The segments of the Fugue in the graph correspond to the three subject versions - original, inverted and augmented - which begin, respectively, at mm.[1, 30 and 62]. In the Prelude, the change of texture and the incisive nature of the stretto that begins at m.[20] would suffice for justifying the division into two segments. It is, though, an aspect of the tonal organization that suggests such division. Tonicized by a strong cadence (V-i with both chords in root position) on the downbeat of m.[20], A flat becomes the seventh of a pile of thirds upon the dominant - B^b, D, F, A^b, C^b. The emphasis given here to the relationship between the dominant and its seventh reflects the importance of the same relationship within the Fugue's subject, where the pitches A sharp and G sharp (the dominant and its seventh in D sharp) are enhanced both by syncopation, and by the characteristic impulse of upward leaps.

It is, indeed, this harmonic implication of the subject that clarifies the prominence of the subdominant within the tonal plan of No.8. In the Prelude, A flat minor, present at mm.[2, 8, 20, 23, 31 and 38], not only explains the division of the piece into two segments, as seen above, but also establishes a parallelism between the introduction and the coda. The first moving of the harmonic progression to the A flat sonority of m.[2] creates the same i-iv-V-i pattern which, upon a tonic pedal, appears in the four last measures of the piece. The Picard closing given to the Prelude, although traditional for pieces in minor, has a connective function in No.8. The major quality of the E flat chord, by generating a certain expectation toward the subdominant, subtly announces its prominence in the piece to come.

The expectation left at the end of the Prelude is answered in the Fugue by a consistent use of G sharp. Whereas in some places it appears as a passing event, in others it assumes definite harmonic functions. At mm.[33, 37, 38, 39, 61 and 84], it results from lines built on the melodic D sharp minor scale. At mm.[2, 4, 6, 9-11, 40-42, 44, 57-60, 76, 78 and 86] G sharp appears as the fourth degree, or the seventh of the dominant. At mm.[14-15, 29 and 53], it acts as the second degree in ii-V-I progressions in F sharp major, the relative of the piece's central tonality. At mm.[25-27], G sharp assumes the dominant-of-the-dominant function preparing the arrival of F sharp major at m.[30]. Yet, it is in the tonic function in the G sharp minor areas of mm.[35-36, 47-50, 63-67 and 72-75] that its importance is confirmed.

Intended to demonstrate the prominent use of the fourth degree, the above description is not, however, a good approach for the linearity which prevails in contrapuntal writing. Regarding fugal subjects, displayed on tonal areas usually committed to a particular plan of presentations, it sometimes becomes difficult to define the function of a specific sonority. An example is offered by the event in augmentation of mm.[67-72]. The subject line in long values is decidedly in F sharp major. The counterpoints to it, from m.[67] to m.[69], are equally in F sharp major. Yet, from m.[69] to m.[72], while the upper line has a B major inflection, the bottom line moves toward G sharp minor. Thus, assertions about tonal areas in the Fugue can lead to misconceptions. Equally dangerous can be the use of analytical symbols, since they are unable to explain how certain sonorities act within the whole of the structure. In No.8, more important than to define the local function is to observe how the events based on two specific pitches, by linking the Prelude to the Fugue, define the proportions of the whole. One of such pitches is A^b/G^#. It not only relates the whole to the Fugue's subject as seen above, but also serves to demarcate the middle of the Prelude. The other pitch is G^b/F^#. At the same time that it is taken at m.[5] of the Prelude for presenting the first contrast to the progression i-iv-V-i of the initial measures, it is used for announcing the enharmonic F sharp major which, in the Fugue, demarcates:

1) the middle of No.8, through the evaded motion of the harmonic progression at m.[14],

3) the golden section of the Fugue which, enhanced by a three-part stretto, suddenly

displays at m.[54] a change from the original to the inverted version of the subject.

Aspects related to phrasing, rhythm, meter and proportions have now to be considered. Also here, the Fugue's subject offers the best point of departure because, emphasized by an upward leap, the syncopation upon the pitch A sharp of the initial motif signals the beginning of a ternary phrasing system that prevails along the piece. Nine half-notes separate that syncopation from the cadence that tonicizes the fifth degree of D sharp on the downbeat of m.[6]. Nine half-notes are also spent from m.[6] to the tonic return on the third beat of m.[10]. This pattern becomes an element of propulsion, since it passes to be progressively enlarged after m.[10]. From the third beat of this measure to the third beat of m.[19], the phrase contains eighteen half-notes. The enlargement of this phrase is due to an event at m.[14]. Instead of allowing the A sharp cadence suggested by the subject to be accomplished, Bach changes the course of the harmonic progression through an evaded cadence which subtly announces the F sharp major of m.[30]. The moving toward m.[30], enhanced by the energy of the stretto that begins at m.[19] and enlarged by the three-beat cadence confirmation of mm.[28-29], comes to contain twenty one half-notes. The overlapping of the first and second segments on the downbeat of m.[30] provides for the continuity expected in a fugue.

The inverted version of the subject predominates along the sixty three half-notes of the central segment - from m.[30] to the third beat of m.[61]. Corresponding, therefore, to twenty one times the basic pattern of three half-notes, this segment contains an uninterrupted gesture of increasing energy. Re-asserting cadences, such as that of mm.[28-30], do not occur, and great impetus is added to the motion by the three-part stretto that begins at m.[52]. A special event takes place within this stretto. At mm.[52-53], the initial portion of the original subject, as configured at m.[3], re-appears, to be suddenly replaced at m.[54] by the inverted version of the subject. For this inverted version, instead of using the descending tonic-to-dominant fourth, like at m.[30], Bach uses the more incisive character of the descending dominant-to-tonic fifth. Thus, he devotes to F sharp major the same gesture he had devoted to D sharp minor in the lowest voice of m.[44]. What is important to observe is that the descending fifth to D sharp demarcates the middle of the Fugue, while the descending fifth to F sharp demarcates the Fugue's golden section.

The increasing activity of the Fugue's central segment is not without consequence. It prepares the arrival of the subject in augmentation at m.[62]. Surrounded by original and inverted subject versions (varied in some cases), three events in augmentation constitute the last segment of the Fugue. Although the three-half-note pattern becomes somewhat altered by overlaps, by the bridges that connect the different tonal areas upon which the augmentations are displayed, as well as by the coda's elaboration, in performance, still is the feeling of a ternary impulse inter-playing with the binary meter that gives the music a flexible and continuous flow. Slightly shorter than the two previous segments, the third acts as an enlarged and grandiose cadence gesture for the whole of No.8.

It is necessary to observe the texture and the use of registers in the Fugue. The material which constitutes the contrapuntal tissue derives mostly from the subject. The step line framed by a fifth - A^#, G^#, F^#, E^#, D^#, which acts as the subject's backbone, generates not only the counterpoint to the subject, as in mm.[3-4], but also the majority of lines that fill up the texture, as the two upper parts of mm.[7-10] illustrate. The dotted figuration which appears in the inner part at m.[24], and accompanies the augmentation at m.[77], is nothing but a variation of the subject. This homogeneity of the raw material creates, in turn, an homogeneous sound basis for the main entrances of the subject. Yet, the subject, instead of being repetitive (as subjects are usually considered), receives at each appearance a distinctive treatment. Bach exploits, for example, the character differentiation that exists between ascending and descending intervals. It suffices to compare the ascending fifth of m.[1] to the descending fifth of m.[44]. Rhythmic values, metrical positioning and tonal areas are also among the elements Bach exploits to make each subject entrance distinct. It is, however, on register that he relies the most. A good example is the way he saves the last augmentation, at m.[77], for the top register of the texture. From these observations comes the understanding that the piece, although written in three parts, contains six voices. Bach employs here a technique similar to the one which creates polyphony in his solo music for violin or cello. Figure 2a) shows how Bach distributes the voices in the different registers of the keyboard, and Figure 2b) lists the voices that correspond to the main subject presentations.

Fig. 2