“The Art of Fugue”的意思、由来-开放百科全书

The Art of Fugue (or The Art of the Fugue; {{lang-de|Die Kunst der Fuge|links=no}}), BWV 1080, is an incomplete musical work of unspecified instrumentation by Johann Sebastian Bach (1685–1750). Written in the last decade of his life, The Art of Fugue is the culmination of Bach's experimentation with monothematic instrumental works.

This work consists of 14 fugues and 4 canons in D minor, each using some variation of a single principal subject, and generally ordered to increase in complexity. "The governing idea of the work", as put by Bach specialist Christoph Wolff, "was an exploration in depth of the contrapuntal possibilities inherent in a single musical subject."^[1] The word "contrapunctus" is often used for each fugue.

Sources

The earliest extant source of the work is an autograph manuscript^[2] of the early 1740s, containing 12 fugues and 2 canons. This autograph is typically referred to by its call number of P200 in the Berlin State Library. Three manuscripts for pieces that would appear in the revised edition were bundled with P200 at some point before its acquisition by the library.

The revised version was published in May 1751, slightly less than a year after Bach's death. In addition to changes in the order, notation, and material of pieces which appeared in the autograph, it contained 2 new fugues, 2 new canons, and 3 pieces of ostensibly spurious inclusion. A second edition was published in 1752, but differed only in its addition of a preface by Friedrich Wilhelm Marpurg.

In spite of its revisions, the printed edition of 1751 contained a number of glaring editorial errors. The majority of these may be attributed to Bach's relatively sudden death in the midst of publication. Three pieces were included that do not appear to have been part of Bach's intended order: an unrevised (and thus redundant) version of the second double fugue, Contrapunctus X; a two-keyboard arrangement^[3] of the first mirror fugue, Contrapunctus XIII; and a chorale harmonization "{{Lang|de|Vor deinen Thron tret ich hiermit}}" ("Herewith I come before Thy Throne"), derived from BWV 668a, and noted in the introduction to the edition as a recompense for the work's incompleteness, having purportedly been dictated by Bach on his deathbed.

The anomalous character of the published order and the Unfinished Fugue have engendered a wide variety of theories which attempt to restore the work to that state originally intended by Bach.

Structure

The Art of Fugue is based on a single subject ({{Audio|KdF Motiv2.mid|play on piano}} or {{Audio|KdFThema.mid|play on organ}}):

The work divides into seven groups, according to each piece's prevailing contrapuntal device; in both editions, these groups and their respective components are generally ordered to increase in complexity. In the order in which they occur in the printed edition of 1751 (without the aforementioned works of spurious inclusion), the groups, and their components are as follows.

Counter-fugues, in which the subject is used simultaneously in regular, inverted, augmented, and diminished forms:

Mirror fugues, in which a piece is notated once and then with voices and counterpoint completely inverted, without violating contrapuntal rules or musicality:

Instrumentation

Both editions of the Art of Fugue are written in open score, where each voice is written on its own staff. This has led some to conclude^[6] that the Art of Fugue was intended as an intellectual exercise, meant to be studied more than heard. The renowned keyboardist and musicologist Gustav Leonhardt,^[7] argued that the Art of Fugue was probably intended to be played on a keyboard instrument (and specifically the harpsichord).^[8] Leonhardt's arguments included the following:^[7]

However, opponents of Leonhardt's theory such as Reinhard Goebel argue that:{{Cite quote|date=August 2017}}

There is also the possibility that The Art of Fugue was not intended for one single (type of) instrument, but instead for whatever instruments were at hand.{{Citation needed|date=August 2017}} This hypothesis is given weight by the modern recording and concert history of the work: it is variously performed by string quartets, wind quartets, solo keyboardists, electronics, and orchestras. See "Notable Recordings", below.{{Original research inline|date=August 2017}}

The Unfinished Fugue

A handwritten manuscript of the piece known as the Unfinished Fugue is among the three bundled with the autograph manuscript P200. It breaks off abruptly in the middle of its third section, with an only partially written measure 239. This autograph carries a note in the handwriting of Carl Philipp Emanuel Bach, stating "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{{music|flat}}–A–C–B{{music|natural}}] in the countersubject to this fugue, the composer died.") This account is disputed by modern scholars, as the manuscript is clearly written in Bach's own hand, and thus dates to a time before his deteriorating health and vision would have prevented his ability to write, probably 1748–1749.^[9]

A number of musicians and musicologists have composed conjectural completions of Contrapunctus XIV which include the fourth subject, including musicologists Donald Tovey (1931), Zoltán Göncz (1992), Yngve Jan Trede (1995), and Thomas Daniel (2010), organists Helmut Walcha, David Goode, Lionel Rogg, and Davitt Moroney (1989). {{Citation needed-span|date=March 2016|text=Ferruccio Busoni's Fantasia contrappuntistica is based on Contrapunctus XIV, but is more a work by Busoni than by Bach. In 2001 Luciano Berio arranged the contrapunctus for orchestra; while Berio did not complete the fugue in the usual sense, he produced a performing version that allows the composition to fade away gracefully.|reason=}} Other completions that do not incorporate the fourth subject including those by the French classical organist Alexandre Pierre François Boëly and pianist Kimiko Douglass-Ishizaka.

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.^[10]^[11]

Douglas Hofstadter's book Gödel, Escher, Bach 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. According to Gödel, 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". 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.

Sylvestre and Costa^[12] reported a mathematical architecture of The Art of Fugue, based on bar counts, which shows that the whole work was conceived on the basis of the Fibonacci series and the golden ratio. The significance of the mathematical architecture can probably be explained by considering the role of the work as a membership contribution to the {{ill|Correspondierende Societät der musicalischen Wissenschaften|de}}, and to the "scientific" meaning that Bach attributed to counterpoint.

Notable recordings

Harpsichord

Organ

Piano

String quartet

Orchestra

Other

See also

Notes and references

1. ^Johann Sebastian Bach, the Learned Musician by Christoph Wolff, p. 433, {{ISBN|0-393-04825-X}}.
2. ^The autograph manuscript bears the title {{Lang|de|Die Kunst der Fuga}}, written in the hand of Bach's son-in-law Johann Christoph Altnickol. This implies that the title was conceived at some point before the printed edition, which is titled {{Lang|de|Die Kunst der Fuge}}, but after the completion of the autograph.
3. ^The printed indication of "a 2 Clav." and the counterpoint of the added voices do not appear to follow Bach's practice, evidencing that the parts were likely included by the editors of the printed edition to bolster the work.
4. ^Helmut Walcha, "Zu meiner Wiedergabe", in Die Kunst Der Fuge BWV 1080, St Laurenskerk Alkmaar 1956 (Archiv Production, Polydor International 1957), Insert pp. 5–11, at p. 7.
5. ^{{cite web|title=The Art of the Fugue|publisher=American Public Media|url=http://pipedreams.publicradio.org/articles/artoffugue/fugue1.shtml|accessdate= 25 November 2010}}
6. ^{{cite web|url=http://pipedreams.publicradio.org/articles/artoffugue/performed.shtml|title=The Art of the Fugue|first=American Public|last=Media|website=pipedreams.publicradio.org}}
7. ^¹{{Cite journal|journal=The Musical Times|first=Gustav|last=Leonhardt|authorlink=Gustav Leonhardt|title=The Art of Fugue – Bach's Last Harpsichord Work: An Argument|volume=39|number=3|date=July 1953|pages=463–466|jstor=740009}}
8. ^D. Schulenberg. "Expression and Authenticity in the Harpsichord Music of J.S. Bach". The Journal of Musicology, Vol. 8, No. 4 (Autumn, 1990), pp. 449–476
9. ^See e.g. the discussion inJohann Sebastian Bach, the Learned Musician by Christoph Wolff, {{ISBN|0-393-04825-X}}.
10. ^University of Auckland News, Volume 37, Issue 9 (May 25, 2007) {{webarchive|url=https://web.archive.org/web/20070926200010/http://www.auckland.ac.nz/uoa/fms/default/uoa/about/newsevents/publications/university%20news/Past%20issues/2007/uninews07_09.pdf |date=September 26, 2007 }}
11. ^The thesis is available online: http://hdl.handle.net/2292/392
12. ^{{Cite journal|last=Loïc|first=Sylvestre|last2=Costa|first2=Marco|year=2011|title=The Mathematical Architecture of Bach's The Art of Fugue|url=https://www.researchgate.net/publication/258507180_THE_MATHEMATICAL_ARCHITECTURE_OF_BACH'S_THE_ART_OF_FUGUE|journal=Il Saggiatore Musicale|volume=17|pages=175–196|via=}}
13. ^Robert Hill: Recordings of Musical Offering & Art of Fugue, bach-cantatas.com
14. ^¹²The recordings by Walcha (1970) and Moroney include both their completion of Contrapunctus XIV and the unfinished original, while Bergel's includes only his attempt.
15. ^¹Partial performances on organ (Contrapuncti I–IX) and piano (I, II, IV, IX, XI, XIII inversus, and XIV).
16. ^The recording, which includes both the unfinished original and Rogg's completion, in the year of its release won the Grand Prix du Disque from the Charles Cros Academy.
17. ^André Isoir: Recordings of Musical Offering and Art of Fugue, bach-cantatas.com
18. ^Published by Accentus Music: CD – J. S. Bach Kunst der Fuge – Zhu Xiao-Mei, Piano, No. ACC 30308
19. ^{{cite web|url=https://ksr-video.imgix.net/projects/3031628/video-802252-h264_high.mp4|title=video|publisher=}}
20. ^Paolo Borciani and Elisa Pegreffi with Tommaso Poggi and Luca Simoncini, as Quartetto Italiano, CD Nuova Era 7342, recording 1985.See
21. ^Except the canons, which are played by harpsichordist Kenneth Gilbert on the recording.
22. ^{{cite web|url=http://www.niederfellabrunn.at/shop/J2ES2EBach3A_The_Art_of_the_Fugue_2D_Die_Kunst_der_Fuge2C_BWV_1080.html|title=J. S. Bach: The Art of the Fugue – Die Kunst der Fuge, BWV 1080|website=www.niederfellabrunn.at}}
23. ^{{YouTube|YcxQdRIY11o|Jack Stratton: Contrapunctus IX (talkbox)}}