The Art of Fugue - AbsoluteAstronomy.com

The Art of Fugue BWV

BWV

The Bach-Werke-Verzeichnis is the numbering system identifying compositions by Johann Sebastian Bach. The prefix BWV, followed by the work's number, is the shorthand identification for Bach's compositions...

1080, is an incomplete work by Johann Sebastian Bach

Johann Sebastian Bach

Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...

(1685–1750). It was most likely started at the beginning of the 1740s, if not earlier. The first known surviving version, which contained 12 fugue

Fugue

In music, a fugue is a compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation and recurs frequently in the course of the composition....

s and 2 canon

Canon (music)

In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

s, was copied by the composer in 1745. This manuscript has a slightly different title, added afterwards by his son-in-law Johann Christoph Altnickol

Johann Christoph Altnickol

Johann Christoph Altnickol, or Altnikol, was a German organist, bass singer, and composer. He was a son-in-law and copyist of Johann Sebastian Bach.-Biography:...

: Die Kunst der Fuga. Bach's second version was published in 1751 after his death. It contains 14 fugues and 4 canons. "The governing idea of the work", as the eminent Bach specialist Christoph Wolff put it, is "an exploration in depth of the contrapuntal possibilities inherent in a single musical subject."

Each of the 14 fugues except the final unfinished one use the same deceptively simple subject in D minor

D minor

D minor is a minor scale based on D, consisting of the pitches D, E, F, G, A, B, and C. In the harmonic minor, the C is raised to C. Its key signature has one flat ....

Structure

In the 1751 printed edition, the various movements are roughly arranged by increasing order of sophistication of the contrapuntal devices used. The Arabic number in the title indicates the number of voices in the fugue, with the exception of the last one, where a 3 Soggetti means "with 3 subjects":

Simple fugues:

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

Inversion (music)

In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

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

Stretto

The term stretto comes from the Italian past participle of stringere, and means "narrow", "tight", or "close".In music the Italian term stretto has two distinct meanings:...

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

Augmentation (music)

In Western music and music theory, the word augmentation has three distinct meanings. Augmentation is a compositional device where a melody, theme or motif is presented in longer note-values than were previously used...

(doubling all note lengths) and diminished

Diminution

In Western music and music theory, diminution has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of shorter, usually melodic, values...

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

10. 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:

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 fugue in 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)

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

BACH motif

In music, the BACH motif is the motif, a succession of notes important or characteristic to a piece, B flat, A, C, B natural. In German musical nomenclature, in which the note B natural is written as H and the B flat as B, it forms Johann Sebastian Bach's family name...

, B - A – C – B ('H' in German letter notation).

Sources of the work

The order of the fugues and canons has been debated, especially as there are differences between the manuscript and the printed editions appearing immediately after Bach's death. Also musical reasons have been invoked to propose different orders for later publications and/or the execution of the work, e.g. by Wolfgang Graeser in 1927, who also published his own "completion" of the final Contrapunctus XIV.

The 1751 printed edition contained — apart from a high number of errors and other flaws — a four-part version of Contrapunctus XIII, arranged to be played on two keyboards (rectus BWV 1080/18,1 and inversus BWV 1080/18,2). It is however doubtful whether the printed indication "a 2 Clav.", and the fourth added voice, that is not mirrored according to Bach's usual practice, derive from him, or from his son(s) that supervised this first edition.

The engraving of the copper plates for the printed edition would however have started shortly before the composer's death, according to contemporary sources, but it is unlikely that Bach had any real supervision in that preparation of the printed edition, due to his illness at the time.

The first printed edition also includes an unrelated work as a kind of "encore", the chorale prelude Vor deinen Thron tret Ich hiermit (Herewith I come before Thy Throne), BWV

BWV

668a, which Bach is said to have dictated on his deathbed.

A 1742 fair copy manuscript contains Contrapuncti I–III, V–IX, and XI–XIII, plus the octave and augmented canons and an earlier version of Contrapunctus X.

Instrumentation

Manuscript copies of the Art of Fugue, as well as the first printed edition, use open scoring, where each voice is written on its own staff. This has led to the assumption that the Art of Fugue was an intellectual exercise, meant to be studied and not heard. However, musicologists today, such as Gustav Leonhardt

Gustav Leonhardt

Gustav Leonhardt is a highly renowned Dutch keyboard player, conductor, musicologist, teacher and editor. Leonhardt has been a leading figure in the movement to perform music on period instruments...

, agree that the Art of Fugue was probably intended to be played on a keyboard instrument. Leonhardt's arguments included the following:

It was common practice in the 17th and early 18th centuries to publish keyboard pieces in open score, especially those that are contrapuntally complex. Examples include Frescobaldi
Girolamo Frescobaldi
Girolamo Frescobaldi was a musician from Ferrara, one of the most important composers of keyboard music in the late Renaissance and early Baroque periods. A child prodigy, Frescobaldi studied under Luzzasco Luzzaschi in Ferrara, but was influenced by a large number of composers, including Ascanio...

's Fiori musicali
Fiori musicali
Fiori musicali is a collection of liturgical organ music by Girolamo Frescobaldi, first published in 1635. It contains three organ masses and two secular capriccios. Generally acknowledged as one of Frescobaldi's best works, Fiori musicali influenced composers during at least two centuries...

(1635), Samuel Scheidt
Samuel Scheidt
Samuel Scheidt was a German composer, organist and teacher of the early Baroque era.-Biography:...

's Tabulatura Nova (1624), works by Johann Jakob Froberger
Johann Jakob Froberger
Johann Jakob Froberger was a German Baroque composer, keyboard virtuoso, and organist. He was among the most famous composers of the era and influenced practically every major composer in Europe by developing the genre of keyboard suite and contributing greatly to the exchange of musical...

(1616–1667), Franz Anton Maichelbeck (1702–1750), and others.
The range of none of the ensemble or orchestral instruments of the period corresponds to any of the ranges of the voices in The Art of Fugue. Furthermore, none of the melodic shapes that characterize Bach's ensemble writing are found in the work, and there is no basso continuo.
The fugue types used are reminiscent of the types in The Well-Tempered Clavier
The Well-Tempered Clavier
The Well-Tempered Clavier , BWV 846–893, is a collection of solo keyboard music composed by Johann Sebastian Bach...

, rather than Bach's ensemble fugues; Leonhardt also shows an "optical" resemblance between the fugues of the two collections, and points out other stylistic similarities between them.
Finally, since the bass voice in The Art of Fugue occasionally rises above the tenor, and the tenor becomes the "real" bass, Leonhardt deduces that the bass part was not meant to be doubled at 16-foot pitch, thus eliminating the pipe organ as the intended instrument, leaving the harpsichord as the most logical choice.

The fact that it is playable on a keyboard at all is evidence for some that this was Bach's intended instrument, as it is not possible to play most of his ensemble pieces on a keyboard instrument.

The unfinished fugue

Contrapunctus XIV breaks off abruptly in the middle of the third section at bar 239. The autograph carries a note in the handwriting of Bach's son Carl Philipp Emanuel Bach

Carl Philipp Emanuel Bach

right|250pxCarl Philipp Emanuel Bach was a German Classical period musician and composer, the fifth child and second son of Johann Sebastian Bach and Maria Barbara Bach...

saying "Über dieser Fuge, wo der Name B A C H im Contrasubject angebracht worden, ist der Verfasser gestorben." ("At the point where the composer introduces the name BACH [for which the English notation would be B-A-C-B] in the countersubject to this fugue, the composer died.") However, modern scholarship disputes this version, in particular because the musical notes are indisputably in Bach's own hand, written in a time before his deteriorating vision led to erratic handwriting, probably 1748–1749.

Many scholars, including Gustav Nottebohm

Gustav Nottebohm

Martin Gustav Nottebohm was a pianist, teacher, musical editor and composer who spent most of his career in Vienna. He is particularly celebrated for his studies of Beethoven....

(1881), Wolff and Davitt Moroney

Davitt Moroney

Davitt Moroney is a British-born and educated musicologist, harpsichordist and organist. His parents were of Irish and Italian extraction – his father was an executive with the Anglo-Dutch Unilever conglomerate...

, have argued that the piece was intended to be a quadruple fugue, with the opening theme of Contrapunctus I to be introduced as the fourth subject. The title Fuga a 3 soggetti, in Italian rather than Latin, was not given by the composer but by CPE Bach

Carl Philipp Emanuel Bach

right|250pxCarl Philipp Emanuel Bach was a German Classical period musician and composer, the fifth child and second son of Johann Sebastian Bach and Maria Barbara Bach...

, and Bach's Obituary actually makes mention of "a draft for a fugue that was to contain four themes in four voices". The combination of all four themes would bring the entire work to a fitting climax. Wolff also suspected that Bach might have finished the fugue on a lost page, called "fragment X" by him, on which the composer attempted to work out the counterpoint between the four subjects.

A number of musicians and musicologists have conjectured completions of Contrapunctus XIV, notably music theoretician Hugo Riemann

Hugo Riemann

Karl Wilhelm Julius Hugo Riemann was a German music theorist.-Biography:Riemann was born at Grossmehlra, Schwarzburg-Sondershausen. He was educated in theory by Frankenberger, studied the piano with Barthel and Ratzenberger, studied law, and finally philosophy and history at Berlin and Tübingen...

, musicologists Donald Tovey and Zoltán Göncz

Zoltán Göncz

Zoltán Göncz is a Hungarian composer who often applies archaic forms and complex structures in his compositions.He graduated from the Ferenc Liszt Academy of Music in 1980...

, organists Helmut Walcha

Helmut Walcha

Helmut Walcha was a blind German organist who specialized in the works of the Dutch and German baroque masters and is known for his recordings of the complete organ works of Johann Sebastian Bach.- Biography :Born in Leipzig, Walcha was blinded at age 19 after vaccination for smallpox...

, David Goode and Lionel Rogg

Lionel Rogg

Lionel Rogg is a Swiss organist, composer and teacher of musical theory. Among many other distinctions, he has recorded the complete organ works of Johann Sebastian Bach three times....

, and Davitt Moroney

Davitt Moroney

. Ferruccio Busoni's Fantasia Contrappuntistica
Fantasia Contrappuntistica
Fantasia contrappuntistica is a solo piano piece composed by Ferruccio Busoni in 1910. Busoni created several versions of the work including several for solo piano, and one for two pianos. It has been arranged for organ and for orchestra since the composer's death.The work is in large part a...

is based on Contrapunctus XIV, but is more a work by Busoni than by Bach.

In 2007, New Zealand organist and conductor Indra Hughes completed a doctoral thesis about the unfinished ending of Contrapunctus XIV, proposing that the work was left unfinished not because Bach died, but as a deliberate choice by Bach to encourage independent efforts at a completion.

Douglas Hofstadter

Douglas Hofstadter

Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...

's book Gödel, Escher, Bach
Gödel, Escher, Bach
Gödel, Escher, Bach: An Eternal Golden Braid is a book by Douglas Hofstadter, described by his publishing company as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll"....

discusses the unfinished fugue and Bach's supposed death during composition as a tongue-in-cheek illustration of Austrian logician Kurt Gödel's first incompleteness theorem. To be more specific, the idea in that theorem is that the very power of a "sufficiently powerful" formal mathematical system can be exploited to "undermine" the system, by leading to statements that assert such things as "I cannot be proven in this system". Because of this twisty kind of self-reference, such assertions are true but unprovable. In Hofstadter's discussion, Bach's great compositional talent is used as a metaphor for a "sufficiently powerful" formal system; however, Bach's insertion of his own name "in code" into the fugue is not, even metaphorically, a case of Gödelian self-reference; and Bach's failure to finish his self-referential fugue serves as a metaphor for the unprovability of the Gödelian assertion, and thus for the incompleteness of the formal system.

A book entitled "Bach: Essays on His Life and Music" includes an article about the unfinished fugue, stating that Bach never intended to write the rest of the fugue on the last sheet of music paper used for the fugue because of the unalignment of the bottom staves. It also says that because of the above-mentioned reason, Bach wrote the rest of the fugue on another sheet of music paper, called "fragment x" that would have completed, or almost completed, the fugue. However, even if there is a fragment x, it has been lost.

The permutation matrix

In 1991 a theory was published by Zoltán Göncz

Zoltán Göncz

Zoltán Göncz is a Hungarian composer who often applies archaic forms and complex structures in his compositions.He graduated from the Ferenc Liszt Academy of Music in 1980...

answering the question of how Bach planned the appearance of the fourth subject, the main subject of the cycle:

In the course of the exposition of the first three subjects (first subject: mm. 1–21, second subject: mm. 114–141, third subject: mm. 193–207), Bach applied a serial sequence of voice entries decided in advance, by which he determined the space and time parameters of the subject entries. The superimposition of the three exposition matrices foreshadows, and develops as a negative, the sequence of the voice entries of the fourth subject. The copying of the four subjects onto each other displays a characteristic construction of Bach's oeuvre occurring mainly in the vocal fugues: that of the permutation fugue.

However paradoxical, it follows from the logic of composing a quadruple fugue that the combinations joining all four subjects (i.e. those combinations which appear last when performing the work) were already completed in the very first stage of composition, because the possibility of overlapping the four subjects (1 + 2 + 3 + 4) is the sine qua non
Sine qua non
Sine qua non or condicio sine qua non refers to an indispensable and essential action, condition, or ingredient...

of writing a quadruple fugue. The process of composition does not proceed in a linear way from the beginning, but with all four parts in view.

One of the striking features of Contrapunctus XIV is that in this movement Bach applied the stretto

Stretto

The term stretto comes from the Italian past participle of stringere, and means "narrow", "tight", or "close".In music the Italian term stretto has two distinct meanings:...

of whole expositions, layering the first two expositions atop each other prior to introducing the third subject. In the exposition of the first three subjects he "programmed" the later permutation stretti, then applied the expositions as "programs", "algorithms". The permutation matrix, apart from originating authentically with Bach, can be proved to have been ready at the time of the genesis of the work (that is, earlier than the surviving section).

The discovery of the permutation matrix was one of the most essential requirements for achieving a reconstruction of Contrapunctus XIV which might approach the original form planned by Bach. (Göncz, Z.: Reconstruction of the Final Contrapunctus of The Art of Fugue, in: International Journal of Musicology Vol. 5, pp. 25–93. 1997 ISBN 3-631-49809-8; Vol. 6, pp. 103–119. 1998 ISBN 3-631-33413-3)

A Pythagorean enigma

The theory is advanced by the cellist Hans-Eberhard Dentler (a pupil of Pierre Fournier

Pierre Fournier

Pierre Fournier was a French cellist who was called the "aristocrat of cellists," on account of his elegant musicianship and majestic sound....

's, and Fellow of the World Academy of Art and Science

World Academy of Art and Science

The World Academy of Art and Science is an international non-governmental scientific organization, an informal and non-official world network of individual fellows elected for distinguished accomplishments in the fields of natural and social sciences, arts and the humanities...

) that the Art of the Fugue was written to display Pythagorean

Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

philosophical principles. The arguments revolve upon Bach's friendship with Johann Matthias Gesner

Johann Matthias Gesner

Johann Matthias Gesner was a German classical scholar and schoolmaster.He was born at Roth an der Rednitz near Ansbach. His father, Johann Samuel Gesner, a pastor in Auhausen, died in 1704, leaving the family in straitened circumstances...

, whom he had known in Weimar and who in 1730 moved to the Thomasschule at Leipzig (where Bach was Cantor) as rector. There Gesner taught Greek philosophy with an emphasis on Pythagorean thought.

Among Gesner's students was Lorenz Christoph Mizler

Lorenz Christoph Mizler

Lorenz Christoph Mizler von Kolof was a German physician, mathematician, and writer on music.-Biography:...

, who became a pupil and friend of Bach's. Bach was one of four distinguished dedicatees of Mizler's 1734 doctoral dissertation on Music as part of a Philosophical Education. Mizler founded the Korrespondierenden Sozietät der Musikalischen Wissenschaften (Corresponding Society of Musical Sciences) in 1738, which Bach joined in June 1747, and of which Handel

HANDEL

HANDEL was the code-name for the UK's National Attack Warning System in the Cold War. It consisted of a small console consisting of two microphones, lights and gauges. The reason behind this was to provide a back-up if anything failed....

and Telemann were also members. The society was concerned with the union of music, philosophy, mathematics and science in Pythagorean theory, and required each member to contribute a practical work in demonstration of this approach, for which Bach produced his Canonic Variations on "Vom Himmel hoch da komm' ich her"

Canonic Variations on "Vom Himmel hoch da komm' ich her"

The Canonic Variations on "Vom Himmel hoch da komm' ich her" , BWV 769, are a set of five variations in canon for organ with two manuals and pedals by Johann Sebastian Bach on the Christmas hymn by Martin Luther of the same name...

for organ, BWV 769, and the Canon triplex a 6 voci. The Society's work commenced with the publication of a Bibliography (in its Musikalische Bibliotek) referencing works of Marcus Meibom, John Wallis, Leibniz, Kepler and Robert Fludd

Robert Fludd

Robert Fludd, also known as Robertus de Fluctibus was a prominent English Paracelsian physician, astrologer, mathematician, cosmologist, Qabalist, Rosicrucian apologist...

.

The points of this analysis are that the work constitutes an enigma

Puzzle

A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...

in the classical sense of a puzzle contained within its structure. This subsists in the numerical and philosophical relations of Unity (one key signature

Key signature

In musical notation, a key signature is a series of sharp or flat symbols placed on the staff, designating notes that are to be consistently played one semitone higher or lower than the equivalent natural notes unless otherwise altered with an accidental...

throughout and the thematic synthesis); Tetraktys (the relation of 1, 2, 3 and 4 as arranged to form the perfect triangle), the mirror or speculum principle, Contrapunctus as derived from Aristotelian

Aristotle

Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

terminology referring to balancing opposites, the Music of the Spheres is possibly reflected in Fugues 1-7, and in the term Fugue

Fugue

In music, a fugue is a compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation and recurs frequently in the course of the composition....

, meaning 'flight', which refers to the flight of the musical phrases.

Against the theory is Bach's apparent indifference to the Society in its early years, and his hesitancy in joining it. The Society had in fact attempted to establish principles for the writing of cantatas which were not in line with his own approach. Since any musical structure was susceptible to Mizler's Pythagorean analysis, the case for any specific precedent influence on The Art of Fugue remains conjectural.

It has also been argued that the hidden theme in Edward Elgar's Enigma Variations

Enigma Variations

Variations on an Original Theme for orchestra , Op. 36, commonly referred to as the Enigma Variations, is a set of a theme and its fourteen variations written for orchestra by Edward Elgar in 1898–1899. It is Elgar's best-known large-scale composition, for both the music itself and the...

may derive from The Art of Fugue.

Films about the Art of Fugue

The documentary film Desert Fugue
Desert Fugue
Desert Fugue is a 90 minute documentary film about Johann Sebastian Bach's Art of Fugue. It was directed by Will Fraser and produced by Fugue State Films. It features organist George Ritchie, Bach scholar Christoph Wolff and organ builders Ralph Richards and Bruce Fowkes...

is a 90 minute documentary about the history of the Art of Fugue and its suitability for performance on the organ. The film features interviews with scholar Christoph Wolff

Christoph Wolff

Christoph Wolff is a German-born musicologist, presently on the faculty of Harvard University. Born and educated in Germany, Wolff studied organ and historical keyboard instruments, musicology and art history at the Universities of Berlin, Erlangen, and the Music Academy of Freiburg, receiving a...

, George Ritchie (organist)

George Ritchie (organist)

George Ritchie is an American organist. His teachers included Helmut Walcha, and like Walcha he is best known for his interpretations of Johann Sebastian Bach's music. Ritchie has recorded Bach's complete organ works, and his recording of Bach's Art of Fugue was reviewed in Gramophone Magazine as...

and organ builder

Organ builder

-Australia:* William Anderson * Australian Pipe Organs Pty Ltd* Robert Cecil Clifton * William Davidson* J.E. Dodd & Sons Gunstar Organ Works* Fincham & Hobday* Geo. Fincham & Son* Alfred Fuller * Peter D.G. Jewkes Pty Ltd...

s Ralph Richards and Bruce Fowkes.

Notable recordings

See http://www.jsbach.org/1080.html and http://www.bach-cantatas.com/NVD/BWV1080.htm#Rec for more complete lists.

Harpsichord:

Gustav Leonhardt
Gustav Leonhardt
Gustav Leonhardt is a highly renowned Dutch keyboard player, conductor, musicologist, teacher and editor. Leonhardt has been a leading figure in the movement to perform music on period instruments...

(1969)
Davitt Moroney
Davitt Moroney
Davitt Moroney is a British-born and educated musicologist, harpsichordist and organist. His parents were of Irish and Italian extraction – his father was an executive with the Anglo-Dutch Unilever conglomerate...

(1985)
Ton Koopman
Ton Koopman
Ton Koopman is a conductor, organist and harpsichordist.Koopman had a "classical education" and then studied the organ , harpsichord and musicology in Amsterdam...

with Tini Mathot (1994), on two harpsichords
Menno Van Delft (1999)
Sébastian Guillot (2006)
Bradley Brookshire
Bradley Brookshire
Bradley Brookshire is an American-born harpsichordist.He earned his undergraduate degree from the University of Michigan School of Music , his Master of Music from Mannes College in New York City , and is a Candidate for the Ph.D...

(2007) includes an additional CD-ROM with score to follow along as MP3s play
Gavin Black & George Hazelrigg (2009) on two harpsichords: voices shared equally throughout. http://www.theartofthefugue.com
Lorenzo Ghielmi
Lorenzo Ghielmi
Lorenzo Ghielmi is an Italian organist and harpsichordist.He teaches old music at the Accademia Internazionale della Musica in Milan and at the "Schola Cantorum Basiliensis" in Basel. He was professor in Trossingen and at the Hochschule für Musik in Lübeck too. Ghielmi also played with Ensemble Il...

on a Silbermann piano and harpsichord with Vittorio Ghielmi
Vittorio Ghielmi
Gamba player, conductor, composer. Born in Milano, Italy, still very young he attracts notice for the intensity and versatility of his musical interpretation and for his new approach to the viol and to the sound of ancient music repertoire...

and "Il Suonar Parlante" viols quartet (2009)

Organ:

Helmut Walcha
Helmut Walcha
Helmut Walcha was a blind German organist who specialized in the works of the Dutch and German baroque masters and is known for his recordings of the complete organ works of Johann Sebastian Bach.- Biography :Born in Leipzig, Walcha was blinded at age 19 after vaccination for smallpox...

(1956, 1970)
Glenn Gould
Glenn Gould
Glenn Herbert Gould was a Canadian pianist who became one of the best-known and most celebrated classical pianists of the 20th century. He was particularly renowned as an interpreter of the keyboard music of Johann Sebastian Bach...

(1962) incomplete
Ensemble Wolfgang von Karajan (1963), on three chamber organs
Lionel Rogg
Lionel Rogg
Lionel Rogg is a Swiss organist, composer and teacher of musical theory. Among many other distinctions, he has recorded the complete organ works of Johann Sebastian Bach three times....

(1970)
André Isoir
André Isoir
André Isoir is a renowned French organist.Isoir studied with Édouard Souberbielle and Germaine Mounier at the École César-Franck and under Rolande Falcinelli at the Paris Conservatoire where he won the first prizes in organ and improvisation in 1960.Thereafter he won several international organ...

(1999) Some movements performed as a duet with Pierre Farago, on the Grenzing organ of Saint-Cyprien
Saint-Cyprien
Saint-Cyprien is the name or part of the name of several places. Most of them are named after Cyprian:-Canada:* Saint-Cyprien, Bas-Saint-Laurent, Quebec, municipality in Bas-Saint-Laurent, Quebec...

in Périgord
Périgord
The Périgord is a former province of France, which corresponds roughly to the current Dordogne département, now forming the northern part of the Aquitaine région. It is divided into four regions, the Périgord Noir , the Périgord Blanc , the Périgord Vert and the Périgord Pourpre...

, France
Wolfgang Rübsam
Wolfgang Rübsam
Wolfgang Friedrich Rübsam is a German-American organist, pianist, composer and pedagogue.-Biography:...

(1992)
Marie-Claire Alain
Marie-Claire Alain
Marie-Claire Alain is a French organist and organ teacher best known for her prolific recording career. She is particularly known for her ability to perform substantial works entirely from memory.-Background and education:...

(1993)
Louis Thiry
Louis Thiry
Louis Thiry , is a French organist, composer and pedagogue.Thiry studied at the Nancy Conservatoire, where he received a first prize in organ at the Nancy Conservatory in 1952, followed by studies with André Marchal at Institut National des Jeunes Aveugles in Paris...

(1993) on the Silbermann organ of Saint Thomas Church (Strasbourg)
Saint Thomas Church (Strasbourg)
The Saint-Thomas Church is a historical building in Strasbourg, eastern France. It is the main Protestant church of the city since its Cathedral became Catholic again after the annexation of the town by France in 1681...

.
Hans Fagius
Hans Fagius
-Biography:Fagius studied organ with Bengt Berg before entering the Royal College of Music, Stockholm where he studied with Alf Linder. After graduating in 1974 he studied organ privately with Maurice Duruflé in Paris. He taught organ in Gothenburg and Stockholm before being appointed professor of...

(2000) on the Carsten Lund organ of Garnisons Church Copenhagen, Denmark.
Kevin Bowyer
Kevin Bowyer
Kevin John Bowyer is an English organist, known for his prolific recording and recital career and his interest in playing unusual, modern and extremely difficult compositions.-Biography:...

(2001) on the Marcussen organ of Saint Hans Church
Saint Hans Church
Saint Hans Church is a church in Odense, DenmarkThe church has a three manual Marcussen organ used by Kevin Bowyer to record the complete organ works of Bach for Nimbus Records....

, Odense
Odense
The city of Odense is the third largest city in Denmark.Odense City has a population of 167,615 and is the main city of the island of Funen...

, Denmark
George Ritchie (organist)
George Ritchie (organist)
George Ritchie is an American organist. His teachers included Helmut Walcha, and like Walcha he is best known for his interpretations of Johann Sebastian Bach's music. Ritchie has recorded Bach's complete organ works, and his recording of Bach's Art of Fugue was reviewed in Gramophone Magazine as...

(2010) on the Richards, Fowkes & Co organ of Pinnacle Presbyterian Church
Pinnacle Presbyterian Church
Pinnacle Presbyterian Church is a Presbyterian Church congregation of more than 1,400 members located in north Scottsdale, Arizona.Pinnacle started Oct. 1, 1989, in the Glenn Moor Clubhouse in Troon Country Club with 25 committed, visionary members...

in Scottsdale
Scottsdale
Scottsdale is the name of several places:* Scottsdale, Arizona, United States* Scottsdale, Tasmania, Australia* Scottsdale Reserve, New South Wales, Australia...

, Arizona
Arizona
Arizona ; is a state located in the southwestern region of the United States. It is also part of the western United States and the mountain west. The capital and largest city is Phoenix...

. This recording includes as a bonus track an alternative take of the final unfinished fugue with the completion by Helmut Walcha
Helmut Walcha
Helmut Walcha was a blind German organist who specialized in the works of the Dutch and German baroque masters and is known for his recordings of the complete organ works of Johann Sebastian Bach.- Biography :Born in Leipzig, Walcha was blinded at age 19 after vaccination for smallpox...

.

Piano:

Richard Buhlig
Richard Buhlig
Richard Buhlig was an American pianist.Buhlig was born in Chicago, where he received his early training. In 1897 he moved to Vienna to study under Teodor Leszetycki. Upon completing his studies in 1900, he gave his first public concert in 1901 in Berlin, and toured extensively in Europe until late...

and Wesley Kuhnle (1934)
Glenn Gould
Glenn Gould
Glenn Herbert Gould was a Canadian pianist who became one of the best-known and most celebrated classical pianists of the 20th century. He was particularly renowned as an interpreter of the keyboard music of Johann Sebastian Bach...

incomplete
Charles Rosen
Charles Rosen
Charles Rosen is an American pianist and author on music.-Life and career:In his youth he studied piano with Moriz Rosenthal. Rosenthal, born in 1862, had been a student of Franz Liszt...

(1967)
Grigory Sokolov
Grigory Sokolov
Grigory Lipmanovich Sokolov is a concert pianist, often considered one of the greatest pianists alive. He was born April 18, 1950 in Saint Petersburg, Russia.-Biography:...

(1982)
Zoltán Kocsis
Zoltán Kocsis
Zoltán Kocsis is a Hungarian pianist, conductor, and composer.Born in Budapest, he started his musical studies at the age of five and continued them at the Béla Bartók Conservatory in 1963, studying piano and composition...

(1984)
Yuji Takahashi
Yuji Takahashi
is a Japanese composer, performer, pianist and author.Studied under Roh Ogura and Minao Shibata at the Toho Gakuen School of Music. In 1960, he made his debut as a pianist by performing Bo Nilsson's Quantitaten. He lived in Europe from 1963 to 1966 where he worked with Iannis Xenakis. He gave the...

(1988)
Tatiana Nikolayeva
Tatiana Nikolayeva
Tatiana Petrovna Nikolayeva was a Russian Soviet pianist, composer and teacher.-Early life:Nikolayeva was born in Bezhitsa in the Bryansk district on May 4, 1924...

(1992)
Andrei Vieru (1994)
Walter Riemer (2006), using a fortepiano of Mozart type
Pierre-Laurent Aimard
Pierre-Laurent Aimard
Pierre-Laurent Aimard is a French pianist. He was born in Lyon, where he entered the conservatory. Later he studied with Yvonne Loriod and with Maria Curcio....

(2008)

String quartet:

Roth Quartet (1934-5) includes conjectural end played by Donald Tovey on keyboard.
Quartetto Italiano (1985)
Juilliard String Quartet
Juilliard String Quartet
The Juilliard String Quartet is a classical music string quartet founded in 1946 at the Juilliard School in New York. The original members were violinists Robert Mann and Robert Koff, violist Raphael Hillyer, and cellist Arthur Winograd; Current members are Joseph Lin and Ronald Copes violinists,...

(1989)
Keller Quartet (1997)
Delmé Quartet (2000), arranged by composer Robert Simpson
Robert Simpson (composer)
Robert Simpson was an English composer and long-serving BBC producer and broadcaster.He is best known for his orchestral and chamber music , and for his writings on the music of Beethoven, Bruckner, Nielsen and Sibelius. He studied composition under Herbert Howells...

, including versions of Contrapuntus XIV unfinished and completed following Tovey
Tovey
-People:* Bramwell Tovey, conductor and composer* Donald Francis Tovey, musical analyst, musicologist* Eric Tovey, wrestler* Frank Tovey, deceased UK musician, who also recorded under the name Fad Gadget* Jessica Tovey, actress...

's version.
Emerson String Quartet
Emerson String Quartet
The Emerson String Quartet is a New York–based string quartet in residence at the State University of New York at Stony Brook. Previously the Quartet was in residence at The Hartt School. Formed in 1976, they have released more than twenty albums and won nine Grammy Awards. Both violinists...

(2003)
Vittorio Ghielmi
Vittorio Ghielmi
Gamba player, conductor, composer. Born in Milano, Italy, still very young he attracts notice for the intensity and versatility of his musical interpretation and for his new approach to the viol and to the sound of ancient music repertoire...

and "Il Suonar Parlante" viols quartet (2009) with Lorenzo Ghielmi
Lorenzo Ghielmi
Lorenzo Ghielmi is an Italian organist and harpsichordist.He teaches old music at the Accademia Internazionale della Musica in Milan and at the "Schola Cantorum Basiliensis" in Basel. He was professor in Trossingen and at the Hochschule für Musik in Lübeck too. Ghielmi also played with Ensemble Il...

on a Silbermann piano and harpsichord

Orchestra :

Hermann Scherchen
Hermann Scherchen
Hermann Scherchen was a German conductor.-Life:Scherchen was originally a violist and played among the violas of the Bluthner Orchestra of Berlin while still in his teens...

with Orchestre de la RTSI (1965)
Karl Ristenpart
Karl Ristenpart
Karl Ristenpart was a German conductor.Born in Kiel, Germany, he studied at the Stern Conservatory in Berlin and in Vienna. He was heavily involved in creating three orchestras in his lifetime, most notably the Chamber Orchestra of the Saar. With this group he created one of the recorded...

with Chamber Orchestra of the Saar (1965)
Neville Marriner
Neville Marriner
Sir Neville Marriner is an English conductor and violinist.-Biography:Marriner was born in Lincoln and studied at the Royal College of Music and the Paris Conservatoire. He played the violin in the Philharmonia Orchestra, the Martin String Quartet and London Symphony Orchestra, playing with the...

with Academy of St. Martin in the Fields
Academy of St. Martin in the Fields
The Academy of St Martin in the Fields is an English chamber orchestra, based in London.Sir Neville Marriner founded the ensemble as The Academy of St.-Martin-in-the-Fields in London as a small, conductorless string group. The ensemble's name comes from Trafalgar Square's St Martin-in-the-Fields...

(1974)
Jordi Savall
Jordi Savall
Jordi Savall i Bernadet is a Catalan viol player, conductor and composer. He has been one of the major figures in the field of Western early music since the 1970s, largely responsible for bringing the viol back to life on the stage...

with Hesperion XX (1986)
Erich Bergel
Erich Bergel
Erich Bergel was a conductor from Transylvania .-Professional career:Bergel was a flutist of the Hermannstädter Philharmoniker age 18. From 1950 to 1955 he studied conducting, organ and composition at the Gheorghe Dima Music Academy of Cluj-Napoca...

with Cluj Philharmonic Orchestra (1991)
Karl Münchinger
Karl Münchinger
Karl Münchinger was a German conductor of European classical music. He helped to revive the now-ubiquitous Canon in D by Johann Pachelbel, through recording it with his Stuttgart Chamber Orchestra in 1960...

and Stuttgart Chamber Orchestra (1965)
Stuttgart Chamber Orchestra (2002)
Rinaldo Alessandrini
Rinaldo Alessandrini
Rinaldo Alessandrini is a virtuoso on Baroque keyboards, including harpsichord, fortepiano, and organ. He is founder and conductor of the Italian early music ensemble Concerto Italiano, performing music of Monteverdi, Vivaldi, Couperin, J. S. Bach, and others...

and Concerto Italiano
Concerto Italiano
Concerto Italiano is an Italian early music ensemble well-known for their interpretations of Monteverdi and Vivaldi, among others.The historically informed performance ensemble was formed by the harpsichordist Rinaldo Alessandrini, and made its Rome debut with Francesco Cavalli's La Calisto in 1984...

(1998)

Other:

Milan Munclinger
Milan Munclinger
Milan Munclinger was a significant Czech flautist, conductor, composer and musical scientist.-Biographical:...

with Ars Rediviva
Ars Rediviva
Ars Rediviva was a Czech instrumental early music group, whose historically informed performances played a key role in the revival of Baroque music in Czechoslovakia.-Ars Rediviva chamber ensemble:...

(1959, 1966, 1979)
Fine Arts String Quartet
Fine Arts Quartet
The Fine Arts Quartet, a distinguished chamber music ensemble founded in Chicago, USA in 1946 by Leonard Sorkin and George Sopkin, has an illustrious history of performing success and an extensive recording legacy. It is one of the few to have recorded and toured internationally for over half a...

and New York Woodwind Quintet
New York Woodwind Quintet
The New York Woodwind Quintet is an ensemble-in-residence at the Juilliard School in New York City, originally appointed in 1987. At Juilliard, the members of the New York Woodwind Quintet present seminars each year for student woodwind ensembles, give regular coachings, and perform.The quintet's...

(1962)
Yuji Takahashi
Yuji Takahashi
is a Japanese composer, performer, pianist and author.Studied under Roh Ogura and Minao Shibata at the Toho Gakuen School of Music. In 1960, he made his debut as a pianist by performing Bo Nilsson's Quantitaten. He lived in Europe from 1963 to 1966 where he worked with Iannis Xenakis. He gave the...

(incomplete) electronic version (1975)
Musica Antiqua Köln
Musica Antiqua Köln
Musica Antiqua Köln was an early music group that was founded in 1973 by Reinhard Goebel and fellow students from the Conservatory of Music in Cologne. Musica Antiqua Köln devoted itself largely to the performance of the music of the 17th and 18th centuries...

(director Reinhard Goebel
Reinhard Goebel
Reinhard Goebel is a German conductor and violinist specialising in early music on authentic instruments. Goebel received his first violin lessons at the age of twelve...

) for string quartet/harpsichord and various such instrumental combinations (1984)
Berliner Saxophon Quartett for saxophone
Saxophone
The saxophone is a conical-bore transposing musical instrument that is a member of the woodwind family. Saxophones are usually made of brass and played with a single-reed mouthpiece similar to that of the clarinet. The saxophone was invented by the Belgian instrument maker Adolphe Sax in 1846...

(1990)
József Eötvös
József Eötvös (musician)
József Eötvös is a classical guitarist, from Pécs, Hungary. Eötvös studied with Roland Zimmer and Franz Just at the Hochschule für Musik "Franz Liszt", Weimar. He won several international competitions between 1985 and 1988...

for two eight-string guitar
Guitar
The guitar is a plucked string instrument, usually played with fingers or a pick. The guitar consists of a body with a rigid neck to which the strings, generally six in number, are attached. Guitars are traditionally constructed of various woods and strung with animal gut or, more recently, with...

s (2002)
Zagreb Guitar Quartet for guitar quartet (2005)
Amsterdam Loeki Stardust Quartet
Amsterdam Loeki Stardust Quartet
The Amsterdam Loeki Stardust Quartet is a professional Dutch recorder quartet which was founded in 1978 by four students of the Sweelinck Conservatory Amsterdam; Daniël Brüggen, Bertho Driever, Paul Leenhouts and Karel van Steenhoven...

for recorder
Recorder
The recorder is a woodwind musical instrument of the family known as fipple flutes or internal duct flutes—whistle-like instruments which include the tin whistle. The recorder is end-blown and the mouth of the instrument is constricted by a wooden plug, known as a block or fipple...

quartet (1998)
Phantasm
Phantasm
Phantasm may refer to:In comics:* Phantasm , a short-lived member of the New Teen TitansIn film:* Don Coscarelli's Phantasm series** Phantasm , a 1979 horror film** Phantasm II...

(director: Laurence Dreyfus
Laurence Dreyfus
Laurence Dreyfus, FBA is a Bach scholar. He was born and raised in Boston, Massachusetts, and attended Cherry Hill High School West in New Jersey. He earned a B.A., Yeshiva U., studied cello under Leonard Rose, at the Juilliard School, later reading Musicology at the Columbia University...

) for viola da gamba four-part consort (1998)
Calefax Reed Quintet for reed instruments (2000)
Fretwork
Fretwork (music group)
Fretwork is a consort of viols based in England, United Kingdom. Formed in 1986, the group consisted of six players, while it is currently five viols...

for Consort of Viol
Viol
The viol is any one of a family of bowed, fretted and stringed musical instruments developed in the mid-late 15th century and used primarily in the Renaissance and Baroque periods. The family is related to and descends primarily from the Renaissance vihuela, a plucked instrument that preceded the...

s (2002)
Aurelia Saxophone Quartet for saxophone quartet (2005)
The Canadian Brass
Canadian Brass
The Canadian Brass is a brass quintet founded by Dr. Charles Daellenbach and Gene Watts in 1970. In addition to maintaining a heavy international touring schedule, the Canadian Brass have recorded over 80 CDs and DVDs...

for brass quintet
Brass quintet
A brass quintet is a five-piece musical ensemble composed of brass instruments. The most common instrumentation is two trumpets or cornets, one horn, one trombone or euphonium/baritone horn, and one tuba or bass trombone....
The electronic art of fugue by Klangspiegel (2005)
The Version of Jacques Chailley instrumentation of Pascal Vigneron for wind quartet, brass quartet and organ (2005)
An electronic version, Laibachkunstderfuge
LAIBACHKUNSTDERFUGE
LAIBACHKUNSTDERFUGE is a concept album by NSK industrial group Laibach...

, by Neue Slowenische Kunst
Neue Slowenische Kunst
Neue Slowenische Kunst , aka NSK, is a controversial political art collective that announced itself in Slovenia in 1984, when Slovenia was part of Yugoslavia. NSK's name, being German, is compatible with a theme in NSK works: the complicated relationship Slovenes have had with Germans...

industrial band Laibach
Laibach (band)
Laibach is a Slovenian avant-garde music group associated with industrial, martial, and neo-classical musical styles. Laibach formed June 1, 1980 in Trbovlje, Slovenia . Laibach represents the music wing of the Neue Slowenische Kunst art collective, of which it was a founding member in 1984...

(2008).

Media

External links

Full discography of The Art of Fugue
Johann Sebastian Bach / L'art de la fugue / The Art of the Fugue - Jordi Savall, Hesperion XX - Alia Vox 9818
Piano Society: JS Bach - A biography and various free recordings in MP3 format, including art of fugue
Web-essay on The Art of Fugue
Introduction to The Art of Fugue
Die Kunst der Fuge (scores and MIDI files) on the Mutopia Project
Mutopia project
The Mutopia Project is a volunteer-run effort to create a library of free content sheet music, in a way similar to Project Gutenberg's library of public domain books.The music is reproduced from old scores that are out of copyright...

website
The Art of Fugue as MIDI files
Image of the ending of the final fugue at external site
Contrapunctus XIV (the reconstructed quadruple fugue) – Carus-Verlag
Malina, János: The Ultimate Fugue, The Hungarian Quarterly, Winter 2007
Contrapunctus XIV (reconstruction): Part 1/2, Part 2/2 (YouTube Video)
Contrapunctus II as interactive hypermedia at the BinAural Collaborative Hypertext
Synthesized realization and analysis of the Art of Fugue by Jeffrey Hall
Hughes, Indra (2006) Accident or Design? New Theories on the unfinished Contrapunctus 14 in JS Bach's The Art of Fugue BWV 1080 The University of Auckland PhD Thesis
“Johann Sebastian Bach’s The Art of Fugue” an article on Bach's Art of Fugue by Uri Golomb, published in Goldberg Early Music Magazine
Ars Rediviva: Sound Recordings Library, The Art of Fugue, Contrapunctus VIII
http://www.fuguestatefilms.co.uk/aof description of documentary film Desert Fugue
Desert Fugue
Desert Fugue is a 90 minute documentary film about Johann Sebastian Bach's Art of Fugue. It was directed by Will Fraser and produced by Fugue State Films. It features organist George Ritchie, Bach scholar Christoph Wolff and organ builders Ralph Richards and Bruce Fowkes...

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.