The Art of the Fugue (Die Kunst der Fuge) was one of the last works of Johann Sebastian Bach, who died in 1750. Apparently he worked on it into the year 1749 but left it incomplete. It is a cycle of fugues; below I shall explain the term fugue. The circumstances of this work's composition and its composer's death have left much room for speculation and debate.
I bought my first recording early in 1965, a performance on the organ by Helmut Walcha. When I started with Contrapunctus 1, a plaintive and monumental piece, I thought of Kennedy's assassination. I was a Republican in those days and I had avoided feelings about that event; now it seemed real to me.
Bach said nothing about the instrumentation for this composition. Over the years I have thought about what instruments I would choose; I have bought various recordings. I shall recommend instrumentations for the various movements.
Bach lived in several towns during his career. From 1723 until his death he was in Leipzig, a major town in Saxony but not its capital. The taxi-drivers I had there did not speak English, and that was incentive for me to rough it auf Deutsch. One, at my request, showed me the Thomaskirche, where Bach was music director.
Bach was born March 21, 1685.
There have been those who assumed this was just abstract music, to be studied but not performed. No, it has some very beautiful music and it is the mature Bach at the height of his powers.
The fugue is a form that could be said to make a science of music. There are conventions and there is terminology. Perhaps it could be compared to a biological drawing. A fugue is polyphonic, i. e. written in several voices. It generally needs 3 or more voices (also called parts) to be considered a legitimate fugue. It is very doubtful that a fugue of more than 6 voices would have artistic merit.
A voice in solo states a melody, the subject. The next voice plays plays an imitation of the subject at a different pitch while the first voice plays something else. In succession all the voices join and this section is called the exposition of the subject. There would not be enough room if all voices were octaves apart; therefore a second key is used, differing from the first by one sharp or flat. The version of the subject in the second key is called an answer. Development of various sorts follows. Often the effect is like a thunderhead; clouds seem to build up and in the end drop rain. An answer that is an exact transposition of the subject is called a real answer. More often, the answer is a little different and is called a tonal answer. In the Art of the Fugue answers are mostly tonal.
Counterpoint is the art of weaving melodies together into a tapestry. In Bach's music everything fits together very well.
This work includes at least 14 fugues as well as 4 canons for 2 voices. Two of the fugues are in 3 voices and the rest are in 4 voices. Bach had a fascination with numerology. With 'H' the 8th letter of the alphabet, his name adds up to 2+1+3+8=14. A performance is about 80 minutes. The first 11 of the fugues are entitled Contrapuncti 1 through 11. There then are 2 pairs of mirror fugues and there is the incomplete Final Fugue. There are a few alternate versions included with the manuscripts. The contrapuncti fall into groups of increasingly complex structure. There is debate about the order and instrumentation of the movements. I am attracted to using the canons as interludes between the groups. Others insert the canons in different places or play them together.
The cycle is built on a principal subject, which has a number of variants. Throughout it is in the key of D minor. Bach often used this key for works of monumental quality, such as the famous Toccata and Fugue and the Dorian Toccata and Fugue.
When I was in college a friend took a law school entrance exam. There was an analogy question, predicated on the assumption that Bach's opus magnum was his Mass in B minor. I took issue with that. At the time I thought his most important works were his many cantatas. There are several large works that could qualify, such as the Art of the Fugue, the Musical Offering, and the Saint Matthew Passion. I do not want to leave this question to writers of standardized tests.
As I said above, my first recording was performed by the blind organist Helmut Walcha, recorded 1956 as part of Deutsche Grammophon Gesellschaft's Archive history of music project. Gustav Leonhardt recorded the work on harpsichord on LP in 1969, without the Final Fugue. I have been inspired by Neville Marriner's recording of 1974, which uses a variety of instrumentations. There is a recording by the group Fretwork (2002) on string instruments of the viol family. Jeffrey Hall has posted an electronic version, with much good commentary.
I promised a proposal of instrumentation. I would make the organ the Alpha and the Omega: Contrapunctus 1 and the Final Fugue. I like the concentration of sound the organ offers. I would vary instrumentions from one movement to the next. Small ensembles are in keeping with the baroque era. Some movements sound good when woodwinds are added to strings. Perhaps viol instruments could be mixed with the violin family, as Bach did in his Sixth Brandenburg Concerto. I do not know how to orchestrate; hence I will make general suggestions or refer to actual orchestrations such as ones by Neville Marriner.
Above I mentioned circumstances that have attracted much speculation and debate about this work. In 1747 in Leipzig Bach joined the Corresponding Society of the Musical Sciences , which expected its members, until age 65, to submit an annual work of music. He may have intended the present work as his contribution for 1749; he turned 65 in 1750. In 1749 he lost his eyesight. He left manuscripts of the work written in his hand. He also ordered an engraved version that was printed in 1751, after his death July 28, 1750. The order and instrumention of the movements have much been debated. Gustav Leonhardt and others have questioned whether the Final Fugue was really part of the Art of the Fugue.
The first group consists of the 4 simple fugues. The first 2 use the standard form of the subject and the second 2 use an inverted form. Voices: B = bass, T = tenor, A = alto, S = soprano.
Contrapunctus 1: organ. The voices enter in the order ASBT. The spirit is one of peaceful resignation.
The subject, which is basic to the entire cycle, is a beautiful melody that begins with a rising D-A. A real answer would begin A-E but A-D sounds better.
Elementary textbooks on counterpoint may say not to cross voices, but Bach did not hesitate to do so in this piece and he knew how. It takes ingenuity to figure out a fingering to play this on a keyboard with 2 hands.
Contrapunctus 2: string quartet. The voices enter in ascending order BTAS. I would use the bright sounds of instruments of the modern violin family. Strings provide a contrast to the organ. I hear a spirit of rejuvenation.
Contrapunctus 3: harpsichord. TASB. This movement, like its successor, uses the inverted form of the subject. This is a slow and grave piece.
All but the 2 mirror fugues can be played by 2 hands on one harpsichord. A reason to use other instruments is to avoid monotony.
Contrapunctus 4: strings and woodwinds. SATB. A lively piece. There is a two-note motiv like a cuckoo call, perhaps good for a woodwind.
Canon alla ottava: harpsichord. 2 voices. This is a jubilant piece.
The next 3 fugues are called contrafugues, as they combine the subject with its inversion. They also use stretto: beginning of the subject by a voice before the previous voice is finished; the voltage is thus stepped up.
I have no quarrel with Neville Marriner's choice of instruments for these 3 fugues but I differ on inserting a canon between Contrapuncti 6 and 7. I think the 3 fugues form a very natural sequence.
Contrapunctus 5: strings and woodwinds. ABST. This is a truly sublime piece of music, especially as Neville Marriner's ensemble performs it. The alto voice opens this fugue with an inverted form of the subject with passing tones added: perhaps the ultimate variant of the subject in beauty.
Contrapunctus 6: harpsichord. BSAT. This uses the subject and its inversion in syncopated forms, termed a la style francaise The subject occurs in diminished forms, i. e. in contracted time.
Contrapunctus 7: strings and woodwinds. TSAB. Subject and inversion are combined with augmented (in slow motion) and diminished (in fast motion) forms. This is a climax piece, an ultimate in interweaving different forms of the subject.
Canon alla decima: organ or harpsichord. 2 voices. This is a sublime piece, good on either instrument. I have worked on playing it. One time a guy heard me play a part of it and said he was surprised how good Bach sounded. If you think Bach just sounds like an exercise you likely have not heard a good performance.
Bach next brings double and triple fugues, having multiple subjects. Each subject enters in an exposition, and only afterward is it combined with other subjects.
Contrapunctus 8: string trio. Triple fugue in 3 voices.
First subject: ABS. This is a new subject, moderate in pace.
Second subject: ASB. This new subject is a brisk one.
Third subject: BSA. Variant form of the inversion of the main subject, with real answer.
With 3 subjects at work, the music gets active.
Contrapunctus 9: harpsichord. Double fugue.
First subject: ASBT. Another new subject, a quick one.
Second subject: STAB. Augmented (slow) version of main subject. This becomes a backdrop for the light-hearted first subject.
Contrapunctus 10: organ. Double fugue
First subject: ASBT. A new subject, with real answer, which bass and tenor invert. Quarter notes are followed by cascades in opposite directions.
Second subject: SATB. This is the subject variant that opens Contrapunctus 5.
Contrapunctus 11: strings and winds. Triple fugue. This is a majestic piece, deserving an orchestration, perhaps including an E-flat (high) trumpet.
First subject: ASTB. This is a rugged variant of the main subject, with a real answer, an inversion of the 3rd subject of Contrapunctus 8.
Second subject: ATBS. Inversion of 1st subject of Cp. 8. This melody seems to wind upward.
Third subject TASB. Variant of 2nd subject of Cp. 8. A quick melody joins 2 slower ones.
Canon alla duodecima: harpsichord. 2 voices. This piece uses a very modified variant of the principal subject.
Contrapunctus 11 is a climax and is followed by the mirror fugues, of a more relaxed nature. Each mirror fugue is followed by its inversion. It is not usually possible to write an invertible fugue in the span of 2 hands on a single keyboard.
Mirror fugue in 4 voices: string quartet. rectus BTAS & inversus SATB. A slow piece.
Mirror fugue in 3 voices:2 harpsichords. rectus ABS & inversus SAB. Subject with inversion. A playful piece. A version for 2 keyboards has an added bass line, like a accompaniment.
Canon per augmentationem in contrario Motu: violin and bassoon. 2 voices. This is a gargoyle of a piece.
Final Fugue: organ.
The first subject enters in ascending order BTAS. Like the main subject it begins D-A and the tonal answer begins D-A. . On the organ it seems to announce that its composer is ready to meet his Maker.
The second subject, ASBT, is a lively one with many notes. Real answer.
The third subject, TASB, starts with the name B-A-C-H. In German notation B is B-flat and H is B natural. Real answer. This subject combines with the first two for about 2 minutes through measure 239. There is a most poignant moment: the music stops.
At the bottom of the page in the manuscript there is a note written by son Carl Philip Emanuel Bach: "Über diese Fuge, wo der Nahme B.A.C.H im Contrasubject angebracht worden, der Verfasser gestorben ist." "When at work on this fugue, where the name BACH appears in the countersubject, the composer died." It seems this is misleading. Bach went blind in 1749 and died July 28, 1750. The music is written in his hand.
It has been assumed that a fourth subject would be the main subject of the entire cycle. Draw a square and divide it into a 4-by-4 array of 16 squares. Since the first subject enters BTAS fill the main diagonal with 1's: rows for voices, columns for order. Do likewise for 2, ASBT, and for 3, TASB. There remain 4 unfilled squares, hinting that the 4th subject should enter as SBTA. This clue was taken by Zoltán Göncz in 1992 when he wrote a completion of the Final Fugue. Jeffrey Hall uses this completion in his electronic version.
There have been other completions. Sir Donald Tovey published his in 1931. Helmut Walcha also recorded a completion. At least one counterpoint textbook has posed completion of this fugue as a problem for students. It has been suggested by some that Bach intentionally left this Final Fugue unfinished as a problem for future musicians.
When Bach died he was considered old-fashioned. His 3 notable sons composed in a more modern style. His widow Anna Magdalena Bach died in poverty. For more than a century the Art of the Fugue did not receive serious attention. Wolfgang Graeser in 1926 published an edition of the work. It was not until the second half of the 20th century that the Art of the Fugue really got an audience.
I have not mastered any musical instrument. I have an electronic keyboard and am beginning to play the fugues' voices individually. When I learn how they sound I can follow recordings against a score. I am especially interested in learning the Canon alla decima and Contrapunctus 5. I have played a very limited amount of Bach, but I find that playing really adds to my appreciation of his music. This is after many years when I just listened to recordings. Enjoy. Many people may want to listen just to small portions at a time.
Anyone know why taxi-drivers in Leipzig and Dresden might not speak English?
Sources:
- Sir Donald Tovey, "The Art of Fugue and Companion to the Art of Fugue." (1931) This book includes a well edited score and an extensive commentary. Tovey includes his own completion of the Final Fugue. He recommends listening and making one's own analysis and then comparing that with his analysis.
- Helmut Wacha (1956, DGG ARC 14077/8). Schnitger organ, St. Laurenskerk, Alkmaar, Netherlands. This recording has been re-issued as part of a box (Archiv 463 712-2) of 12 CD's: organ works of Bach performed by Walcha. The latter set includes Walcha's completion of the Final Fugue (1970) on the organ of Saint-Pierre-le-Jeune, Strasbourg.
- Gustav Leonhardt, harpsichord. (1969, Pro Arte, BL-2000) Final Fugue not included.
- Neville Marriner, Academy of St. Martin in the Fields. (1974, Phillips, 6747 172) This recording is re-issued on CD (Decca 442 556-2) along with Bach's 'Musical Offering.'
- Fretwork. (2009, Harmonia Mundi, HMX 2907296) Viols.
- Website by Jeffrey Hall. 'The Art of Fugue, BWV 1080, by Johann Sebastian Bach' Includes electronic realization.