Witting and Unwitting Allusion in JSBach

Texts and Contexts

Witting and Unwitting Allusion inCertain Keyboard Music of J. S. BachPeter Williams

Can one see apparent subtleties, seeming allusions, possible signifi-cances, in the music of such a composer as Bach and simply be unsurewhether they are deliberate or accidental, orto use better wordswitting or unwitting? I think the answer to that must be Yes. Perhaps,since some puzzles of this kind can be solved more confidently than oth-ers, it might be useful to categorize the different levels of certainty, todistinguish various steps between the "plausible or likely" and the"rather far-fetched" among the possible allusions in his music. Admirersof Bach could be more than usually anxious not to miss the significancesthe symmetries, golden sections, symbolisms, references to number,and stylistic imitationswhile being wary of seeing more than is reallyjustified. It also seems to be true that one can find other speculations lessconvincing, other "conclusions drawn from the evidence" more assertiveor even more pedantic, than one's own.

Bach scholarship today often gives the impression of being assertor-ial, using what it has collected as evidence in order to assert such thingsas that the B-Minor Mass is a vocal quintet, or that the harpsichord toc-catas are for organ, or that Bach used organ and harpsichord together inchurch for the basso continuo. At least such hypotheses draw on whatseems to be concrete evidence, rather than the free speculation offeredby many a study of gender in Cantata 140 or social hierarchy in theBrandenburg Concertos or rhetoric in the Musical Offering. But what ex-actly is "concrete evidence"? The problem seems to me not so much thatin a given topic contrary evidence can usually (always?) be assembled,but that what is evidencein any historical question whateveris aquestion that can only ever be answered conditionally.

We construct history from what we take to be facts and events, butcan do so only according to our understanding: Michael Oakeshott issurely right to claim that "evidence is not something, coming to us fromthe past, which has merely to be accepted," and that by definition, what

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Alliision in Bach's Keyboard Music 757

we call evidence cannot be anything more than "the testimony of oth-ers' experience." And because it is only this, it "can never take us out-side our own world of experience." Even when it comes to dealing witha historical fact or event, "anyone who has considered the matter knowswell enough how arbitrary the individuality of an historical event is."1The construct that is history is only ever part of a whole story, and, as Ihope to show from the following examples, often the most one can do isdistinguish between one kind of speculation and another, leaving ques-tions asked but not answered.

Numbers

In its settings of Lutheran chorales, the third volume of J. S. Bach's key-board music published in 1739 (Clavierubung 111) incorporated in variousways various allusions to the Holy and Undivided Trinity. For example,in the opening chorales the composer cited particular Kyrie tropes (Godthe Father, God the Mediator, and God the Spirit); and then he set theTrinity hymn "Allein Gott in der Hoh' " three times, rising in keys so asto circumscribe a major third (F, G, A) and developing three voices soas to produce three different kinds of trio.2 It could well have been partof this allusive program that he begins and ends the volume as a wholewith a piece in three flats (E-flat major); that each of these has threethemes; and that the total number of pieces in the volume is 3 X 3 X 3(27). Rather than some profound symbolism in these allusions, however,one might see merely a composer's way of reminding himself of (or per-haps inwardly saluting) the three-in-oneness that music is peculiarlyable to demonstrate. He must have been aware that of all things, musicoffers the clearest illustration of the dogma of the Trinity, its triple coun-terpoint the best analogy there is to the idea of three in one.

Such allusion is straightforward and has of course been the stuff ofcountless commentaries over the last half century, supported by varioushistorical "facts." One of these is that for full organ music of that period,E-flat major was uncommon and in fact rather new, not the kind ofthing a composer would do by accident, nor a key for which most organswould have had an acceptable tuning.3 Furthermore, some reasonablespeculations about the bar-by-bar workings of the prelude and fuguemight suggest that E-flat major was not the original key in which theywere conceived: D major is much more likely on grounds of style (anouverture-like prelude, an alia breve fugue), tuning (the passage in E-flatminor then becomes one in D minor), and playing manner (D major ismore idiomatic for the fingers, as players can test for themselves).


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758 The Musical Quarterly

Clearly, if that is the case and extra trouble was taken in this way, thenthe three flats look more than ever like a witting allusion, though againthere is hardly a symbol here, more a simple cipher. All this would stillbe so even if the pieces were actually conceived in their present key, forif D major is a kind of norm for such music, then it could mean that animaginative composer was, as it were, inwardly transposing as he com-posed his piece in E-flat. In addition, if he had recently got to know theE-flat ouverture in Francois Couperin's twenty-fifth Ordre (1730), thenanother kind of allusiveness might be operating, not so much to Couperinpersonally but to the up-to-date idea of having such music in any key.

In the case of the total number of pieces being 3 X 3 X 3 , otherfactors have to be borne in mind. Amongst the twenty-seven piecesare twenty-one chorales, as there can also be twenty-one movements inthe classical French organ mass (e.g., the five masses of Andre Raison[1688], probably known to Bach).4 So it is not out of the question thatthere is some allusion here to the "authority" of earlier organ music,though the twenty-seven could also and always remind the Lutheran or-ganist of the twenty-seven books of his New Testament. But in any case,if the three flats and the twenty-seven pieces can or do both functionas allusion, they do so in two different categories, visual and aural: threeflats are not heard and can only be seen and counted on the page. Per-haps one could argue that in listening to or playing the volume, one ishardly counting twenty-seven pieces either, but obviously they exist inthe way that three flats (mere notational tokens) do not. So do the threethemes of the prelude and the three sections of the fugue.

Amongst the other numbers arising in connection with ClavieriihungIII is one more puzzling: the curious fact that, as is often pointed out, thetitle page of a volume published when the composer was fifty-four yearsold contains fifty-four words. Perhaps one should resist smiling at thevery possibility that this was deliberate, since indeed it is not out of thequestion that a pious Lutheran would acknowledge his Maker's gift oflife by alluding to the number of years he had lived. But such a refer-ence, if that is what it is, would be in a different category from the oth-ers. For one thing, to make fifty-four, the words have to be counted oneway rather than another (i.e., with or without hyphens); for another, thenumber alludes to the composer's self, so it would be out of step with thevolume's other allusions; and for a third, any wordplay of this kind on atitle page can hardly have the same status as a large-scale musical planrunning to dozens of pages.

But note: fifty-four is twice twenty-seven, and thus the number ofwords on the title page of Clavieriibung III is twice the number of piecesit contains. One might feel obliged to assume that there are some further


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Allusion in Bach's Keyboard Music 759

significances here if only one could find them. For example, would anysuch doubling be in any way connected to the volume's pairs of choralesettingsa small setting following a larger, a pairing of the kind gener-ally said (though only conjecturally) to correspond to Luther's Greaterand Lesser Catechisms? But is doubling comparable to pairing? If so, arewe to bear in mind other classical dichotomies, such as good and evil,light and dark, Old Testament and New, Adam and Eve, major and mi-nor keys? Or is all this nonsense? Or, to put it more kindly, a conjecturetoo far? I think so, but it is the type of conjecture one often does meet inwritings on Bach, leaving one to ask just where it all stops.

B-A-C-HMany a simple allusion turns out not to be simple. Consider the appar-ent reference within certain works of Bach to the notes B, A, C, and H.Over the last two and a half centuries many instances of this group ofnotes in the contrapuntal lines of Bach's works have been observed, in-cluding suggestions that this or that instance is a transposed or reversedB-A-C-H, although one could claim that any kind of alteredB-A-C-H is a contradiction in terms.

Already in 1732, J. G. Walther had pointed out that these fournotes are, as he says, "melodic in their order," and went on to attributethis observation to "the Leipzig Bach," that is, Johann Sebastian (cor-recting this later to the Jena Bach, Johann Nicolaus).5 Clearly, B-A-C-His easy to recognize both as eponymy and as musical motif and must havebeen familiar enough amongst German organists of that time and place,appealing to their interest in musical games of various kinds, acrostics,puzzle canons, number symbolisms, quodlibets, and so forth. One won-ders whether the significance of these notes when they easily occur inthe natural order of thingsespecially in C major, F major, D minor,or even G-minorwould have struck earlier Bachs such as JohannChristoph (d. 1703) or Johann Michael (d. 1694), as they set choralesin these keys and produced lines with a glancing B-A-C-H in themfrom time to time.6

One questionable sighting can stand for others. In the Neue-BachAusgabe's Canonic Variations, the editor has been allowed to write"B A C H" into the closing bar, as shown in Example I.7 But this isspecial pleading. Not only are the four notes divided between twovoices, but, because they are, it was not necessary in the conventionsof the time to cancel the B-flat in one voice by writing in a B-naturalin another.8 In other words, neither is there a B-A-C-H motif in themusic nor is there one even in the notation, in either the print or the


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alia strcttaI \ a

Example J. Canonic Variations on "Vom Himmel hoch," BWV 769.5, closing measures, from NeueBach Ausgabe, ser. 4, Bd. 2, ed. Hans Klotz (Kassel: Barenreiter, 1957), 211. Reproduced by kind per-mission of Barenreiter Verlag.

autograph manuscript (see Ex. 2 for the print). So although the notesthemselves are there, any speculation (however charming) that theycontain a witting allusion has little down-to-earth support. It happensthat in C-major cadences, marked as they often are by a touch of chro-maticism, these particular notes are not at all unlikely to arise, and itcould be that no one needed special nudging to hear allusions here.9But that too may be a speculation too far.

A second simple puzzle about B-A-C-H also speaks for many oth-ers. When a Bach pupil came to write a fugue on a theme beginning onor containing only B-A-C-H he had a problem, because the motif be-longs to no obvious key. The opening note (B-flat) makes sense neitheras tonic nor dominant (the usual notes with which a fugue subject be-gan), nor even as leading note (which sometimes appears, as in F-sharpmajor in book 2 of The Well-Tempered Clavier (WTC II). Consequently,the pupil would have done best to follow the master's own policy in thetriple fugue of the Art of Fugue: this policy was to use it as a counter-point (i.e., a second or third subject, not a first) and to round it off witha cadence figure that fixed its key.10 Example 3a shows the completedsubject. Now it happens that in this form the fugue subject uses all sixnotes of the chromatic fourth, D-C-sharp-C-natural-B-B-flat-A,changing their order and so paraphrasing them as he so often did, butnow in a new way, and all the time remaining in D minor, which hadlong been the classic key of this ancient motif. The key itself, even per-haps the whole idea, of the Art of Fugue is probably to be seen as allu-sive: to mode 1 of antiquity, the first tone, tonus primus, le premier ton.This had also been the key of the five fugues sur le mesme sujet (same but


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Example 2. Canonic Variations "Vom Himmel hoch," BWV 769.5, closing measures, from a copy ofthe print Einige canonische Veraenderungen (Nuremberg: Schmid, [1747-48]).

B A C H

IJ r

Example 3a. Fugue subject from The Art of Fugue, BWV 1080.19, m. 193

Chromatic fourth

Example 3b. A rising chromatic fourth in the first tone

varied, like the Art of Fugue's) at the end of Jean-Henry d'Anglebert'sPieces de clavecin (1689), whose ornament table had been copied out byBach while he was still in his twenties.

Hence the second puzzle arising from B-A-C-H: did the composerwittingly expand it into a paraphrased chromatic fourth, as shown inExample 3 ? Perhaps, for he uses no more and no fewer than those sixnotes, and very many of his previous works in D minor had incorporateda conspicuous chromatic fourth, plain or paraphrased, often in the latterstages of a work. For French composers, the fugue grave in D minor hadbecome traditionally associated with the chromatic fourth, actually re-ferred to by Gilles Julien as les cromatiques dans le premier ton (Livred'orgue [1690], preface). This fourth is otherwise rare in the twentypieces of the Art of Fuguestrange, considering how many chromaticfugues in D minor there had been since the time of Frescobaldi or John


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Bull. It must have seemed a worn-out compositional idea, redeemed inthis instance by incorporating into it B-A-C-H.

Major and MinorIn turning to the books of The Well-Tempered Clavier, one finds manypuzzles, even as to whether one is right to speak of a Well-TemperedClavier, book 2, at all. Either way, both books begin in C major, but why?For organists the classic first key had been D minor, which traditionallyalso had neither flats nor sharps. (Nor of course did the first scale pro-pounded by many earlier theorists, the one beginning with the first letterof the alphabet, A.) Even if Bach was following recent convention instarting with C major as the first key for a set of secular keyboard fugues,as he was, it was not inevitable that it would be followed by the minorversion of the same key, this by the next major key up a half step, andso on, even if all twenty-four keys were by now involved.11 A fantasiaby the Dresden musician Friedrich Suppig, exactly contemporary withWTC I and going "through all keys major and minor," was composedwith a much more logical order in its keys, one of several possible butparticularly useful here for modulating in the course of a single piece ofmusic:

C-a-F-d-B-flat-g-E-flat-c...For whatever reason, previous collections by Bach himself had followedother key orders:

C-c-d-D-e-E-F-C-sharp-c-sharp-e-flat-f

for the preludes in the Clavierbuchlein W. F. Bach that are found again inother versions in the WTC I; and

C-d-e-F-G-a-b-B-flat-A-g-f-E-E-flat-D-c

for both the two-part and three-part inventions in the same volume.12That the WTC's order is not musically compelling or even logical,

though neat enough on paper, is now largely forgotten, so thoroughlyhas it governed perceptions more or less ever since.13 It is the wordwohltemperirt that has attracted and still attracts most attention. Butperhaps there is a fundamental misunderstanding herein seeing TheWell-Tempered Clavier as being about tuning and temperament, or insurmising that its purpose was to show what or how one could play inall twenty-four keys on a keyboard suitably tuned. The whole questionof temperamentwhat "well-tempered" means in this instance, how totune it, and how these pieces once and for all vindicate (and were meant


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to vindicate) the twenty-four key diatonic systemis now deeply en-trenched in a wide range of musicological and organological thinking.The composer's liking for all keys was remarked on in his Obituary and issupported by the evidence that he transposed several pieces for theWTC, doubtless more than extant sources now suggest.14 It is not sur-prising, therefore, that writers have been (and still are) drawn to varioustemperament minutiae in connection with the WTC.

But something else is surely much more likely: that an intenselycreative composer would find tuning and temperaments nothing like asinteresting as another pressing musical detail brought out by thesepieces, namely the difference between major and minor. Here, "differ-ence" refers not so much to how the triads and keys are tuned as to howthey behave, how they stimulate very different musical compositions,how they feel under the fingers. For example, notice how patently themajor triads and minor triads are sounded at the beginning of severalpreludes, including the opening chord of the C major, with its doubledmajor third in the sensitive part of the aural spectrumone cannot get amore major sound than this. Or how very differently the triads of, say,the G-major or C-sharp-major preludes are laid out from those in E-flatminor and B-flat minor. Every player responds to this difference, wit-tingly or unwittingly.

The composer's title page supports the idea that the major-minordifference was in his mind, for there he spells out what major and minorthirds are and yet says nothing about actual tuning.15 Furthermore, as ifconfirming the point, he spells out the thirds by means of the old sylla-bles, which writers of the previous generation such as Speer or Niedt hadeither rejected or ignored.16 In addition, the two "Rules for GeneralBass" in the Anna Magdalena Book of 1725, though very brief, also sug-gest that what was important was the difference between major and mi-nor, especially perhaps to people still exposed daily to music not yet to-tally diatonic: their quasi-modal hymns and motets. The first of theserules, written by J. C. F. Bach, describes the two scales (major and mi-nor) and two triads;17 the second, written by A. M. Bach, describes thetwo triads and their notation.

It is perhaps in the nature of literate studyreading, writing, learn-ing, teachingthat a formal title such as Well-Tempered comes to pro-vide more of a focus than the intimate details of the music itself, wherethe contrast between tonal dialects is rather to be felt than defined. Butnote that the two points I have made so far about The Well-TemperedClavier are.already different in weight: the aim of the volume is rathermore speculative than why it begins in a particular key. And there areother questions open only to speculation.


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Hexachords?

One question I have asked myself is what significance, if any, there is inthe strange fact that the opening fugue subjects of the two books (in Cmajor) derive from no more and no fewer than the first six notes of thescale of C major (Ex. 4). The second of these is especially ingenious: de-spite its length, it never goes above or below the same notes andcanthis be accident?could hardly be more different from the first, in pre-senting a canzonetta-like subject in an up-to-date time signature.18

Now these six notes, C, D, E, F, G, and A, are specific and have avenerable history. They constitute the hexachord of early medieval mu-sic theory, used for the notated examples in the ninth-century MusicaEnchiriadis and called the "natural hexachord" by later theory (a termi-nology ultimately reflected in modern usage when we speak of C majoras having no sharps or flats but only naturals). Whether it was from earlyinstruction in the rudiments or from more recent reading that Bachknew of such traditions is unclear to me, but it could have been throughAndreas Werckmeister (with at least some of whose other writings hewas intimate), or his cousin and colleague in Weimar, Johann GottfriedWalther, or even the recent gossipy references to music of antiquitymade by Mattheson.19 Some recent writers had been discarding the sixsyllables of old theory and pedagogy, finding them less useful as aids forteaching than the seven or eight note names as we now have them.20That Bach, however, was wittingly acknowledging tradition is suggestedby the old syllables mentioned on the title page of The Well'TemperedClavier (see note 15). Perhaps there was a conscious allusion here toKuhnau's Clavierubung title of thirty years earlier, both in the syllablesand in the reference to thirds:

Partien aus dem Ut, Re, Mi, oder Tertia majore eines jedweden Toni.(Kuhnau)durch alle Tone und Semitonia, sowohl tertiam majorem oder Ut Re Mianlagend. (Bach)

Note that the predecessor is again being superseded: the younger com-poser is making use of Semitonia as well as Toni, and indeed all of them.

On a title page written in much the same part of Germany, Fried-rich Suppig (mentioned earlier) had used only the up-to-date terms ornote names, no longer the old sol-fa syllables.21 Saluting old traditionsis something one can easily imagine of J. S. Bach, but he would also bejoining those earlier composers who had composed C-major fugues withsubjects apparently derived from the same six syllables. Examples probably


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Natural Hexachord

Example 4- Subjects of the fugues in C major, WTC 1 and WTC 11, with the notes of the hexachordumnaturalis

known to him include one or two by Buxtehude (the praeludium BuxWV138 and the canzonetta BuxWV 167). It could be, therefore, that anysuch examples by J. S. Bach are "modernized" versions of the old Ut-Re-Mi-Fa-Sol-La fugue subjects of such composers as Froberger (Fanta-sia I [1649]) and, though of course less and less likely to be known to J.S. Bach, his predecessors Frescobaldi, Sweelinck, Bull, and Gibbons.22

In the case of Samuel Scheldt's Tabulatura nova of 1624 (part 2), allfive free-fugal movements had been based on subjects apparently derivedin much the same way from various hexachords, not C-D-E-F-G-A inthis case but A-B-C-D-E-F or G-A-B-flat-C-D-E-flat or G-A-B-C-D-E. Perhaps Scheldt knew the second volume of Zacconi's Prattica dimusica (1622), whose chapters 52 and 53 recommend the ascending anddescending hexachords as contrapuntal subjects. Athanasius Kircher'sMusurgia universalis of 1650 (pp. 466 ff.) had also used the same Fro-berger fantasia as a model of keyboard music (see more on this later).Was it ultimately such books as these, and/or the tradition they them-selves reflected, that lay behind hexachordal fugue subjects in later andvery different music, such as Reincken's Hortus musicus (c. 1687) or Al-binoni's Suonate a tre (1694), both in part arranged or recomposed byBach? Albinoni's are in A major and B-flat, keys more at home withstrings than the keyboardist's C major, into which key the latter hasbeen transposed, presumably by Bach (BWV 946). This is also the keyof one of C. F. Pollaroli's two capricci copied in the Andreas Bach Bookby J. C. Bach (the other in D major), both of them built on the samesix notes.

Such a parade of names suggests that if Bach did not derive the C-major fugue subjects of The WelUTempered Clavier from the six genera-tive notes of antiquity, and if the second of them was not created topresent maximum difference while using the same notes as the first, thenwe have a startling coincidencein fact, two. That is hard to believe,especially since other C-major fugues in other genres, such as the organ


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praeludia BWV 531, 545, and 547, the sonata BWV 529, the orchestraloverture BWV 1066, and the violin sonata BWV 1004, have subjectsthat appear to be as free as those in any other key, with fewer or morenotes than the natural hexachord. The opening C-major fugue of J. K. F.Fischer's collection Ariadne musica of 1702 is close to being hexachordal,and since WTC I seems to share some theme types with Ariadne musica,Bach's subject looks like some allusion.23 Perhaps he even had a particu-lar predecessor in mind: the extraordinary survey of stretti in the C-majorfugue in WTC J might have been originally inspired by certain incipientbut undeveloped stretti in Froberger's Fantasia I (see Ex. 5a and 5b). Thefantasia is likely to have been known in the Bach family circle, for notonly was Froberger evidently admired by Sebastian (see Beisswenger, 285n. 4) but it was one of the few German fugues available in print, its pub-lication in Kircher's Musurgia ensuring a wide, influential, and lastingcirculation.

Perhaps there are two respects in which the opening C-major fugueof WTC I can be seen as a particular instance of the "anxiety of influ-ence." I take this now famous phrase to be appropriate to J. S. Bach notin the sense of a poet's troubled desire to put right what previous poetshave written (anxiety, a "mode of melancholy")24 but in the more posi-tive sense of anxiety: the composer is anxious (is very keen, as we mightsay) to take up Froberger's ideas for stretti, and this for two reasons. First,to pursue them more thoroughly and concisely, using a comparable butupdated hexachordal subject and developing its stretti to such a degreethat the fugue (including the exposition) is irregular, exceptional, andquite impractical as a model for the student. His subsidiary motifs or six-teenth-note figurae are also very similar to Froberger's, as Example 5shows. Secondly, to do so for purposes of publication. If the WTC I (inits form as a fair-copy compilation complete with title page) had beeneven partly planned to succeed Fischer's Ariadne musica as a publishedcollection, all the more reason to allude in its first fugue to long-standingtradition: to the first of Froberger's fantasias, itself surely an allusion tothe first of Frescobaldi's published collection of Capricci (1624), whichwas also based on the natural hexachord.

Tetrachords?The hexachord is not the only token of ancient authority one mightdiscern in the mature keyboard work of J. S. Bach. Amongst the twenty-seven pieces in Clavierubung III is the puzzling penultimate group of four,the so-called Four Duets, models of fugal and imitative composition, per-haps included in the volume for this very reason.25 The keys of E minor,


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- ^ J J*" J * J_J ir r ' v :

^ J, ^jl^J-LJ t i t /

r r r L-^

j

Example 5a. J. J. Froberger, Fantasia no. 1 (1649 book), from m. 54 (note values halved)

r-y-

Examp/e 5b. J. S. Bach, Fugue no. 1 (WTC /, BWV 846.2), from m. 14

F major, G major, and A minor (or the notes E, F, G, and A) seem tohave some significance, bearing in mind that key sequences of variouskinds are found elsewhere in these volumes. Rising by step over fournotes is clearly the result of witting organization, but is there more?Perhaps an allusion to one of the old tetrachords as they had been trans-mitted by many intervening theorists? In J. G. Walther's Lexicon of 1732,for example, upper- and lower-octave versions of these same four notesare described and illustrated, here rather more clearly than in Walther's


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earlier treatise, the Praecepta of 1708.26 In both of Walther's references,these particular four notes are conspicuous by being the top of theknown Greek scale, the tetrachordum excellentium.

Why there might be a rising tetrachord behind the keys of the FourDuets is a question open to various answers. To allude in this way wouldbe to share some of the tetrachord's authority, or at least to acknowledgeancient authority in a manner concordant with other didactic aims ofthe twenty-seven-piece volume. Some of these aims are obvious: thebook includes music in characteristic German, Italian, and French styles,some ancient, some new; its melodies are associated with Luther's Ger-man paraphrases of Latin texts and even the Greek Kyries; there is bothstrict counterpoint and free, with various examples of stile andco and stilemoderno, of Palestrinian textures and galant chamber trios; and there isa whole catalog of essays in two crucial musical forms (ritornello andfugue). The Four Duets are extraordinarily strict pieces of two-voicecounterpoint, entirely unconnected with the Lutheran chorales in thevolume and not explicitly part of the volume's liturgical plan at all.27Instead, they offer paradigms of contrapuntal imitation, such as that thefirst, in E minor, is a demonstration of (amongst other things) a doublefugue of invertible counterpoint so tightly organized that every note init derives from subject or countersubject.28

The Duets of Clavierubung III are learned pieces as even the com-plex Kyries at the beginning of the book are not, and yet at the sametime they are practical, playable, striking, original, self-contained, andquite different from any textbook's examples and indeed from the Two-Part Inventions and much older duo genres such as Pachelbel's Magnifi-cats. To salute the tetrachord of ancient musical theory with four exam-ples of new musical practice (Ubung) is appropriate in a way characteristicof the composer, especially as the four notes when given modern form astonics produce symmetrically arranged modes (minor, major, major,minor). Had the keys or diatonic tonalities been differentsay, E major,F major, G minor, and A minorthe argument on behalf of tetrachordswould be far weaker. In addition, that they are a close-knit group is sug-gested by the four different time signatures (surely deliberate, part of thecomprehensive "survey" the Four Duets provide), as is the possibilitythat in both theory and practice they were calculated to have the samepulse or beat. (This last may well have been the case already with thethree movements of the Italian Concerto in Clavierubung II.)

There is another possibility arising from these four notes, E, F, G,A, but more speculative and without obvious musical point. The volumeas a whole begins with a piece in E-flat major, which ends on the tonic;and eventually, following the Four Duets, it closes with a fugue that be-


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gins on a B-flat. Now between E-flat and B-flat lie the Duets' four notes,E, F, G, and A, so that the opening E-flat rises to the final B-flat via atextbook tetrachord. But so odd a progression results that to suggest thecomposer wittingly arranged it seems another speculation too far. Whenthe harpsichord partitas follow a key order (B-flat, C, A, D, G, and E)that moves logically to the very next chord that Bach published (Fmajor, at the beginning of the Italian Concerto), the order is rational,straightforward, and even strikingly melodious. Furthermore, somesuch link between the volumes of Clavierubung 1 and 17 is suggestedby the original announcement of a seventh partita, which either neverappeared or became (part of) Clavieriibung 11 as we know it.29 Clearly,key sequence was an important means of organization for J. S. Bach.

But for Clavierubung 111 to incorporate the order E-flat, E-natural,F, G, A, and B-flat is not straightforward, partly because twenty-oneother pieces come between the first and second, and partlythis is astronger objection, I thinkbecause the order makes no musical sense.These notes belong to no scale, and I cannot imagine what the order'stheoretical or practical significance might be, although doubts, ghosts offears that one might be missing something here, do still linger.

Clavieriibung''s French PiecesThe title Clavierubung, signifying "practical music for keyboard" andappearing to be quite self-effacing, was doubtless an allusion to publica-tions appearing in Leipzig from a previous and highly respected Thomas-kantor.30 Together, Bach's four volumes produce a monument to key-board music at its most elevated: suites (I and II), variations (IV), aconcerto (II), fugues (all four), canons (III and IV), preludes (I and III),ouvertures (all four), trios (I, III, and IV), and chorales con e senza pedale(III), all as varied between themselves as the genre parameters would al-low, and across an intricate range of styles greater than that adopted byany other composer during the whole of their period. There are manyunknowns about the volumeswhether, for instance, some or even allwere composed for or had some connection with Bach's eldest andbeloved son Wilhelm Friedemann, whether the third volume is a kindof written-out model organ recital, as often claimed today, whether theGoldberg Variations originated as the anecdote says and are correctlycalled "Part IV" (as made conventional by the Bach-Gesellschaft andNeue Bach Ausgaben), and so on. Musical questions abound, such aswhether the six partitas, arguably the most original in conception of allharpsichord suites, were a response (again under the "anxiety of influ-ence" already mentioned) to one or another set of recent publications in


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Paris, or to a set of interestingly galant violin sonatas published nearby inthe same period.31 If the partitas were such a response, they soon lostsight of what they were responding to.

But there is a quite different puzzle about the Clavierubung. In themiddle of all four volumes, and nowhere else, there is a movement solelyin the French style, a piece in the form of an ouverture (I, II, and IV) ora fugue (III): the fourth of six partitas (I), the second of two pieces (II),the fourteenth of twenty-seven organ pieces (III), and the sixteenth ofthirty variations (IV). (The fugue of Clavierubung 111 anticipates the onein the Art of Fugue that the 1751 print labeled in Stylo Francese, withwhat authority is not known. Note that in the autograph version, thistoo is a middle movement: no. 7 of thirteen regular fugues.) The symme-try within the Clavierubung volumes is there to be seen on paper and isprobably more theoretical than practical, that is, a timed performance ofthe complete volumes need not find those pieces at the halfway point.But they do largely occur halfway through the paginations: in book I, onpage 33 out of a total of 73 pages; in book II, on page 14 out of 29 pages;in book III, on page 39 out of 77 pages; and in book IV, on page 16 outof 32 pages. The only one not literally halfway through the page count isthe first, leading to a speculation that Bach, having spotted the physicalnear-symmetry of the first volume when the six separate pieces were col-lected together in one publication, makes sure that the other three vol-umes were more "accurate" in this respect. Especially since more thanone engraver was at work, it has to be possible that the composer over-saw the pagination in some way.

From the point of view of symmetry the Goldberg Variations areparticularly striking, as there are thirty-two pages and thirty-two pieces,each of which contains thirty-two (or sixty-four) bars developed from astandard chaconne bass of eight bars. In addition, each movement is intwo equal halves (thus 16 + 16, which is not at all common in binaryform), and an ouverture is piece no. 16 on page 16. Furthermore, themusic of each variation has a phrasing of two and four measures (evensometimes one measure), much more explicit than is usual with Bach,and only his inexhaustible invention prevents this from being tiresomelyobvious. But note: all these twos and fours represent not so much num-ber symbolism as simple symmetry, an orgy of binary multiples that issurely the product of calculation, though one by no means forced on theplayer's attentionnot even visually (the last of the thirty-two move-ments is not written out, being a da capo). Nor can all the factors of twobe serving as some arcane allusion to the volume's number IV, for thisdoes not appear.


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Allusion in Bach's Keyboard Musk 771

As to the idea of a French overture halfway through a volume, thears rhetorica in its various manifestations had long recognized the ideathat a "new start" could be made at the midpoint of a presentation ofsome kindan advocate's appeal, a pastor's sermon, and so on. This isthe so-called inner exordium of the Latin rhetoricians, who pointed outwhat those planning any kind of speech or lecture learn: that as you ad-dress an assembly, there can be a great effect in (as it were) starting againhalfway through, returning to an opening idea and now developing itwith new emphases or in new directions. Perhaps in this way a composermight be consciously alluding to classical rhetoric such as it was taughtin universities (Leipzig, Jena), choir schools, and gymnasia. That noneof the four volumes is a single or unified "work" as a sermon or speechwould be, with a single coherently organized beginning, middle, andend, need not affect any paper plan it might have had: organizationclear to the eye need not be to the ear.

But the idea of the inner exordium does not help one solve anotherpuzzle. Consider the four volumes of music opened in the middle: fourpieces in French overture style, the first in D major, the second in B mi-nor, the third in E minor, and the fourth in G major. In the order of thevolumes these are relative keys: D major-B minor, E minor-G major.Now is that deliberate or accidental? Why would a composer do sucha thing? Would he really plan, in the course of sixteen years or so, fourmajor volumes with this in mind? The keys are even symmetrical inanother way: the outer are dominant arid tonic in the major (D and G),the inner dominant and tonic in the minor (B and E). If one went fur-ther and pointed out that the four notes can also be so ordered as to pro-duce one of the Gregorian Te Deum's characteristic and returning motifs(B-D-E-G), few musicians now would not think this a speculation toofar. But whatever the explanation, the relatives and dominants are thereto be seen.

The point here is that if the key plan of the four French overtureswas calculated, then we have to say that the Goldberg Variations are inG major because the middle movement of a volume published over adecade earlier was in D major. But that is unbelievable, especially sinceit is clear that the Goldberg's bass is related to other variation works inG major, including sets by Purcell (Ground, Z 645), J. C. Bach (d. 1703;a sarabande), Handel, and Gottlieb Muffat (Componimenti, [1739]).32It looks as if there had been some kind of common-property chaconnetheme in G major circulating from the later seventeenth century onwardand useful for improvisations, a musical idea of which Bach was quiteaware and to which he alluded once again by "extending" it beyond


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recognition. His theme of thirty-two measures was four times as longas the other examples, as they in turn had been twice as long as theirancestorthe original descending tetrachord of many an earlierchaconne, including one in this G major form (G-F-sharp-E-D) for thefinal piece in Corelli's widely circulating Sonata a tre, op. 4-

Now just as there were good "external" reasons why the Goldbergwas in G major, so there were for the keys of the three other Frenchmovements in Clavieriibung. D major for the first fits in with the planof the six partitas (B-flat, C, A, D, G, and E); B minor for the secondmay have been created specially for the volume (to be as remote fromthe Italian Concerto's F major as possible); and E minor for the thirdmatches other key schemes in the book (thus the pair D-E for the Credochorales matches E-D for the following Paternoster chorales). So thereseem to be two choices. If the Goldberg's G major is not the result ofsome long-term plan, then this particular symmetry in Bach's four vol-umes is accidental, and the pattern of keyswhich is a purely musicalidea, without religious or other nonmusical allusionhas been the resultof chance and is not even incontrovertible. If, on the other hand, by thetime of the fourth volume of Clavierubung, the composer had spotted theemerging pattern and wanted to keep it up, he wittingly developed atheme for the variations that had long had traditional associations withG major. Which is the more credible?

Perhaps the best way to think of such puzzles is that chance is thewrong word: we would do better to think in terms of witting and unwit-ting, and conclude that Bach was the kind of thinker who could createpatterns both wittingly and unwittingly. He could begin deliberatelywith one pattern, as with the keys of the partitas, and this could gener-ate other patterns not at first planned in the same way. Or he couldknowingly inherit an idea, such as that a collection of fugues begins witha C-major hexachordal subject, while at the same time have his ownhabits of which he might not always have been aware (e.g., for a piece inF major he would often introduce E-flat as its first accidental; see WTCI, Prelude no. II).33 Even in vocal music, whose whole raison d'etre is toallude to the text and mark it in some way, one can distinguish betweenthe specific use of a purely musical device (sudden octaves for "all atonce together," in the opening chorus of BWV 201) and the automaticuse of certain intervals or harmonies long associated with portmanteauwords (Kreuz, weinen, resurrexit, seufzen, jauchzet, etc.). Much can beand frequently is written about these last associations, but so ingrainedand conventionalized are theyfar more than any of the symmetries de-scribed herethat one cannot always take them to have been wittinglymade use of by the composer.


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Notes1. Michael Oakeshott, Experience and Its Modes (Cambridge: Cambridge UniversityPress, 1933), 116-17, 122.2. A cantus firmus, a trio, and a fugue. Significantly or not, the first of these is the onlypiece in the volume to be headed a 3 although some other chorale settings are in threeparts.

3. Johannes Mattheson, Grosse Generalbass'Schule oder exemplarische Organistenprobe(Hamburg, 1731), 244, points out that the key was unfamiliar to most organists, un-known in the repertory (including hymns), and unsuitable for some organs.4. It is not quite that the "theme of the Passacaglia" BWV 582 is possibly derived fromthe "theme" of a Christe in Raison's second mass (so described in Kirsten Beisswenger,]ohann Sebastian Bachs hlotenbibliothek [Kassel: Barenreiter, 1992], 369), but that the sub-ject of the passacaglia's fugue is the Christe's ostinato bass, now transposed to C minor.The distinction is important, for the latter suggests that BWV 582 may have begun as a"fugue in C minor on a theme of Raison." If die five sets of hymn variations in De Grigny'sLivre d'Orgue (1699; copied by Bach) are counted as five single pieces, there are twenty-seven in total.

5. Johann Gottfried Walther, Musicalisches Lexicon (Leipzig, 1732), 64: "in ihrer Ord-nung melodisch." For the correction to Johann Nicolaus, see Werner Neumann andHans-Joachim Schulze, eds., Bach-Dokumente, vol. 2 (Kassel: Barenreiter, 1969), 231-32. In his earlier Praecepta (see note 19), Walther thought that Guido could have beenreferring to his own name when he introduced the bottom or gamut G-clef; thus Waltherwas linking a personal name to a note name.

6. E.g., Johann Michael Bach's two settings of "Ich ruf' zu dir" in the so-called Neu-meister Collection.

7. Hans Klotz, ed., Die Orgelchorale aus der Leipziger Originalhandschrift, ser. 4, Bd. 2 ofJohann Sebastian Bach, Neue Ausgabe sdmtUcher Werke (Kassel: Barenreiter, 1957), 211(BWV 769, original print). For some reason, Klotz does not add it at the correspondingmoment in the MS version on p. 105 (BWV 769a, autograph). On the other hand, hemarks it in another movement of BWV 769a (p. 112), but not at the correspondingpoint of BWV 769 (m. 207).8. I.e., in this instance, in either the printed or the manuscript version.

9. See, e.g., the last five bars of the C-Major Sonata for Organ, BWV 529.10. It seems likely that W. F. Bach was correct when he said (as reported in PhilippSpitta, Johann Sebastian Bach, 2 vols. [Leipzig, 1879], 2:685), that only here did hisfather, being "no fool," make use of his name as a fugue subject.11. The tendency for collections of liturgical organ music to begin in modes 1, 2, or 3(D, G, or A minor) is clear in Frescobaldi and Froberger, who in other kinds of musicwould begin in C major (Frescobaldi's twelve capriccios of 1624 and Froberger's sixfantasias of 1649).12. Suppig: "Durch alle Tonos nemlich durch 12 duros and 12 molles, zusammen 24Tonos." See Friedrich Suppig, Labyrinthus musicus Calculus musicus: Facsimile, ed. RudolfRasch (Utrecht: Diapason, 1990). The Three-Part Inventions (Sinfonie) are lacking thepresumed last piece, plus half of the penultimate. Vestiges of the Clavierbiichleiris order of


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preludesminor before major when it has a simpler key signaturecan be seen in anearly copy of WTC I (SBB P 401, of 1722-23).13. As in modern editions. Starting at C major and going up by step is the order stillfound in the newest Buxtehude edition (Dietrich Buxtehude: The Collected Works, vol. 15,ed. Michael Betotti, [Williamstown, Mass., 1999]. Presumably, it was the Neue Bach Aus-gabe volumes of the free organ works that established this new and quite anachronisticordering.

14. Hans-Joachim Schulze, ed., Bach-Dokumente, vol. 3 (Kassel: Barenreiter, 1972), 88.15. "[D]urch alle Tone und Semitonia, So wohl tertiam majorem oder Ut Re Mi anlagend,als auch tertiam minorem oder Re Mi Fa betreffend."

16. For Speer, see note 20. That it was J. S. Bach who used Friderich Erhard Niedt'sMusicalische Handleitung oder griindlicher LJnterricht, vol. 1 (Hamburg, 1700) in thefigured-bass treatise Vorschriften (1738; see Beisswenger, 366) is more conjectural thanoften appears, for example in Pamela Poulin,}. S. Bach's Precepts and Principles (Oxford:Clarendon, 1994). Niedt's teacher was Johann Nicolaus Bach, referred to earlier.17. The minor scale described here is C-D-E-flat-F-G-A-flat-B-ftat-C, up and down.Here too the fourth is described as klein, the fifth and octave as vollig, i.e., the fourth hasalways to be tuned smaller than it should be because the fifth is always tuned perfect. Butthat sounds impractical.

18. Canzonette or canzone as understood by German organists post-Buxtehude arelively keyboard fugues in almost unbroken semiquavers and with a "bright" cadence,such as the Canzon in C Major, BuxWV 166, whose subject too shares some characteris-tics with Bach's. I have outlined the possible significance of duple time signatures in"Considerations sur la nouvelle mesure a 2/4 au debut du XVIIIe siecle," in he mouvementen musique a lepoque baroque, ed. Herve Lacombe (Metz: Serpenoise, 1996), 85-98.19. Hexachord syllables mentioned briefly in, e.g., Werckmeister, Musicalische Paradoxal-Discourse (Quedlinburg, 1707), 45. On the composer's familiarity with Werckmeister, seePeter Williams, "J. S. Bach: Orgelsachverstandiger unter dem Einfluss Andreas Werck-meisters?" Bach-Jahrbuch 68 (1982): 131-42. For Walther's treatise of 1708, see JohannGottfried Walther, Praecepta der musicalischen Composition, ed. Peter Benary (Leipzig:Breitkopf und Hartel, 1955), 36. For Mattheson's correspondence with Fux in 1717-18and other writings, see his Criticae musicae tomus secundus (Hamburg, 1725), 185-210,265-66.

20. E.g., Daniel Speer, Grundrichtiger . . . Unterricht der musicalischen Kunst (Ulm,1697), 10.21. So "durch alle Tonos nemlich durch 12 duros und 12 molles, zusammen 24 Tonos":see note 12.

22. Gibbons's Fantasia of Four Parts, published in Parthenia (1613), is particularly inter-esting in its use of the same six notes, because of its modal ambiguity: is the subject in Cmajor or in A minor (the key in which it closes)?23. Note that Fischer's next collection, the Blumenstrauss of 1732, was ordered accord-ing to the old framework of eight tonos ecciesiosticos and thus begins in D minor.

24. The prime application of the term in Harold Bloom, The Anxiety of Influence: ATheory of Poetry (London: Oxford University Press, 1973), e.g., 25.


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25. Two other speculations about them are (1) that their musical idiom suggests domes-tic music making on harpsichord and (2) that they contain hidden allusions, such as tothe cross in the contrapuntal invertibility of the F-Major Duet. See Albert Clement, "Dieideelle Grundlage der vier Duette BWV 802-805?" in Die seelsorgliche Bedeutung JohannSebastian Bachs: Kantaten zum Thema Tod und Sterben, ed. Renate Steiger (Heidelberg:Internationale Arbeitsgemeinschaft fiir theologische Bachforschung, 1993), 193-226.26. As too in Sebastien de Brossard's Dictionaire de musique, 2d ed. (Paris: Chez C. Bal-lard, 1705), 161, a source for German lexicographers. Walther, Praecepta, 63-64, andLexicon, 600-1.

27. That the subjects can be made to resemble paraphrases of one or another choralemelody is shown in K. Ehricht, "Die zyklische Gestalt und die Auffiihrungsmoglichkeitdes III. Teiles der Klavieriibung von J. S. Bach," Bach-Jahrbuch 51 (1949-50): 40-56.28. Other contrapuntal, formal, and allusive devices in the Four Duets are suggested inmy Johann Sebastian Bachs Orgeluierke, vol. 1 (Mainz: Schott, 1996), 397-404.29. Newspaper notice in Schulze, 202. Since the B-minor "partita" (BWV 831) appearsto be a revised, transposed version of BWV 831a in C minor (though many questions areraised by this assumption), one wonders if the transposition was made in order to be asfar from F major as possible. If so, there may be some justification for speculating that theE-flat major prelude and fugue of Clavierubung III were transposed likewise for "external"reasons.

30. The two sets of seven keyboard suites of Johann Kuhnau, published in Leipzig in1689 and 1692, and also in a tonal order: in Kuhnau, C, D, E . . . , major then minor;in Bach, B-flat, C, A . . . , major and minor mixed.31. None of the harpsichord volumes of Rameau, or sonatas for violin of J. G. Graun(Merseburg, 1726?), Wilhelm Friedemann's violin teacher in the operative period(1726-27), is listed in Beisswenger, Notenbibliothek.32. Compare the opening bass of the Goldberg with that of Handel's Chaconne in Gmajor, HWV 442 (composed c. 1703-6), and the Variations in G Major, HWV 435.33. Some examples I have noticed: BWV 213i, 540i, 540ii, 59Oi, 600, 651, 703, 833,971i,1046iv, and 1095.


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Witting and Unwitting Allusion in JSBach

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