The Galaxy – Demonstrating the art of the fugue

A portrait which may show Bach in 1750

Bach, possibly from c. 1750 (Image via Wikipedia)

I enjoy my annual celebration of Bach’s birthday (he would be 327 years old on March 21st), if for the simple reason that it gives me a convenient excuse to take a good, hard listen to any one of his numerous masterpieces.  The one risk that I run is the trap of unwittingly playing the same pieces every year.  That is hard to avoid, as Bach wrote some of the most easily appropriate music for the Easter religious holiday, which by happenstance usually falls near the 21st (this year’s observance is three weeks afterwards), and several of his works rank among the truly great musical compositions.  So, in the end, while I do strive for musical variety, I don’t worry about it.  If I choose one week out of the year to play some of the greatest music that the world has ever heard, the greatness of said music remains undiminished.

So it is with that very lack of reservation that I bring out Bach’s Art of Fugue for this year’s birthday show, even though I think I may have done the same last year.  The very brilliance of the work makes the suggestion hard to refuse.  A little background: Bach began the composition of the piece at some point during the early 1740s, although it could possibly have been earlier.  This was a period where Bach was writing pieces that encapsulated everything that he had done up to that point (i.e. The Musical Offering), or revising earlier pieces so that the craft would be to his satisfaction (the two Passion works, Wohltemperierte Clavier, B Minor Mass).  One might say that Bach saw himself as having reached the sunset of his life, and he wanted to have made a grand statement.  He was quite successful, as he was able to produce, either through revisions or through original composition, three truly epic masterpieces within the three years prior to his death: The B Minor Mass, St. Matthew’s Passion, and the Art of Fugue.

The basic subject of Bach's Art of Fugue

The basic subject of Bach's Art of Fugue

While each work has its own special qualities, the Art of Fugue is quite interesting, from a compositional standpoint.  Bach started with a simple musical phrase, seen above, which is stated unequivocally in the first section.  He then ran through all of the different potential ways that he could rephrase and reorganize the statement.  What he did (I use here Wikipedia’s excellent discussion of the compositional methods Bach used):

1. Contrapunctus I, and

2. Contrapunctus II: Simple monothematic 4-voice fugues on main theme, accompanied by a ‘French’ style dotted rhythm motif.

3. Contrapunctus III, and

4. Contrapunctus IV: Simple monothematic 4-voice fugues on inversion of main theme, i.e. the theme is “turned upside down”

Counter-fugues, in which a variation of the main subject is used in both regular and inverted form:

5. Contrapunctus V: Has many stretto entries, as do Contrapuncti VI and VII.

6. Contrapunctus VI, a 4 in Stylo Francese: This adds both forms of the theme in diminution (halving note lengths), with little rising and descending clusters of semiquavers in one voice answered or punctuated by similar groups in demisemiquavers in another, against sustained notes in the accompanying voices. The dotted rhythm, enhanced by these little rising and descending groups, suggests what is called “French style” in Bach’s day, hence the name Stylo Francese.

7. Contrapunctus VII, a 4 per Augmentationem et Diminutionem: Uses augmented (doubling all note lengths) and diminished versions of the main subject and its inversion.

Double and triple fugues, with two and three subjects respectively:

8. Contrapunctus VIII, a 3: Triple fugue.

9. Contrapunctus IX, a 4 alla Duodecima: Double fugue

Contrapunctus X, a 4 alla Decima: Double fugue.
11. Contrapunctus XI, a 4: Triple fugue.

Mirror fugues, in which the complete score can be inverted without loss of musicality:


Contrapunctus 12 (Image via Wikipedia)

12. Contrapunctus XII, a 4: The rectus (normal) and inversus (upside-down) versions are generally played back to back.

13. Contrapunctus XIII, a 3: The second mirror fuguein 3 voices, also a counter-fugue.

Canons, labeled by interval and technique:

14. Canon per Augmentationem in Contrario Motu: Augmented canon in inverted motion.

15. Canon alla Ottava: Canon at the Octave. The two imitating voices are separated by an octave.

16. Canon alla Decima in Contrapunto alla Terza: Canon at the tenth, counterpoint at the third.

17. Canon alla Duodecima in Contrapunto alla Quinta: Canon at the twelfth, counterpoint at the fifth.

An arrangement of Contrapunctus XIII, see below.

18. Fuga a 2 (rectus), and Alio modo Fuga a 2 (inversus)

J.S. Bach's The Art of Fugue, breaks off abrup...

J. S. Bach: unfinished last fugue from "Kunst der Fuge", last page. Source: Deutsche Staatsbibliothek Berlin, Mus. ms. autogr. Bach P 200 (Image via Wikipedia)

Unfinished quadruple fugue:

19. Fuga a 3 Soggetti (Contrapunctus XIV): 4-voice triple, possibly quadruple, fugue, the third subject of which is based on the BACH motif, B♭ – A – C – B♮ (‘H’ in German letter notation).

The aforementioned unfinished quadruple fugue was quite the fitting capstone to the piece.  One must understand how interested Bach was in numerology and musical symbolism – there are a number of pieces where Bach spells out his name musically, such as he did here.  But this is just the beginning of how brilliant the fugue is.  A number of modern musicologists have suggested that Bach may have intended to use a restatement of the original theme as the fourth, missing section.  This may be, and is certainly logical, but we shall never know.

Further Reading

Tonight’s recording, made by Gustav Leonhardt in 1953, is also special in and of itself, as it is the first full recording of the piece on harpsichord.  When he made the recording, there was some argument as to whether it was actually written for harpsichord (the autograph score does not specify).  Now, there is little doubt, but this is probably in some part due to the work of performer/musicologists such as the eminent Leonhardt.  Leonhardt culminates the discussion thusly:

“The Art of Fugue has been written with an extraordinary knowledge of the technical possibilities of ten fingers on a keyboard.  The work does not only show Bach on his immense creative height, but also as the grandiose master of the keyboard.”

English: Gustav Leonhardt at the MAfestival in...

Gustav Leonhardt at the MAfestival in Bruges (Image via Wikipedia)

(postscript: I am utterly aghast to read, during the writing of this blog piece, of the passing of Gustav Leonhardt back in January.  The contribution that Mr. Leonhardt made to music in general, and to our understanding of the brilliance of Bach, cannot possibly be overestimated.  Leonhardt was brilliant on both organ and harpsichord, and he has been the subject of many Galaxy broadcasts over the course of the 16 years that I’ve been broadcasting.  He would have a place in musical history if just for this one recording that we’ve played tonight, but his career went far beyond this one recording.  Mr. Leonhardt, you will be missed.)

Related articles

For our second piece of the evening, we heard a cantata for solo voice, BWV 82, Ich Habe Genug (trans: “I have enough”).  The cantata was written for the Feast of the Purification of the Virgin Mary, and sung on the feast day, February 2, 1727.  This was during his Leipzig period, the height of his career, and came during an extended period of amazing output (at one point he was writing a cantata every week; in this manner he wrote three complete cycles of cantatas to cover the Lutheran calendar).  Tonight’s cantata is unusual, one of a select few that he wrote for solo voice, without other soloists or choir.  It was first written for solo bass (that version in C minor), but in later years Bach revised it for other voice types – for soprano in E minor in 1730-31, and for alto in C minor.  He also revisited the cantata at some point in the 1740s, bringing it close to the form of the original.

Lorraine Hunt Lieberson

Lorraine Hunt Lieberson (Image from

Tonight’s recording, from 2002, also features a special talent, Lorraine Hart Lieberson.  She passed away from cancer a few years later, but left behind some gorgeous samplings of her ability, of which this is one (and a particularly beautiful one at that).  I don’t know if the selection of the specific cantatas was purposeful, but the libretto makes quite a statement for someone experiencing such an illness:

Ich habe genug,
Ich habe den Heiland, das Hoffen der Frommen,
Auf meine begierigen Arme genommen;
Ich habe genug!
Ich hab ihn erblickt,
Mein Glaube hat Jesum ans Herze gedrückt;
Nun wünsch ich, noch heute mit Freuden
Von hinnen zu scheiden.

I have now enough,
I have now my Savior, the hope of the faithful
Within my desiring embrace now enfolded;
I have now enough!
On him have I gazed,
My faith now hath Jesus impressed on my heart;
I would now, today yet, with gladness
Make hence my departure.


One comment on “The Galaxy – Demonstrating the art of the fugue

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