Ordering Problems in J. S. Bach's "Art of Fugue" ResolvedAuthor(s): Gregory ButlerSource: The Musical Quarterly, Vol. 69, No. 1 (Winter, 1983), pp. 44-61Published by: Oxford University PressStable URL: http://www.jstor.org/stable/741800Accessed: 26/09/2010 22:50

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Ordering Problems in J. S. Bach's Art of Fugue Resolved

GREGORY BUTLER

ONE of the most tantalizing enigmas in Bach research has to do with Bach's final intentions concerning his last, posthumous publica-

tion, the Art of Fugue. Among the intriguing mysteries surrounding this collection is that involving the ordering of its various composi- tions. Almost all of the numerous proposals on this subject' to date have necessarily been highly speculative because concrete source evi- dence which might shed light on the question is almost completely lacking. However, vital evidence has recently been discovered which will be discussed in this essay.

The obvious place to begin any inquiry into the ordering prob- lems is with the augmentation canon2 which in the present disposi- tion of the print precedes the other three canons. It appears on three pages, 48, 49, and 50-recto, verso, and recto faces respectively. But this composition is clearly out of order in the print, for where there should be a page turn in the present pagination scheme, at the end of page 48, there is none. Yet, at the end of page 49, where no page turn is required, since pages 49 and 50 are facing pages, a page turn has been set up at the point where a half rest occurs in the upper part.3 (See Plate

This essay was presented at the Annual Meeting of the American Musicological

Society in New York, November 4, 1979. I am indebted to Christoph Wolff for several

valuable suggestions on the present text.

i The most recent thorough discussion of ordering problems in the Art of Fugue is that of

Wolfgang Wiemer, Die wiederhergestellte Ordnung in Johann Sebastian Bachs Kunst der Fuge (Wiesbaden, 1977), a detailed source-critical study of the original print.

2 Canon per Augmentationem in Contrario Motu, BWV 1080,4. 3 See Richard Koprowski, "Bach 'Fingerprints' in the Engraving of the Original Edition,"

in "Bach's Art of Fugue: An Examination of the Sources," Seminar Report in Current Musicol-

ogy, XIX (1975), 66. For his interpretation of this important piece of source evidence, see Wiemer,

p. 54. Wiemer, in his reordering scheme, has placed the augmentation canon at the end of the series of four canons simply on the basis of this discrepancy in layout.

44

Bach's Art of Fugue 45

I.) Clearly, in the original pagination scheme, these three pages must have occupied the opposite faces to those which they now occupy, that is, verso, recto, and verso faces. In such a disposition, the page numbers for the three pages in question would have been odd-, even-, and odd-numbered and further, what is more important for this study, these original numbers would have occupied the opposite upper corner of the plates to those which the present page numbers occupy, that is, the upper left-, right-, and left-hand corners.

I had been involved in detailed research into the engraving of Bach's Dritter Teil der Klavieriibung (1739)4 and one important aspect of that research centered on the erasure of original page numbers on the plates and the subsequent reengraving of corrected page numbers. In such a process, I found that inevitably telltale signs of erased page numbers remained in evidence, since the procedure of erasure is a delicate one with the danger of damaging the plates ever present. Thus, if the impression of the engraving tool in the copper is deep, at the deepest point of penetration the original incision remains, is filled with ink, and appears in the print.

In all cases I had dealt with in this earlier Bach print, the subse- quent reengraving of the emended page numbers had been over the original page numbers. But in the case of the Art of Fugue, I reasoned that if by fortuitous chance any of the original page numbers for these three plates had been engraved before the decision to change the position of this work in the ordering scheme, the same telltale signs of these original page numbers would be in evidence in the opposite upper corners to those in which the present corrected page numbers appear. With this in mind, I made a detailed examination of the pertinent pages in as many of the extant copies of the original print as possible. I was not disappointed.

I had noticed with considerable interest in a facsimile copy of the first page of the augmentation canon from the copy of the print in the Sibley Music Library, Eastman School of Music, Rochester,5 what appeared by all accounts to be a partially erased number in the upper left-hand corner of the plate immediately to the left of the "C" which opens the title. A closer examination of the original undertaken in the

4 In my as yet unpublished article, "New Research on J. S. Bach's Dritter Teil der

Klavieriibung," presented at the Annual Meeting of the American Musicological Society in Minneapolis, October 28, 1978.

5 Vault. M3.3.B118K. I wish to thank the Sibley Music Library, Rochester, for permission to photograph this source and for generous assistance.

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Bach's Art of Fugue 47

summer of 1979 confirmed my original suspicions. A close-up photo- graph of the partially erased number which initially had caught my attention was clearly a 7 (see Plate II) and a blowup of this erased number revealed more details. (See Plate III.) In the process of the erasure, the incision made by the engraving tool in the copper still remains below the surface of the plate and shows up as a telltale clear area with fairly well-defined borders. These "ghosts" were clearly in evidence here at the bottom of the downstroke in the seven, in the wedge-shaped period following it, and, most important, in an almost completely erased number preceding the seven.

This first digit of the original page number is almost indeciphera- ble, but there is definitely a clear area corresponding to the top half of this number. A painstaking study of this clear area suggests that it may represent the remains of an original 5. Certainly the diagonal upper- most stroke is uniquely characteristic of this engraver. The certain identification of the first digit of the original page number for what is now page 48 is not possible from the source evidence at hand. How- ever, for the purposes of this study, let us proceed on the supposition that the number in question is a 5 and that this page was originally

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48 The Musical Quarterly

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50 The Musical Quarterly

Figure 1

Present Ordering Scheme, Subsidiary Original Ordering Scheme, Section 2 Pagination Page 45 to End

32 Contrapunctus 11. a 4 1

33 2 34 3 35 4 36 5 37 Contrapunctus inversus 12 a 4 6 38 7 39 Contrapunctus inversus a 4 8 40 9 41 Contrapunctus a 3 10 42 11 43 Contrapunctus inversus a 3 12 44 13 45 Contrap: a 4 14 45 [Contrapunctus 14] 46 15 46 47 16 47 48 Canon per Augmentationem 17 48

in Contrario Motu 49 18 49 50 19 50 51 Canon alla Ottava 20 51 Canon all Ottava 52 21 52 53 Canon alla Decima 22 53 Canon alla Decima

Contrapuncto alla Terza Contrapuncto alla Terza 54 23 54 55 Canon alla Duodecima 24 55 Canon alla Duodecima

Contrapuncto alla Quinta Contrapuncto alla Quinta 56 25 56 57 Fuga a 2. Clav: 26 57 Canon per Augmentationem

in Contrario Motu 58 27 58 59 Alio modo Fuga a 2. Clav. 28 59 60 61 Fuga a 3 Soggetti 62 63 64 65 66 Wen wir in hoechsten Noethen

Canto Fermo in Canto 67

Bach's Art of Fugue 51

paginated as 57. Is such a pagination consistent with other internal and source evidence at our disposal?

If what is now page 48 was originally paginated as 57 as hypothe- sized, then the augmentation canon would originally have been in- tended to follow the other three canons as the last in the group of four. (See Fig. I.) Actually, this ordering accords with current thinking among Bach scholars for whom the placement of the augmentation canon in the print before the other three canons as the first of the group has always seemed most illogical. After all, in the autograph score of the work, P200,6 the augmentation canon comes after the octave canon as the fourth composition in a group of four. Also, from a theoretical and compositional standpoint, it is by far the most com- plex of the four canons, and as such would seem to serve as a logical and fitting culmination to the group.

In my unsuccessful search for traces of the original page numbers of the last two pages of the augmentation canon, I made another interesting discovery. In the empty upper right-hand corner of the second verso page, what is now page 49, there seemed to be a very small number engraved in the corner of the plate.7 (See Plate IV.) Even unmagnified the first digit was clearly a 2, while the second digit was unclear owing to the presence of a small fiber in the paper at this point. On magnification, the second digit was clearly a 7. The number 27 here would seem to be all that is left of a series of minute, hastily scrawled series of numbers indicating the correct sequence of the plates to the paginator.s This discovery serves to verify the pagination in Bach's hand which appears in the upper left-hand corner of each of the three pages of the Abklatschvorlage of the augmentation canon-

6 Deutsche Staatsbibliothek, Berlin, Mus. ms. Bach P200, Beilage 1.

7 This same detail of engraving is to be found in all of the exemplars of the print I have been able to examine, some ten in number. As for the erased original page number, it is clearly visible in only a small fraction of the sample examined. The copy in the Sibley Music Library, Rochester, which was used in this study and the copy of the second edition in the Gemeente Museum, The Hague, are outstanding in this respect. In some copies the erasures are only partially visible and in others not visible at all. This state of affairs is consistent with similar evidence in the Dritter Teil der Klavieriibung. It is also completely in keeping with the whole printing process, for such erasures would naturally be most clearly visible in the later impres- sions only.

8 There is an earlier precedent among the Bach prints for this procedure. In the third edition of the original print of Bach's Erster Teil der Klavieriibung (1731), a similar sequential aid is employed by the printer, in this case a series of letters rather than numbers. See Richard Jones, Neue Bach-Ausgabe, V/1 Krit. Bericht, p. 18.

52 The Musical Quarterly

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PLATE IV. J. S. Bach, Canon per Augmentationem in Contrario Motu, BWV 1080, 14 showing upper right-hand corner of page 49 magnified (Sibley Music Library, Rochester Vault.M3.3.B118K.)

26, 27, and 28.9 In light of the discovery of the original pagination of the Art of Fugue, a reexamination of this now verifiable subsidiary pagination scheme is clearly in order.

Employing the pagination 26, 27, 28 for the three pages of the

augmentation canon, if we count backward as the print is presently ordered, we arrive at the third page of Contrapunctus 8, the first triple fugue as page 1. This makes no sense at all.'0 If however we restore the

augmentation canon to its hypothesized position in the print, that is, occupying pages 57, 58, and 59, and count backward, substituting for these page numbers, 26, 27, and 28, we arrive at page 32 of the print, the first page of Contrapunctus 11, the second triple fugue. (See Fig. 1.) It

9 For facsimile reproductions of these pages, see Koprowski, p. 63, Plate III, and Wiemer, p. 78, Abbildung 1.

10 Wiemer's explanation is no less puzzling; see Wiemer, p. 14. He claims that the subsidiary pagination scheme relates to those plates for which J. S. Bach himself prepared the Stichvorlage. In doing so, he is forced not only to reorder the canons but to include at least one work, Contrapunctus 2, of which Bach is not the scribe.

Bach's Art of Fugue 53

can hardly be coincidental that it is precisely from this point in the print on, excluding the works transcribed and engraved after Bach's death," that Bach himself takes over as the scribe of the Stichvorlage with a minimal and mechanical contribution by his next-to-youngest son Johann Christoph Friedrich. 2

It is also significant that it is with page number 32 that the engraver of the page numbers begins to add a period after each page number and does so until the end of the print with the exception of pages 33, 34, 38, 39, 40, 52, 53, 54, and 61. Having drawn on precisely this sort of evidence in my study of the engraving and printing of the Dritter Teil der Klavierifbung,13 I concur completely with Wiemer who interprets this as an indication that the plates were paginated and therefore engraved in two distinct sections." However I believe that Wiemer's interpretation in this case, that the second of these sections begins only at the point where all page numbers have periods, is too narrow and arbitrary. Actually, all page numbers have periods from page 42 on (with the above exceptions), the second page of the recta version of Contrapunctus 13, the second mirror fugue, yet Wiemer arbitrarily and conveniently chooses page 45 as the first page of his second section.

However, it is the point where the periods first appear, page 32, which is significant, and this meshes with the two other pieces of evidence presented above. Pages 1 to 31 are the work of at least five different scribes'5 including J. S. Bach and Johann Christoph Fried- rich and constitute an earlier layer in the engraving. When Bach took over the exclusive preparation of the Stichvorlage of the second section of the work from page 32 on, he employed a subsidiary pagination scheme in which the first page of Contrapunctus 11 became page 1.

I I See Koprowski, p. 64. 12 See Koprowski, p. 66. This conclusion is supported and strengthened by Wiemer; see

Wiemer, pp. 63-64, n. 36. I refer to Johann Christoph Friedrich's contribution in the case of the mirror fugues as minimal and mechanical because it would seem most logical that J. S. Bach prepared the Stichvorlage for Contrapunctus 121 and Contrapunctus 131 as models for his son who then mechanically carried out the operation of melodic and contrapuntal inversion on each, probably with P 200 as a guide. This logical hypothesis would immediately establish the ordering of the pairs of mirror fugues in the original print as highly suspect, for J. S. Bach would almost certainly have prepared the Stichvorlage for the recta, and not the inversa member of each pair.

13 In this case, to establish that pp. 16 and 17 were engraved last of all in section I of the print and that their engraving was separated somewhat in time from that of the rest of the plates.

14 Wiemer, pp. 25-26. On the basis of paper studies, it is clear that the Dritter Teil der Klavieriubung was similarly pulled in two sections.

15 See Koprowski, p. 65, Chart 1.

54 The Musical Quarterly

The evidence brought to bear above strongly supports my initial tentative identification as a 5 of the almost indicipherable initial digit of the original page number for what is now page 48. Reordering of the augmentation canon to occupy its originally intended position in the print as the last in the series of four canons and the restoration to it of its original pagination, pages 57, 58, 59, raise certain questions. Another composition must originally have occupied the three pages now left vacant. This may have been an original composition which does not appear in P200 (like Contrapunctus 4 and the two canons at the tenth and twelfth, for instance) which was planned for in the original pagination scheme but which was never finished or was lost after Bach's death. Or, like Contrap: a 4, the original version of Contrapunctus 10-the second double fugue and the Fuga a 2 Clav:- an arrangement for two keyboards of the second mirror fugue, the composition which originally occupied these pages, was a duplica- tion of material already presented earlier and mistakenly included after Bach's death. In this case, the duplication may have been discov- ered, the composition removed, and the augmentation canon reor- dered to insert in its place.

Alternatively, the reordering may have occurred as a result of the decision taken after Bach's death to add the arrangement for two keyboards of the second mirror fugue after the canons. The obvious layout for each of the two versions, occupying two pages as they do, was on facing verso and recto pages of an opening. Since in the original ordering the augmentation canon which this posthumously added work would have followed ended with a verso page and since such a layout would have been impossible, the augmentation canon was simply reordered as the first of the series of four canons.

However, such hypotheses all involve decisions and operations which would have taken place only after Bach's death when, in fact, the original pagination of the augmentation canon in the print as pages 57, 58, and 59 was clearly part of Bach's pagination scheme. This is substantiated by his subsidiary pagination scheme. Since Contrap: a 4, presently occupying the three pages immediately preced- ing the augmentation canon, pages 45 to 47 inclusive, presents the version of the second double fugue found in P200, and thus duplicates material which appears earlier in the print, Bach could never have intended it to be included in the collection. Therefore, in his original ordering scheme, something else must have been intended to fill the gap of six pages, from page 45 to page 50 inclusive.

Bach's Art of Fugue 55

The earlier version of the second double fugue, Contrap: a 4, then must have been included by mistake after Bach's death. The arrange- ment for two keyboards of the second mirror fugue, the "unfinished" Fuga a tre soggetti and the compensatory chorale, Wenn wir in h6chsten N6ten sein, are all in the hand of the same scribe and must also have been added after Bach's death, since he would never have included an arrangement of material presented earlier in the collec- tion, an incomplete work, or an unhomogeneous chorale. Of these four posthumous pieces only one could conceivably have been des- tined for inclusion in the collection had Bach lived to see it through the press. And it is this work which would, I submit, have occupied the six pages between the mirror fugues and the canons--the incomplete quadruple fugue.

Christoph Wolff has established conclusively that this composi- tion was, in fact, virtually finished at Bach's death and that it was definitely to have been included in the Art of Fugue.'" As it appears in the print in its incomplete state, this work occupies five pages. It seems clear that the finished version would have fit nicely on six pages. If we examine the relative proportions of the three extant sections of this fugue, we notice a consistent diminution in the lengths of successive sections. Moreover, section 2 (78 measures) is almost exactly two- thirds the length of section 1 (115 measures), and section 3, not quite complete, occupies forty-six measures and conceivably in its complete state would have occupied approximately two-thirds the length of section 2 (52 measures). Adhering to the same proportions, section 4 may well have occupied approximately two-thirds the length of sec- tion 3, that is, approximately thirty-four measures. (For a schematic diagram of the fugue's sectional structure, see Fig. 2.) This would leave approximately forty-six measures for the concluding sixth page which is exactly the average number of measures per page for the first five pages as they appear presently in the print.

But, one will surely argue, this quadruple fugue was to have been the culmination of the work, a fitting close to the collection, citing the fact that it is the last work from the collection to appear in the print. But it has been established that not only the inclusion but the ordering of those works in the hand of the last of the numerous scribes must be regarded as highly suspect. In fact, that this fugue was intended by

16 "The Last Fugue: Unfinished?, in Bach's Art of Fugue: An Examination of the Sources," Current Musicology, XIX (1975), 71-77.

56 The Musical Quarterly

115 mm. 78 mm. 52 mm.? 34 mm.?

m. 1 m. 115 m. 193 m. 245? m. 279?

I, i II, I/II III, III, IV, I I/II/III I I/II/III/IV I

Figure 2. Schematic diagram of the quadruple fugue as completed

Bach to have been the concluding piece is I believe simply another of the Romantic misapprehensions attending this work.'7 Nowhere in the various contemporary documentary sources referring to it is it ever once referred to as the last work in the collection, but always as the last

fugue: Preface to the first edition-"die letzte Fuge"18 Preface to the second edition--"seiner letzten Fuge"19

Nekrolog-"in die vorletzte Fuge und die letzte"20 In fact, in the original ordering, the quadruple fugue was to have been the last fugue in the collection, but not the last work. This position was reserved for the complex augmentation canon.

If we restore the incomplete quadruple fugue to its proposed position in the collection, the logic of the resulting structure becomes evident at once.21 (See Fig. 3.) We have an unbroken series of fourteen

Contrapuncti followed by a group of four canons.22 The whole con-

17 For a similar Romantic misapprehension and its demolition, see Wolff, "Johann Sebas- tian Bach's 'Sterbechoral': Kritische Fragen zu einem Mythos," in Studies in Renaissance and Baroque Music in Honour of Arthur Mendel, ed. Robert L. Marshall (Kassel, Basel, Tours,

London, Hackensack, N. J., 1974), pp. 283-97. 18 Bach-Dokumente, hera usgegeben vomr Bach-Archiv Leipzig, Supplement zu Johann

Sebastian Bach Neue-Ausgabe saimtlicher IVerke. Band III: I)okumente zum Nachwirken Jo- hann Sebastian Bachs 1750 bis 1800, ed. and comm. Hans-Joachim Schulze (Leipzig, Kassel, 1972), p. 12.

19 Bach-Dokumente, III, p. 15. 20 Bach-Dokumente, III, p. 86. 21 For a discussion of ordering principles at work in this collection, see Wolff, "Ordnungs-

prinzipien in den Originaldrucken Bachscher Werke," in Bach-Interpretationen, comp. Martin Geck (G6ttingen, 1969), pp. 160-64.

22 This is, at least as far as the concluding canonic complex is concerned, consistent with Bach's approach in other late works. The Handexemplar of the Goldberg Variations, the Variations on Vom Himmel Hoch, and the Musical Offering all present intense canonic

Contrapunctus 1 (single fugue) Contrapunctus 2 "

Contrapunctus 3 "

First Contrapunctus 4 First SubSection Section

Contrapunctus 5 (stretto fugue) Contrapunctus 6. a 4 in Stylo Francese "

Contrapunctus 7. a 4 per Augment et Diminut:

Contrapunctus 8. a 3 (triple fugue) Contrapunctus 9. a 4 alla Duodecima (double fugue) Contrapunctus 10. a 4 alla Decima "

Second Contrapunctus 11. a 4 (triple fugue) Second SubSection Section

Contrapunctus inversus 12 a 4 (mirror fugue) Contrapunctus inversus a 4

Contrapunctus a 3

Contrapunctus inversus a 3

[Contrapunctus 14] (quadruple fugue

Canon alla Ottava (canon) Third

Canon alla Decima " Section

Canon alla Duodecirna Canon per Augmentationem in Contrario Motu

Figure 3. Structure in Original Ordering Scheme

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58 The Musical Quarterly

sists of three large sections each divided into two subsections.

Throughout the three initial subsections of each section a relatively simple fugal treatment of an ever-increasing number of subjects is

presented. Each of the three second subsections presents a more com-

plex, arcane, and recherche fugal type-stretto fugues with diminu- tion and augmentation of the subject in the first, mirror fugues in the second, and canons in the third.

From the evidence and conclusions provided above, I think we can draw further conclusions concerning the final stages in the history of the print. Before Bach's death, the completed plates for section 2, unpaginated, were put in order by the engraver, Johann Heinrich Schdibler in Zella23 with clear instructions concerning the pagination scheme. The paginator of the plates engraved all the page numbers on the ordered plates leaving a space of six pages for the as yet incomplete quadruple fugue. Meanwhile the Stichvorlage for the quadruple fugue may have been prepared by Bach. How much, if any, was ever

completed is impossible to say. Bach died and the quadruple fugue remained in an incomplete state even though its conclusion almost

certainly existed, at least in some rough sketch. Since Plates 51 to 59 had already been paginated, Schfibler was left with a gap of six pages in the original scheme. Whether he asked Bach for material to fill out the collection or whether manuscript material on Bach's work table after his death was sent to the printer by Bach's family is not clear. At

any rate, Schfibler decided to fill in the gap of six pages in the original ordering with material at hand. Since the quadruple fugue was in an

incomplete state, it could not be inserted in its originally intended

position, and for aesthetic reasons it was decided that it should appear at the end of the collection. The remaining compositions received, the earlier version of the second double fugue and the arrangement of the second mirror fugue, would clearly occupy three and four pages respectively and could not be used to fill the space.

Further source evidence, only recently come to light, suggests that

Schibler at one time considered inserting the chorale setting, Wenn wir in hochsten Noten sein, in this gap of six pages. Since, as indicated

"epilogues." As a whole, the organization in the Art of Fugue, as suggested in this study, has much in common with, and may well have been influenced by, the disposition of the section on

fugue in Johann Mattheson's Der vollkommene Capellmeister (Hamburg, 1739), where a long discussion of fugal writing involving an increasing number of subjects is followed by a conclud-

ing section on canon. 23 For the identification of the engraver, see Wiemer, pp. 39 ff.

Bach's Art of Fugue 59

earlier, Bach could never have intended to include this chorale setting in the collection, aspects of the layout and engraving of the work have never been really considered. However, it seems strange that the pages occupied by this work are not, as would be most logical, verso and recto faces so as to fill an opening and render a page turn for the work unnecessary. Recently, a close examination of the copy of the original edition in Bologna24 revealed the same telltale signs of an erased page number immediately to the left of the title of the chorale in the upper left-hand corner of what is now page 66 of the print. (See Plate V.) The period is clearly evident here, and the second digit' is quite clearly decipherable as a 7 identical in form with those in page numbers of the last layer of engraving in the collection. Unfortunately the first digit has been almost totally erased: all that remains is the prominent termination of a downstroke at the baseline and what would appear to be the beginning of a leftward descending diagonal stroke above and slightly to the left of this partial downstroke. Considering the form and position of the partial downstroke, it can only be part of one of two numbers, a 1 or a 4. The first possibility can be ruled out since the 1 of this engraver finishes at the baseline in a prong. This leaves the second possibility of a 4. The hint of a leftward descending diagonal would support this as would the resulting original pagination of 47, for such a pagination would place the chorale setting on the second of the three openings constituting the six-page gap. Although again this erased original page number poses problems of decipherment, the evidence strongly supports an original pagination for the chorale setting of pages 47 and 48. With what material Schiibler originally planned to flank the chorale setting on either side is impossible to say.

The idea was finally hit upon to reorder the augmentation canon, placing it before the other three canons while still retaining the grouping. This reordering could be achieved simply by erasing the original page numbers on three plates of the augmentation canon and by repaginating them with their present page numbers. The three- page gap still remaining was filled by the earlier version of the second double fugue entitled simply "Contrap: a 4." Finally, the arrangement of the second mirror fugue was inserted between the last of the canons and the incomplete quadruple fugue with its compensatory chorale.

I use the indefinite "Ordering Problems" in the title of this essay

24 Civico Museo Bibliografico Musicale. DD 72. I wish to thank the Civico Museo Bibliog- rafico Musicale, Bologna, for furnishing photographs from this source and for kind assistance.

60 The Musical Quarterly

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1 : . :•i,;:• i•': .

PLATE V. J. S. Bach, Art of Fugue. Upper left-hand corner of page 66, life-sized and enlarged. Civico Museo Bibliografico Musicale, Bologna. DD 72.

Bach's Art of Fugue 61

advisedly, for other problems remain. There is, for example, the obvious problem of the ordering within the two pairs of mirror fugues25 (not to mention their correct titles) which remains to be resolved satisfactorily. There are also further less obvious but no less puzzling questions.26 However, the above does offer compelling evi- dence establishing the position of the augmentation canon in the original ordering scheme and in so doing confirms what has until now been merely speculation. At the same time, based on this evidence, it posits a convincing hypothesis regarding the position of the enig- matic incomplete quadruple fugue in this original ordering scheme, a placement which until now has never been considered, largely, I believe, because of the Romantic aura of the "unvollendete" which has for so long attended it.

25 See n. 8 above. 26 Koprowski, p. 66.