Analysis of Bach Fugue in D Minor Essay

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Analysis of Bach Fugue in D Minor


The fugue can be defined by Schulenberg as ‘A contrapuntal composition (or section or movement of a larger work) in which a theme, called a subject, is introduced in one voice and then imitated repeatedly at different pitch levels or in different keys by all of the parts’. The fugue originates from the Renaissance motet, an instrumental piece from the 16th and 17th centuries usually with a title such as ‘fantasy’. Contrapuntal style during this time was used within the constraints of the modal system, but the majority of contrapuntal features and devices of fugue style were still available to these earlier composers such as Corelli and Vivaldi. The earliest use of the word fugue in the 16th century actually meant canon strictly applied. This then developed into the fugue as known today. This is evident in the works of Josquin and Buxtehude, imitative contrapuntal ideas evolved in some of their works. At the time of The Well-tempered Clavier certain fugal features are defined. In the exposition a second voice or countersubject almost always follows the subject the countersubject is frequently at the pitch of the dominant.

Regular countersubjects pre-dominate in order that the unity of the fugue may be emphasised. A third voice may enter with the subject generally after a slight delay. There many also be an inverted countersubject. Episodes are generally included in fugues, these are connecting passages between two expositions and their function is to prepare for the next entry. Although the fugue is typically known as a baroque era style of music, composers such as Mozart, Beethoven and Braham’s have extended the style of the fugue. A prominent feature in their fugues is the episode. The episode is generally used and developed more, it normally occurs straight after the exposition. J.S. Bach is well known as the leading composer of fugues and keyboard music in the Baroque era. Bach developed the fugue as it is known today. The Well-tempered Clavier book one and book two contain 48 preludes and fugues in all the keys of the chromatic scale.

It is widely accepted the Bach’s The Well-tempered Clavier was modelled on J.C.F. Fischer’s Ariadne musical, a set of 20 short preludes and fugues in a chromatic key order ascending from C-B. The prelude always preceeds the fugue and is a dance which is generally associated with arpeggiated movement. Bach began writing the ‘Well Tempered clavier book one’ during his Cothen Period, where he was director of chamber music. It was completed in 1722. The second book was written during his Leipzig period. Bach had many influences in writing his fugues.

Michael Praetorius was one of these; he was an influential renaissance composer who discussed the traits of the fugue and its beginnings. Joachinn Bureister was another influence; he organised and studied contrapuntal music in the way that it is studied today. Bach was also strongly influenced by the composer Dietrich Buxtehude, as a youth Bach would visit Buxtehude in which he would gain an ‘outpour of creativity’. Some of the features Buxtehude uses are evident in Bach’s early organ fugues such as the five section Prelude and Fugue in A minor.

Book 1, Fugue in d minor

In Bach’s time the final liberation of the key of D minor from the Dorian mode was completed. Bach used this new tonality in some of his most significant works, including the ‘Organ Toccata’ and the ‘Chromatic Fantasy and Fugue’. The intense feeling created by this key can also be heard in this fugue. The prelude preceding this fugue is light and delicate with mainly arpegiated movement. This provides contrast. This fugue along with fugue number six and fifteen and from book II number six can be classified according to Groocock as ‘a fugue for three voices with stretto’. The fugues in this group have stretto as an important part of formal organisation; this is when the answering or imitating voice need not wait until the previous entry has been completed to make its own entrance. The answering or imitation voice does not need to wait until the previous entry has been completed to make its own entrance. Even though there’s is fuller use of stretto these fugues still have episodes but just in smaller numbers.


The counterpoint in this fugue is among the strictest in The Well-Tempered Clavier. It has very little dissonance throughout. It is also one of the most unified fugues written by Bach, there is no new thematic material introduced after bar 4 and the four episodes are formed from figures in the subject and counter-subject.

The subject last for just over two bars and ends on the dominant but without modulating. The subject rises from the tonic and then with a leap to the 6th breaks off and turns back to the 5th. It is important to note that on the 6th the b flat a staccato sign appears, it appears on the original autographed copy of the fugue. Bach also carries the staccato sign throughout the entire fugue. This shows he perceived the subject to be aggressive and powerful. There are ten entries of the subject after it is first played, but only one is bar 28 is exactly like the opening. In many instances the subject is played but the 3rd is sharpened or flattened, this occurs in bars 17, 18, 34, 39 and 40. This is seen below, the subject occurs in the bass, the 3rd in the 2nd bar is sharpened, the subject also starts in the dominant A major.

The subject unusually in bar 35 starts on F sharp, the leading note to G minor, this is very far away form the original key. This is seen below in the soprano part.

There are five entries of the subject that are inverted and they are in varying positions of the scale.

In this example of an inverted subject the middle voice starts on E, which as the supertonic of D minor, it has a falling 5th instead of a falling 6th in the second bar. In bar 29 the bass starts on an A as the dominant in D minor, which becomes the supertonic in G minor and using a falling fifth as in the example above from bar 14. The countersubject never reappears in its original form. Its presence is felt all through the fugue, in spite of the amount of stretto used. The counter-subject is a semiquaver figure and it appears fourteen times within the fugue.

A common alteration made by Bach to the countersubject throughout the fugue is that only half of the countersubject is played. This happens twelve out of the fourteen times the countersubject appears. An example is shown here in bar 17. The soprano has the second half of the counterpoint. The first half was hinted at in the bar previous, but not continued. In bars 6-7 the countersubject is transferred between the soprano and the middle voice. This is the only instance of this happening in this fugue.

There are four major episodes in this fugue. The first three episodes involve and inverted subject. Episode one from bars 10-13 has the upper voice repeat the end of the subject, in a falling sequence. The bass repeats the end of the counter-subject and in bar 12 the middle voice hints at the inverted subject.

In episode two from bars 25-27 the soprano makes a rising sequence contrary to episode one. The third episode appears from bars 21-25 and comes out of the previous entry and is a free inter-change of the first episode. The final episode is from bars 36-39 developed from the changed ending of the previous soprano entry. In a rising sequence the soprano repeats the figure of the first bar of the counter-subject, while the lower voice in thirds repeats the first half of the inverted subject.

Bach is generous in his use of stretto; there are six examples of it in this fugue. There are four instances of stretto with two voices. In bar 17 the bass is followed by the middle voice in bar 18, with a development towards the cadence. In bars 21-25 there are only two voices but they provide three entries, the bass in bar 21, the soprano in bar 22 and the bass again in bar 23. This is seen in the example below.

In bars 34 and 35 there is again a two-part stretto and again in bars 39-42 there is a two-part stretto that is the same as bars 17-20 but now in the tonic key, with an extension towards the final cadence. There are then two examples of stretto with three voices. The first appearing in bars 13-16, Bach hints at stretto in bars 12 and 13 but is fully employed in bar 14 with the middle voice entry. The final instance of stretto for all three voices happens in bars 27-31, with the soprano entering in bar 27, the middle voice in bar 28 and the bass in bar 29.

To round off the fugue a coda is employed in the final two bars of the piece. The coda makes an allusion of the subject; it is direct and inverted, with thirds added. These are heard on a tonic pedal.


The fugue in d minor was one of the earlier fugues written by Bach during his time at Cothen. Many fugual devices are included in this fugue including stretto, episodes, a countersubject and three main voices. These were all heavily influenced by other composers of the time such as Buxtehude and Bureister. The main idea of the Well Tempered Clavier was taken from J.C.F. Fischer’s Ariadne musical. Dispite this The Well Tempered Clavier is regarded as one of Bach most famous works; it has survived time, and is played regularly today by keyboard students.


Malcolm Boyd, Oxford Composer Companions: J.S. Bach (Oxford university Press 1999)

Joseph Groocock, Fugal Composition, A Guide to the Study of Bach’s ‘48’ (Dorone Groocock 2003)

Hermann Keller, The well-tempered clavier by Johann Sebastian Bach (Allen & Unwin 1976)

Ralph Kirkpatrick, Interpreting Bach’s Well-Tempered Clavier (Yale University Press 1984)

David Schulenberg, Music of the baroque (Oxford University Press 2008)

[ 1 ]. Malcolm Boyd, Oxford Composer Companions: J.S. Bach (Oxford university Press 1999) p.181 [ 2 ]. ibid
[ 3 ]. Boyd, Oxford Composer Companions: J.S. Bach (Oxford university Press 1999) pp.181-182 [ 4 ]. Hermann Keller, The well-tempered clavier by Johann Sebastian Bach (Allen & Unwin 1976) p. 31 [ 5 ]. ibid p.32

[ 7 ]. Boyd, Oxford Composer Companions: J.S. Bach (Oxford university Press 1999) p.515 [ 8 ]. Ralph Kirkpatrick, Interpreting Bach’s Well-Tempered Clavier (Yale University Press 1984) p.6 [ 9 ]. Daniel Shannahan Lecture of Tuesday 24th of February

[ 10 ]. Ibid
[ 11 ]. Boyd, Oxford Composer Companions: J.S. Bach (Oxford university Press 1999) p.181 [ 12 ]. Hermann Keller, The well-tempered clavier by Johann Sebastian Bach (Allen & Unwin 1976) p.67 [ 13 ]. ibid

[ 14 ]. Joseph Groocock, Fugal Composition, A Guide to the Study of Bach’s ‘48’ (Dorone Groocock 2003) p. 63 [ 15 ]. ibid
[ 16 ]. Hermann Keller, The well-tempered clavier by Johann Sebastian Bach (Allen & Unwin 1976) p.69 [ 17 ]. J.S. Bach, Prelude and fugue no.6 in D minor BWV851 Edited by Franz Kroll (Leipzig: Brietkopf & Hartel 1866) [ 18 ]. ibid

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