1411:. 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.
194:
1255:}". For example, Contrapuncti 1 and 2 both switch repeatedly between the keys of A minor and D minor; Contrapuncti 2 and 3 in addition enter F major and G minor, Contrapunctus 2 also visiting B-flat major once in a further "tonal remove": all three begin and end in D minor. He concludes that "Analyses of fugues should focus on continuous, dynamic, organic processes that evolve over time, rather than on the static and discontinuous dismemberment into strictly delineated sections."
731:
471:
44:
33:
1113:
803:: 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
1131:("fugue in three subjects"), also called the "Unfinished Fugue" and Contrapunctus 14, was contained in a handwritten manuscript bundled with the autograph manuscript Mus. ms. autogr. P 200. 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
1278:, rather than by any action an individual can take. Eggebrecht noted the presence in fugue 3 of the presence of the composer's surname Bach in its theme, the sequence of notes B-A-C-H-C#-D. In Eggebrecht's view, this could mean that the composer is not just signing the work, but is placing himself by his grave, accepting
429:
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 two new fugues, two new canons, and three pieces of ostensibly spurious inclusion. A second edition was published in 1752, but
437:
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
746:
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
337:
Bundled with the primary autograph are three supplementary manuscripts, each affixed to a composition that would appear in the first printed edition. Referred to as Mus. ms. autogr. P 200/Beilage 1, Mus. ms. autogr. P 200/Beilage 2, and Mus. ms. autogr. P 200/Beilage 3, they are written under the
2338:
1390:
In her 2007 doctoral thesis about the unfinished ending of
Contrapunctus 14, the New Zealand organist and conductor Indra Hughes proposed that the work was left unfinished not because Bach died, but as a deliberate choice by Bach to encourage independent efforts at a completion.
1139:
in the countersubject, 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.
882:: Canon in which the following voice is both inverted and augmented. The following voice, running at half-speed, eventually lags the first voice by 20 bars, making the canon effect hard to hear. Three versions have appeared in the autograph Mus. ms. autogr. P 200:
2331:
2324:
417:." ("At the point where the composer introduces the name BACH in the countersubject to this fugue, the composer died.") The following page contains a list of errata by Carl Philipp Emanuel Bach for the first printed edition (pages 21–35).
358:
crossed out. The manuscript contains line break and page break information for the engraving process, most of which was transcribed in the first printed edition. Written on the top region of the manuscript is a note written by
2132:
1436:
406:
is presented in a two-stave keyboard system, instead of with individual staves for each voice. The fugue abruptly breaks off on the fifth page, specifically on the 239th measure and ends with the note written by
1593:
Gustav
Leonhardt's 1969 liner notes for Harmonia Mundi HM 30 950 XK: Johann Sebastian Bach, Die Kunst der Fuge , 3–8.; also for Deutsche Harmonia Mundi's CD edition 77013-2-RG (an extensive summary of his 1952
508:
2172:
1840:
1230:
Dominic
Florence proposes that a concept he calls "opposition" governs all the methods that Bach uses in Contrapuncti 1, 2, 3, and 5 to create variety. These include changes in "melody (contrary motion),
2355:
2474:
459:
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 the state originally intended by Bach.
2418:
1083:, 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.
509:
2817:
2347:
2200:
1135:, stating "Über dieser Fuge, wo der Name B A C H im Contrasubject angebracht worden, ist der Verfasser gestorben." ("While working on this fugue, which introduces the name
2562:
2002:
2812:
2423:
2351:
1037:
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
2667:
1483:
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.
88:
1837:
64:
2242:
371:, er hat es aber wieder ausgestrichen auf der Probe Platte und gesetzet wie forn stehet N.B. The late father had written on the copper plate the following title,
2781:
1979:
1431:
701:
860:
Mirror fugues, in which a piece is notated once and then with voices and counterpoint completely inverted, without violating contrapuntal rules or musicality:
2598:
1198:, but it develops Bach's ideas to Busoni's own purposes in Busoni's musical style, rather than working out Bach's thoughts as Bach himself might have done.
2542:
2375:
2102:
2491:
499:
1408:
456:, 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.
2557:
2552:
2547:
1985:
984:: four-voice triple fugue (not completed by Bach, but likely to have become a quadruple fugue: see below), the third subject of which begins with the
679:
660:
2827:
2802:
2479:
2402:
641:
622:
603:
584:
565:
546:
527:
489:
252:, the autograph contains twelve untitled fugues and two canons arranged in a different order than in the first printed edition, with the absence of
89:
1811:
Majewski, Józef (2019). "Musica theologica
Religious Aspects of Die Kunst der Fuge, Musikalisches Opfer, and Goldberg Variations of J. S. Bach".
65:
1672:
has been recorded by Walcha himself, in his Stereo recording of the complete organ works by Bach for Archiv (1956–1971); and by Walcha's pupil,
2436:
1282:
as he reaches towards the tonic note, which marks the end of the fugue and symbolically the end of his life. Further, the six-note fragment is
1090:
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
2587:
2220:
2316:
395:
in the first printed edition respectively. Like
Beilage 1, the manuscript served as a preparatory edition for the first printed edition.
77:
2065:
1403:
discusses the unfinished fugue and Bach's supposed death during composition as a tongue-in-cheek illustration of the
Austrian logician
702:
53:
2504:
2499:
2464:
2459:
2453:
2448:
2431:
1891:
1729:
1656:
1609:
1467:
779:
Stretto-fugues (counter-fugues), in which the subject is used simultaneously in regular, inverted, augmented, and diminished forms:
2249:
1570:
2822:
507:
2509:
2390:
2385:
2380:
2305:
2095:
453:
360:
1777:
2681:
2150:
2137:
1066:
The range of none of the ensemble or orchestral instruments of the period corresponds to any of the ranges of the voices in
680:
661:
438:
unrevised (and thus redundant) version of the second double fugue, Contrapunctus X; a two-keyboard arrangement of the first
1070:. Furthermore, none of the melodic shapes that characterize Bach's ensemble writing are found in the work, and there is no
2522:
642:
623:
604:
585:
566:
547:
528:
490:
734:
2622:
2145:
1959:
1420:
2648:
2029:
2807:
2535:
2088:
1773:
1346:
1190:
427:
Die / Kunst der Fuge / durch / Herrn Johann
Sebastian Bach / ehemahligen Capellmeister und Musikdirector zu Leipzig
234:
1967:
2514:
2204:
1673:
1617:
1132:
1121:
1079:
431:
408:
1271:, which he agreed was impossible to prove: that the work illustrated in musical terms the Christian doctrine of
193:
2582:
1914:
1264:
172:, and generally ordered to increase in complexity. "The governing idea of the work", as put by Bach specialist
138:
2070:
2739:
2655:
1060:
398:
Mus. ms. autogr. P 200, Beilage 3 contains a fragment of a three-subject fugue, which would be later called
180:
possibilities inherent in a single musical subject." The word "contrapunctus" is often used for each fugue.
2721:
2702:
2268:
1878:
1399:
1283:
1165:
1056:
134:
1544:
2688:
2527:
2360:
2295:
2112:
1857:
Hughes, Indra (2006). "Accident or Design? New
Theories on the unfinished Contrapunctus 14 in JS Bach's
1556:
1522:
1021:
was intended as an intellectual exercise, meant to be studied more than heard. The renowned keyboardist
700:
142:
98:
1514:
2661:
2606:
2183:
2177:
2161:
1289:
The
Russian musicologist Anatoly Milka suggests that the various numbers embedded in the work have a
1038:
844:: double fugue, with two subjects occurring dependently and in invertible counterpoint at the twelfth
817:
213:
1951:
414:
Ueber dieser Fuge, wo der Nahme BACH im Contrasubject angebracht worden, ist der Verfasser gestorben
242:
2767:
2753:
2641:
2397:
2167:
2155:
1286:, denoting sinful humanity, whereas the work as a whole is diatonic, symbolising God's perfection.
850:: double fugue, with two subjects occurring dependently and in invertible counterpoint at the tenth
689:
678:
659:
640:
621:
602:
583:
564:
545:
526:
488:
32:
2715:
2051:
1873:
1626:
1394:
1294:
1252:
1240:
737:
2233:
1157:
2290:
1942:
1887:
1725:
1652:
1463:
1236:
165:
2760:
2208:
1820:
1781:
1363:
1220:
1185:
1091:
1022:
1973:
1844:
1648:
1459:
1244:
1181:
443:
375:, but had struck it out again on the proof sheet and restored the title as it was formerly
173:
204:
The earliest extant source of the work is an autograph manuscript possibly written from
2674:
2038:
1177:
1173:
1071:
1048:
1043:
1017:, where each voice is written on its own staff. This has led some to conclude that the
670:
651:
1219:
counts, which shows that the whole work could have been conceived on the basis of the
763:: four-voice fugue on principal subject, accompanied by a 'French' style dotted rhythm
402:
in the first printed edition. Unlike the fugues written in the primary autograph, the
2796:
2259:
1920:
1883:
1774:"Opposition as a guiding principle for performance in J.S. Bach's Die Kunst der Fuge"
1743:
1492:
1404:
1290:
1161:
1102:
It is now generally accepted by scholars that the work was envisioned for keyboard.
632:
613:
594:
575:
556:
537:
518:
480:
247:
169:
157:
1112:
769:: four-voice fugue on principal subject in inversion, employing intense chromaticism
728:
is based on a single subject, which each canon and fugue employs in some variation:
2746:
2574:
2300:
2275:
2006:
1717:
1678:
1480:
1224:
1153:
439:
177:
149:
is the culmination of Bach's experimentation with monothematic instrumental works.
1990:
17:
1929:
1910:
1692:
699:
677:
658:
639:
620:
601:
582:
563:
544:
525:
506:
487:
87:
63:
2709:
1272:
1248:
1216:
1169:
1030:
775:: four-voice fugue on principal subject in inversion, employing counter-subjects
1098:
as the intended instrument, leaving the harpsichord as the most logical choice.
747:
works of spurious inclusion), the groups, and their components are as follows.
347:
Mus. ms. autogr. P 200, Beilage 1 contains a final preparatory revision of the
2695:
2023:
2016:
2012:
1298:
1095:
1014:
985:
821:
717:
110:
1148:
Several musicians and musicologists have composed conjectural completions of
199:
Die / Kunst der Fuga / di Sig.o Joh. Seb. Bach. / (in eigenhändiger Partitur)
1232:
856:: triple fugue, employing the three subjects of Contrapunctus 8 in inversion
212:, usually referred to by its call number as Mus. ms. autogr. P 200 in the
1824:
1437:
List of compositions by Johann Sebastian Bach printed during his lifetime
1029:
was intended to be played on a keyboard instrument, and specifically the
379:
Mus. ms. autogr. P 200, Beilage 2 contains two-keyboard arrangements of
1785:
1500:
1211:
Loïc Sylvestre and Marco Costa reported a mathematical architecture of
787:
279:
and canons in the following order: , , , , , an early version of , , ,
161:
2057:
1630:
2080:
1160:(1992), Yngve Jan Trede (1995), and Thomas Daniel (2010), organists
367:
N.B. Der seel. Papa hat auf die Platte diesen Titul stechen lassen,
1610:"Expression and Authenticity in the Harpsichord Music of J.S. Bach"
838:: triple fugue with three subjects, having independent expositions
828:
192:
153:
1856:
1996:
209:
205:
197:
The title page of Mus. ms. autogr. P 200, which bears the title
2320:
2084:
1332:
a symbol of Christ's cross (lines B---C intersecting A------H).
1838:
University of Auckland News, Volume 37, Issue 9 (May 25, 2007)
1549:– Bach's Last Harpsichord Work: An Argument – Did Bach intend
888:
297:
222:
1945:– A biography with free recordings in MP3 format, including
469:
42:
1152:
which include the fourth subject, including musicologists
2424:
Sonatas for viola da gamba and harpsichord, BWV 1027–1029
736:
Audio playback is not supported in your browser. You can
2243:
Ueber Johann Sebastian Bachs Leben, Kunst und Kunstwerke
2173:
Canonic Variations on "Vom Himmel hoch da komm' ich her"
904:, the third of which appears on the second supplemental
425:
The first printed version was published under the title
2033:
2480:
Canonic Sonata for oboe, violin and continuo, BWV 1040
452:" ("Herewith I come before Thy Throne"), derived from
2419:
Six Sonatas for Violin and Harpsichord, BWV 1014–1019
2003:
Contrapunctus XIV (the reconstructed quadruple fugue)
1077:
The fugue types used are reminiscent of the types in
275:
The autograph manuscript presents the then-untitled
2731:
2633:
2597:
2573:
2490:
2411:
2376:
Sonatas and Partitas for Solo Violin, BWV 1001–1006
2368:
2219:
2121:
1575:– Bach's Last Harpsichord Work: An Argument (1952)"
1359:
4 canons; fugues in each block in groups of 4 and 3
305:presented in two staves and then on one, with the
1499:, St Laurenskerk Alkmaar 1956 (Archiv Production,
1362:4 beasts in Revelation chapter 4 (animals of the
1297:, the last book of the Bible which describes the
1267:suggested a possible religious interpretation of
831:, employing two and three subjects respectively:
1806:
1804:
1802:
1767:
1765:
1033:. Leonhardt's arguments included the following:
931:Canon alla Duodecima in Contrapunto alla Quinta
824:versions of the main subject and its inversion.
365:
2818:Classical musical works published posthumously
1503:International 1957), Insert pp. 5–11, at p. 7.
1479:The printed indication of "a 2 Clav." and the
430:differed only in its addition of a preface by
2782:List of compositions by Johann Sebastian Bach
2332:
2151:Picander's 1728–29 cycle of cantata librettos
2096:
2066:"Le concert d'Irena Kosikova a fait un tabac"
1432:List of compositions by Johann Sebastian Bach
1305:Anatoly Milka's numerological interpretation
373:Canon per Augment: in Contrapuncto all octava
369:Canon per Augment: in Contrapuncto all octava
309:form of the fugue written directly below the
8:
2475:Sonata for two flutes and continuo, BWV 1039
1938:– Jordi Savall, Hesperion XX – Alia Vox 9818
1598:– Bach's Last Harpsichord Work: An Argument)
1330:The surname BACH, taking A=1, B=2, C=3, H=8;
447:
412:
2523:Sinfonia for violin and orchestra, BWV 1045
1645:Johann Sebastian Bach, the Learned Musician
1456:Johann Sebastian Bach, the Learned Musician
1342:Two blocks of 7 fugues (according to Milka)
947:: alternate version of the last 22 bars of
914:: canon in imitation at the octave; titled
875:Canons, labeled by interval and technique:
2339:
2325:
2317:
2103:
2089:
2081:
880:Canon per Augmentationem in Contrario Motu
145:. Written in the last decade of his life,
2563:For two harpsichords in C minor, BWV 1060
1986:International Music Score Library Project
1744:"The Mathematical Architecture of Bach's
233:, which was written by Bach's son-in-law
2813:Musical compositions completed by others
1303:
1111:
898:Canon al roverscio et per augmentationem
323:Canon al roverscio et per augmentationem
31:
2255:(Vol. I: 1873; Vol. II: 1880)
1863:, The University of Auckland PhD thesis
1448:
1327:14 fugues (basic structure of the work)
757:: four-voice fugue on principal subject
2133:Printed during the composer's lifetime
2024:Completion (in quarter-comma meantone)
1742:Loïc, Sylvestre; Costa, Marco (2011).
1124:that the composer died at this point.
902:Canon p. Augmentationem contrario Motu
884:Canon in Hypodiatesseron, al roversio
801:Contrapunctus 6, a 4 in Stylo Francese
715:
293:Canon in Hypodiatesseron, al roversio
176:, "was an exploration in depth of the
108:
2588:Orchestral Suite in G minor, BWV 1070
1120:fragment, with a handwritten note by
937:Alternate variants and arrangements:
36:Title page of the first edition, 1751
27:Musical work by Johann Sebastian Bach
7:
2505:Violin Concerto in E major, BWV 1042
2500:Violin Concerto in A minor, BWV 1041
2011:Contrapunctus XIV (reconstruction):
842:Contrapunctus 9, a 4, alla Duodecima
2045:, article Uri Golomb, published in
1351:or 7 trumpets = 4 plagues + 3 woes
933:: canon in imitation at the twelfth
442:, Contrapunctus XIII; and an organ
291:in the first printed edition), , ,
2510:Concerto for Two Violins, BWV 1043
1917:(video and background information)
1571:"images of front and back covers;
848:Contrapunctus 10, a 4, alla Decima
716:Problems playing these files? See
481:Contrapunctus 1, principal subject
141:of unspecified instrumentation by
109:Problems playing these files? See
25:
2543:Keyboard concertos, BWV 1052–1065
2032:as interactive hypermedia at the
1368:see also the 4+3 symbolism above
1273:redemption by God's grace alone,
1263:In 1984, the German musicologist
1086:Finally, since the bass voice in
927:: canon in imitation at the tenth
449:Vor deinen Thron tret ich hiermit
421:First and second printed editions
2583:Orchestral Suites, BWV 1066–1069
2403:Partita for Solo Flute, BWV 1013
2034:BinAural Collaborative Hypertext
1855:The thesis is available online:
1668:Walcha's conclusion to the last
1000:('H' in German letter notation).
820:(doubling all note lengths) and
811:Contrapunctus 7, a 4 per Augment
697:
675:
656:
637:
618:
599:
580:
561:
542:
523:
504:
485:
85:
61:
2828:Unfinished musical compositions
2803:Fugues by Johann Sebastian Bach
2306:Johann Sebastian Bach Institute
1972:(scores and MIDI files) on the
1722:A Companion to the Art of Fugue
961:: two-keyboard arrangements of
894:e per augmentationem, perpetuus
361:Johann Christoph Friedrich Bach
333:Mus. ms. autogr. P 200, Beilage
303:e per augmentationem, perpetuus
152:This work consists of fourteen
2205:Bach-Gesellschaft edition
1778:University of British Columbia
1:
2668:Everything's Gonna Be Alright
2047:Goldberg Early Music Magazine
1495:, "Zu meiner Wiedergabe", in
870:Contrapunctus inversus 13 a 3
865:Contrapunctus inversus 12 a 4
356:Augmentationem contrario Motu
343:Kunst / der Fuga / von J.S.B.
1625:(4 (Autumn, 1990): 449–476.
1421:The Art of Fugue discography
1409:first incompleteness theorem
1379:See the 4+3 symbolism above
1293:significance related to the
733:
283:with its two-stave solution
2682:Jesu, Joy of Man's Desiring
2398:Cello Suites, BWV 1007–1012
1886:. pp. 79–81, 86, 671.
1843:September 26, 2007, at the
1813:Gdański Rocznik Ewangelicki
1643:See e.g. the discussion in
1497:Die Kunst Der Fuge BWV 1080
1386:Unfinished Contrapunctus 14
1376:Fugues in groups of 4 and 3
239:(in eigenhändiger Partitur)
2844:
2558:No. 4 in A major, BWV 1055
2553:No. 2 in E major, BWV 1053
2548:No. 1 in D minor, BWV 1052
1911:The Art of Fugue, BWV 1080
1772:Florence, Dominic (2006).
1676:, in the documentary film
1519:– Types of Fugues, Part 1"
1418:
1347:Horsemen of the Apocalypse
1207:Principles of construction
1191:Fantasia contrappuntistica
963:Contrapunctus inversus a 3
918:in Mus. ms. autogr. P 200.
235:Johann Christoph Altnickol
2777:
2286:
2039:"Johann Sebastian Bach's
1618:The Journal of Musicology
1259:Religious interpretations
1133:Carl Philipp Emanuel Bach
1122:Carl Philipp Emanuel Bach
1080:The Well-Tempered Clavier
959:Alio modo. Fuga a 2 Clav.
448:
432:Friedrich Wilhelm Marpurg
409:Carl Philipp Emanuel Bach
381:Contrapunctus 13 inversus
260:(two-keyboard version of
1930:Johann Sebastian Bach /
1915:Netherlands Bach Society
1334:These digits sum to 14.
1265:Hans Heinrich Eggebrecht
1063:(1702–1750), and others.
829:Double and triple fugues
393:Alio modo Fuga a 2 Clav.
349:Canon in Hypodiatesseron
327:Canon in Hypodiatesseron
321:format, and a two-stave
101:on organ and harpsichord
2823:Compositions in D minor
1697:Rudolf Barshai Memorial
1094:, thus eliminating the
1061:Franz Anton Maichelbeck
738:download the audio file
139:incomplete musical work
2722:A Whiter Shade of Pale
2703:Sheep may safely graze
2269:Bach-Werke-Verzeichnis
2162:Clavier-Übung III
2058:Bach, Alphametics and
2052:Electronic realization
1943:Piano Society: JS Bach
1874:Hofstadter, Douglas R.
1752:Il Saggiatore musicale
1144:Attempts at completion
1125:
1116:The final page of the
1057:Johann Jakob Froberger
925:Contrapunto alla Terza
500:1, whole contrapunctus
474:
413:
377:
201:
189:Mus. ms. autogr. P 200
168:of a single principal
130:
47:
37:
2716:Trio Sonata, BWV 525a
2529:Brandenburg Concertos
2361:Johann Sebastian Bach
2296:Neue Bachgesellschaft
2252:Johann Sebastian Bach
2156:Clavier-Übung II
1913:: performance by the
1732:, page 177 footnote).
1724:(2013 Dover reprint,
1557:American Public Media
1523:American Public Media
1115:
1009:Both editions of the
916:Canon in Hypodiapason
854:Contrapunctus 11, a 4
671:11, principal subject
652:10, principal subject
473:
325:—a second version of
313:form, with the same
281:Canon in Hypodiapason
218:Die / Kunst der Fuga
196:
143:Johann Sebastian Bach
46:
35:
2740:Bach's Greatest Hits
2662:Bach-Busoni Editions
2608:The Musical Offering
2465:in E major, BWV 1035
2460:in E minor, BWV 1034
2454:in C major, BWV 1033
2449:in A major, BWV 1032
2432:in B minor, BWV 1030
2178:The Musical Offering
2146:Clavier-Übung I
1936:The Art of the Fugue
1825:10.48540/gre.2019.11
1608:Schulenberg, David.
836:Contrapunctus 8, a 3
633:9, principal subject
614:8, principal subject
595:6, principal subject
576:5, principal subject
557:4, principal subject
538:3, principal subject
519:2, principal subject
270:Canon alla duodecima
216:. Bearing the title
214:Berlin State Library
126:The Art of the Fugue
2768:Switched-On Bach II
2754:Jazz Sebastian Bach
2642:Air on the G String
2168:Goldberg Variations
2149:(1726–1730; 1731);
2140:Gott ist mein König
2022:Contrapunctus XIV:
1926:, bach-cantatas.com
1879:Gödel, Escher, Bach
1400:Gödel, Escher, Bach
1306:
2272:(1950; 1990; 1998)
2201:Four-part chorales
2071:La Dépêche du Midi
1969:Die Kunst der Fuge
1786:10.14288/1.0092827
1693:"The Art of Fugue"
1395:Douglas Hofstadter
1304:
1295:Book of Revelation
1176:(1989), conductor
1126:
977:Incomplete fugue:
475:
351:, under the title
202:
164:, each using some
131:Die Kunst der Fuge
99:David Ezra Okonşar
48:
38:
18:Die Kunst der Fuge
2808:1750 compositions
2790:
2789:
2314:
2313:
2291:Bach Gesellschaft
2184:Schübler Chorales
2074:, 11 August 2014
1932:L'art de la fugue
1553:to be performed?"
1383:
1382:
1251:), and tonality (
1196:Contrapunctus XIV
1150:Contrapunctus XIV
1129:Fuga a 3 Soggetti
1118:Fuga a 3 Soggetti
1107:Fuga a 3 Soggetti
1055:(1624), works by
982:Fuga a 3 Soggetti
922:Canon alla Decima
912:Canon alla Ottava
742:
703:
691:Fuga a 3 Soggetti
681:
662:
643:
624:
605:
586:
567:
548:
529:
510:
491:
400:Fuga a 3 Soggetti
289:Canon alla Ottava
285:Resolutio Canonis
266:Canon alla decima
90:
66:
16:(Redirected from
2835:
2761:Switched-On Bach
2616:The Art of Fugue
2442:
2441:
2363:
2352:orchestral works
2341:
2334:
2327:
2318:
2209:New Bach Edition
2196:The Art of Fugue
2115:
2105:
2098:
2091:
2082:
2077:
2060:The Art of Fugue
2041:The Art of Fugue
2030:Contrapunctus II
1992:The Art of Fugue
1984:: Scores at the
1981:The Art of Fugue
1962:The Art of Fugue
1960:Introduction to
1954:The Art of Fugue
1923:The Art of Fugue
1898:
1897:
1870:
1864:
1859:The Art of Fugue
1853:
1847:
1835:
1829:
1828:
1808:
1797:
1796:
1794:
1792:
1769:
1760:
1759:
1746:The Art of Fugue
1739:
1733:
1714:
1708:
1707:
1705:
1703:
1689:
1683:
1666:
1660:
1641:
1635:
1634:
1614:
1605:
1599:
1596:The Art of Fugue
1591:The Art of Fugue
1588:
1582:
1581:
1579:
1573:The Art of Fugue
1567:
1561:
1560:
1547:The Art of Fugue
1540:
1534:
1533:
1531:
1529:
1517:The Art of Fugue
1510:
1504:
1490:
1484:
1477:
1471:
1453:
1315:The Art of Fugue
1307:
1269:The Art of Fugue
1221:Fibonacci series
1213:The Art of Fugue
1186:Ferruccio Busoni
1088:The Art of Fugue
1068:The Art of Fugue
1025:argued that the
1023:Gustav Leonhardt
999:
998:
993:
992:
949:Contrapunctus 10
726:The Art of Fugue
705:
704:
683:
682:
664:
663:
645:
644:
626:
625:
607:
606:
588:
587:
569:
568:
550:
549:
531:
530:
512:
511:
493:
492:
472:
451:
450:
416:
262:Contrapunctus 13
251:
147:The Art of Fugue
120:The Art of Fugue
92:
91:
79:The Art of Fugue
68:
67:
55:The Art of Fugue
45:
21:
2843:
2842:
2838:
2837:
2836:
2834:
2833:
2832:
2793:
2792:
2791:
2786:
2773:
2727:
2629:
2593:
2569:
2531:, BWV 1046–1051
2516:Triple Concerto
2486:
2443:major, BWV 1031
2439:
2438:
2407:
2364:
2359:
2345:
2315:
2310:
2282:
2281:
2224:
2215:
2214:
2123:
2117:
2111:
2109:
2075:
2054:by Klangspiegel
2026:(YouTube video)
2019:(YouTube video)
1974:Mutopia Project
1921:Discography of
1907:
1902:
1901:
1894:
1872:
1871:
1867:
1854:
1850:
1845:Wayback Machine
1836:
1832:
1810:
1809:
1800:
1790:
1788:
1771:
1770:
1763:
1741:
1740:
1736:
1720:'s comments in
1715:
1711:
1701:
1699:
1691:
1690:
1686:
1667:
1663:
1649:Christoph Wolff
1642:
1638:
1612:
1607:
1606:
1602:
1589:
1585:
1577:
1569:
1568:
1564:
1542:
1541:
1537:
1527:
1525:
1512:
1511:
1507:
1491:
1487:
1478:
1474:
1460:Christoph Wolff
1454:
1450:
1445:
1428:
1423:
1417:
1388:
1367:
1350:
1349:+ 3 calamities,
1333:
1331:
1261:
1209:
1204:
1182:Daniil Trifonov
1146:
1110:
1053:Tabulatura Nova
1013:are written in
1007:
1005:Instrumentation
996:
995:
990:
989:
973:, respectively.
790:entries, as do
784:Contrapunctus 5
773:Contrapunctus 4
767:Contrapunctus 3
761:Contrapunctus 2
755:Contrapunctus 1
750:Simple fugues:
744:
743:
741:
723:
722:
714:
712:
711:
710:
709:
708:MIDI renditions
706:
698:
695:
686:
685:
684:
676:
673:
667:
666:
665:
657:
654:
648:
647:
646:
638:
635:
629:
628:
627:
619:
616:
610:
609:
608:
600:
597:
591:
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589:
581:
578:
572:
571:
570:
562:
559:
553:
552:
551:
543:
540:
534:
533:
532:
524:
521:
515:
514:
513:
505:
502:
496:
495:
494:
486:
483:
476:
470:
465:
444:chorale prelude
423:
389:Fuga a 2. Clav:
335:
254:Contrapunctus 4
245:
191:
186:
174:Christoph Wolff
116:
115:
107:
105:
104:
103:
102:
96:
93:
86:
83:
74:
73:
72:
69:
62:
59:
49:
43:
28:
23:
22:
15:
12:
11:
5:
2841:
2839:
2831:
2830:
2825:
2820:
2815:
2810:
2805:
2795:
2794:
2788:
2787:
2785:
2784:
2778:
2775:
2774:
2772:
2771:
2764:
2757:
2750:
2743:
2735:
2733:
2729:
2728:
2726:
2725:
2718:
2713:
2706:
2699:
2692:
2685:
2678:
2675:Feel My Rhythm
2671:
2664:
2659:
2652:
2645:
2637:
2635:
2631:
2630:
2628:
2627:
2626:
2625:
2612:
2603:
2601:
2595:
2594:
2592:
2591:
2585:
2579:
2577:
2571:
2570:
2568:
2567:
2566:
2565:
2560:
2555:
2550:
2540:
2539:
2538:
2525:
2520:
2512:
2507:
2502:
2496:
2494:
2488:
2487:
2485:
2484:
2483:
2482:
2477:
2469:
2468:
2467:
2462:
2457:
2451:
2446:
2434:
2428:Flute Sonatas
2426:
2421:
2415:
2413:
2409:
2408:
2406:
2405:
2400:
2395:
2394:
2393:
2388:
2383:
2381:Partita No. 1
2372:
2370:
2366:
2365:
2356:transcriptions
2346:
2344:
2343:
2336:
2329:
2321:
2312:
2311:
2309:
2308:
2303:
2298:
2293:
2287:
2284:
2283:
2280:
2279:
2273:
2264:
2256:
2247:
2238:
2229:
2228:
2226:
2217:
2216:
2213:
2212:
2188:
2128:
2127:
2125:
2119:
2118:
2110:
2108:
2107:
2100:
2093:
2085:
2079:
2078:
2063:
2055:
2049:
2036:
2027:
2020:
2009:
2000:
1988:
1977:
1965:
1957:
1949:
1940:
1927:
1918:
1906:
1905:External links
1903:
1900:
1899:
1892:
1865:
1848:
1830:
1798:
1761:
1734:
1709:
1684:
1674:George Ritchie
1661:
1636:
1600:
1583:
1562:
1543:Anon. (n.d.).
1535:
1513:Anon. (n.d.).
1505:
1485:
1472:
1447:
1446:
1444:
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1440:
1439:
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1427:
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1419:Main article:
1416:
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1340:
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1335:
1328:
1325:
1321:
1320:
1317:
1311:
1260:
1257:
1235:(contrapuntal
1208:
1205:
1203:
1200:
1178:Rudolf Barshai
1174:Davitt Moroney
1145:
1142:
1109:
1104:
1100:
1099:
1084:
1075:
1072:basso continuo
1064:
1049:Samuel Scheidt
1044:Fiori musicali
1006:
1003:
1002:
1001:
975:
974:
955:Fuga a 2 Clav:
952:
935:
934:
928:
919:
909:
873:
872:
867:
858:
857:
851:
845:
839:
826:
825:
808:
805:Stylo Francese
798:
792:Contrapuncti 6
777:
776:
770:
764:
758:
735:
732:
730:
713:
707:
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688:
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674:
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631:
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579:
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560:
555:
554:
541:
536:
535:
522:
517:
516:
503:
498:
497:
484:
479:
478:
477:
468:
467:
466:
464:
461:
422:
419:
334:
331:
243:Georg Poelchau
237:, followed by
231:Joh. Seb. Bach
190:
187:
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182:
106:
94:
84:
76:
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70:
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52:
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41:
40:
39:
26:
24:
14:
13:
10:
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6:
4:
3:
2:
2840:
2829:
2826:
2824:
2821:
2819:
2816:
2814:
2811:
2809:
2806:
2804:
2801:
2800:
2798:
2783:
2780:
2779:
2776:
2770:
2769:
2765:
2763:
2762:
2758:
2756:
2755:
2751:
2749:
2748:
2744:
2742:
2741:
2737:
2736:
2734:
2730:
2723:
2719:
2717:
2714:
2711:
2707:
2704:
2700:
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2530:
2526:
2524:
2521:
2519:
2517:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2497:
2495:
2493:
2489:
2481:
2478:
2476:
2473:
2472:
2471:Trio Sonatas
2470:
2466:
2463:
2461:
2458:
2455:
2452:
2450:
2447:
2444:
2435:
2433:
2430:
2429:
2427:
2425:
2422:
2420:
2417:
2416:
2414:
2410:
2404:
2401:
2399:
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2379:
2378:
2377:
2374:
2373:
2371:
2367:
2362:
2357:
2353:
2349:
2348:Chamber music
2342:
2337:
2335:
2330:
2328:
2323:
2322:
2319:
2307:
2304:
2302:
2299:
2297:
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2292:
2289:
2288:
2285:
2277:
2274:
2271:
2270:
2265:
2262:
2261:
2260:Bach-Jahrbuch
2257:
2254:
2253:
2248:
2245:
2244:
2239:
2236:
2235:
2231:
2230:
2227:
2222:
2218:
2210:
2207:(1851-1899);
2206:
2203:(1765–1787);
2202:
2198:
2197:
2192:
2189:
2186:
2185:
2180:
2179:
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2170:
2169:
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2158:
2157:
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2141:
2135:
2134:
2130:
2129:
2126:
2120:
2114:
2106:
2101:
2099:
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2087:
2086:
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2073:
2072:
2067:
2064:
2062:
2061:
2056:
2053:
2050:
2048:
2044:
2042:
2037:
2035:
2031:
2028:
2025:
2021:
2018:
2014:
2010:
2008:
2004:
2001:
1998:
1994:
1993:
1989:
1987:
1983:
1982:
1978:
1975:
1971:
1970:
1966:
1964:
1963:
1958:
1956:
1955:
1952:Web-essay on
1950:
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1944:
1941:
1939:
1937:
1933:
1928:
1925:
1924:
1919:
1916:
1912:
1909:
1908:
1904:
1895:
1893:0-14-005579-7
1889:
1885:
1884:Penguin Books
1882:. Middlesex:
1881:
1880:
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1869:
1866:
1862:
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1842:
1839:
1834:
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1807:
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1803:
1799:
1787:
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1779:
1775:
1768:
1766:
1762:
1757:
1753:
1749:
1747:
1738:
1735:
1731:
1730:0-486-49764-X
1727:
1723:
1719:
1713:
1710:
1698:
1694:
1688:
1685:
1681:
1680:
1675:
1671:
1670:Contrapunctus
1665:
1662:
1658:
1657:0-393-04825-X
1654:
1650:
1646:
1640:
1637:
1632:
1628:
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1601:
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1552:
1548:
1539:
1536:
1524:
1520:
1518:
1509:
1506:
1502:
1498:
1494:
1493:Helmut Walcha
1489:
1486:
1482:
1476:
1473:
1469:
1468:0-393-04825-X
1465:
1461:
1457:
1452:
1449:
1442:
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1425:
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1414:
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1410:
1406:
1402:
1401:
1396:
1392:
1385:
1378:
1375:
1372:
1371:
1365:
1364:4 evangelists
1361:
1358:
1355:
1354:
1348:
1344:
1341:
1338:
1337:
1329:
1326:
1323:
1322:
1319:Significance
1318:
1316:
1312:
1309:
1308:
1302:
1300:
1296:
1292:
1291:numerological
1287:
1285:
1281:
1277:
1276:
1270:
1266:
1258:
1256:
1254:
1250:
1246:
1243:), density (
1242:
1238:
1234:
1228:
1226:
1222:
1218:
1214:
1206:
1201:
1199:
1197:
1193:
1192:
1187:
1183:
1179:
1175:
1171:
1167:
1163:
1162:Helmut Walcha
1159:
1155:
1151:
1143:
1141:
1138:
1134:
1130:
1123:
1119:
1114:
1108:
1105:
1103:
1097:
1093:
1092:16-foot pitch
1089:
1085:
1082:
1081:
1076:
1073:
1069:
1065:
1062:
1059:(1616–1667),
1058:
1054:
1050:
1046:
1045:
1040:
1036:
1035:
1034:
1032:
1028:
1024:
1020:
1016:
1012:
1004:
987:
983:
980:
979:
978:
972:
968:
967:forma inversa
964:
960:
956:
953:
950:
946:
943:
940:
939:
938:
932:
929:
926:
923:
920:
917:
913:
910:
907:
903:
899:
895:
891:
890:
885:
881:
878:
877:
876:
871:
868:
866:
863:
862:
861:
855:
852:
849:
846:
843:
840:
837:
834:
833:
832:
830:
823:
819:
815:
812:
809:
806:
802:
799:
797:
793:
789:
785:
782:
781:
780:
774:
771:
768:
765:
762:
759:
756:
753:
752:
751:
748:
739:
729:
727:
721:
719:
694:
692:
672:
653:
634:
615:
596:
577:
558:
539:
520:
501:
482:
462:
460:
457:
455:
445:
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435:
433:
428:
420:
418:
415:
410:
405:
401:
396:
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370:
364:
362:
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328:
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308:
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97:Performed by
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2759:
2752:
2747:Back to Bach
2745:
2738:
2615:
2614:
2607:
2528:
2515:
2301:Bach Archive
2276:Bach Digital
2267:
2266:Schmieder's
2258:
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2195:
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2122:Music /
2116:publications
2069:
2059:
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2007:Carus-Verlag
1991:
1980:
1968:
1961:
1953:
1947:Art of Fugue
1946:
1935:
1931:
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1877:
1868:
1858:
1851:
1833:
1816:
1812:
1789:. Retrieved
1755:
1751:
1745:
1737:
1721:
1718:Donald Tovey
1712:
1700:. Retrieved
1696:
1687:
1679:Desert Fugue
1677:
1669:
1664:
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1616:
1603:
1595:
1590:
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1572:
1565:
1551:Art of Fugue
1550:
1546:
1538:
1526:. Retrieved
1516:
1508:
1496:
1488:
1481:counterpoint
1475:
1455:
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1398:
1393:
1389:
1345:7 seals = 4
1314:
1288:
1279:
1274:
1268:
1262:
1239:), harmony (
1229:
1225:golden ratio
1212:
1210:
1202:Significance
1195:
1194:is based on
1189:
1158:Zoltán Göncz
1154:Donald Tovey
1149:
1147:
1136:
1128:
1127:
1117:
1106:
1101:
1087:
1078:
1067:
1052:
1042:
1027:Art of Fugue
1026:
1019:Art of Fugue
1018:
1011:Art of Fugue
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1008:
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440:mirror fugue
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178:contrapuntal
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137:1080, is an
125:
124:
119:
118:
117:
95:(31 minutes)
78:
71:(40 minutes)
54:
29:
2634:Adaptations
2623:discography
2225:scholarship
2211:(1954–2007)
2076:(in French)
1861:, BWV 1080"
1819:: 181–202.
1280:sola gratia
1275:sola gratia
1249:syncopation
1247:), rhythm (
1215:, based on
1180:(2010) and
1170:Lionel Rogg
1166:David Goode
1039:Frescobaldi
1031:harpsichord
786:: has many
387:, entitled
246: [
241:written by
2797:Categories
2696:Lady Lynda
2618:, BWV 1080
2610:, BWV 1079
2590:(doubtful)
2518:, BWV 1044
2456:(doubtful)
2445:(doubtful)
2278:(2010–...)
2263:(1904–...)
2191:After 1750
1758:: 175–196.
1702:6 February
1462:, p. 433,
1443:References
1415:Recordings
1405:Kurt Gödel
1299:apocalypse
1253:modulation
1241:dissonance
1096:pipe organ
1015:open score
986:BACH motif
886: [
822:diminished
814:et Diminut
718:media help
295: [
287:(entitled
220: [
111:media help
2656:Ave Maria
2492:Concertos
2250:Spitta's
2240:Forkel's
2221:Biography
1876:(1980) .
1284:chromatic
1237:inversion
1233:polyphony
818:augmented
463:Structure
166:variation
156:and four
129:(German:
2649:Alphabet
2440:♭
2412:Ensemble
2354:by, and
2234:Nekrolog
2199:(1751);
2181:(1747);
2175:(1747);
2171:(1741);
2165:(1739);
2159:(1735);
2143:(1708);
2138:cantata
2017:Part 2/2
2013:Part 1/2
1841:Archived
1528:28 April
1426:See also
1397:'s book
1223:and the
1184:(2021).
1156:(1931),
1047:(1635),
997:♮
991:♭
454:BWV 668a
319:inversus
307:inversus
228:/ di Sig
81:, part 2
57:, part 1
2358:after,
2223: /
1976:website
1791:8 March
1682:(2010).
1501:Polydor
1313:Use in
1245:texture
906:Beilage
816:: uses
788:stretto
693:, motif
353:Canon p
184:Sources
170:subject
162:D minor
2732:Albums
2575:Suites
2246:(1802)
2237:(1754)
2187:(1748)
2124:lyrics
1890:
1728:
1655:
1629:
1466:
1310:Number
1172:, and
994:–A–C–B
965:, the
942:Contra
900:, and
385:rectus
338:title
315:rectus
311:rectus
268:, and
158:canons
154:fugues
2599:Fugal
2536:No. 5
2391:No. 3
2386:No. 2
1999:files
1631:63530
1627:JSTOR
1613:(PDF)
1578:(PDF)
971:recta
892:]
301:]
250:]
226:]
123:, or
2710:They
2437:in E
2369:Solo
2350:and
2113:Bach
1997:MIDI
1888:ISBN
1793:2024
1726:ISBN
1716:See
1704:2021
1653:ISBN
1530:2012
1464:ISBN
1137:BACH
969:and
957:and
794:and
446:on "
404:Fuga
391:and
383:and
210:1746
206:1740
2689:Joy
1995:as
1821:doi
1782:doi
1647:by
1458:by
1407:'s
1217:bar
1188:'s
1051:'s
1041:'s
988:, B
945:a 4
889:sic
411:: "
341:Die
298:sic
264:),
223:sic
208:to
160:in
135:BWV
133:),
2799::
2193::
2153:;
2136::
2068:,
2015:,
2005:–
1934:/
1817:13
1815:.
1801:^
1780:.
1776:.
1764:^
1756:17
1754:.
1750:.
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1366:);
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256:,
248:de
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2340:e
2333:t
2326:v
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2090:v
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1896:.
1827:.
1823::
1795:.
1784::
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1706:.
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1633:.
1623:8
1580:.
1559:.
1545:"
1532:.
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1470:.
1373:3
1356:4
1339:7
1074:.
951:.
908:.
807:.
796:7
740:.
720:.
317:–
113:.
20:)
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