount is the work’s concern for teaching, some commentators suggest, that its musical integrity has been compromised. Schulenberg writes that ‘The Art of Fugue eschews tonal variety, the order of movements being determined by the contrapuntal technique illustrated in each’, and he criticises the ‘retrospective’ style, concluding that the work was written ‘to serve pedagogic and theoretical, not practical, ends’.[12] Wallace Brockway and Herbert Weinstock agree that The Art of Fugue has greater merit when used for teaching purposes than when employed in performance.[13] According to Richard Jones, however, Bach synthesised both practical and theoretical aspects in order to please his audience [14], and any idea that The Art of Fugue is not a practical work is ‘a serious misapprehension’.[15] Furthermore, C. P. E. Bach suggested that it was precisely because Bach’s lessons were ‘practical, and omitted all the dry species of counterpoint that are given in Fux and others’ [16], that they taught so well. Therefore The Art of Fugue is qualified to teach because, even when creating music for the performer, Bach had the student in mind.
In order to show what The Art of Fugue teaches I will compare an analysis of a Contrapunctus movement with a definition of fugue. Contrapunctus 4 has been chosen since this typically represents [17] the type of fugal writing which Bach appears to have invented and also used in the Well-Tempered Clavier. Stanley Sadie defines ‘fugue’ as follows:
In the opening section, the ‘exposition’, the main theme or ‘subject’ is announced in the tonic, after which the second ‘voice’ enters with the answer, i.e. the same theme but at the dominant (or subdominant) pitch . . . while the first may proceed to a counter-subject. This procedure is repeated at different octaves until all the voices have entered and the exposition is complete. [18]
Contrapunctus 4 [Example 1] clearly follows this model. The exposition (bars 1-18) begins with the eight-note subject in D minor in the treble at bar 1, the alto answering tonally, a fifth below, in bar 5. As the alto enters the soprano begins the regular counter-subject, characterised by an ostinato quaver figure derived from the last four notes of the subject. Although delayed by an extension in bars 9 and 10, the tenor gives a real answer in bar 11, with the notes unaltered from the subject. The bass answer occurs in bar 15, copying the alto answer but at the octave below.[19] The appearance of the subject in all four voices, together with a counter-subject, creates a complete exposition, ‘the only essential for the definition of a piece as a fugue’[20]. Therefore The Art of Fugue teaches the basic process of fugue composition.
Sadie’s definition mentions several additional conventions of the fugue: a ‘counter-exposition’; further subject entries with ‘episodes’ derived from the exposition; a set of ‘middle entries’ that vary the theme in keys ‘other than the tonic or dominant’; and a final subject entry in the tonic.[21] All of these features can be seen in Contrapunctus 4 [Example 1]. A counter-exposition runs from bars 27 to 42, with the redundant entries occurring in bars 27 (treble), 31 (alto), 35 (tenor) and 39 (bass). Prior to this is an episode, from bars 19 to 26, in which the tenor and bass parts are derived from the counter-subject quaver figure of the exposition; by the end of the second episode (bars 43-60) the quaver figure has permeated all four parts. During the middle entries (bars 61-80) there is variation as the subject has altered from its appearance in the exposition. The intervals between notes 3 to 5 of the theme are not major third - semitone but major/minor third - minor third, and apart from the alto none of the subject entries appear in the tonic. However, the modulatory fourth episode (bars 81-106) ensures that the tonic is regained by bar 107, where the theme returns in D minor in the tenor to signal the return. The final entry of the subject, in the alto at bar 133 and following the fourteen-bar fifth episode, is in the tonic, although the eighth note is raised to create a tierce di picardie cadence in bar 138 after a four-bar tonic pedal.[22] From this analysis it is evident that Contrapunctus 4 includes the aspects described by Sadie; therefore, especially for the modern student, The Art of Fugue teaches not only the rules of fugal texture but also the conventions of the genre.
However, as suggested by his choice of ‘Contrapunctus’ rather than ‘Fugue’ for the movement titles [23], Bach’s lessons in The Art of Fugue extend beyond fugue technique to instruct on good compositional practice in general. Bach’s 1723 Preface to his Inventions, also didactic pieces, includes his petition for copyists ‘not only to be inspired with good inventions, but properly to develop them’.[24] Contrapunctus 4 [Example 1] includes several examples of melodic invention and development. Firstly, Bach uses stretto in lower and then upper parts to introduce the return at bar 107. Secondly, a ‘cuckoo-like upbeat figure’ [25] which appears in Episode 1 is employed throughout the fugue: as octave imitation in bars 31-2 (bass and treble) and 40-41 (treble and alto); as a counter-ostinato on D and B-flat in bars 35-6, in the middle entries in three parts at once during bars 61-6, and in the lower parts during bars 73-4 and 77-9 where it is extended by a note and used as an ‘imitative’ ostinato.[26]
The third good general compositional technique demonstrated by Contrapunctus 4 [Example 1] is the use of sequence in every episode. While the sequence in Episode 1 could be viewed as a modulatory device, other episodes suggest that sequence is important melodically as well as harmonically. The four bar ascending sequence of bars 47 to 50 (Episode 2) is inverted by the six bar sequence beginning Episode 4, and treated to a varied reprise in bars 119 to 123 of Episode 5. The quaver figures from Episode 1 are treated antiphonally in a rising sequence from bars 53 to 57 of Episode 2, and then treated imitatively in bars 87 to 93 of Episode 4.[27] This shows that, through the use of sequence, imitation and inversion, the later episodes develop the melodic inventions of the earlier episodes. Therefore The Art of Fugue uses the fugue texture as a vehicle to teach good compositional techniques in general.
While Contrapunctus 4 effectively demonstrates teachings through simple fugue design, it is important to examine the more advanced fugal techniques exemplified by other movements. In Contrapunctus 7 [Example 2] the subject is answered (in stretto) by an inversion of the theme, creating counter-fugue, which is augmented so that each note value doubles. The alto entry in bar 3 is back in rectus form and has undergone diminution to return it to crotchet meter, but the inversus bass entry at bar 5 is massively augmented, so a crotchet becomes a semibreve and the original subject of one-and-a-half bars takes nine bars to execute.[28] Mirror fugue is demonstrated by Contrapunctus 12 [Example 3], where the inversus form of the theme in the Contrapunctus, beginning A, D in the treble, becomes the rectus form in the Contrapunctus Inversus, beginning D, A in the bass.[29]
Other Contrapuncti teach the techniques of multiple fugue. Contrapunctus 9 [Example 4] is a double-fugue, with two subjects, and also demonstrates invertible counterpoint; this is seen in bar 45 where Subject I sounds a twelfth higher than its appearance in bar 35, and where Subject II has been switched below to provide the bass line. Contrapunctus 11 [Example 5] is a triple fugue; its three subjects appear in bar 146, and are all later inverted.[30] According to Jones, Contrapunctus 14 [Example 6] was to teach quadruple fugue[], although only three subjects, including the notorious motive in which Bach ‘identifies himself by name’ [32], have been exposed before the work ends unfinished. Therefore The Art of Fugue was able to teach the advanced contrapuntal techniques of stretto, counter-fugue, augmentation, diminution, invertible counterpoint and inversion all subjects, mirror fugue and multiple fugue.[33]
Because of its comprehensive nature, though, The Art of Fugue goes beyond the teaching of particular compositional methods; Bach’s efforts provide a model for other composers wishing to produce encyclopedic reference works. Although each movement exemplifies different techniques, all are united by a theme which itself is varied, as Christoph Wolff demonstrates, by rhythm.[34] John Butt calls this synthesis of unity and variation ‘a dynamic specific to Bach’s music’ [35]; therefore something from which other composers could potentially learn. Copyists could benefit from what Donald Jay Grout calls ‘Bach’s desire to fulfil thoroughly the potentialities . . . inherent in any musical situation’.[36] Just as the philosopher Leibnitz saw a world built from single ‘monads’, each of which implied the whole world [37], so Bach produced encyclopedic composition manuals in line with Vollkommenheiten, the German term for perfection and completeness [38]. With unity and variation making up a complete whole, therefore, The Art of Fugue teaches how to create a comprehensive musical reference manual.
The series of lessons in The Art of Fugue were, in Bach’s mind, ‘naturally restricted to those of his own time and, at best, the immediate future’.[39] Several factors support Daw’s provocative view that the work has minimal use for students today. Although students are still asked to write in the style of Bach, the idea of an actual ‘copying repertoire’ [40] has fallen from fashion, as educators strive to find more creative teaching methods. Also, although the Contrapuncti exemplify the main fugue techniques, not all of them demonstrate typical harmonic practice. Contrapunctus 4 [Example 1] moves to chord III after the first episode, so does not follow the standard I-V-vi-I fugue progression. This suggests that The Art of Fugue may be more useful to history students studying Bach’s own fugal technique, than to composition students learning fugal technique in the abstract. Moreover, uncertainties concerning the ordering of movements [41] undermines the view of progressive difficulty in the work, and the ambiguity over editions [42] distances all of Bach’s lessons from us.
Nevertheless, The Art of Fugue is still able to teach an encyclopedic range of fugal techniques and composition methods, thanks to its full notation and didactic intent. Whatever its failings, it certainly has more use to composition students of today than the didactic ‘textbook’ works of Fux, Rameau or Mattheson.[43] Instead of continuing the treatise tradition Bach chose to instruct through an actual musical work which, as shown by the Associated Board 2002 Keyboard Edition, still has great practical application. As Marpurg noted in 1752, ‘natural and cogent thoughts maintain their worth in all times and places’.[44]
NOTES
[1] David Yearsley, ‘Alchemy and Counterpoint in the Age of Reason’, Journal of the American Musicological Society 51 No.2 (Summer 1998), p.214.
[2] ibid, p.215.
[3] Marpurg, ‘Preface’ to The Art of Fugue (1752) in The Bach Reader: A Life of Johann Sebastian Bach in Letters and Documents. Revised Ed. eds. Hans T. David & Arthur Mendel (New York: Norton, c.1945) pp.267-8.
[4] Stephen Daw, ‘Bach as Teacher and Model’ in The Cambridge Companion to Bach ed. John Butt (Cambridge: Cambridge University Press, 1997), pp.195-6.
[5] David Schulenberg, The Keyboard Music of J. S. Bach (London: Victor Gollancz, 1993), p.344.
[6] ibid, p.345.
[7] Richard Jones, ed. J. S. Bach The Art of Fugue/Die Kunst der Fuge BWV 1080 (London: The Associated Board of the Royal Schools of Music (Publishing) Ltd, 2002), p.8.
[8] C. P. E. Bach quoted by Jones, ed., p.9.
[9] Schulenberg, p.346.
[10] Richard D. P. Jones, ‘The Keyboard Works: Bach as Teacher and Virtuoso’ in Butt, ed., p.150.
[11] Martin Zenck, ‘Re-Interpreting Bach in the Nineteenth and Twentieth Centuries’ in Butt, ed., p.239.
[12] Schulenberg, pp.344-5.
[13] Wallace Brockway & Herbert Weinstock, Men of Music (London: Methuen & Co. Ltd., 1959), p.200.
[14] Jones in Butt, ed., p.144.
[15] Jones, ed., p.9.
[16] C. P. E. Bach, quoted by Daw in Butt, ed., p.198.
[17] Schulenberg, p.354.
[18] Stanley Sadie, ed., ‘Fugue’, The Grove Concise Dictionary of Music (London: Macmillan, 1994), p.292.
[19] Jones, ed., p.105.
[20] Sadie, p.292.
[21] ibid, p.292.
[22] Jones, ed., pp.105-6.
[23] Christoph Wolff, Johann Sebastian Bach: The Learned Musician (Oxford: Oxford University Press, 2000), p.436.
[24] J. S. Bach, Preface to Inventions (1723) quoted by Daw in Butt, ed., p.198.
[25] Citation needed.
[26] Jones, ed., pp.105-6.
[27] ibid., p.106.
[28] ibid., p.107.
[29] ibid., p.110.
[30] ibid., pp.107-8, 109-110.
[31] ibid., p.111.
[32] Marpurg in David & Mendel, eds., pp.267-8.
[33] Jones, ed., p.9.
[34] Wolff, p.435.
[35] John Butt, ‘"A Mind Unconscious That It Is Calculating"? Bach and the Rationalist Philosophy of Wolff, Leibnitz and Spinosa’ in Butt, ed., p.64.
[36] Donald Jay Grout, A History of Western Music Rev. Ed. (London: J. M. Dent & Sons, 1973), p.421.
[37] Butt in Butt, ed., p.62.
[38] John Butt, ‘Bach’s Metaphysics of Music’ in Butt, ed., p.57.
[39] Daw in Butt, ed., p.202.
[40] ibid., p.199.
[41] ibid., pp.346-350.
[42] Jones, ed., pp.6-8.
[43] Schulenberg, p.344.
[44] Marpurg in David & Mendel, eds., pp.267-8.
BIBLIOGRAPHY
Brockway, Wallace & Herbert Weinstock. Men of Music. London: Methuen and Co., 1959.
Butt, John. ‘Bach’s Metaphysics of Music’ in The Cambridge Companion to Bach, ed. John Butt. Cambridge: Cambridge University Press, 1997.
________. ‘“A Mind Unconscious That It Is Calculating”? Bach and the Rationalist Philosophy of Wolff, Leibnitz and Spinosa’ in The Cambridge Companion to Bach, ed. John Butt. Cambridge: Cambridge University Press, 1997.
David, Hans T. & Arthur Mendel. The Bach Reader: A Life of Johnann Sebastian Bach in Letters and Documents. Rev. Ed. New York: Norton, c.1945.
Daw, Stephen. ‘Bach as Teacher and Model’ in The Cambridge Companion to Bach, ed. John Butt. Cambridge: Cambridge University Press, 1997.
Dickinson, A. E. F. Bach’s Fugal Works: With an Account of Fugue Before and After Bach. London: Sir Isaac Pitman & Sons Ltd, 1956.
Grout, Donald Jay. A History of Western Music. Rev. Ed. London: J. M. Dent and Sons, 1973.
Jones, Richard D. P. ‘The Keyboard Works: Bach as Teacher and Virtuoso’ in The Cambridge Companion to Bach, ed. John Butt. Cambridge: Cambridge University Press, 1997.
________________, ed. J. S. Bach The Art of Fugue/Die Kunst der Fuge BWV 1080. London: The Associated Board of the Royal Schools of Music (Publishing) Ltd, 2002.
Sadie, Stanley, ed. ‘Fugue’, The Grove Concise Dictionary of Music. London: Macmillan, 1994. 292-3.
______________. ‘Counter-fugue’, The Grove Concise Dictionary of Music. London: Macmillan, 1994. 190.
Schulenberg, David. The Keyboard Music of J. S. Bach. London: Victor Gollancz, 1993.
Siepmann, Jeremy. The Piano: The Complete Illustrated Guide to the World’s Most Popular Instrument. London: Carlton Books Ltd, 1996.
Wolff, Christoph. Johann Sebastian Bach: The Learned Musician. Oxford: Oxford University Press, 2000.
Yearsley, David. ‘Alchemy and Counterpoint in the Age of Reason’. Journal of the American Musicological Society 51 No.2 (Summer 1998): 201-244.
Zenck, Martin. ‘Re-Interpreting Bach in the Nineteenth and Twentieth Centuries’ in The Cambridge Companion to Bach, ed. John Butt. Cambridge: Cambridge University Press, 1997.