Bach’s first keyboard collection was published in 1731 under the title Clavir Übung Theil 1, Opus 1 (hereafter CÜ I).26It comprised six partitas,five of which had been published earlier as individual units: Partita 1 in 1726 (BWV 825), Partitas 2 and 3 in 1727 (BWV 826–7), Partita 4 in 1728 (BWV 828) and Partita 5 in 1730 (BWV 829).27 In spite of a public announcement in 1730 advertising a seventh Partita, the collection was published as a whole with only six Partitas, the sixth Partita never being sold separately.28In 1735 Bach published a second keyboard collection, the
24
D-B Mus. ms. Bach P 219. NBA KB Source C, c. 1724. 25 SeeChapter 3and theAppendix. 26Schulenberg, Keyboard Music, 321–46. 27
NBA KB V/1.
28BD II, Doc. 277. Leipzig, 1 May 1730:‘The Fifth part of Bach’s Clavier Übung is now ready and with the remaining two the whole work will be completed for the up-coming Michaelmas Fair.’
second part or Zweyter Theil der Clavier Übung, (hereafter CÜ II), which consists of just two works: a three-movement Italian Concerto (BWV 971) and an eleven-movement French Overture (BWV 831).29The omission of any reference to its opus in the title suggests that Bach intended it to be associated with CÜ I. The numerical construction confirms this idea.
Together the forty-one movements of CÜ I and the fourteen movements of CÜ II have 3120 bars. Table 6.8 shows how these 3120 bars form a symmetrically arranged large-scale 1 : 2 proportion with 1040 : 2080 bars in a 2 : 3 proportion formed by three continuous sections in publication order, dividing the second Partita and the Italian Concerto into two parts. A permutated B-A-C-H pattern can be seen in the keys of four of the eight works. Furthermore, six sections have 2088 bars and four 1032 bars, exactly parallel to the 2088 bars of WTC I and 1032 bars of AA.
Table 6.9illustrates the layers of large-scale structural parallels between the two parts of the Clavier Übung and Bach’s first pair of keyboard collections. When he published CÜ II in 1735, Bach united, for the second time, two contrasting keyboard collections into a set with 3120 bars, thereby creating a mega double 1 : 1 construction from 1 : 1 sets made up of 2 : 2 keyboard collections in 3120 : 3120 bars, with each set having the same large-scale 1 : 2 proportion in 1040 : 2080 bars. There are, Table 6.8Symmetrical 1 : 2, 2 : 3 and B-A-C-H signature. CÜ I & CÜ II (1735)
BWV Partita Bars 1 : 2 Key Bars Bars 825 1 in B♭ major 249 249 B♭ 249 826/1 2 in C minor 90 TS 90 C 90 826/2–6 2 in C minor 288 288 288 827 3 in A minor 342 342 A 342 828 4 in D major 422 422 422 829 5 in G major 391 391 391 830 6 in E minor 396 396 396 971/1–2 Italian Concerto 241 241 241 971/3 Italian Concerto 210 210 210 831 French Overture 491 491 B (H) 491 Totals 3120 1040 : 2080 B-A-C-H 2088 1032
No copies have survived of the sixth and seventh and it is therefore assumed that neither was published individually.
however, fewer smaller-scale layers of proportion within the CÜ I and II pair. This is a natural consequence of the fact that Bach could not, without enormous expense, adjust the structures of thefirst five partitas which had already been printed and sold individually.
The barring in the engraving of CÜ I and CÜ II is very clear, and the 3120 bars are those written rather than repeated. The only notational anomaly that affects the numerical result is the‘Sinfonia’ of the C-minor Partita, BWV 826/1, where at bar 29 there is the dual count of a time signature as bar line, a TS feature.30Instead of a bar line there is simply a new time signature where the movement changes fromc to34, rendering its length both 90 and 91 bars. There is a similar case in bar 163 of the French Overture, but since it affects the bar total only when the movement is repeated it is irrelevant to the 3120-bar structure.
The spelling of the title words Clavier Übung is inconsistent in the various published partitas. The first title page used in 1726 for Partita 1 (BWV 826) uses the form‘Clavier’. The same plate was reused for the title page of thefifth partita in 1730, with a judicious change of the numeral I to V. The title pages for the individually published partitas 2, 3 and 4, however, use the form‘Clavir’, without an ‘e’. When Bach had a new plate engraved for the title page of the complete collection, Opus 1, he chose the form ‘Clavir Übung’, perhaps because of its satisfying numerical value, 123,31 parallel both to his own name, as 3 x 41, and as a B-A-C/2-1-3 number, and to the overall bar total of 3120.32The 1032-bar total of the Table 6.9Proportional integration of two sets of two keyboard collections
1722/3 & 1726–35 1 : 1 1 : 1 1 : 1 1 : 2 1 : 1 1 : 1 1 : 1 AA 1032 1032 1040 : 2080 1040 2080 WTC I 2088 2088 CÜ I Sinfonia BWV 826/1 [French/Italian] 90 CÜ II [French/Italian] 942 CÜ I all but BWV 826/1 2088 CÜ I 2178 1040 : 2080 1040 2080 CÜ II 942 Totals 3120 : 3120 1032 : 1032 2088 : 2088 3120 : 3120 1040 : 1040 2080 : 2080
30Explained inChapter 1. 31CLAVIR: 3+11+1+20+9+17=61 UBUNG: 20+2+20+13+7=62. 32SeeChapter 2.
first two partitas has the same 2-1-3 allusion. Evidence from the early versions of the partitas and the numerical structure suggests how Bach worked to create this perfectly proportioned plan.
Early versions of works in the collection
The earliest copy of the A-minor Partita (BWV 827) can be found in Anna Magdalena’s second Clavierbüchlein (P 225),33 dated 1725, written care-
fully by Bach onto the first seventeen pages of his wife’s new leather- bound book.
When preparing this partita for publication Bach renamed the first movement‘Fantasia’, inserting two new bars between bars 117 and 118 of the original, and adding a 32-bar Scherzo between the Menuetto and Gigue, Table 6.10, shaded column +/, thus transforming its six movements in 308 bars into seven movements and 342 bars. He also wrote the E-minor Partita (BWV 830) on pages 18–41 of the 1725 music book, immediately after the A-minor Partita. When he prepared this partita for publication he changed the title of the first movement from ‘Prelude’ to ‘Toccata’, and increased its length by inserting two bars between bars 73 and 74, adding a bar between thefinal and penultimate bars, and a new 32-bar ‘Air’, Table 6.10, shaded column +/. Two movements of the E-minor Partita were reused from earlier compositions: 116 bars came from the recently revised Sonata for violin and harpsichord (BWV 1019a/3), St 162 (Table 5.9), which he renamed ‘Corrente’, and 32 bars from BWV 1019a/5, which
Table 6.10Partitas in A and E minor. Autograph, P 225, and Print, BWV 827, 830
A-minor Partita, 1725 E-minor Partita, 1725–30
Movement P 225 Title 1/ CÜ I Movement P 225 Title 1/ CÜ I Prelude 118 Fantasia +2 120 Prelude 105 Toccata + 3 108 Allemande 16} 16} Allemande 20} 20 Corrente 56} 56} Corrente 116} 116 Sarabande 28} 28} Air — + 32 32 Menuetto 40} Burlesca 40} Sarabande 36} 36 Scherzo — +32 32} Tempo di Gavotta 32} 32 Gigue 50} 50} Gigue 52} 52 Totals 308 +34 342 361 + 35 396
he transcribed for keyboard and set as a‘Tempo di Gavotta’. Bach’s neat handwriting and attention to detail as he copied these two partitas onto the first forty-one sides of his wife’s new book reflect the care he took over their composition.34 They were not just beautiful to behold, they were carefully constructed as a perfectly proportioned pair. The 223 bars of the first movements form a 1 : 2 proportion with the 446 bars of the remaining movements (seeTable 6.11).
Anna Magdalena’s book began with a perfect presentation set of two partitas, proportioned 1 : 2, in keys a perfectfifth or 2 : 3 apart. Nonethe- less, when Bach grafted these movements into his published collection he destroyed this perfection and unity by increasing their length by 69 bars. One can understand the additional bars and the two extra movements as improvements motivated by musical considerations. However, I suspect this was matched by his motivation to create a new perfect numerical structure on a larger scale.
There are clues in the evolving numerical structure of CÜ I to suggest that Bach always intended the published keyboard collection to comple- ment hisfirst unpublished set of keyboard works from 1722/3.
Table 6.12shows that the first two published partitas, including their repeats, have 1032 bars, the same total as the two-part Inventions and Sinfonias. The parallel implies that Bach may have planned to add a further 2088 bars, to create a collection with 3120, parallel to the 1032 and 2088 bars of his earlier set. The perfected A- and E-minor Partitas (P 225) have 1115 bars including repeats. Had Bach used these towards the projected total of 2088 bars, he would have had only 973 bars for thefinal partitas. There is no source evidence to suggest that he had composed the French Overture before 1730. However, if he had, and if by then he had planned to Table 6.111 : 2 proportion in Partitas in A and E minor. Autograph, P 225, 1725
pp. 1–41 Prelude Allemande Corrente Sarabande Menuetto Gigue Totals 1 : 2 A minor 118 16 56 28 40 50 (308) E minor 105 20 116 36 32 52 (361) 446
[669] 223 Totals 223 36 172 64 72 102 (446) 669
34
Kobayashi dates the handwriting of the E-minor Partita in P 225 to between 1725 and 1730. Notenschrift, NBA 9/2 (1989) 208. It was possibly C. P. E. Bach who paginated the two partitas much later.
include this eleven-movement‘partita’ in the collection, its 982 repeated bars (excluding the
D
of Gavotte/Passepied/Bourée) could easily have been adjusted by nine bars to 973 bars to make afive-partita set of 3120 bars. But this did not happen, and it is in any case unlikely that the French Overture had eleven movements by this time. The reconstruction in Table 6.12suggests that the hypothetical 1032 : 2088 scheme would have been too limiting and musically restricting. By using the number of written rather than repeated bars, Bach could increase the scale of his collection and still use the good idea of the 3120, 1040 : 2080 construction, with 1032 and 2088 visible in two parts parallel to the 1723 keyboard pair. (seeTable 6.8).Hints of the construction procedure
The two works in CÜ II were composed significantly earlier than their 1735 publication date might suggest. Anna Magdalena made a very neat copy of the French Overture in C minor,35BWV 831a, P 226,36for which Bach wrote the title,‘Ouverture pour le Clavecin a 2 Clav. composée par J. S. Bach’. Based on the handwriting and watermarks, the copy can be dated to c. 1732–5 or possibly to the middle of 1733.37It is possible that a shorter, early version of the French Overture could have been the adver- tised seventh Partita.38 The Italian Concerto, BWV 971, was composed even earlier than the French Overture.39Two manuscript copies based on a pre-publication version have survived. The first was made by Johann Christoph Oley (1738–89) before 1762, and has the title Concerto en Table 6.12Evolving plan, including repeats, to mirror AA and WTC I?
BWV Date Score Work Bars Bars 3120 [19] 825 1726 Print Partita 1 in B♭ major 477 477 826 1727 Print Partita 2 in C minor 555 555 827a 1725 P 225 Partita 3 in A minor 498 498 830a c. 1725 P 225 Partita 6 in E minor 617 617 831a pre-1728 pre-P 226 ‘French’ Partita in C minor 982 982 Totals 1032 2097 1032 :2088
35NBA KB V/2, 14; source 2 B. 36D-B Mus. ms. Bach P 226 fascicle 9, 41–65. 37
NBA KB V/2, 15 and 48. Kobayashi, Notenschrift, 208. 38
BD II, Doc. 276, Leipzig, 1 May 1730.
39K. Beißwenger,‘An Early Version of the First Movement of the Italian Concerto BWV 971’, in Bach Studies 2, ed. D. Melamed (Cambridge University Press, 1995), 1–19.
F dur.40 Its bar structure is identical to the published version, with afirst movement of 192 written bars. A second copy was made by Leonhard Scholz (1720–98) and represents an even earlier version of the concerto. The layout of the first movement is unique: it is written with a
D
indication after bar 163.41This is a striking parallel to the 163 bars of the first movement of the French Overture, which would become its compan- ion in CÜ II. When Bach prepared the Italian Concerto for publication, however, he wrote out the da capo section in full, making afirst movement with 192 bars. This 192 bars was essential to form the 1040 : 2080 propor- tion shown in Table 6.8. Perhaps it was this numerical coincidence that gave Bach the idea of including the Concerto in the Clavier Übung collec- tion, and expanding the collection beyond partitas? The 1 : 1 proportion in 163 : 163 bars also suggests that he had some concrete means of recalling the length of works he had composed earlier.The key of the Italian Concerto may also have played a part in its inclusion in the Clavier Übung series. Christoph Wolff has pointed out a logical expanding major-minor key pattern across CÜ I:
We do not know why the planned seventh Partita was not published. At any rate, according to Bach’s well-ordered tonal plan, it must have been intended to be set in F major. . .[Bach] did not use an ascendingly ordered succession of keys as he had in the Well-Tempered Clavier and the Inventions and Sinfonias; instead he chose a sequence based on gradually expanding upward and downward intervals . . . Without the seventh Partita, the consistent logic of the original plan was, of course, destroyed. Yet the end result forms a hardly less logical order: one piece in the major mode, followed by two in minor for the second half, for a total of three pieces in major and three in minor modes.42
The numerical evidence shows that Bach designed the two parts of the Clavier Übung as a unit, and therefore if Wolff’s observation reflects Bach’s conscious patterning, Bach did indeed continue the logic of the key pattern. The already composed Italian Concerto with itsfitting 163-bar first move- ment was in F major. The minor-mode French Overture continued the major–minor patterning. Bach decided to transpose it to B minor, which lay centrally between the E and F of the penultimate works in the set, and also completed the B-A-C-H signature across the set.
40NBA KB V/2, 14; Oley’s copy is source A: Boston Public Library Ms M 200.12(2). 41
D LEb Rar Ib, 58, formerly D Gb Ms.Scholz 5.2.3, reads‘Da Capo all Segno’, and D LEb Rar Ib, 59, formerly D Gb Ms.Scholz 5.2.4 reads‘Da Capo d’al Segno’: image in Beißwenger, ‘Italian Concerto’, 2–3.
42Wolff,‘The Clavier-Übung Series’, Essays, 189–90.
At what point and for how long Bach planned a seven-partita collection is not known– the rumour may have been nothing more than a simple advertising ploy or mistake. At what point he devised the structure of this two-collection set to make it a precise parallel to hisfirst keyboard set is also unclear. A block of 1700 written bars suggests a possible compos- itional timeline.
If the 1700-bar block shown inTable 6.13is evidence of Bach’s organisa- tional planning it could help reconstruct the order in which Bach worked. By 1727 he had published thefirst, second and third partitas and probably also composed the Italian Concerto. This gave him 1420 bars. With hindsight it is easy to see that all he needed to reach the desired total of 3120 was an additional 1700 bars. However, although theoretically possible, it seems highly unlikely that as early as 1727 Bach would have decided to include a concerto in a collection of partitas. It is more likely that the 1700-bar block dates to early 1731 or late 1730, when he was preparing the sixth partita for publication. Having a draft of the French Overture to hand, and the Italian Concerto on his desk, he saw how he could create a perfect set of two complementary collections of 3120 bars each. The 1700-bar block may have acted as a structural guide as he made minimal additions to Partita 6 before publication in 1731 of CÜ I as a set of six, while he calculated the number of bars needed to revise and graft the French Overture into the structure. An earlier version of the French Overture may well have been the advertised seventh Partita, but Bach changed his plan. Thefinal touch to his perfect scheme was to create the B-A-C-H key pattern by transposing the French Overture to B minor, some time after mid-173343 and probably shortly before its publication as part of CÜ II in 1735.
The intentionality of Bach’s design is further suggested in a 1032 and 2088 structure, parallel to WTC I and AA, formed by the unconventional Table 6.13A 1700-bar block, without repeats, suggesting early ordering
BWV Date Score Work Movements Bars 828 1728 Print Partita 4 in D major 7 422 829 1730 Print Partita 5 in G major 7 391 830 1731 Print Partita 6 in E minor 7 396 831 173? P 226 French Overture in C minor 11 491
Totals 32 1700
43The estimated date of Anna Magdalena’s copy in P 226 based on her handwriting and the watermarks of the paper, NBA KB VIII/1, 71f.
C minor Sinfonia of the second partita. Its opening dotted section sets the expectation of a typical French overture, but within seven bars something quite different happens, and again at bar 29, when it unexpectedly changes to3
4 metre, almost but not quite in the style of an Italian Sinfonia. 44 The
proportional integration can be seen in Table 6.9, where its 90 bars (counted as TS) combine with the 942 bars of the Italian Concerto and French Overture of the second part of Clavier Übung to make a total of 1032 bars. Thefirst part of Clavier Übung, without the C minor Sinfonia, has 2088 bars.Table 6.14shows a further remarkable numerical feature of the completed two-collection set – the bar total of the final four works, when counted at the repeat, form an exact block of 2800 bars. The constructional significance of this 2800-bar block becomes apparent when one sees the 2800-bar block Bach had formed by 1741 with the third and fourth parts of the Clavier Übung series. The distinct blocks of 2800 bars and 1700 bars suggest that while Bach was constructing his collections he was aware of both the written and repeated bar totals.
Changes to bars, movements and key transposition are a normal part of compositional revision procedure. Regrouping works into a collection to create a new artistic constellation is part of normal planning procedure. Usually such revisions and regrouping are necessary because compositions are in a rough and ready state. This was not the case for Bach when he constructed the first two parts of his Clavier Übung series. Neither tech- nical nor musical reasons can explain his extension to the A-minor and E-minor Partitas: they were already excellent. Nor was there a practical or acoustical reason why Bach should transpose the French Overture from C minor to B minor. It too was already excellent in its original key. Table 6.14A striking 1 : 1 proportion suggesting a large-scale working plan
BWV Collection Work Bars 1 : 1 829 CÜ I/5 Partita in G major 687 687 830 CÜ I/6 Partita in E minor 680 680 971 CÜ II/1 Italian Concerto 451 451 831 CÜ II/2 French Overture 982 982
CÜ III German Organ Mass 1840 1840 988 CÜ IV Goldberg Variations 960 960
Totals 5600 2800 : 2800
44Schulenberg, Keyboard Music, 327.
The changes were motivated by Bach’s desire to bring his first published two-set collection into harmonious order. Its layers of larger and smaller- scale proportions demonstrate empirically its numerical kinship and unity with his earlier unpublished two-set collection. The words Zweyter Theil and his omission of Opus 2 on the title page confirm his intention. His two publications created a unity with harmonious proportions that would never be heard,45 but which Bach hoped would delight his neighbour and lead to greater devotion to God.