SmArt Art – the fugue

Posted on November 12, 2013


In my previous blog entry about the origins of instrumental music I explored how polyphonic music and the emergence of bass accompaniment led to the development of new genres. Harmonic thinking, based on Pythagorean pitch relationships, with notes organised in chords (played simultaneously based on the harmonic triad – tonic / dominant / median) started to become increasingly prevalent in music. On the other hand, there was a rich heritage of polyphonic music (several overlapping melodies), and highly developed methodology about the rules of combining melodies, called counterpoint, outlined in the influential treatises of the era (e.g. Prattica di musica by Lodovico Zacconi in 1619 and later Gradus ad Parnassum by Johann Joseph Fux in 1725). All this cumulative knowledge fueled the efforts of the greatest composers to create music that would display the highest level of organisation possible.

The fugue developed in the sixteenth century from other genres based on contrapunctal writing. Earlier musical forms, such as the fantasia, canzona and ricercare incorporated canonic writing, where the same melodic passage is repeated in different voices, overlapping with each other. A very popular early canon is the one composed by Johann Pachelbell – Canon in D – played by the London Symphony Orchestra in the video:

Also, these pieces included free counterpoint, where different melodies are running in parallel in a way in which their notes harmonise with each other. Such a piece is Jan Pieterszoon Sweelink’s Fantasia chromatica – a beautifully creative, stimulative piece played by Prof. Juergen Kursawa in the video below:

Fugues typically include passages of imitative (canon-like) and free counterpoint, organised in structures similar to mathematical formulae. The basic element of the fugue is its subject (or subjects, as often there is more than one subject), a melodic phrase that is examined in its fine details, such as pitch relationships, steps, leaps, harmonic structure etc. These characteristics will then be applied to the overall build-up of the fugue, determining its organising principles such as harmonic relationships between different voices and modulations occurring in the piece. Also, the melodic material presented in the fugue is usually derived from the subject, the entire subject or parts of it doing all sorts of acrobatics, such as turning upside down (inversion), moving backwards (retrograde), overlap with each other (stretto) or running at a faster or slower tempo (diminution or augmentation). The character of the subject, its leaps and rhythms would also determine the emotional colour and dynamic “temperament” of the piece.

According to the predefined methodology used in the sixteenth century, the fugue consists of several passages of exposition of the subject, alternating with episodes, where the subject is further developed. In its first exposition, the subject is presented in a single voice (monophonic texture), followed by the introduction of the same subject in all the other voices, usually transposed to different keys. Once the subject is introduced in each voice, the exposition is ended, and links to the first episode, which allows more creative freedom for the composer. Expositions and episodes alternate with each other several times, usually leading to a short ending passage (coda), which closes the fugue.

Johann Sebastian Bach – Fugue No. 10, The Well-Tempered Clavier, Book I

The Well-Tempered Clavier is one of the cornerstones of instrumental music written for the keyboard by Bach, providing study material for generations of young musicians. It became a stepping-stone towards fame for a young piano virtuoso called Beethoven in his first years in Vienna. Mozart and Haydn closely studied Bach’s preludes and fugues, finding new dimensions for their music, it was a source of great inspiration for Mendelssohn and a nurturing subject for the talents of the young Chopin and many other pianists and composers.

The term Well-Tempered Clavier covers two collections of 24 preludes and fugues, written 20 years apart from each other (the first Book in 1722 and the second one in 1742). The pieces are successively arranged in ascending order along the 12 notes of the Western tuning system, one piece for major and one for minor tonality, each piece consisting of a prelude and a fugue.

To demonstrate the nature of the fugue as a genre I have chosen Fugue number 10 from Book I. My choice was rather intuitive, as I noticed an interesting contrast between the slower, lyrical prelude and the energetic, stimulating fugue. It turned out that this piece perfectly exemplifies Bach’s methodical way of thinking, as he “calculated” the right place for every single note in this piece. Beyond the mathematics, the individuality of the piece seems to lie entirely within the character of the subject and in the ingenious way these characteristics are infused into the entire piece.

The piece is arranged in two voices, an upper and a lower melodic line on the keyboard. The main body of the piece consists of 38 measures, followed by 4 measures of closing material. The main portion of 38 measures is split in two equal parts, consisting of 19 measures each. Each measure in the first part is related to a measure in the second part, e.g. the melodic content of measures 3-4 corresponds exactly to measures 22-23, but the melody in the upper line swaps position with the lower line, and both lines are transposed up one fourth (F♯minor in the upper line becomes B minor in the lower line and B minor in the lower line is converted into E minor in the upper line

There appear to be two melodies of similar importance. The first subject is presented in the upper line of the first two measures (in the key of E minor), followed by the second subject in F♯ minor (countersubject) in the following two measures (also in the upper voice). The introduction of the second subject is paralleled in the lower voice by the re-statement of the first one, transposed into B minor.

In the following score I marked Subject 1 with red and Subject 2 with blue(kind of blue).  The phrases belonging to the episodes – marked with black ink – have been noted as E1 – 4. I also noted the key in which they appear, aiming to demonstrate the logic in the harmonic buildup.

Fuga X - part 1Fuga X - part 2

When we look at the melodic contour of the two subjects, we can notice that the interval of the fourth plays an important role – in the first subject there is a chromatically descending line from E to B (one fourth apart) and in the second subject a descending diatonic stepwise movement from F♯to C♯ (also one fourth apart). Notes of the minor scales dominate the two melodies. Of course, saying that a passage is “in minor” only means that it contains mainly notes of the minor scale, but not exclusively.  They also include notes that would be part of the major counterpart of the minor scale, as well as chromatic bridging notes. This balance between minor and major, with a bias towards minor, is reflected in the larger structure of the piece, i.e. in the harmonic choices underlying the episodes. Also, there is an interesting ending of the first subject, the last two notes being one step lower than E, i.e. two Ds one octave apart. This is reflected in the harmonic underpinnings of the second episode, where there is a modulation moving one step down – from D major in mm 16-17 to C major in m 18-19 in the upper line, paralleled in the lower line by a movement from A major in mm 15-16 to G major in mm17-18. There is a similar modulation from A major to G major in the fourth episode.

A similar calculated relationship applies to the melodies in the episodes – there are four phrases (on the score I notated them with E1-4).  The episodes of part one correspond exactly to those in part two, with the two voices swapped with each other and transposed up a perfect fourth.

Listening to different pianists playing the Prelude and Fugue No.10 it was striking that compared to the very poetical, ethereal prelude the fugue often sounded quite mechanical. I think to play it well the pianist would need find ways to soften up a bit the fugue, turning into a more “organic” conversation between two parallel voices. This is perfectly realised by the András Schiff in the recording inserted above.

Tibor Kovacs

References and interesting links:

Burkholder, J. P., Grout, D. J., Palisca C. V. (eds.) (2005) A history of Western music. 7th ed. New York: W.W. Norton & Company Inc.

Greenberg, R. (2011) How to Listen to and Understand Great Music. 3rd ed. United States of America: The Teaching Company

Wikipedia (2013) Fugue [online] Wikipedia website. Available from: [Accessed 7th November 2013]

The Canons and Fugues of J. S. Bach [online] – website edited by Timothy A, Smith. An amazing website with lots of detailed and technically elaborate analyses available from [Accessed 7th November 2013]

Posted in: Part 5