1.1 What features in your piece help you to determine the prelude type?

Music is often defined as a sequence of sounds which are arranged chiefly on three levels:

-	on the horizontal level,	the up and down in a tune, called pitch pattern;
-	on the vertical level,	several pitches forming ensembles, called harmonies;
-	on the level of time,	with longer or shorter, regular or irregular time spans from the beginning of one tone to that of the next, called rhythm.

 
Within the context of this very general setting, each of these levels is usually carefully organized.

-	The horizontal level distinguishes melodic units, phrases and sections. This is what we are after if we analyze structure.
-	The vertical level distinguishes the ways in which simultaneous voices relate to each other. This is called texture.
-	Finally, on the level of time, the multitude of rhythmic values is packed into bars of usually equal length in an orderly way, with a definite hierarchy between their beats. This is called metric organization.

Although any piece of music will obviously feature most if not all of these components, a composer usually seeks particular expression of his artistic idea by molding these components in such a way that a certain design is recognizable. For such a design there is one basic choice to make: does he want to compose along the lines of a standard model which can be recognized as such, or does he want his piece to sound more like a spontaneous improvisation?

In the case of established form. models there are certain rules by which a composer must abide – e.g. dances require certain metric and rhythmic features, a canon requires a specific texture, sonata form requires a particular sequence of material. In the case of a composition sounding more like an improvisation, he may choose one or two of the six components mentioned above and shape his piece primarily according to these. In a prelude, i.e. in a composition carrying a name which does not reveal anything about the content of the piece, discovering this determining force is therefore of vital importance for both listeners and interpreters.

a) Pieces determined mainly by harmonic processes

Whenever melody and rhythm are negligible or neutral, harmony is the ruling factor this rule of the thumb sounds simple enough. But are melody and rhythm not always present?

Of course that is true. Yet, while rhythm is never actually "absent", it can be described as neutral if all rhythmic values are of the same length, or if different note values in different voices are arranged in such a way that their combined pattern amounts to completely regular motion. (This is called a complementary rhythm.)

Similarly, pitch will Of course never be absent – but it does not necessarily build melodies. A broken-chord pattern, whether created by one voice alone or jointly by complementary voices, is not primarily a melodic feature. (It could turn out to be melodic – as it often does in themes of the Viennese Classical style – if it gives way soon enough to a more lyrical continuation. However, if the same broken-chord pattern is carried through many bars, these will be judged as lacking genuine melodic features.)

b) Pieces determined mainly by processes of motive or figure development

Motive	is the name for a small melodic unit which is individual enough to be immediately recognized when it occurs again. (By common agreement, such a unit is actually only called a motive if it does appear more than just once.)
Figure	is the term preferred whenever such a unit is "unsingable", i.e. with a rhythm so fast or a pitch pattern so unmelodious that, while we might recognize it as a whole, we may not necessarily become aware of each single detail contained in it.

 
Motivic development occurs whenever such a unit is taken up repeatedly and under varying circumstances which prompt it to adjust some of its features. A composition would be described as "determined mainly by motivic development" if its material relies predominantly on a (usually small) number of motives, i.e. if, in a major part of a piece, there is always at least one voice which can be seen to derive from those melodic units.

c) Pieces following the outlines of "invention" or "fugue"

Both invention and fugue are standard form models which commonly appear bearing the heading "fugue" or "invention". A prelude, undeterminable in form and texture from its title, can be composed in such a way that it abides by the rules of these models.

How can we distinguish between "motivic development" and these established forms?

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Whenever a prelude is conceived as a strictly contrapuntal composition (i.e. in a texture of two or three voices all of which are independent from each other and all of which are continued consistently throughout the piece); and whenever it relies mainly on one melodic idea, then it is probably either an invention or a fugue.

If we wish to investigate further, how can we distinguish between the two standard models? In both cases, the "main idea" may occur accompanied by a "counter" idea; in both forms, the "main idea" may retreat for a while and then return. We are therefore looking for other features which might aid distinction.

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If the "main idea" enters in all voices successively, and if these imitations commence alternately from the tonic and the dominant, we can speak of a fugue. This is particularly the case whenever there are counter-subjects which, like the subject, wander through all voices. (Where a "prelude in the style of a fugue" may differ from a "real" fugue is at the beginning: instead of commencing with an unaccompanied subject statement it may introduce its main idea surrounded by a few harmonizing notes or chords.)

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If none of the above-stated conditions is given, we can speak of an invention. This is particularly the case whenever the "main idea" appears not only in imitation but also in sequence.

d) Pieces determined mainly by a small number of rhythmic patterns

There are preludes which seem determined by a few small motives – of a particular kind. These motives constantly change pitch, so that we may recognize the composition as being based on rhythmic patterns. It is consequently this little repertoire of rhythmic models which should find its way into the listener's memory.

e) Pieces determined mainly by metric organization

Whenever a piece appears determined mainly by its metric features, we can be sure that it is meant to convey a certain undefinable atmosphere, rather than the impression of an intricate play with structures or material development. In such a piece it will be the regular pulse – or any very simple, fairly monotonous variation on this pulse – which dominates anything else.

Such music was traditionally used (and is still being used in this way in many non Western cultures) to instill in the audience a meditative mood, if not to create a mesmerizing effect in the listener's mind. In the context of western music, such a meditative piece often precedes a composition which its author regards as too profound to be grasped immediately by an unprepared mind. The metrically-determined prelude thus serves to relax the listeners and empty their minds of too much activity.

1.2 What factors determine the overall design of a prelude?

Every piece of traditional music is horizontally structured, i.e. it consists of several sections each of which is determined by a rounded harmonic progression. Simple forms, like some dances and songs, may be made up of only two sections which may be more or less analogous ("binary") or contain a recurrence of the first A B A ("ternary"). They often feature repeat marks which clearly indicate at least one of the part endings. Preludes, however, are very often designed as a chain of phrases. The length of these phrases tends to be much more irregular than in simple forms where even-numbered bar patterns are preferred.

a) Where does the first section end?

When trying to determine the first structurally relevant cadential close, one is looking for a dominant (V) immediately followed by a tonic (1). This combination should be preceded somewhere by a chord on either IV or 11. While the dominant may appear with various additions (e.g. with a seventh or even a ninth) and may then sometimes come without its root (vii⁷), the tonic is less volatile: it never lacks its basis and is not normally mixed with additional notes.

Whether this first cadence indicates a separate structural section, or whether it serves only as an introduction to a larger portion, depends mainly on the melodic design so far. This can be easily determined by considering the following:

-	If the first cadential progression supports a single melodic unit complemented by an "answer" in the following bars, a more encompassing structural portion must be assumed.
-	If melodic design is either absent or arbitrary, the first cadence qualifies for the closure of an independent structural section. (Exception: In cases where one of the main voices – the top line or the bass – fails to truly take part in this initial phrase, e.g. by sounding a pedal note, and thus suspends the real beginning, a larger context is again implied.)

b) The second cadential progression

The second cadential progression in a piece usually departs from the home key of the composition towards a new tonal center which will again be confirmed by a perfect cadence. This modulating passage is nearly always more prolonged than the initial harmonic progression. Its end usually marks the conclusion of a structural section, irrespective of the function of the previous cadence.

c) The sections

The number of structural sections in a prelude is theoretically not restricted, although finding more than six parts is rare. Their boundaries are always delineated as described above: a conclusion in the harmonic progression coinciding with a conclusion in the melodic line if there is one.

d) What exactly constitutes a "structural analogy"?

Structural analogies recall the simpler binary and ternary designs and are therefore a very popular building principle in preludes. Such an analogy may consist of as little as two or three bars, or it may extend to the length of a complete section which is in some way recapitulated.

The simplest, but also least frequent, manner of creating an analogy is by literally repeating several bars. More ingenious and more widely used are variation, transposition and analogy.

i	Variation In a variation, a number of bars recur with modified features. Several details may be altered: - One or several of the voices may be written in a more elaborate pitch and/or rhythmic pattern; - the main tune may transfer to another voice; - an accompanying voice may present a different pattern. The features which will always remain exactly the same in literal variation are the key, the overall harmonic progression and the length of the analogous segments.
ii	Transposition The simplest form of transposition is that which keeps all the original details intact but merely transfers them to a new tonal environment. If there are, in addition, more than arbitrary changes in the details, we would speak of a transposition + variation.
iii	Analogy In an analogy, the structural design is taken up in principle rather than literally. The changes on the surface may be so considerable that they make it difficult to spot the analogy at first sight. For a good understanding of the structure, however, analogies are just as important as other correspondences, especially as they are much more frequent. Imagine, for instance, the following structural pattern in an early section: "two-bar model with sequence + modulation to a new key + cadential close with two bar closing formula".

Let us assume that the analogous segment at a later stage of the piece is initiated by a different two-bar model, which is then sequenced, that the modulation takes an extra bar to get where it is heading, and that the closing formula, although of equal length, also uses a different melodic design in the treble voice. This is a very subtle way of creating an analogy – and very rewarding to detect. Understandably, such analogies only make sense if the surface design – pitch pattern, rhythm and texture – is neutral enough to draw sufficient attention to structural processes.

1.3 How do you express the character of the prelude

a) What features help you in determining the basic character of the prelude?

The character of a composition (often called the basic character) is obviously conveyed through its material. Determining this basic character may at first seem a difficult task since Bach's scores contain almost no indications of dynamics, touch or articulation, or tempo. There are very few exceptions in the Well-Tempered Clavier. Single wedges and slurs occur occasionally (see e.g. the subject of the fugue in D minor, vol. 1), and tempo is designated three times (both the fugue in B minor from vol. 1 and the prelude in G minor from vol. 11 are marked Largo, and the prelude in B minor from vol. 11 is headed Allegro.)

In the absence of verbal hints we must assume that musicians of Bach's era were capable of deducing the character from the basic information contained in the music itself – i.e. from the rhythmic patterns used and from the design of pitch. If we try to imagine ourselves in their place, we would therefore ask: what kind of rhythmic and intervallic structure distinguishes a rather calm character from a rather lively spirit? The answer is simple enough and worth remembering:

-	On the one hand, the predominance of steps or leaps helps distinguish the contrasting characters; leaps are regarded as more energetic and stepwise motion as more emotional.
-	On the other hand, the character is expressed in simple or complex rhythm; a complex rhythm requires time to unfold whereas a simple rhythm invites virtuosity and might even sound less interesting when played too calmly.

Once you have established the basic character, you need to translate this fairly abstract concept into practical performance features. Here are some hints concerning the conclusions to be drawn regarding tempo and articulation:

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Whenever the material of a composition represents the rather calm basic character, the tempo can be anywhere between moderate and very slow. The general articulation is legato. Exception: non legato for cadential-bass patterns and any occasional consecutive leaps (more than one at a time).

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Whenever the material of a composition represents the rather lively basic character, the tempo can be anywhere between moderately flowing and very fast. The appropriate articulation is legato (or correctly: quasi legato) for the shorter note values, non legato for the longer values'. Main exception: an appoggiatura is always inseparably linked to its resolution, and the keynote leading note / keynote (do si do) formula is always legato. (These so called longer notes in a rather lively piece need further specification whenever we are dealing with notes prolonged by a dot or tie while certainly "longer" are played detached only whenever the prolongation (i.e. the value of the dot or tie) is itself of "longer" duration. If the time value of the prolongation equals one of the "shorter" notes in this composition, the note will be linked to the following one in quasi legato. Thus in a composition where non legato quarter-notes and quasi legato eighth-notes are a rule, a half-note prolonged by a dot or tied into a quarter-note would be detached from the following note; but a dotted quarter-note or any note prolonged in an eighth-note tie would not be detached.)

b) How do you make decisions regarding ornament realization?

Ornaments in polyphonic compositions of the Baroque era are, more often than not, decisive features in the material which they decorate. Their convincing execution depends on a smooth beginning, a motion which relates to the rest of the piece, and an appropriate ending.

The most common ornament in Bach's fugues is the long trill, indicated by one of several symbols: the abbreviations tr or t, the mordent symbol or one of the signs for compound trills). Here is how the long trill is played:

-	It regularly (i.e. according to the basic rule for ornaments) commences on the upper neighboring note. However, there is a very frequent exception: * Whenever the trill note is approached stepwise, i.e. whenever the main note is preceded by the interval of a second, from above or below, the trill will begin on the main note. * Another exception, although much less frequent, applies whenever an ornament decorates the first note of a phrase (see e.g. the initial note of the G minor prelude from Book 1). In this case, too, the ornament commences on the main note.
-	The trill motion is related to the general motion in the composition in such a way that the speed of the trill notes is twice as fast as that of the fastest written-out note values. While trills beginning on the upper neighboring note enjoy regular motion throughout, those which begin on the main note (and which therefore contain an uneven number of notes) hold the first note twice as long as the other trill notes, i.e. in such a way that all further upper auxiliaries fall on the stronger pulses within the trill (thus evoking the effect of a long appoggiatura).
-	Whenever the note following the trill, the harmonic resolution, falls on a strong,beat, the end of the trill should include a suffix, i.e. a turn to the lower neighboring note and back to the main note. * Exceptions: There are three cases in which no suffix is needed or even desirable: if the resolution appears too late, or too early, or not at all. The first is the case if the trill is prolonged with a tie; in this case the shake stops short on the last main note before the end of the bar, so that the tie can be fully appreciated. The second case occurs in dotted note patterns; here the shake stops preferably shortly before the dot. Finally, if the trill is succeeded by a rest, the shake should continue up to the very end of the ornamented note value, ending again on the last main note.

Any ornament which appears in the subject or one of the counter-subjects must be regarded as integral to this component of the material. Regardless of whether or not the composer repeats the ornament symbol with each entry of this material, the performer should retain such a trill throughout the work (provided the subject or counter-subject does not appear in drastically modified shape).

1.4a How do you deal with preludes determined mainly by harmonic processes?

i

Harmonic progressions and the development of dynamic tension When trying to find a valid interpretive concept in pieces determined primarily by harmonic processes, the basic facts to be considered are the tension generated by each of the chords, and the dynamic relation in consecutive chords. There is quite a simple rule for defining such relations: - The tension increases with every active step, i.e. with every step moving away from the relevant tonic. - The tension decreases with every passive step, i.e. with every step moving towards a resolution. Thus, in the simple harmonic progression with perfect cadence, the subdominant chord (or its substitute) as the active step represents the highest harmonic tension; the dominant chord with its clearly determined tendency to resolve follows with less tension, and the tonic is most relaxed. This natural design is enhanced whenever a function appears as a seventh or ninth chord (i.e. a IV7 carries even more tension than the simple IV; a V7 tends even stronger towards its resolution. Last but not least, the degree by which the harmonic tension (and with it the dynamic level which depicts this tension) increases is related to the "audacity" of the harmonic step.

ii

Secondary features Beyond these basic considerations of chord relationships there are two secondary features which must be given special attention since they will regularly repeal the rule mentioned above: the sequence and the pedal note. The term sequence describes the process by which a model – this can be a melodic unit or, in the case of a harmonically-determined composition, a group of chords – is repeated once or several times on different pitch levels. In such a case, the dynamic process between the chords is always established in the model. The sequential groups can but follow the same pattern, or else the relationship would not be comprehensible. The model thus sets an example which will be observed in each sequence, regardless of the actual harmonic relationships there. The pedal note also creates a law of its own. It consists of a bass note, usually entering on the dominant of the home key, which is sustained (or – more common on instruments other than the organ – reiterated) for several bars, while the harmonies made up by the other voices seem reluctant to surrender to the truth that the piece is soon to come to an end. Pedal notes obviously have their roots in Baroque organ music. Yet, while a sustained or reiterated note on the organ will, without doubt, objectively maintain a constant dynamic level, subjectively or psychologically it will work its way deeper and deeper into the listener's consciousness. This is how a basically simple event – that of a sustained or reiterated note – insinuates a gradual, smooth but persistent increase of tension. Finally, any truly melodic event suspends the processes of tension in pieces determined by harmonic relationships. If a melodic unit, however small, has enough character of its own, it may create motions that are momentarily independent from the underlying harmonic process.

1.4b How do you deal with preludes determined mainly by motivic elements?

i

The relevant motives, their character and dynamic design Finding the motives on which a piece is built would seem fairly easy. However, their scope should be determined carefully to guarantee a correct idea of structure and phrasing. Remember that at the beginning of a motive, occasional variations in subsequent appearances may occur. The ending may also include some pitfalls: on the one hand, the final note may appear in various versions but still belong, as a rhythmically necessary element, to the motive; on the other hand, notes repeatedly succeeding the motive may still be no more than an extension – and thus not generate anything of their own. They may not belong to the motive at all, and should then be clearly separated in color and/or phrasing.) The basic character of any such motive results from the same ingredients as it does in all other polyphonic compositions in this style: - A predominance of stepwise motion (interrupted, if at all, only by a "high tension interval") evokes a rather calm basic character; so does a complex rhythmic structure with a variety of note values, including syncopations, dotted and tied notes. - Frequent leaps (of a fourth or more) or broken chords as part of the motive indicate a rather lively basic character; so does a melodic pattern in simple rhythmic structure. Spelled out ornaments are another indicator for 'lively' basic character. Within each motive or figure, any of the following details can trigger a rise in tension: - an active harmonic step - an appoggiatura - a leading-note - a high-tension interval - a syncopation or other rhythmic feature As far as the development of motives or figures is concerned, the most frequent processes are: - sequence a unit is repeated on a different step of the scale, usually with some of its intervals adjusted; - imitation a unit is repeated in another voice, starting on any degree of the scale; - inversion a unit sounds upside down; - partial sequence varied sequence extended sequence the original idea (or a recognizable fraction of it) recurs but has been changed in shape and/or length.   The overall expressive value created by each of these processes can be very generally described as follows: - Rising sequences usually cause an increase of tension and falling sequences cause a decrease; - imitations, variations and inversions have in themselves no influence on the increase or decrease of intensity; - stretto formations and parallels represent heightened emotional intensity; - abridged and extended sequences tend to represent a loosening of the grip of tightly organized material, thus a relaxation.

ii

The development of tension For the overall dynamic design, You would consider similar factors as in a fugue. The development of tension is determined above all by the density of Prominent material. This density can be achieved horizontally or vertically. (For more details refer to the in depth discussion below under 2.7.) Another factor is the change of mode or, rarely, the change of character due to inversion.

1.4c How do you deal with Preludes which follow the outlines of "invention" or "fugue"?

 If you find that your prelude contains the determining features of a fugue, refer to questions and information nos. 5 11 for further guidance. You can actually also use most of this information if your prelude is an invention. However, the following differences between the two standard models exist, either in terminology or in design.

i

The material The "main idea" of an invention is commonly not named a subject but a motive – although either name will serve its purpose in furthering your understanding. (Also, possible contrapuntal "companions" could then be referred to as "counter-motives", a term which, though consistent, does not seem to have found its way into common usage.)

ii

The design The rules concerning an accepted order and grouping of entries in a fugue do not apply to an invention. The initial motive, after being stated clearly (with or without accompaniment) at the very beginning of the composition, is followed by a number of sequences and imitations. It may then be shortened to leave a less individual figure, or engender new combinations of its two halves. It may or may not give way to secondary motives. Most certainly, in the course of this neutralizing process, it will modulate to either its dominant or (if the home key is in minor mode) to its relative major key and come to a transitory halt in a full cadence. The second section commences in this new key, often with the same or similar presentation of material in inverted voices. In terms of structure, almost every possible continuation seems acceptable if we want to take Bach's own fifteen inventions as a guarantor. As far as the material serving as accompaniment to the main motive is concerned, everything is possible – from notes or chords representing nothing but a harmonic pattern, through simple quasi-independent yet not very individual lines, and up to counter motives with all the characteristics of what would be the counter-subject in a fugue. Even stretto imitations, although infrequent, could occur.

 

1.4d How do you deal with preludes determined mainly by rhythmic patterns?

i	The rhythmic patterns and their interrelations Rhythmic patterns can be analyzed in a way similar to motivic ones: whenever a particular sequence of note values is * significant enough to be easily recognized, * independent from other sequences, and * repeatedly taken up, we can call it a rhythmic pattern. It should usually come in varying pitch arrangements otherwise we might just as well identify it as a "motive". The sequence of note values which combined provide a rhythmic pattern is, in addition, determined by two factors: by its metric position (i.e. it may commence on a downbeat or be conceived as from weak to strong beat), and by its length. Whenever both the metric position and the length of two patterns within a composition are identical, we call them interrelated.
ii	Modifications and developments of the material The different melodic guises in which a rhythm pattern appears can usually best be described in terms of motion e.g. "leap up, four steps down, last note up" to allow for easy identification of minor variations. Whenever even such a very broad definition does not apply we should start distinguishing between pattern I a and pattern I b. The means of development which the composer may use when playing with these patterns are basically the same as those used for melodically determined motives: variation of detail, inversion, abbreviation and extension, augmentation and diminution, stretto and parallel.
iii	Tension curves  Build ups and declines of tension are initiated mostly by either the pitch level of sequences (rising sequences increase tension, falling sequences diminish tension) or the density of texture. In addition, dynamic climaxes can also be created by features beyond the main rhythmic patterns, especially by an unusual harmonic step.

1.4e How do you deal with preludes determined mainly by metric organization?

i

The pulse The dominant pulse can be any note value other than the fastest one appearing in the piece. You can usually find it by checking whether any one of the other rhythmic values is constant in one of the secondary voices, or whether it is given additional emphasis by double stems. (E.g. if the first note in each group of four sixteenth-notes carries a second voice stem, the pulse of the piece is most likely to be one of quarter-notes.)

ii

Secondary features and the development of tension The secondary features beyond this pulse include, above all, melodic lines, harmonic progressions and texture. These are also the only elements which can bring about tension buildups. Climaxes, however, tend to be fewer and more gradually prepared than in other pieces (not surprising in view of the "meditative" mood these compositions generally have). Particularly in pieces with a quarter-note beyond sixteenth-note structure, as described above, the ornamental nature often allows the piece to flow without too much change in sound intensity.

2.1 What exactly is the "subject"?

"Subject" is the term used for the leading idea of a fugue. This idea is always introduced at the very beginning of the piece. At this opening, it regularly appears unaccompanied, i.e. there are rests in the other voices so that the listener can gain a very clear and distinct understanding of this most important component of the thematic material. Throughout a fugue, the subject sounds many times. These appearances are called "statements", "subject entries" or "entrances".

a) How long is the subject?

If we compare the musical language with the verbal idiom, as we do e.g. when we talk about "statements," then the structure of a musical phrase would have to meet a corresponding set of requirements as does a verbal phrase. In any complete sentence, we expect a certain number of components without which the message would appear incomplete; and while there are many options how a clause may begin, we usually expect it to end with a full stop. Corresponding processes determine a musical phrase – here: the subject.

-	A subject can commence at any point of a bar. When interpreting a fugue it is worth establishing whether the beginning falls on a weak or strong beat (or between beats) because this may influence the character of the entire piece.
-	While the melodic details to be found in a subject abide by no rule Oust as the choice of words in a sentence is not prescribed), the functions these melodic steps represent in terms of the harmonic progression follow a certain order (as would the grammatical components of a clause).
-	The equivalent in music to a full stop in language is the perfect cadence. The conclusion of a complete musical phrase – such as the subject in a fugue – is therefore represented by the harmonic resolution from dominant to tonic (or from V to 1). In addition, you may consider the metric position. While the conclusion of a phrase could theoretically fall on any beat in a bar, subject endings on a down beat or middle beat are strikingly more frequent than others.

 
If you have always looked for the end of the subject by comparing the first bars of the piece with two or three later entries of the subject – seeing how many notes remain the same – you should know that this method is not entirely safe.

-	The final note may sometimes appear varied and therefore seem not the same in all entries; e.g. an original ending on the third degree may later be replaced by a conclusion on the keynote.
-	The notes immediately following the end of the subject but do not actually belong to it may appear similarly after some of the later statements and thus mislead you.

b) What is a phrase, and what are sub-phrases?

Continuing our comparison of a phrase in music with a clause in verbal language, we can state: Just as a sentence may consist of a single clause or contain sub-clauses of different order, so can a musical statement be of simple or more complex structure.

The existence of sub-phrases can most often be detected by looking for one of the following three features:

-	sequences
-	changes in pitch level
-	changes in rhythmic pattern

It also helps to think of singers or wind instrumentalists. If they would breathe somewhere during the course of the subject, then this breathing is most likely to represents the point of "phrasing".

Whenever a subject consists of a single indivisible phrase, the musical tension unfolds in a single, unbroken rise and fall. Whenever a subject contains sub-phrases, the message is only correctly transmitted if the musical line is structured.

Generally speaking, a fugue subject is always conceived as a unity, a oneness. Thus even if it does consist of several sub units, these should never appear as equally important, rivaling segments. Instead, a subject will always have one predominant center: the focusing point or climax. In a structured subject, this climax may either be reached in several consecutive sweeps each of which brings about higher dynamic tension, or the resolution of tension after the climax may occur in several gradually descending curves. In other cases, a "main clause" is preceded or followed by a "side thought" or "afterthought".

c) When you report the pitch outline in the subject, what are you looking for?

The pitch outline in Baroque polyphonic pieces usually fits in one of two categories:

-	A piece may either be distinguished by a variety of intervals including several larger leaps and occasional broken chord patterns; in this context, groups of shorter note values often represent written out ornamental figures (turns, mordents, inverted mordents).
-	Or there may be a predominance of small intervals (stepwise motion) combined with only an occasional single "high tension" leap. These high tension intervals include especially the minor sixth, the minor seventh, the tritone (augmented fourth / diminished fifth) and the diminished fourth.

 

d) When you analyze the rhythmic pattern, what are you looking for?

The rhythmic features of polyphonic pieces can be roughly grouped into two categories: 

-	The rhythmic pattern of a piece may be simple, with two predominant note values in the relevant material.
-	Or it may be rather complex, including a variety of note values, dotted and tied notes and syncopations.

 

e) What is most important in a harmonic progression?

When asked to investigate into the harmonic background of a subject you can proceed in two ways: you can either limit yourself to the essential details which you know to be relevant to the build up and decline of dynamic tension, or you can thoroughly analyze each harmonic step underlying the subject. As the second option is fairly complicated and needs some experience, let us begin with the first. There are actually only two "essential details" in a harmonic progression:

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Where is the active harmonic step that is the step from the tonic – that is the step from the tonic chord to the subdominant or its substitute, i.e. I – IV or I – ii? Look out for any conspicuous fourth or sixth degrees of the scale. (In C major, e.g., you would try to find any F or A falling on a strong beat or on a syncopation.)

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Is this active step followed directly by the passive step V – I (dominant – tonic), or is there a modulation to another key? In the case of a modulating subject, you will find a raising accidental suddenly cropping up, most often before the fourth scale degree. So, if the first unaccompanied bars of your fugue show a sharpening accidental (i.e. an additional sharp in any key signature with sharps, or a neutralized final flat in any key with flats) then this is where the shift is taking place. In this situation, when determining the end of the subject you are not looking for your original tonic chord but for the tonic in the new key. (This is almost always the dominant.)

In case you choose the second option and decide to undertake a more detailed analysis, here is some help: Most subjects are built on the steps of a simple progression, i.e. on tonic / subdominant / dominant / tonic in the setting I IV (1) V I or 111 (1) V 1; you would therefore do best to take note of those chords first. (In C major, these would be: C-E-G, F-A-C or D-F-A, G-B-D, C-E-G.)

Now identify in your subject all those notes which fall directly on a beat and determine their harmonic background. You will realize that, apart from the first and fifth degrees of the scale (i.e. C and G in C major), all notes can be clearly attributed to one of the harmonic steps.

The following peculiarities should be noted:

-	The dominant often appears as a seventh chord (e.g. G B D F).
-	The basic progression may appear harmonically ornamented; in this case, a function builds something like a "harmonic inverted mordent" with the chord normally preceding it, e.g.: I-V-I-IV-V-I or I-IV-I-IV-V-I.
-	In a minor key cadence, both the tonic and the subdominant (I + IV) are in minor mode. The dominant, however, uses the note of the harmonic minor scale, particularly the leading note. It is thus regularly a major chord and will therefore feature an accidental (e.g. in C minor: C-Eb-G, F-Ab-C , G-B-D, C-Eb-G).

   

f) Which are the features likely to increase tension within a phrase?

Several features in the three areas of harmony, melody and rhythm may contribute to heightened tension.

-	Active harmonic steps These are above all the steps from the tonic to the subdominant (I-IV) and tonic to supertonic or relative minor of subdominant (I-II or I-ii).
-	Appoggiaturas These are notes which "withhold" or "delay" the melodic resolution into the main harmonic step. Whenever the unaccompanied subject seems to imply a change of harmony on a weak beat, it is wise to double check the harmonic background compare with that in later subject statements. You will probably find that the harmonic change occurs on the strong beat, but that there is a melodic note purposefully lagging behind thus creating extra tension.
-	Leading-notes, particularly artificial ones A natural leading-note is a degree of the scale which is a semitone neighbor to a tonic chord note; it thus has a tendency to "lead" into it. (In a major scale the leading-notes are: the 7th leading up to the octave and the fourth degree leading downwards to the third; e.g. B-C and F-E. In a minor scale they are: the harmonically raised 7th leading up to the octave and the sixth degree leading down to the fifth; e.g. B natural-C and Ab G.) Artificial leading notes are semitones created with the help of an accidental (e.g. in C major: F# G).
-	High-tension intervals. These include above all the minor sixth, minor seventh, tritone and diminished fourth.
-	Syncopations or other rhythmic prolongations Syncopations are deliberate distortions of the metric order: a weak beat is prolonged (by a dot, a longer note value or a tie) in such a way that it "swallows" the following stronger beat and its accent.)

2.2 What is the importance of the subject in the fugue?

It has often been observed that it would seem wrong to say a fugue has a subject; one should rather say there is a subject which has generated a fugue. The perfect little musical entity which we call subject is in fact at the origin of the fugue. Its 11 companions" are dependent on it to the largest imaginable extent: were the subject any different, they too would not be what they are. The subject is responsible for the feelings of density and relaxation in the fugue, and it is the main force in creating structure. Whenever it rests for a while, its absence is distinctly felt.

Although this basic truth is valid in all fugues, the degree of impact exercised by the subject on its surroundings may vary slightly in each piece. Some of the common constellations are:

-	The subject can be spread regularly across the piece and always come accompanied by other prominent musical ideas. Thus, although leading, it will appear as "one in a group".
-	As the subject retreats momentarily, other characteristic motives may develop. Thus, the subject may appear as the leader of one "team" which is contrasted by another (admittedly less important) "team" representing a different color
-	Last but not least, the subject may not have the same importance at all times but, e.g., demand more and more attention as the fugue develops. It may do so by presenting its statements in more powerful variations, or by appearing in several voices almost at once.

a) When you discuss the subject statements, what are you looking for?

A fugue can contain any number of subject statements the twenty four entries in the first fugue of the Well Tempered Clavier represent by no means the largest number. These statements are usually named after the voice in which they sound. The following conventions are practical:

-	In a four-part fugue, the established names for the voices are those of the vocal ensemble: soprano, alto, tenor, bass (abbreviated S A T B).
-	In a three-part fugue, since using a selection from this four-part combination would seem arbitrary, a good solution is to refer to the voices as upper voice, middle voice and lower voice (abbreviated U M L).
-	In the few five-part fugues, the least problematic choice is to be to count them from v1 for first or uppermost voice to v5 for fifth or lowest voice. (The attempt made by some analysts to retain the vocal terms by introducing alto I and alto II or tenor I and tenor II has led to lengthy arguments among scholars. Such a quarrel seems somehow quite beside the point, and the v1 to v5 option may prevent further disputes.)

 

b) What kind of changes can you expect to occur in the subject?

In the course of the fugue, the subject may appear in various guises. This is important to remember when trying to locate all the subject statements.

-	One of its intervals may be modified to adjust to a different harmonic background. In many fugues, this is the case in the second and fourth entries, i.e. in the answer, the entries beginning on the dominant. An entry with such an interval adjustment is called a "tonal answer" – as opposed to the "real answer" in which all intervals remain exactly the same.
-	The end or the beginning of the subject (or both) may feature variations in pitch and rhythm. Frequent are prolonged or shortened first notes and delayed final resolutions.
-	Part or all of the subject may appear in rhythmic variation (e.g. showing dotted note figures where the original was in regular motion) or in metric variation (e.g. beginning on a weak instead of a strong beat – or vice versa – and continuing slightly "off beat").
-	The subject may appear upside down. This is called an "inversion".
-	Finally, the speed may appear changed in such a way that all note values are doubled and the subject is twice as long. This modification is called the "augmentation". Also possible, although less frequent, are entries in "diminution" where the time value of all notes is decreased and the subject therefore takes only half the time it did originally.

 

c) What are "stretto " and "parallel"?

There are certain rules dictating the way in which subject statements follow each other. These are stricter at the beginning of the piece perhaps to guarantee the opportunity for the listener to distinguish all aspects of the material. Thus in the first section of a fugue each voice is expected to wait for the conclusion of the previous statement. Only then is it allowed to launch a new entry. Later in the fugue, however, it may occur that a voice becomes "impatient" and embarks on a subject statement while another is still in the middle of it. This is called a "stretto"; it always indicates heightened tension. Strettos may occur between two or more voices, and between original and varied statements of the subject.

As polyphonic compositions stress the independence of all voices, a "parallel" where the subject sounds simultaneously in two voices is a very special feature. A parallel statement indicates a very high state of exaltation. Like the "stretto", it can also involve different versions of the subject.

Talking of grouped entries, a final means of intensification is the "repeated entry" in which one voice, after having stated the subject, does not give way to another voice but immediately launched the subject all over again. It usually does so either on a different harmonic step or by using any of the above mentioned variations – as if to add a new side or aspect to its argument.

2.3 What exactly are counter-subjects?

A counter-subject is a more or less consistent companion to the subject. It may enhance the character of its leader or rival him. But, like a faithful companion, it is bound to the subject in such a way that it will not usually appear in its entirety at times when the subject is resting. (There are fugues in which a prominent musical idea is introduced only after one or more sections have already passed, and then sounds both against the subject and on its own. This is called a "second subject", and in very special cases you may even find a "third subject". A fugue featuring more than one subject is called "double fugue", "triple fugue" etc.)

In a regularly built fugue, the first counter-subject will be introduced in the voice which launched the piece, and sound against the subject entry in the subsequent voice. Similarly, the second counter-subject (if the fugue has one) can be expected to appear first against the third subject entry, etc. One possible beginning of a four-part fugue is therefore (S = subject, CS = counter-subject):

(Don't forget, however, that there are fugues with no counter-subject at all; this happens if the subject is so dominant that it does not accommodate any rivaling ideas. In other cases, a counter-subject may come in later than expected, or it may accompany only a few subject statements.)

When trying to find out whether a line qualifies as a counter-subject you should ask yourself the following questions:

Is it independent?	A line which duplicates part of the subject in either rhythm or pitch pattern is not regarded as independent.
Is it melodic?	A scale segment in regular motion or a melodically meaningless group of notes would not be recognized.
Does it recur?	A melodic detail which only sounds once will not be given a formal name.

 

a) How can you determine the length of a counter-subject?

The length of a counter-subject will always roughly correspond to that of the subject. Where exactly it begins and ends can best be decided when compared with later appearances.

b) What phrase structure can you expect to find ?

The phrase structure of a counter-subject can vary considerably. We might find anything from an indivisible unit to complex phrases with sequences or other combinations of sub-phrases. Note particularly that the phrase structure of a counter-subject will often not coincide with that of the subject in answer to the demand of independence.

c) When determining the dynamic tension, what features you are looking for?

The development of tension represented in a particular counter-subject can be initially determined along the same lines as that in the subject. However, one important aspect to be kept in mind is that, given the request for independence, the climax of one will, in most cases, not coincide with that of the other. (For performers, this is very important to remember. It is vital to play each element with dynamic independence, despite the seeming difficulty of the task. Parallel dynamic movements, although easier to perform, often make it hard, if not impossible, for a listener to distinguish the elements of a fugue. This is a pity since "helping the audience to understand" is the essential task of the interpreter.)

d) What should a sketch featuring the phrase structure and the dynamic tension in the primary material of the fugue show?

Sketches, though certainly rather tedious to draw, are an invaluable help for two reasons: designing them makes things clearer in your head, and the visual image is a much better guide during the performance than some intellectual concept.

-	Write out the subject juxtaposed with all its counter-subjects, using a separate staff for each.
-	If any part of the material does not consist of a single unit, add a little hook or tick after the last note of each sub-phrase.
-	Now draw underneath each staff the opening and closing "hairpins" which in music represent the increase and decrease of tension.

 

2.4 How do you find the episodes in a fugue?

Those bars in a fugue where the subject is temporarily resting are called "subject free passages" or "episodes". A good way of marking them is by numbering them throughout the fugue (E1, E 2 etc.). Where their range is to be determined outside the score, "bars 5-7 may sometimes be clear enough, whereas in other case you may wish to specify "bars 5m-7d", meaning "from the middle of bar 5 to the downbeat of bar 7".

a) How many episodes can you expect?

The number of episodes in a fugue is not restricted. Theoretically, there could be an episode after each subject entry, although this is not often the case. Also, there are some very special episodes which, from their material, appear divided into two or more distinct segments. In such cases the composer will often use episode patterns which have already been clearly established. Whenever this occurs, special attention should be given as such subdivisions are frequently of importance to the structural design of the piece.

b) When ascertaining the material of an episode, what are you looking for?

There are basically three types of episodes:

-	The first type is directly related to the subject in terms of the material it draws on. It uses either the "head" or the "tail" of the subject and then plays with it in patterns of sequence (same voice, different pitch) or imitation (different voice, any pitch). Such episodes are often virtually inseparably linked to the preceding or following subject entry.
-	The second type of episode is characterized by one or more unique motives which set it distinctly apart from the main material. Such an episode motive is usually a rather short melodic figure which recurs several times and is characteristic enough to be easily recognizable. As with all other material in a polyphonic composition, it can move through all the voices and may even be varied or inverted. The character of such an episode motive is determined by the same features as that of the subject and its counter-subjects: by its design of pitch and its rhythmic features. If a motive is closely related to any part of the primary material, its character and dynamic curve will convey this. On the other hand, motives which are clearly independent should sound as different as possible from the main portions of the fugue.
-	The third type of episode fulfills a different function. In some instances, the stretch of music between the end of one subject entry and the beginning of the next conveys no message whatsoever of its own. Instead, it merely extends the cadential close of what happened before. Often it will be recognizable either by the typical cadential-bass pattern, or by a closing formula in one of the other voices. Typical patterns for such closing formulas are shown under ex. 1. (Some experts deny such cadential extensions the term "episode". Whatever you call it, remember that it indicates the end of a major segment of the fugue.)

 

(ex. 1)

 

c) In which way can one episode be related to another one?

Episodes in analogous sections of a fugue are often very closely related. An episode may

-	take up the material of an earlier episode, either literally, varied, transposed, or in exchanged voices;
-	feature an additional voice added to a previous thinner texture;
-	extend or shorten the material of an earlier episode, or develop it freely.

 

d) What are the possible roles of an episode in the overall development of tension?

An episode can establish three crucial relationships to its surroundings:

-	it can link two subject statements by leading from one towards the next;
-	it can be conclusive by resolving tension that was built up by the preceding subject statement;
-	it can represent a different register, appearing basically independent of its surroundings and serving as a color contrast.

   
The two former types usually feature material which is closely related to the subject. The contrasting type may contain independent episode motives or motives related to one of the counter-subjects.

2.5 Performance practice in Baroque polyphonic style

a) The basic character

The basic character of a fugue, just like that of a prelude, is conveyed through its material; you will therefore find a detailed discussion of this aspect above under 3a). Let us recall here only the rule of thumb:

-	A predominance of stepwise motion and a complex rhythmic pattern indicate a rather calm basic character.
-	Frequent leaps (intervals of a fourth or more), possibly combined with ornamental figures in the faster note values, and a fairly simple rhythmic pattern indicate a rather lively basic character. (You have, actually, already collected all the necessary information under 2. 1 c and 2. 1 d above.)

Let us assume that your performance already portrays most aspects of structure. How do you express abstract aspects like character, mood, intensity in a way which every listener will be able to grasp?

The predominant means by which a performer conveys character are: tempo, articulation and touch. All three work together in shaping and shading the character; they may do so in different combinations but should obviously not appear to contradict each other.

While touch may enhance slightly different nuances in each composition, tempo and articulation are directly connected with the basic character of a piece and can thus be determined more objectively.

b), d) Tempo, articulation and ornament realization

For all details regarding the adequate choice of articulation and execution of ornaments, please refer back to the discussion of these aspects under 1.3a).

c) How do You decide which relation to choose between the tempo of the prelude and that of the fugue?

All through the Baroque and Classical era, pieces of music which together form a larger work (i.e. the movements of a sonata or suite, or prelude and fugue, Prelude and toccata, etc.) were conceived as being related in their metric organization. This concept is comparable to the much more familiar demand of "rhythmic relationship" in architecture. Imagine a group of buildings constructed in the same style but to the order of different patrons and therefore with unrelated measures (height and width, angle of roof, pattern of windows and doors, etc.). Such buildings will appeal to the eye as individual houses, each of them a unit in its own right. A complex of related buildings, however, such as a castle, temple district or similar structured ensemble, will display a subtle yet very definite relationship between all the measurements.

As music unfolds in time which is measured in pulsations, the equivalent factor of "rhythmic relationship,, is created by proportions of the metric values. For this purpose, any of the several pulses which are conveyed in a piece of music can be used as a point of reference: the actual metric value indicated in the time signature, the larger unit of a half or whole measure, or the smallest note value appearing in the piece. 

A tempo proportion is then created in such a way that one note value of the first piece relates to Any value of the next by being either equally fast, or half or twice as fast (1:2 / 2:1), or three times as fast or slow. Even an implied but not actually sounding value, like the triplet fraction in a piece not featuring triplets, can be related to a pulse in another movement; this may be preferable particularly in the case of successive pieces of the same time signature and rhythmic organization which might otherwise present too little distinction. To give a few examples (out of many possible ones):

The quarter-note beat of a fugue may equal

-	a quarter-note in the prelude
-	an eighth-note in the prelude,
-	a half-note in the prelude, etc.
-	an entire bar of whatever duration in the prelude
-	three eighth-notes /three quarter-notes /three sixteenth-notes in the prelude an assumed (not occurring) triplet eighth-note or triplet quarter-note in the prelude.

 

2.6 What determines the design of a fugue?

As you will have already found out, the subject statements of a fugue can appear one after the other, or they can be divided by episodes. Whatever the pattern, obviously these elements do not simply pass by as a shapeless, disorganized chain of events. 

On the contrary, Bach's fugues are all constructed with very carefully balanced "sections". Since this design or structural layout is slightly different in each fugue and of vital importance to an understanding of the composition, it is useful to develop some secure method of analysis.

a) Which of the structural features are basic traits of a fugue? Which help to determine the particular design?

Remember the nursery explanation of the structure of a fugue?

It's like a conversation: one speaker brings up a topic and his friends pick it up one after another. The "first round" ends after each of them has added his comment. It is, however, possible for one of them to make a "sum up remark". (In the fugue, this is called a "redundant entry".) After a relaxation, with or without some contrasting talk, the discussion of the main topic resumes.

In each consecutive round, these are the rules:

-	The minimum number of speakers is two. (A monologue is no conversation!)
-	Nobody should speak twice unless he sums up one round. (Exceptions occur in intensifications where an additional entry reinforces another without making a "statement" of its own. Thus "stretto", "parallel" or "repeated statement" are counted as one "group entry".)
-	The maximum number of speakers is again "all plus one" (e.g. with four friends it is 4 + 1 = 5, one being allowed to comment twice).

This rule of thumb will almost always help to determine the length of the first section (or "exposition"); it often even enlightens the entire plan of the composition, with all its consecutive rounds. Concerning the number of "rounds", you can expect at least two. As for the maximum, there is no established rule. (There was a time when people, influenced by theories of the late nineteenth century, tried to detect a three section structure in every fugue. Despite the fact that this has long since been unmasked as a misconcept originating in sonata and ternary forms, these theories still seem to abound.)

As soon as each voice in your fugue has entered with the subject, the full ensemble is reached. However, while the "musical debate" relaxes (as in an episode) or embarks on a fresh start (as at the beginning of a new section), one of the voices often takes a rest. A subject statement which sounds accompanied by less than the full number of voices may therefore indicate the beginning of a new section.

Analogies in a fugue are not necessarily obvious at first sight, although some are. What is required is that a sequence of events (like a number of subject entries, accompanied by other material, perhaps including an episode) recurs later in the piece in the same or very similar order. This similarity does not refer to the position of the material in the ensemble; so the order may be the same with different voices being used to present the material – which is why some analogies are hard to find.

b) What do the harmonic features tell us about the design?

While a larger part of the piece will always appear closely related to the main key, there are usually passages which show a harmonic digression to either a different tonal area and/or to the opposite mode (to minor in a major fugue and vice versa).

To determine the harmonic background of a subject entry, it is best to look at both its beginning (i.e. the first two or three notes, to avoid misinterpretations in tonal answers) and its end. Subject entries within one section often appear in tonic / dominant / tonic / dominant progression. A change in this pattern is worth noting. Significant cadences are usually those which appear as obvious formulas or cadential-bass patterns outside the main material of the fugue.

c) How to sketch the design of a fugue?

Such a design is usually sketched using a horizontal column for bar numbers and corresponding horizontal columns for each of the voices. Here, "bricks" (which can be of different thickness or shade, according to the hierarchy of material) represent the subject and counter-subject entries, e.g.:

b.	1	2	3	4	5	6	7	8	9	10
S							S		epi-
A					S		CS1		so-
T			S		CS1		CS2		de
B	S		CS1		CS2		CS3		(rest)

 

2.7 Which factors determine the development of tension

The development of tension is the way in which the intensity, density and dramatic vigor develop, between the first and the last note of the composition.

Here are some of many possible patterns:

-	Some fugues begin by presenting their material in a very condensed manner. Later, however, the subject takes frequent rests, appears in a weaker mode (i.e. where the subject sounds less dramatic) or in weaker surroundings (e.g. with the other voices resting or sounding neutral lines, instead of counter-subjects).
-	In the first sections of other fugues, the material is introduced in more of a matter of fact way. It is only after the exposition that more and more intensity starts building up.
-	Yet other fugues are conceived along symmetrical lines.

 

a) What do you take into consideration when trying to decide whether or not (and how much) the tension rises within a section?

The development of tension within any segment of the fugue is determined above all by the density of prominent material. This density can be achieved horizontally or vertically as follows:

-

Horizontally, a group of subject statements in which the entries follow each other without delay will create more urgency than scattered statements interrupted by episodes. Even more so, both the rare but very effective "repeated entry" and the subject "augmentation" invite special attention since the statement is doubled in length.

-

Vertically, a subject entry which comes accompanied by characteristic counter-subjects in each of the remaining voices creates more intensity than one which has only one serious contestant, or one which is surrounded merely by neutral lines. Particularly effective in the build up of tension are strettos and parallel entries; they create an effect of breathlessness or of forces joined in battle respectively.

   

b) When discussing how the sections of your fugue relate to each other in terms of tension, what are the relevant factors?

The way in which the sections within the whole composition relate to each other depends above all on the factors mentioned above the density of prominent material and secondly on the harmonic progression. Note, however, that the minor mode does not always soften the character of the material, just as the major mode does not necessarily convert an introverted atmosphere into one more extroverted.