Bach’s autograph score of the six Cello Suites (BWV 1007–12) has not survived. The primary copy on which modern editions are based, P 269,41 was prepared by Anna Magdalena Bach for Georg Heinrich Ludwig Table 5.11Parallels between two violin collections. P 967 and P 229
Six Solos P 967 Proportions Six Sonatas P 229 2400 bars 1 : 1 2400 bars 1600 : 800 bars 2 : 1 1600 : 800 bars 4 : 2 works 2 : 1 4 : 2 works
B-A-C in 1600-bar block B-A-C in 1600-bar block Italian title page 1 : 1 Italian title page (St 162) Solo 1 : 2 Duo
40The results are remarkable, even though one set includes repeats and the other does not. 41D-B Mus. ms. Bach P 269.
Schwanberg (1696–1774).42 The watermarks indicate that the batch of paper she used was the same as her husband used between autumn 1727 and winter 1731.43It is thought that Bach compiled the collection in Cöthen before 1720, and that he may have composed some of the suites when he lived in Weimar.44In this section the numerical structure and the characteristics of proportional parallelism will help ascertain the extent to which Bach had revised and perfected the collection of cello suites to a publication-ready state when Anna Magdalena made the copy.
Anna Magdalena’s copy of the Six Solos, P 268, and her copy of the Cello Suites, P 269, were originally a single two-part set. A comparison between P 268, and Bach’s autograph manuscript, P 967, shows how carefully Anna Magdalena emulated her original model when she copied the violin solos. Following the same line, scholars have therefore surmised that her copy of the Cello Suites ought to be relatively true to Bach’s lost original, yet found it wanting.45Schulze cites her erroneous misnaming of the Allemande (BWV 1011/2) as Courante, and the unusual comment La Fin. des Suixttes, as examples that must have deviated from Bach’s original, a trait of her copying that caused Bach to check her work.46 Other anachronistic features in her score that modern editors assume to be copying errors include (1) clear repeat indications in movements traditionally not repeated, (2) the inaccurateflow of slurs, and (3) her omission of the literal da capo indication after Bourée 2 in the fourth suite, interpreting her Verte as an indication to turn back to Bourée 1.47
Bach’s assignation ‘Libro Primo’ in the title page of the Six Solos implies that it was to be thefirst part of a comprehensive project.48Anna Magda- lena’s copies of the solo collections for violin and cello, P 268 and P 269, were given a united title page by Schwanberg, who used the words‘Pars 1’ and ‘Pars 2’, which has since been interpreted to mean that Bach intended the two solo collections to belong together. The precision of the numerical correlation between thefinal version of the Six Sonatas, P 229, and the Six Solos, seen above, strongly suggests that Bach saw the Six Sonatas as part of a large-scale two-part set. The following discussion of the numerical structure of the Cello Suites will shed light on the extent to which this collection too may have been revised to integrate a third collection into the string collec- tions project.
42Schulze, Bach-Überlieferung, 96–101. 43 Ibid., 97. 44
J. Butt,‘Cello Suites’, in J. S. Bach, ed. Malcolm Boyd. Oxford Composer Companions (Oxford University Press, 1999).
45NBA KB VI/2, 27. 46 Schulze, Bach-Überlieferung, 97 and 100. 47 NBA KB VI/2, 77. 48NBA KB VI/2, 18.
Evidence from the score
Table 5.12shows the numerical structure of the six Cello Suites P 269, with 1975 written bars and 140 bars of da capo, which brings the total to 2115 bars, and 4000 bars when all the repeats and da capo indications are included. The shaded column shows a clear double 2 : 1 proportion within the 2115 bars, with 4 : 2 Suites in 1410 : 705 bars.
The pattern of the keys, D-C-E♭, is in the same intervallic relationship as the self-referential B-A-C, although a minor third higher; some may wish to see this as a signatorial reference. But it is when all the repeats that Anna Magdalena included are counted that the total becomes 4000 bars and the collection seen to be in perfect numerical relationship with the two violin collections. The 4000 bars can be seen only when Anna Magdalena’s repeat instructions are followed precisely, including the curious repeats she marked for the preludes of suites 2, 3, 4 and 5, even though they make little musical or editorial sense. Repeats in the movements marked with a da capo are not observed, as seems to have been customary; and the dal segno indication of Gavotte 1 (BWV 1012/5) is followed literally, so that the opening 4-bar refrain is repeated every time it is performed (i.e. 8 + 16 + 8 + 16 + 8 bars), hence 56 and not 48 bars.49In addition to the possible self- reference in the key relationships, the G-major Suite has 410 performed bars, which may be an allusion to Bach’s name. There are also several layers of perfect proportion in the structure which, combined with the double 2 : 1 structure in 1410 : 705 bars, suggest that P 269 was a faithful copy of Bach’s lost original, and that the original had been numerically revised.
Table 5.13shows the proportional planning within the D-major Suite (BWV 1012). It has a 1 : 1 : 1 structure in 3 : 2 : 2 movements in blocks of 200, and a 1 : 1 proportion in the first three movements, 144 : 144 bars. This numerical ordering demonstrates that Bach understood Mattheson’s fifth rule of charm, ‘the precise observation of the correct proportion of all parts of a melody with one another’.50
Its many units of multiples of 200 bars strongly indicate compositional revision. Unfor- tunately no early version of the cello collection has survived. However, traces of evidence in the numerical structure suggest an earlier plan, and
49
Many modern scores adopt a rational layout of this Gavotte, disguising the performance implication by removing the four-bar refrain indicated by Anna Magdalena’s (presumably also Bach’s original) dal segno symbol.
Table 5.12Bar structure of Cello Suites: 1975, 2115 and 4000 bars
BWV Key Suite Movement Bars
D
Bars 2 : 1 Bars* Totals D-C-Eb 1007/1 G major 1 Prélude 42 238 238 42 410 1007/2 Allemande 32 64 1007/3 Courante 42 84 1007/4 Sarabande 16 32 1007/5 Menuet 1 24 48 1007/6 Menuet 2 24 48 1007/5 Menuet 1D
24 24 1007/7 Gigue 34 681008/1 D minor 2 Prélude 63 295 295 126 [AMB] 566 D 1008/2 Allemande 24 48 1008/3 Courante 32 64 1008/4 Sarabande 28 56 1008/5 Menuet 1 24 48 1008/6 Menuet 2 24 48 1008/5 Menuet 1
D
24 24 1008/7 Gigue 76 1521009/1 C major 3 Prélude 88 408 408 176 [AMB] 788 C 1009/2 Allemande 24 48 1009/3 Courante 84 168 1009/4 Sarabande 24 48 1009/5 Bourée 1 28 56 1009/6 Bourée 2 24 48 1009/5 Bourée 1
D
28 28 1009/7 Gigue 108 2161010/1 E♭ major 4 Prélude 91 329 329 182 [AMB] 706 E♭ 1010/2 Allemande 40 80 1010/3 Courante 64 128 1010/4 Sarabande 32 64 1010/5 Bourée 1 48 96 1010/6 Bourée 2 12 24 1010/5 [Bourée 1
D
] [48] 48 1010/7 Gigue 42 841011/1 C minor 5 Prélude 223 469 469 446 [AMB] 902 C 1011/2 Allemande 36 72 1011/3 Courante 24 48 1011/4 Sarabande 20 40 1011/5 Gavotte 1 36 72 1011/6 Gavotte 2 22 44 1011/5 Gavotte 1
D
36 36 1011/7 Gigue 72 144 1012/1 D major 6 Prélude 104 376 376 104 628 D 1012/2 Allemande 20 40 152 d e m o n s t r at i o n simply that the 4000-bar version was an intermediate solution before Bach had time to create a more perfect parallel to the Six Solos and the Six Sonatas.
(a) A 4000–bar structure and many layers of perfect proportion
The bar totals of the six suites do not fall into large-scale proportion, either in the configuration 3 : 3 or 4 : 2 suites. However,Table 5.14shows that when the collection is viewed by movement, the bar totals form a large- scale double 1 : 1 proportion with 4 : 4 movements and 2000 : 2000 bars. The Gigue movements have exactly 800 bars. and these form a second layer of proportion with the 1200 bars of Courantes, Menuets/Gavottes/Bourées Table 5.12 (cont.)
BWV Key Suite Movement Bars
D
Bars 2 : 1 Bars* Totals D-C-Eb 1012/3 Courante 72 144 1012/4 Sarabande 32 64 1012/5 Gavotte 1 28 56 1012/6 Gavotte 2 20/4 56 1012/5 Gavotte 1D
28 28 1012/7 Gigue 68 136 Totals 1971/5 140[88] 2115 1410 : 705 4000 4000 * including repeatsTable 5.13Evidence of proportional planning in BWV 1012
Including Anna Magdalena’s repeat indications, P 269
BWV Movement Bars 1 : 1 : 1 1 : 2 1 : 1 1012/1 Prélude 104 104 104 104 1012/2 Allemande 40 40 40 40 1012/3 Courante 144 144 144 144 1012/4 Sarabande 64 64 64 1012/5 Gavotte 1 56 56 56 1012/6 Gavotte 2 56 56 56 1012/7 Gigue 136 136 136 Totals 600 200 : 200 : 200 200 : 400 144 : 144
1 and their repeat after Menuets/Gavottes/Bourées 2. Further parallel layers of proportion can be found within movement types.
(b) Layers of proportion within 4000 bars: 1600 : 2400.
Table 5.15 shows a second large-scale proportion in the 4000 bars: 2400 bars in the shaded area and 1600 bars formed by the 1076 bars of Préludes and the 524 bars of the sixth suite (BWV 1012), excluding the 104 bars of Prélude already counted. Bach must have adapted the preludes and the sixth suite to achieve this exact total. Of all the movements in this Table 5.14A double 1 : 1 proportion in 4000 bars formed between movements
Including Anna Magdalena’s repeat indications, P 269
Movements in BWV 1007–12 Bars 1 : 1 2 : 3 1. Préludes 1076 1076 2. Allemandes 352 352 3. Courantes 636 636 636 4. Sarabandes 304 304 5. Menuets/Gavottes/Bourées 1 376 376 376 6. Menuets/Gavottes/Bourées 2 268 268 Da Capo of Menuets/Gavottes/Bourées 1 188 188 188 7. Gigues 800 800 800 Totals 4000 2000 : 2000 800 : 1200
Table 5.15Large-scale 3 : 2 proportion with 2400 : 1600 bars across movements
Including Anna Magdalena’s repeat indications, P 269
BWV Prélude Allemande Courante Sarabande Men/1 Men/2
D
Gigue Bars Totals 1007 42 64 84 32 48 48 24 68 (368) 1008 126 48 64 56 48 48 24 152 (440) 1009 176 48 168 48 56 48 28 216 (612) 1010 182 80 128 64 96 24 48 84 (524) 1011 446 72 48 40 72 44 36 144 (456) 2400 1012 104 40 144 64 56 56 28 136 1600 Totals 1076 352 636 304 376 268 188 800 4000 154 d e m o n s t r at i o n scollection, it is the opening preludes that display the greatest compositional diversity and thus offered Bach the greatest freedom as he strove to reach a specific bar total.51Table 5.16shows this more clearly, with the Préludes in
Suites 1–5 and the 628 bars of Suite 6 making 1600 bars, which contain another layer of double proportion with 3 : 3 groups in 400 : 1200 bars. The next column shows how movements 2–7 of Suites 1–5 have 2400 bars, and a double 1 : 1 proportion with 980 : 980 bars. These two large-scale 2 : 3 proportions in 1600 : 2400 bars, several smaller layers of proportion, and an implied signature in both the keys and as the total of the G-major Suite (BWV 1007), suggest that this collection too had been numerically per- fected. If these results show that Bach found a way of making the collection perfectly proportioned, even if it meant introducing repeats in preludes where none are expected, Anna Magdalena’s reputation as an inaccurate copyist needs to be reviewed.
Evidence of an early 1800-bar structure
The collection has 1975 bars when the repeats are not observed: 1375 bars in Suites 1, 3, 5 and 6 (214, 380, 433 and 348 bars) and 600 bars in the D-minor and Eflat-major Suites forming a building block typical of Bach’s numerical construction. This 600-bar block suggests that Bach may have originally planned an 1800-bar construction, with a double 1 : 2 proportion in 2 : 4 suites and 600 : 1200 bars. Such a structure would have formed a Table 5.16Compositional blocks and proportions within the Cello Suites 2400 : 1600 bars
Including Anna Magdalena’s repeat indications, P 269
BWV Bars 1 : 3 BWV Bars 1 : 1 1007/1 42 42 1007/2–7 368 368 1008/1 126 126 1008/2–7 440 1009/1 176 176 1009/2–7 612 612 1010/1 182 182 1010/2–7 524 524 1011/1 446 446 1011/2–7 456 456 1012/1–7 628 628 980 : 980 Totals 1600 400 : 1200 2400
3 : 4 proportion in 1800 : 2400 bars with the Six Solos, and 1 : 1 in 6 : 6 Solos : Suites. Table 5.17 shows that a 2 : 1 proportion is formed when the extensive 223-bar C-minor Prélude (BWV 1011/1) is replaced by a prelude with 48 bars. Although hypothetical, the possibility warrants further investigation.
The 223-bar version of the Prélude from the Suite in C minor (BWV 1011) has survived in both P 269, and in an autograph transcription for lute (BWV 995) with a dedication to ‘Monsieur Schouster’.52The water- marks and writing indicate that the lute transcription was made at exactly the same time as P 269, between autumn 1727 and winter 1731. Schulze suggests that Bach made the dedicated transcription spontaneously, intending to have a second fair copy made by someone, such as Anna Magdalena, before handing it over to the sponsor.53If this was the case, it is highly likely that his wife would have had both the cello version and Bach’s lute transcription to hand when she made P 269.
The C-minor Prélude of thefifth suite is more than twice the length of any of the other preludes in the collection. This discrepancy suggests that it did not originally belong to the collection, and was probably the means by which Bach generated the perfect 1600 : 2400 structure described above. Had the length of the C-minor Prélude been 48 and not 223 bars, as in Table 5.17, the 1800-bar collection would have an exact double 2 : 1 proportion with 4 : 2 suites in 1200 : 600 bars, matching the double 2 : 1 proportion in the Six Solos and in the Six Sonatas. Furthermore,Table 5.18 Table 5.17Speculative reconstruction exchanging BWV 1011/1 with a 48-bar Prelude
Bars counted as written, i.e. without repeat or da capo indications
BWV Prélude Allemande Courante Sarabande Men/1 Men/2 Gigue Bars 2 : 1 1007 42 32 42 16 24 24 34 214 214 1008 63 24 32 28 24 24 76 271 271 1009 88 24 84 24 28 24 108 380 380 1010 91 40 64 32 48 12 42 329 329 1011 48* 36 24 20 36 22 72 258* 258 1012 104 20 72 32 28 24 68 348 348 Totals 436 176 318 152 188 130 400 1800 1200 : 600
52Bibliothèque Royale, Bruxelles. Ms II.4085 (Fétis Nr. 2910). 53Schulze, Bach-Überlieferung, 101.
shows that it would have been proportioned movement-wise 1 : 2 : 3, with 400 bars of Gigues, 600 bars of Courantes, Sarabandes, and the second Menuets/Gavottes/Bourées, and 800 bars of Préludes, Allemandes and the first Menuets/Gavottes/Bourées, with 1 : 2, 2 : 3 and 3 : 4 proportions formed between the groups of movements.
It must be emphasised that this is a hypothetical reconstruction and that no 48-bar cello Prélude in C minor has survived, although a copy of an undated 48-bar Prélude in Eflat major for lute (BWV 998) from the 1730s has.54 Had BWV 998 originally been for cello in minor mode, it would havefitted perfectly into the implied 1800-bar plan. If Bach intended it to be copied into P 269, Anna Magdalena did not fulfil his primary wishes. It is not difficult to appreciate how a distracted copyist, however experienced, might have confused an instruction about two different lute preludes.55If Bach checked Anna Magdalena’s work,56and if he noticed the error, he let
it stand.
I suspect that this plausible and simple 1800-bar structure may have been the original plan for the Cello Suites, and that when the error had been noticed, practical expediency caused the last-minute introduction of repeat marks to the Préludes to create a perfectly proportioned collection for Schwanberg.
Table 5.18Perfect proportions in P 269 with a hypothetical 48-bar Prelude in BWV 1011
Bars counted as written, i.e. without repeat or da capo indications Movements Bars 1 : 2 2 : 3 3 : 4 1. Préludes* 436* 436* 436* 2. Allemandes 176 176 176 3. Courantes 318 318 318 4. Sarabandes 152 152 152 5. Menuets/Gavottes/Bourées 1 188 188 188 6. Menuets/Gavottes/Bourées 2 130 130 130 7. Gigues 400 400 400 Totals 1800 400 : 800 400 : 600 600 : 800
* indicates the hypothetical structure with a 48-bar prelude for the C minor suite
54
Ueno Gakuen College, Tokyo (J-Tuu). No callmark. Lute solo (BWV 998), copyist J. S. Bach. 55
Bach himself seems to have done the same in 1739 when he made the error in P 28, the fresh score of the St John Passion. SeeChapter 12.
The perfection of the 2400 : 2400 parallel between the Six Solos and the Six Sonatas suggests furthermore that, although the collection of Cello Suites in its 4000-bar version of P 269 had been perfected, Bach may have wished to revise its alternative, written total of 1975 bars by adding a further 425 bars. To do this, he would probably have expanded several of the freely structured prelude movements to create a simpler double 2 : 1 structure in 1600 : 800 bars and 4 : 2 movements, relating it more perfectly to the two violin collections, just as he expanded the early fugal movements in the Six Solos. I suggest therefore that, because of the perfect numerical parallel between the Solos and Sonatas, and the title-page association between the Solos and the Suites, Bach’s 4000-bar solution was an intermediate one for the Cello Suites, left in the hope of afinal revision that never materialised.
Although Bach composed other works for stringed instruments, some of which have survived in his handwriting, none besides these three were compiled and left as best fair copy collections. Proportional parallelism demonstrates the intentional perfection of the structure of each collection, despite the proposed interim solution of the Cello Suites. Furthermore, the numerical evidence confirms that the copies by Altnickol, P 229, and Anna Magdalena, P 269, represent Bach’s wishes faithfully, and that, aside from surface blemishes in the orthography, they bear the same numerical characteristics as an autograph manuscript, or publication overseen by Bach. The clues to Bach’s handiwork, implied in the constructional order of Kellner’s copy of the Five Solos, also show that P 804 is far more than a random collection offive works for solo violin.
There will always be those who desire an explanation or interpretation of the specific numbers that recur in these three related collections: 400, 800, 900, 1600, 2400 and 4000.57 Although a parallel meaning could be found for every number in these collections, it would be inconsequential compared with the eternal significance of the Harmony in Bach’s exquis- itely executed layers of 1 : 1 and 2 : 1 proportions.
57See J. ab Unterberg, Tractatus Historicus. . . Tractatus Philosophicus . . . Tractatus Theologicus De Mystagogia, sive de Mysteriis Numerorum (Augsburg: Klugheimer, 1734) for a
contemporary interpretation of numbers.
Well-Tempered Clavier Book One (BWV 846–69)
Inventions and Sinfonias (BWV 772–801)
Clavier Übung Part I (BWV 825–30) Clavier Übung Part II (BWV 831 & BWV 971)
Wann ich dann von unterschiedlichen Freunden, wie solche harmonia einzurichten sey, bin ersuchet worden, und ich meinem Nechsten mit der Gabe so mir Gott gegeben hat, zu dienen mich schuldig befinde: so habe nicht allein die Vortheile zum Bau diese harmoniae, sondern auch die Grundsätze zur Composition insgemein durch Mathematische demonstrationes, Gott zu ehren, und meinem Nechsten zum Nutz heraus zu geben nicht unterlassen können.
A. Werckmeister, 1701
The subject of this chapter is four collections for keyboard instruments. The first two have their origins in Cöthen or possibly earlier, and were revised and polished around the time the Bach family moved to Leipzig in 1723. The second two collections were born, revised and published amidst the intensity of Bach’s first twelve years in Leipzig.