Charles Gounod was not alone in hearing the opening prelude of the Well-Tempered Clavier as a wandering accompaniment in search of a melody—surely, we have all heard performers play it that way. But early eighteenth-century musicians certainly heard the prelude differently, as various modern analysts have explained. Edward T. Cone has demonstrated that the arpeggiation pattern, like many Baroque continuous-rhythm figurations, is far more intricate than a mere accompaniment.1 And thanks to one of Schenker's Graphic Analyses, we know that the prelude clearly expresses a descending octave scale in the bass and a dominant pedal framed by opening and closing tonic prolongations.2
That latter aspect of the prelude already appears in print in the mid-eighteenth century in C. P. E. Bach's instructions on improvisation near the end of his 1762 Versuch über die wahre Art das Clavier zu spielen, zweyter Theil, where he explains that an improvisor extemporizing a prelude "fashions the bass out of the ascending and descending scale of the prescribed key, with a variety of figured bass signatures, and may . . . perform the resultant progressions in arpeggiated or sustained style . . . A tonic organ point is convenient for establishing the tonality at the beginning and end. The dominant organ point can also be introduced effectively before the close."3
Carl Philipp Emanuel likely learned this description of how to create a prelude from his father, who perhaps used as cases in point not only the Well-Tempered Clavier's C-major Prelude, but three of the ensuing preludes in the same volume: those in C minor, D major, and E minor. These four preludes form a "mini-series" within Volume 1 of the Well-Tempered: all contain recurring figurations over very similar basses. And all were substantially recomposed in relation to their earlier versions in the Clavierbüchlein vor Wilhelm Friedemann Bach when Johann Sebastian decided to include those preludes in the Well-Tempered, Volume 1.4 Indeed, of the eleven preludes that journeyed from the Clavierbüchlein to the first volume of the Well-Tempered, only these four underwent substantial changes.
These four preludes merit close study and comparison, for their common factors and differences, their relationship to the eighteenth-century ideas that elucidate their structure, Johann Sebastian's revisions of their earlier versions for inclusion in the Well-Tempered, and the order in which they appear in the Well-Tempered all offer a glimpse into Bach's compositional and pedagogical procedures not only for these pieces, but for a vast range of his compositions, suggesting various applications that might enliven our own teaching.
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Thoroughbass versions of all four preludes appear in Example 1. Each thoroughbass uses whole notes to indicate the main harmonic goals, half notes to highlight the bass notes that participate in scales connecting these main notes, and solid note-heads for other chords. The slurs group together bass notes and chords that fulfill a single role in the prelude (as discussed in the next paragraph).
Example 1. Annotated Thoroughbass Renderings of J. S. Bach, Preludes in C major, C minor, D major, and E minor, Well-Tempered Clavier, 1.
When laid out in this manner, each prelude clearly illustrates just what Carl Philipp Emanuel recommends. The preludes open and the two preludes in C close with what I call the "frame": a tonic-defining progression, either a literal "tonic organ point" as C. P. E. suggests, or a closed, tonic-prolonging "imitated cadence" (to paraphrase Rameau's contemporaneous term for a cadential progression such as tonic-supertonic-dominant-tonic that is not a conclusive cadence because the chords are inverted or because the melody fails to arrive on the tonic).5 The remainder of each prelude features one or two descending octave scales followed by a dominant pedal, with some brief neighboring progressions linking the end of the scale or scales to the beginning of that dominant pedal.
The preludes appear—both in the Well-Tempered and in Example 1—in order of increasing complexity, with each prelude in the series building on the ideas of its predecessors. The simplest prelude is that in C major. It appears to express its structure—opening frame, octave scale, dominant pedal, and closing frame—with little excess fuss. Its pattern is unvarying until the last two measures. And it marks its progress through both its single octave scale and dominant pedal by dividing both into two parts, of which the second is similar to the first part: as noted on Example 1, the second half of the octave scale ends with a literal transposition of the first half; and the second half of the dominant pedal likewise ends with the same harmonies as its first half.
The C-minor Prelude is quite similar to that in C major, but at every stage is considerably more complex. Like the C-major Prelude, its basic pattern recurs each half-measure; but the pattern's details change frequently, and not every measure repeats the pattern literally. In addition, the C-minor Prelude features several dramatic changes in tempo and texture that make some of its underlying structural features less obvious than parallel features in the C-major Prelude. For instance, the recurrence of the opening frame at the end of the C-minor Prelude is not as obvious as the similar recurrence in the C-major Prelude because in the Prelude in C minor that recurrence spans the change in texture and tempo from Adagio back to Allegro and is interrupted by a cadenza-like passage. In addition, because the second prelude is in the minor mode, its bass octave scale is broken at scale-step 3, resulting in an uneven and therefore more complex division that does not lend itself to the sort of structural parallelism between two halves of the scale such as that in the C-major Prelude (where the bass scale is broken midway at scale-step 5). And the second prelude's dominant pedal is not simply two parts, of which the second is like the first, as in the C-major Prelude; instead, the dominant pedal in the C-minor Prelude is broken by the change to Presto.
The D-major Prelude is even more complex, with many of those complexities building on elements in the previous two preludes. Although there is a recurring pattern here too, it is less easy to specify precisely, since its details change frequently. And there are two bass scales, not just one. The first bass scale breaks at scale-step 5 (as in the C-major Prelude) and also pauses for a long time on scale-step 3 (which is the articulation-point in the C-minor Prelude—but of course scale-step 3 is more distant in the major mode than in the minor). Then there is a second octave scale in the bass; this one broken at scale-steps 6 and 4. As in the C-minor Prelude, the dominant pedal spans a major break in texture—here because of what I call "the cadenza." And unlike either of its predecessors, the D-major Prelude literally transposes its opening measures at a later point. Specifically, mm. 1-6 (the entire texture of the opening framing progression plus the movement to the dominant) recur transposed to conclude the second octave scale in mm. 20-25. This suggests several compositional possibilities far larger in scope than a mere prelude based on an octave scale: perhaps a multi-part movement in which the opening recurs in the subdominant (which is a structure that Bach uses in preludes as varied as that in E major in the Well-Tempered, in the Adagio of the G-minor Solo-Violin Sonata, and in the Preludio of the E-major Solo-Violin Partita—all pieces composed around the same time). Or perhaps the transposition of the opening suggests a ritornello-type movement in which the key-defining opening recurs in different tonalities.
The E-minor Prelude is the most complex of the four, once again building upon structural aspects of its predecessors. There are two octave scales, with the second inflected toward the subdominant side (as in the D-major Prelude). There is a recurrence of the opening frame on the arrival on the subdominant (again as in the D-major Prelude), but because it occurs at the arrival of the Presto (a tempo and texture change reminiscent of the middle of the dominant pedal in the C-minor Prelude) and with a texture different from that at the opening, the parallelism between the opening and its transposed recomposition is both less obvious than in the literal transposition of the opening "ritornello" in the D-major Prelude, and more like the manner in which Bach will sometimes begin two movements in a suite with similar underlying progressions. The most striking difference between the E-minor Prelude and its predecessors is its ornamented melody—for the first time in this mini-series of preludes, the patterned element is the accompaniment for a more prominent textural component. Yet even this new element (namely, the melody) is reminiscent of the melodic style during the Adagio portion of the C-minor Prelude.
In effect, this mini-series of preludes is a composition lesson in creating progressively more complex pieces from a common—and, in early eighteenth-century terms, commonplace—foundation. Students and advanced players of the time were familiar with the Rule of the Octave (a common mnemonic showing the usual harmonies to be played over a bass scale), bass pedals, and other ubiquitous thoroughbass patterns. As they learned these preludes, they would probably have recognized immediately how Bach had created a wide range of stylistic surfaces on that simple bass structure.
I believe that Bach created this compositional lesson quite purposefully when he inserted these preludes into the first volume of the Well-Tempered, since the earlier versions of all four preludes as they appear in the Clavierbüchlein are invariably simpler and much closer in structure to one another. There, the C-minor and E-minor Preludes lack their tempo and texture changes, the D-major and E-minor Preludes lack their second octave scales, and the E-minor Prelude lacks its melody—the right hand merely features block chords each half-measure. Probably, when Johann Sebastian first wrote these pieces for Wilhelm Friedemann to copy into his Clavierbüchlein, Johann was merely content to demonstrate to his young son the variety of textures that one could create to enliven very similar basses. But when Johann Sebastian reworked these four preludes for incorporation into the first volume of the Well-Tempered, he was likely hoping that the resulting pieces would, as he wrote on the title page of the contemporaneous collection of the Inventions, teach "those desirous of learning . . . not only to have good inventiones [ideas], but to develop the same well."6
In order to do so, he had to fulfill several agendas. First, he had to expand each prelude to match the scope of the fugues with which he paired them. Second, in the process of making them suitable to precede compositions as strict as fugues, he had to tighten up their internal relationships by creating various parallelisms between sections in a manner that is missing from the earlier versions. And as he created those parallelisms, he invariably worked from the same structural principle that he used to determine their ordering within the Well-Tempered: the principle of heightening complexity. Just as the subject of the opening fugue in the first volume of the Well-Tempered (that in C major) is totally diatonic and the concluding fugue's subject contains all twelve tones (and not the other way around); and just as the variations within each of the sections of his solo-violin Chaconne feature increasingly complex combinations of rhythms, voice leadings, chromaticisms, and the like; and just as he invariably situated contrapuntal devices within his fugues so that they occur in increasing order of complexity, often leading to a contrapuntal tour-de-force near the end—so in these preludes, whenever material returns, it is reworked into more complex form.
Consider the C-major Prelude. The Clavierbüchlein score, containing at least two different versions of the prelude, appears in Facsimile 1.7 But whatever those earlier versions are, the prelude as it appears in the Well-Tempered is a more tightly organized work. Consider first the way that Johann Sebastian reworked the octave scale so that in the Well-Tempered both portions of the scale have the parallel structure noted above; the versions in the Clavierbüchlein lack that parallelism which tightens the structure of the Well-Tempered version. Second, Johann Sebastian doubled the length of the dominant pedal from four measures to eight creating the other parallelism noted above—again making the structure more self-referential. Third, the Well-Tempered version rounds off the prelude by ending with a recomposition of the opening framing progression (in contrast to the Clavierbüchlein version that simply halts on a single tonic chord after the dominant pedal).
Facsimile 1. The C-major Prelude from J. S. Bach's Well-Tempered Clavier as it appears in the Clavierbüchlein vor Wilhelm Friedemann Bach. The first three systems appear on the recto side of a page; the last system appears on the verso.
In all three recompositions just cited (creating the parallelism within the portions of the octave scale, doubling the length of the dominant pedal, and ending the prelude with a recomposition of the opening frame), the recurring music is more complex than the first statement. The first part of the octave scale is entirely diatonic in the key of its cadence (G major), and uses exclusively consonant triads or seventh chords built upon consonant triads. The second part of the octave scale, by contrast, introduces three chromatic pitches (, , and ), all of which are chromatic to the key of both the preceding and following cadences. And two diminished-seventh chords join the harmonic vocabulary.
For the expansion of the dominant pedal, Bach essentially repeated the harmonic progression of the first four measures with one crucial change: the first harmony. The changed chord is the most dissonant harmony of the piece, a five-voiced chord with no less than six dissonances: an augmented second (-), two tritones (-A and C-), a major seventh (G-), major ninth (G-A), and a perfect fourth over the bass (G-C).
When the opening harmonic frame recurs to end the piece, a chromaticism appears and the progression is over a bass pedal, heightening the dissonance level. In addition, the E-F-F-E melody of the opening, although present again in the last four measures, is not the top voice at the very end. Lastly, the figuration pattern that characterizes all the other measures in the prelude disappears in the penultimate measure.
Similar structural changes characterize the revisions of the other pattern-preludes discussed above. In each case, the reworked sections heighten the levels of activity.
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We know about J. S. Bach's compositional pedagogy through the reports of his pupils, including his sons.8 We know that he demanded a solid grounding in thoroughbass, and built further instruction upon that foundation. He may not have left for posterity a prose composition treatise. But in his pedagogically-organized cycles—such as these preludes from the Well-Tempered, as well as the Inventions—he surely wrote many if not all of the musical examples that allow us to re-create the essence of his compositional pedagogy.
Early eighteenth-century musicians, likewise with a grounding in thoroughbass, would likely have seen these preludes in order according to the ideas introduced here. We know that theirs was a period before the adoration of masterworks. They probably did not revere these pieces as exemplars of "The Masterwork in Music." Rather, they would have respected them as demonstrations of how to put the building blocks of composition to good use. Across this mini-series of preludes, they might well have marvelled at Bach's ability to begin with the near-extemporization of the C-major Prelude, and then at his ability to build in the following preludes in this mini-series a wide range of textures and formal types out of the first prelude's simple improvisational building-blocks: even including cadenzas, accompaniments to spun-out melodies, and hints at ritornellos and binary construction. After all, this is what Friedrich Erhard Niedt explicitly taught in his turn-of-the-century thoroughbass treatise—supposedly Bach's favorite thoroughbass treatise—when he built upon several closely related thoroughbasses a suite of eleven dances, plus a prelude and a chaconne.9 But whereas Niedt's text and examples are often pedantic (he was, after all, a lawyer by profession), Bach's exemplary pieces are unfailingly inventive. An astute eighteenth-century musician might well have recognized why: namely, Bach's remarkable ability to open with a small amount of thematic or motivic material and work with that material in ever-more complex ways to create rhetorical musical arguments. Indeed, this is such a consistent feature of Bach's style that it is hard to imagine he did not discuss it when he taught composition.
We too can teach from these pieces just as he must have in Leipzig in the 1720s, 30s, and 40s. Just as we use Bach's chorales to exemplify harmony, voice leading, and structural properties, we can use the notions discussed here—especially recycling conventional thoroughbass patterns and using small amounts of thematic material in evermore complex ways—to illustrate compositional technique and prowess. For instance, after our students become aware that surfaces as different as those of the C-major and E-minor Preludes are built on the same foundation, we can show them how the various dances of the D-minor Solo-Violin Partita all share underlying thoroughbasses no less similar to one another than are the underlying thoroughbasses of these four pattern-preludes. Example 2a contains the opening bass lines and chord notes of the first four dances in that partita. The bass lines are notated in real rhythms, the chord notes in solid noteheads. The vertical alignment highlights the similarities (or identities) among these movements. For instance, the allemande and corrente have pretty much the same bass and chords from their openings through their cadences in F (m. 6 in the allemande, m. 12 in the corrente). But the corrente, which is in a faster tempo, expands some motions. Mm. 2-3 of the corrente, for instance, prolong the D chord by its dominant before resuming the path of the allemande; and mm. 7-9 prolong the chord in similar fashion. Some other harmonies appear in different inversions: the G-minor seventh chord in m. 2 of the allemande and m. 3 of the corrente, for instance.
Example 2. Annotated Thoroughbass Renderings of the opening portion of movements from Bach's Partita in D minor for solo violin
The sarabande takes a new turn in m. 3 (and then continues in its own direction). But the new progression (encircled in Example 2a) recurs in the giga as an expansion of the motion between the comparable D and G chords in the allemande and corrente. In brief, the relationships among these dance movements is akin to the relationships discussed earlier between four pattern-preludes in the Clavierbüchlein and the first volume of the Well-Tempered. The D-minor Solo-Violin Partita seems to relate its individual movements to one another in this manner more closely than Bach's other suites (whether for keyboard, violin, cello, or orchestra). Awareness of this close variational relationship among these movements makes one appreciate that it is no mere coincidence that Bach placed his most extended one-movement variation cycle—the chaconne—at the end of that D-minor Solo-Violin partita, his suite that most fully exemplifies the older meaning of the word "partite" (literally, little parts or variations, akin the seventeenth-century English term "divisions").10 As Example 2b shows, the theme of the chaconne (the bass and progression in mm. 1-4) is closely related to the openings of the partita's four dance movements.
Our students will also realize that the conventional progressions of the Well-Tempered's pattern preludes—harmonic frames, bass scales, dominant pedals, and the like—are part of a fairly limited vocabulary of such conventional formulas that occur in virtually all of Bach's music. The thoroughbasses illustrated in Example 2, for instance, all begin with a tonic-defining progression akin to the harmonic frames opening the pattern preludes in Example 1. Indeed, the Chaconne's basic progression is nothing more than a harmonic frame. And consider the D-major Prelude from the second volume of the Well-Tempered, whose opening appears in Example 3. The D-major Prelude is in binary form with an extended modulatory section after the double bar followed by a recapitulatory section in which all the materials of the first reprise recur in order in the tonic key. Yet despite the proto-sonata-form structure and almost galant style of this 1740s work, the opening bass and outer voices are strikingly similar to those of the C-major Prelude from Volume 1. These harmonic conventions were the building blocks Bach knew.
a. J. S. Bach, Prelude in D major, Well-Tempered Clavier, 2, mm. 1-8: score
b. same in thoroughbass
c. J. S. Bach, Prelude in C major, Well-Tempered Clavier, 1, mm. 1-11 in thoroughbass
Did Johann Sebastian discuss with little Wilhelm Friedemann his recompositions of the simpler preludes in his son's Clavierbüchlein when Johann reworked them just a year or two later for inclusion in the Well-Tempered? I imagine that the answer is yes, even though I cannot prove it. For we do have in the Clavierbüchlein a concrete example of Johann Sebastian the composition teacher at work revising what must be one of Wilhelm's earliest composition exercise. That lesson, even without any accompanying text, shows how skilled Johann Sebastian was at adapting the formulaic aspects of a piece to the demands of the immediate motivic materials, and developing those motivic materials within those formulaic contexts. I refer to that strange three-reprise Allemande from the Clavierbüchlein that appears in Example 4.
Example 4. J. S. Bach and W. F. Bach (?), Allemande in G, BWV 836
Most probably, Johann gave Wilhelm the opening five-measure reprise and told him to compose a second reprise to conclude the piece—which Wilhelm notated as the current mm. 6-12. Young Wilhelm's well-intentioned enthusiasm does not quite compensate for his glaring compositional errors and immaturities. Seeking to impress his father with his ability to compose dramatic music, Wilhelm immediately jumped to the highest register of his keyboard—hitting three high Cs within two measures (not to mention the high C within the mordent on in m. 6). Then, as only an inexperienced composer seeking cheap thrills could imagine, he introduced the most exciting thing he could think of: the utterly new chromatic scale in m. 7 over a chromatic bass. Unfortunately, he miscalculated the size of the interval to be filled by the chromatic scale in m. 7, and would have arrived on F natural (!) on the next chord had he not inserted the extraneous A at the end of the second beat. Further chromatic scales appear in mm. 10 and 11, again requiring the turn-around at the end to avoid arriving on the wrong note on the following beat.
The brand new left-hand figure in m. 11 causes the repeated cadence in 11-12 to be shifted metrically. But the chromatic scale and that new left-hand figure in m. 11 are far from the only new material in this reprise. Even the very first motive, the descending scale that opens m. 6, is new. To be sure, it outlines the same descending fifth A-D that ends the melody of the first reprise; but set with a new rhythm, register, and key, and accompanied by a new left-hand rhythm in m. 6, any connection between the two descending A-D fifths is relatively weak. Finally, amidst all his care in creating new and exciting effects, Wilhelm Friedemann failed to notice that he had ended in the wrong key—his final cadence is in the dominant, rather than back in G minor!
In sum, this second reprise is a poor conclusion, flitting between new ideas without relating these ideas either to one another or to those of the first reprise. Overall, it strives for momentary effects (chromaticism, high register, and so forth) without an overall argument.
Johann Sebastian may have worked with his son or may have simply presented his son with the more fitting conclusion that is the third reprise in the Clavierbüchlein. This reworking manages to incorporate each of Wilhelm's ideas, but masterfully puts each in its proper place, both within this reprise and within the allemande as a whole. If we apply what we know about the older Bach's music and pedagogy, we can imagine the issues he might have explained to his son. He might have acknowledged that it is good to want something new and exciting to begin a new reprise. But the idea must continue the argument from before; and a good beginning of a second reprise also often relates to the very opening of the piece. If the A-D fifth opens the second reprise in the same register as the first reprise ends, and is accompanied with the left-hand rhythm from mm. 1-3, the rhythms of melody and harmony will bring back the essence of the opening measures, and the resolution of the C- suspension in the middle of m. 13 will be strongly reminiscent of the middle of m. 1. In that context, a careful listener will hear that the descending fifth is, after all, the underlying melodic motion of mm. 1-2.
He might have proceeded to explain that it certainly is exciting to rise to a new register and include chromaticism. But instead of jumping into a new register and adding a new chromatic idea, as Wilhelm had done, a steady ascent over three measures going around that old formula, the circle of fifths, swiftly moves the music into distant keys. Getting to over an F-minor triad in m. 15 at the culmination of the registral ascent is far more dramatic and directed than Wilhelm's insertion of a chromatic riff in m. 7.
Likewise, concerning the final cadence, Johann must have explained that replacing the undirected chromatic scale in m. 10 and new left-hand figure connecting the two cadences with an extension of the descending motion within the main theme to an octave in m. 18, brings the high register of mm. 15-16 down to the principal register of the piece. The continuous sixteenth-note passage in m. 19 then intensifies the tag to the main theme.
Johann Sebastian's reprise picks up the continually intensifying elements of the first reprise and takes them to new heights. He shows that no compositional element need be truly extraneous; any notion—chromaticism, registral shifts, and the like—can belong to any piece, if only they grow out of previous material . . . and if they join in the intensifying rhetoric within each reprise and over the piece as a whole.
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Thoroughbass formulas combined with the rhetorical use of thematic materials to create ever-new music are the sum and substance of Bach's compositional techniques, both within single sections, over entire movements, and even across multiple movements. Leonard Ratner has discussed the notion of composition by using conventional materials in his 1980 book Classic Music, and William Renwick has discussed the pervasive role of paradigms throughout Bach's fugues in his recent book Analyzing Fugue.11
Formulaic harmonic progressions and rhetorical approaches to thematic continuity had disappeared from contemporaneous compositional practice by the time Bach's music was rediscovered early in the nineteenth century. And phenomena as varied as Charles Gounod's Ave Maria and the aimless sewing-machine style of Bach performances are the result. Only by educating a generation of young musicians to see how Bach used seemingly dull conventions and seemingly long-dead notions like rhetoric to create ever-vibrant conventional rhetorical music will we begin to develop the performing traditions that his music demands. I personally never cease to marvel at the extent to which Bach's music is always not only formulaic, not only rhetorically persuasive, and not only eternally imaginative . . . but all of those at the same time.
1Edward T. Cone, Musical Form and Musical Performance (New York: W. W. Norton, 1968), 63-65.
2Heinrich Schenker, Five Graphic Analyses (Vienna: Universal, 1932; reprint, ed. Felix Salzer, New York: Dover, 1969).
3Carl Philipp Emanuel Bach, Versuch über die wahre Art das Clavier zu spielen, zweyter Theil (Berlin, 1762; numerous later editions), Chapter 41; English translation by William Mitchell as Essay on the True Art of Playing Keyboard Instruments (New York: W. W. Norton, 1949), Chapter 7.
4Johann Sebastian Bach and Wilhelm Friedemann Bach, Clavierbüchlein vor Wilhelm Friedemann Bach, manuscript begun in 1720. Published in Johann Sebastian Bach neue Ausgabe sämtlicher Werke, V/5; facsimile edition (New Haven: Yale University Press, 1959).
5A discussion of Rameau's ideas on cadences appears in Joel Lester, Compositional Theory in the Eighteenth Century (Cambridge: Harvard University Press, 1992), Chapter 3.
6An English translation of the complete title page to J. S. Bach's manuscript of the Inventions appears in The Bach Reader, ed. Hans David and Arthur Mendel (New York: W. W. Norton, 1945; revised ed. 1966), 86, as well as in some editions. Laurence Dreyfus explores the concept of "invention" in J. S. Bach's compositional process in Bach and the Patterns of Invention (Cambridge: Harvard University Press, 1996).
7The obviously inserted measures were either erroneously omitted when the prelude was copied into the Clavierbüchlein, or were added at some later point as Johann Sebastian emended the prelude. (It is more likely, of course, that the inserted measures represent a later emendation, since the odds of W. F. Bach having omitted solely these two parallel measures are low.) A separate indication of multiple versions of the prelude in the Clavierbüchlein score comes from the custos (the mordent-shaped figures at the end of each line on the first page of the prelude in the Clavierbüchlein that indicate the notes that begin the next line). The custos at the end of the last staff system on the first page refers to the chord that actually appears in the Well-Tempered versionnot the chord that appears in the first measure on the reverse side of the page. Clearly, at one time there was an additional (unbound) leaf inserted here that contained a different ending of the preludeprobably a version close to that appearing in the Well-Tempered. (A similar inserted leaf must have also contained the original ending of the D-major Prelude, which simply breaks off in the Clavierbüchlein at the arrival of the dominant pedal.)
8E.g., an English translation of Carl Philipp Emanuel Bach's 1775 letter to Nicolaus Forkel (author of the first book-length biography of J. S. Bach) describing his father's teaching appears in The Bach Reader, ed. Hans David and Arthur Mendel (New York: W. W. Norton, 1945; revised ed. 1966), 279.
9Friedrich Erhard Niedt, Musicalische Handleitung, 3 vols. (Hamburg, 1700-1707; second edition ed. Johann Mattheson, Hamburg, 1710-21; English translation by Pamela Poulin and Irmgard Taylor as The Musical Guide, Oxford: Clarendon Press, 1988). The chapters in the second volume focus on variation of thoroughbass progressions.
10Bach occasionally used the term partite to denote sets of variations on chorales, as in Partite sopra Christ der du bist der helle Tag (BWV 766) and Partite sopra O Gott du frommer Gott (BWV 767). Various English publications of the mid and late seventeenth century use the term "division(s)" to refer to variation(s), the most prominent being The Division-Violist; or, an Introduction to the Playing upon a Ground by Christopher Simpson (London, 1659; facsimile edition, ed. Nathalie Dolmetsch, New York: G. Schirmer, 1955).
11Leonard Ratner, Classic Music (New York: Schirmer, 1980); William Renwick, Analyzing Fugue (Stuyvesant: Pendragon, 1995).