I/11.1.1 The prelude-type

This prelude, written in almost consistent two-part texture, is determined by a figure made up of consecutive broken chords with occasional auxiliary and passing notes. Invented in sixteenth-notes with twenty-four values to each bar of compound time, this figure dominates the entire piece without a single interruption.

I/11.1.2 The overall design of the prelude

The first cadence appears at the end of the figure's first statement, i.e. shortly before the end of bar 2; this harmonic close thus defines the material itself and should therefore not be regarded as a structural close. The next harmonic progression brings forth a modulation to the relative minor key, which is firmly reached in bar 6m. Contrary to the first cadential close which only marked the end of the figure, this one indicates the completion of a structural process.

There are altogether three structural sections:

The F major prelude contains one striking symmetry in its first two sections:

I/11.1.3 Practical considerations for performers

As the entire prelude consists of broken-chord patterns – both in its sixteenth-note figures and their eighth-note accompaniment – and does not contain any truly melodic passages, a very swift tempo is indicated. An ideal rendition is one which allows the listener to feel the four-beats-to-a-bar meter implicit behind the written compound-time designation. The appropriate articulation requires a light non legato for the eighth-notes and quarter-notes and a very light, leggiero-style touch for the sixteenth-notes.

The most noticeable ornaments in this prelude are the compound trills on the half-notes in bars 3, 4, 9, 10, 12, 13; the long trill in bars 14/15 may be included here as it fulfills basically the same function. The execution is as follows:

-	the speed of all these ornaments is in thirty-second-notes;
-	each of them ends with a suffix (the ones in U: bars 4 and 9 including the raised lower neighbor notes B natural and F# respectively);
-	the beginning is as indicated by the curved lines: Concave curves signify a beginning from the upper neighbor note, followed by main note/ lower neighbor/ main note and then the usual trill motion, convex curves signify a beginning from the lower neighbor note, followed by main note/ upper neighbor/ main note and then the usual trill motion.

In other words, the ornaments begin with the following notes:

(It is interesting to observe that Bach's basic idea seems to be that of a trill "from below"; but wherever such beginning from the lower neighbor note would clash with a pitch just heard before, he substitutes this beginning for the opposite one; see e.g. in U: bar 4, a beginning on the lower neighboring note B would clash with the Bb in the preceding figure; in U: bar 9, a beginning on F^# would sound wrong after the recent F natural.)

The ornament in the final bar is a point d'arrêt trill, consisting only of a four-note shake followed by a stop before the final sweep. The same applies to the ornament in U: bar 17 which should stop well before the end of the dotted-quarter-note value because the resolution is delayed by a tie-prolongation.

The example below gives the execution for one representative of each ornament-type.

(ex. 52)

 

I/11.1.4 What is happening in this prelude

There is only one relevant figure, the broken-chord sixteenth-note figure introduced in the upper voice in bars 1/2. For the purpose of gaining a better understanding, it can easily be reduced to the harmonic progression shown.

(ex. 53)

 

This figure describes a sequence of chords in which a harmony turns seventh or ninth chord and resolves, only to find the resolution itself now turning seventh chord and resolving again. The dynamic development equivalent to this harmonic process is twofold: the slight waves of tension-increase and relaxation appear under the umbrella of an overall diminuendo, either from the beginning of the entire figure to the return to the tonic (as in bars 1/2) or, in the shorter versions later on, only through a single chord/seventh-chord/resolution group.

In its development, the figure is shortened and complemented by a trill; as such, it occurs in stretto imitation (see bars 3/4). As the harmonic progression departs from the tonic, the expected resolution is substituted in several cases by an entirely foreign note (see the C major seventh chord followed by C^#) without changing the basic pattern.

The dynamic outline of the first section presents an S-curve. After a fairly assertive beginning and the two-bar tension-decrease mentioned above, the modulation to D minor features an increase, with each figure in the stretto beginning slightly louder than the previous one. This leads to a climax (which should, however, be gentle enough not to rival the section-beginning) followed by a gradual decrease until the end of the section.

The second section commences similarly with a two-bar decrease in tension (see bars 6m-8d). The passage which brings the development of the figure is preceded by an extra bar (bar 8) which initiates the increase of tension, although it does not contribute to the forthcoming modulation. From the middle of bar 10 onwards, a gradual decrease in tension leads to the end of the second section.

The third section sets out with two stretches of one-and-a-half bars length each; both feature continuous ornamental motion in one hand and a new development of the figure in the other, and in both cases the harmonic progression moves in active steps (i.e. in a pattern of ascending fourths; see bars 12m-13: g⁷-C-F-B*, bars 14-15m: d⁷-g⁷-C⁷-F). These developments engender a rise in tension much stronger than any of the previous ones, with the climax of the composition falling on the middle beat of bar 15. In the final descent, the "false imitation" which begins in L: bar 16m should be given some extra emphasis, but neither the trills nor the eighth-notes in bars 17/18 should interrupt the gradual relaxation which continues through to the last bar. The prelude ends on a very gentle note.

I/11.2.1 The subject

The subject of the F major fugue is slightly less than four bars long. It begins with a eighth-note upbeat and ends on the downbeat of bar 4 where the A represents the resolution onto the tonic, after the dominant harmony of bar 3.

The material of this subject includes two features which indicate sub-phrasing; both occur in bar 2 after the downbeat:

firstly,	there is a change in the rhythmic pattern – the continuous eighth-notes give way to sixteenth-note runs with eighth-notes only at their ends;
secondly,	there is a considerable shift in the pitch level – so far the notes had circled narrowly around the C on which the subject commences; thus the sixteenth-note-run from a sixth lower sounds almost like a new beginning.

The rhythmic pattern is very simple, consisting only of eighth-notes and sixteenth-notes. The interval structure contains no surprises either; apart from the above-mentioned shift in pitch level, all intervals in the subject are seconds. It might be interesting, however, to detect that there is a hidden superimposed line, created by the downbeats of the four bars in the subject: D-C-B^b-A. Harmonically, the steps of this line represent the steps of a simple cadence.

When pondering the dynamic outline of this subject, three questions demand an answer:

-	What is the shape in each of the two subphrases?
-	How do the two subphrases relate to one another?
-	How does the line created by the four downbeats influence the overall shape?

All these questions are relatively easy to answer. Within the first subphrase, the D on the downbeat of bar 1 represents harmonically the subdominant, and as no rivaling melodic or rhythmic features claim attention, this D is the obvious choice for a climax. Within the second subphrase, the eighth-note Bb represents the dominant-seventh chord; it is also the only longer note value and, because of the ascending scale leading to it, the note with the greatest melodic emphasis.

The combination of the two subphrases results in two structurally very similar curves. The first is more exposed both harmonically (the step to the subdominant being more active than that to the V⁷) and rhythmically (the eighth-notes sounding more forceful than the ornamental or scalar sixteenth-notes). So far, the dynamic outline is therefore as shown here (ex. 54):

 

When taking into consideration the line created by the four downbeats, the above concept may be modified slightly so as to accommodate the continuity behind the two-subphrase structure. This means that the C in bar 2 is no longer the almost complete relaxation which it would be if seen only as the end of the first subphrase, but appears integrated in the superimposed diminuendo D-C-Bb-A. The result, which incorporates the peak-note structure without abandoning the individual shaping of the subphrases, is this (ex. 55):

 

I/11.2.2 The statements of the subject

There are fourteen statements of the subject. 

(ex. 56)

 

Besides the adjustment of the initial interval in the answer – an adjustment occurring only once (compare U: bars 4/5 with M: bars 0/1), the subject allows for two other variations. Both are introduced towards the end of the fugue.

-	Three statements feature a fill-up sixteenth-note immediately after the second climax (see bars 49/51/53: L, M, U); the second subphrase thus consists only of sixteenth-notes, reinforcing the contrast to the all-eighth-note first subphrase.
-	The final statement introduces even more sixteenth-note variation by substituting the four eighth-notes in the upbeat and the first bar with an ornamental line (see U: bar 64, from last sixteenth-note C, and bar 65).

On three occasions, statements follow each other with considerable overlapping (see statements nos. 6/7, 8/9/10 and 11/12/13). In the latter two groups, strictly speaking, the third statement is not in stretto with the first one; however, the fact that the two consecutive voices in each compressed group repeat the leading statement literally (on the same step of the key, with the same variation) supports a stretto-group interpretation. Parallel subject entries do not occur.

I/11.2.3 The counter-subject

There is only one companion to the subject in this fugue, and it is not a particularly steady one. It is introduced in the middle voice against the second subject statement (see bar 4, second sixteenth-note G, to bar 8d C). Already when accompanying the third subject statement (bars 9-13), CS appears shortened at its beginning. The fourth statement then finds a considerably distorted version of CS shared between two voices (see M: bars 18/19, complemented by L: bars 19-21, from C onwards). The fifth statement again features the complete counter-subject as a companion. The two following statements, which build the first stretto, are surrounded by what can be clearly recognized only as the second half of CS (see U: bars 26-29). Hereafter, the counter-subject is no longer heard.

The phrase structure of the counter-subject displays one indivisible unit; the sequence inherent in the first two bars is ornamental in nature. With regard to the dynamic shape, the swift three-eight meter clearly favors the downbeats, and in the absence of any special tension-enhancing features, the climax will fall on that downbeat which is highest in pitch (e.g. on E in bar 6).

A sketch showing the phrase structure and dynamic design in subject and counter-subject follows in ex. 57.

 

I/11.2.4 The episodes

There are altogether six subject-free passages in this fugue:

None of the subject-free passages is immediately related to the subject; however, material from the counter-subject appears in partial (see E1, where the first bar from CS is anticipated in the upper and middle voices) or even whole quotation (see E2, lower voice).

No genuine episode motives are newly invented, but short sequence-models appear several times:

-	in E2 the model established in bar 13, U+M, is sequenced in bars 14, 15;
-	in E3 the complementary model which picks up the end of S/CS is introduced in bars 31/32, U+M, and sequenced in bars 33/34;
-	in E5 a little one-bar figure (see M: bars 56/57) is imitated through all voices (bars 57-61 and 63/64).

E4 consists of nothing but a cadential close. The same holds true for the first segment of E5, which repeats this cadence in varied transposition (compare bars 54-56 with bars 44-46). The final episode of the fugue is also in reality only a slightly more elaborate cadential formula. This relationship between the cadential closes aside, the episodes in this fugue show neither analogies nor other structurally relevant patterns.

The role each episode plays in the development of this composition can be easily deduced from what has been observed so far:

I/11.2.5 Character, tempo, articulation, ornament realization

The simple rhythmic pattern in this fugue, together with the scalar or ornamental structure of the sixteenth-notes, clearly speaks for a rather lively basic character. The tempo should be fast enough to reflect the bouncing character of the eighth-notes and the ornamental nature of the sixteenth-notes. The appropriate articulation is legato for the sixteenth-notes and non legato for all eighth-notes except those in appoggiaturas and closing-formulas (i.e. in bars 45, 55 and 71 where the ornamented notes in the upper voice are not detached from the notes which follow; likewise in the middle voice, the do-si-do (keynote / leading-note / keynote) figure in bars 55/56 is legato despite the eighth-note-note values).

The relative tempo of the prelude to the fugue poses a little problem because of the inherent triple meter in both movements. The simple proportion, given below under (a), is certainly possible. It strings the two pieces together very firmly, but almost to the point of blurring the confines of each. Also, there is the danger of monotony in two consecutive pieces which both feature mainly two note values in exactly the same pulse. Another proportion may seem complicated but has the advantage of giving a more lively, interesting result; see (b) below:

 The different speed of all note values in the second concept helps considerably to differentiate the touch and color in the (heavier) eighth-notes of the fugue from those (lighter ones) in the prelude.

The F major fugue contains mainly two kinds of ornaments: a long trill on the second-to-last note of the counter-subject and mordents in the typical closing-formulas.

-

The trill in the counter-subject abides by the same rules that would apply to a similar trill in the subject: * it is approached stepwise and thus begins on the main note; * its speed is in thirty-second-notes as these are twice as fast as the shorter written-out note values; * it ends in a suffix before resolving stepwise.

-

The ornaments in the closing-formulas (see bars 45, 55 and 71) are short mordents because their resolutions are in each case anticipated and fall before the next strong beat, thus demanding a point d'arrêt: * they all begin on the upper neighbor note; * their speed can be in thirty-second-notes (or slightly faster); * in the two cases with dotted-note rhythmic figures, the ornament stops short before the third eighth-note beat.

The ornament in bar 28 is a variation of the long trill mentioned above (since the upper voice in bars 26-29 features a variation of CS); although shorter here, its beginning, speed and end are as described for the long trill.

Finally, the mordent in bar 48 (see U: bar 48d) contains four notes; commencing on the upper neighbor note, it fills the note value with four swift sixty-fourth-notes. (As this ornament seems somewhat out of keeping with the remainder of the piece, it may be worth considering whether one might ignore the indication.)

I/11.2.6 The design of the fugue

There are several features in this fugue which give indications as to its design.

-	The subject statements which begin in bars 21 and 46 appear in reduced number of voices and should be earmarked for possible section beginnings. In a third instance, the stretto which commences in bar 36 is accompanied by a sustained pedal (see L: bars 36-40) and thus also creates the effect of not actively involving all three voices.
-	The episodes between the second and third statements (E1) and between the third and fourth ones (E2) are both related to the primary material insofar as they quote the counter-subject; they thus suggest a link between consecutive entries of a single structural section. Furthermore, both episodes have an ascending pitch outline. E3, on the contrary, serves as a kind of extension to the preceding subject statement and shows a descending pitch line.
-	The triple stretto + closing-formula in bars 36-46 is structurally analogous to the triple stretto + closing-formula in bars 46-56. Furthermore, the final cadential close of the fugue is also built along the same pattern as the two preceding ones (compare particularly bars 71/72 with bars 45/46).

Harmonically, the fugue remains rooted in F major until bar 31. The subsequent bars describe a shift to D minor (see bar 32, reinforced by its dominant, the A major chord in bars 34 and 36), which becomes the basis of the triple stretto from bars 36 onwards. A cadence in this relative minor key closes this segment in bar 46.

The following bars pick up the triple stretto in inverse order of entering voices and in G minor (the relative minor to the subdominant); this key is also closed with an explicit cadence (see bar 56). Two bars after this cadence (bar 58) the fugue is back in the home key of F major, in which the final, varied subject statement appears. This is again rounded off with a cadence formula similar to the two previous ones. The design which becomes apparent from these observations is unusual insofar as it reveals a fugue consisting of "parts" rather than "sections".

-

The first part, encompassing two sections, is united by the home key; its two sections are glued together by the bridging power of E2 (which does not allow for phrasing before the fourth statement, although the entering order would suggest this) and by the density of material immediately afterwards (which does not allow for phrasing after the fourth statement either, although the reduced texture would suggest this). This "part" is rounded off by the relaxing episode in descending sequences which introduces the modulation (see E3).

-

Although the second "part" does not literally encompass several sections, the explicit closing-formulas in E4 and E5a give the impression that this part consists of three segments.

For a sketch showing the design of the fugue in F major, see ex. 58.

I/11.2.7 The development of tension

Any discussion of the development of tension in the F major fugue must deal with a multiple-layered composition, i.e. with the sections or segments within each "part", with their combination into a "part", and with the relationship of the two halves of the fugue into a whole.

I

Within the first "part" (i.e. within the combined first two sections of this fugue), the dynamic outline is that of a gentle rise. It is gentle not because the mood or spirit of the piece is anywhere near mild, but rather for the opposite reason: since the first unaccompanied subject statement is already energetic and almost rustic, very little intensification of character takes place with the entry of the other two voices; at the same time, there is a complete lack of any active harmonic development. This gentle rise in tension created by the increasing ensemble is carried through the first two episodes which bring only a slight color change but no relaxation. The fourth entry of the subject may, because of its pitch position, give a false impression of the soprano entrance in a four-part fugue. Although any performer who has analyzed the piece knows that this is a deception, the fact that Bach has composed in this way and has designed the preceding episode as a bridge (both in material and rising direction and tension) is a good reason to play this statement as the first climax. The ensuing subject entry is presented in reduced number of voices and thus suggests a dynamic level which is a bit more relaxed than that in the preceding bars. It is followed by the first stretto which thus brings forth the second and slightly more prominent climax. The first "part" of the fugue is then rounded off with the third episode which is the first passage in the piece to insinuate a release in tension because of its material, descending lines, and harmonic shift. However, the imperfect cadence with which the new key D minor is confirmed in bar 36 discourages a complete relaxation. (Note that the eighth-notes in L: bars 34-36 had better not be played, as is sometimes heard, as a "false entry". Such a rendition would be both melodically and structurally confusing for the listener.)

II

The second "part" of the fugue is much more straightforward: it consists of three truly powerful buildups of tension, each followed by definite declines. With regard to the succession of the three segments, two conclusions are possible: - One concept is to begin the triple stretto in D minor as the absolute climax of the fugue, followed by a slightly less outgoing triple stretto in G minor and a softer shaded episode (bars 56-64), into which the varied subject statement is then blended like an afterthought. - Another concept is to regard the triple stretto in G minor as a confirmation and fortification of the one in D minor, and the fifth episode with its ascending eighth-note scales as a final powerful run for the crowning climax which then arrives with the final statement of the subject.

In the first case, the fugue in its overall shape describes an almost perfect curve; the final cadence returns to a level of tension similar to that from which the fugue commenced. (Such a result may delight us in our need for balance, but it seems somehow too smooth for this fugue).

In the second case, the entire fugue expands in two grand sweeps and the final cadence is still filled with the triumphant power of the towering last subject statement.