WTC I: Fugue No. 1 in C Major, Part III

Starting with WTC I: Fugue No. 1 in C Major, Part I, I began a discussion of the fugue portion of Bach's Prelude and Fugue in C Major from Book I of his Well-Tempered Clavier. I continued the discussion in Part II by talking about the first two of the five cadences Bach uses in this fugue. Now I'd like to extend that discussion by describing the remaining three cadences.

You will get the most out of the discussion if you open this web page in a separate browser window or tab. It contains a Macromedia presentation of the fugue as played by David Korevaar and as analyzed by him and by music scholar Timothy Smith. The presentation includes the score in musical notation, measure by measure, and also a timeline giving an overview of the score.

As I said in the previous post, a cadence is basically a sequence of two chords. The root note of the first chord is typically, but not always, of a higher scale degree than that of the second. Hence, the progression of chords is usually a "falling" one — the word cadence comes from a Latin word for "falling."

For example, C: V - I⁶ is the first cadence in the fugue. It starts on the "FOUR" beat of measure six with the notes G-B-D (the V or "five" chord of the C Major scale; count "one" for C, "two" for D, on up to "five" for G, the root note of the G Major triad). It moves from there to C-E-G-A (the I⁶ or "one sixth" chord, since A, the sixth note in the C Major scale, is added to the basic C-E-G triad that has the keynote of the C Major scale as its root). These notes do not occur all at once, but are spread out, in what amounts to an arpeggio, over all of measure seven.

Prior to this quasi-arpeggio, the notes E and G are heard together on beat "ONE" of the seventh measure, in what can be considered the official completion of the C: V - I⁶ cadence. In a Bach fugue, some notes of the completing chord of a cadence are ofttimes delayed in this fashion.

This C: V - I⁶ cadence thus spans the transition from the sixth to the seventh measure of the fugue, where the exposition section of the music ends and the first development section commences.

The effect of this cadence is to tell the ear:

• what the keynote or tonal center of the music is (specifically, the note C);
• what scale is being used (C Major); and
• what is happening in terms of the structure of the fugue (a new section is beginning)

Because it is a variety of the generic V - I cadence, musicologists call the V - I⁶ cadence an "authentic" cadence — though, as explained in the previous post, this one is an "imperfect authentic cadence" (IAC) and not a "perfect authentic cadence( (PAC). There are other types of cadences, but in this fugue only IACs and PACs are heard.


At the start of the third development section in the timeline, at the transition between measures 18 and 19, we see dm:V - i. Here, the V and i chords of the key of D minor confirm an ongoing modulation into that key.

Two measures later, in the middle of the same section, straddling the bar line between measures 21 and 22, G: V - I betokens a new key of G Major — which happens to be the major key built on the fifth degree of the original "home" key of the fugue, C Major. This is appropriate, because in the run-up to the coda, C: V - I brings us back to that home key. These are the three cadences I'll be discussing in what follows.

I'll get back to dm:V - i and G: V - I presently. For now, I'll skip ahead to C: V - I.

We hear in the tenor, alto, and soprano voices, respectively, the notes D, G, and B at the very beginning of measure 23. Well, the V chord of C Major is ... wait for it ... a G triad made of notes G, B, and D! So when the timeline shows C: V - I at this point, this is the start of it.

You can hear this G-B-D triad by clicking on the timeline at measure 23. Bear in mind that when you do so, the first two notes you hear are, for some reason, the final two sixteenth notes of the previous measure. Only then do you hear the actual G triad — played atop a sixteenth note on F which commences a run of similarly brief notes up and down the scale in the bass voice. This run is a capricious sort of "free association" exercise; it extends a similar one in the soprano voice in the previous measure.

The business of accomplishing the impending V - I cadence, meanwhile, is left to the other three voices: the soprano, the alto, and the tenor.

The rest of measure 23 gives us a musical picture of G-B-D, the V chord of C Major, preparing to morph into the I chord of C Major, C-E-G, at the outset of measure 24. If you look closely at the tenor, alto, and soprano voices, you can see that the notes B, G, and D — the notes which make up the V chord — keep reappearing throughout the remainder of measure 23.

That said, there is also a sort of prefiguration of the resolution of the cadence at beat "THREE" of measure 23, when we hear (from bass to soprano) the notes E, G, E, and C, which describe the upcoming I chord in an inverted variation — i.e., the lowest note is not the root note of the triad, C.

Then, following beat "FOUR," the very last "and" beat of measure 23 has a B in the soprano voice, a D in the alto (which actually began sounding on the "FOUR" beat) and a G in the tenor (which also began on the "FOUR" beat). Meanwhile, the free-form bass run has itself joined in the fun, settling onto a low G note.

At last comes the first notes of measure 24, which (from bass through soprano) are C, G, E, and C: a C Major triad in root position. The G is actually the one that commenced sounding on beat "FOUR" of the prior measure. But the B and D from before are now transformed into C and E. The C: V - I cadence is complete. Bring on the coda!

The coda, the brief section which wraps up this fugue, is also known as the peroration. It consists of measures 24 - 27 of the piece. Through these final four measures the bass voice plays just one long, sustained note, on C. This is called a "pedal" note, and it is no coincidence that the pedal is the keynote of the home key of the fugue. Nor is it a coincidence that the final notes heard in the fugue find C being played, in different octaves, by the bass, tenor, and soprano voices, while the alto voice bifurcates into E and G, so that in addition to the keynote of the home key, C Major, we also hear its most basic three-note chord, the C Major triad, one last satisfying time.


Now, back to the two cadences I skipped over, dm:V - i and G: V - I.

The dm:V - i cadence spans the transition between the second and third development sections of the fugue, lying as it does across the bar line that separates measures 18 and 19. From the "dm" notation that is shown in the timeline, we expect first to find in the score the V chord of the D minor scale, which is the major triad A-C♯-E. Then we expect to find D-F-A, the i chord in the same, D minor scale (written with a lowercase "i" because it is a minor triad).

The easiest way to approach finding this progression as we look at the score itself is to look in measure 18 for a sharp ("♯") sign on one or more notes. Since in the key signature of the fugue there is no sharp sign on C — there are no sharps or flats whatsoever in this fugue's key signature — the C♯'s will have to be notated with "accidental" sharp signs.

Indeed, we find three C♯'s: one in the tenor, and two in the alto. The first of these to be played occurs on the 18th measure's "TWO" beat. It is in the alto, and is accompanied by an E (a held-over note) in the tenor along with an A in the soprano. These three voices are at this juncture combining to play an A Major triad, which is, by no coincidence whatever, the V triad of the D minor scale.

Notice that the bass voice, meanwhile, is doing its own thing. Its note at this point is F, which is not part of the A Major triad. As we saw when we analyzed the C: V - I cadence above, the bass is capable of engaging in a sort of sleight-of-hand diversion from the main business of establishing the beginning of a dm:V - i cadence. But in this case what the bass voice is doing is yet more important: reprising the subject of the fugue.

That bass note, F, is the seventh note to occur in the subject motif ... which may be a bit difficult to detect, in this particular repetition, since the first note is stretched out in length, from its customary eighth note, into a quarter note. I hear this stretching as a sort of hesitancy on the part of the bass voice to launch into the subject motif at all.

At any rate, now that we've found the V chord, A-C♯-E, we're looking next for D-F-A, the i chord of the key of D minor — which, since it is the i chord, is a D minor chord. Not surprisingly, we find it on the "FOUR" beat of the same measure, measure 18. The bass voice has now decided to cooperate with the cadence by playing the A note of this chord, while the tenor voice shuts up briefly. Meanwhile, F and D are played by the alto and soprano voices, respectively.

How quickly things change! On the "and" beat just before the "THREE" in measure 18, we have just heard an A and a C♯, two of the notes from the V chord, along with a sixteenth note on G which migrates hastily to E, the V chord's third note, on the micro-beat between the "and" and the "THREE." In other words, just prior to "THREE" in measure 18 there is another instance of the V chord ... and then, all of a sudden — with the A note on the "and" beat being sustained to become the A note on the "THREE" — the i chord arrives.


But the "THREE" beat of measure 18 is not the actual conclusion of the dm:V - i cadence. That distinction is reserved for the chord that is heard of the "TWO" beat of the next measure, measure 19. There, the notes we hear are, from bass to soprano, D, D, F♯, and D.

Just prior to that chord, on the "and" beat, we hear the V chord again: A-C♯-E. When we hear D-F♯-E on "THREE," we take it to be the i chord at the end of a perfect authentic cadence which began with the V chord. This is so despite two objections.

The first objection is that the note A which, at a perfect fifth interval above the tonic of D, is supposed to be part of this i triad is absent. The is no big problem, because Bach soon has the F♯ which is played as part of the chord ascend, in the alto voice, to A (albeit by way of the intervening G). This happens in the course of having the alto restate the subject of the fugue. Accordingly, the ear hears order restored to the cadential conclusion at the heroic hands of the fugue's own subject — very pleasing, that.

The second objection is that the supposed i chord is not really a minor triad, as it seemingly ought to be if D minor is to be the new temporary key of the fugue. If it were a minor triad, it would be D-F-E, not D-F♯-E. F is a diatonic (scale-based) note in the D minor scale; F♯ is not. What's up with that?

Joseph Kerman's The Art of Fugue

According to Joseph Kerman in his excellent book The Art of Fugue: Bach Fugues for Keyboard 1715-1750, this raising of F to F♯ in measure 19 produces a "novel effect" that

... seems to arise from a compound of the unexpected D-major harmony — with F♯ — the pause on the pedal D [bass note], brief as it is, and the way the two inner voices [i.e., the alto and tenor] ease their way or glide across the cadential downbeat [on "THREE"]. ... The progression conveys something of the mood of an interrupted, or deceptive, cadence, though technically it cannot be called that, of course. (pp. 7-8)

An interrupted or deceptive cadence is one that does not arrive at the I or i chord (depending on whether the scale is major or minor) but winds up on (for instance) the chord based on the sixth degree of the scale. This is not that, but Kerman says it feels like it anyway. He continues:

... to call the D-major chord a tierce de Picardie also seems odd, for Picardy mode-change is supposed to happen to the tonic chord at the end of a composition ...

Here, he's referring to a so-called "Picardy third," a device Bach and others used by means of which to end a minor-key fugue on a major chord by raising the chord's 3rd degree — as F to F♯. That's what he's doing with this chord: raising the 3rd. But it's being done not to the tonic chord here, but to "the dominant of the dominant," says Kerman.

The "dominant" is the 5th degree of a scale. If the scale is C Major, the dominant is G (count: C-D-E-F-G). Then, taking G as the tonic, its dominant — the "dominant of the dominant" — is (G-A-B-C-)D. The triad built on it ought to be (since F and not F♯ is in the original C Major scale) D-F-A. Here, however, Bach exercises the prerogative of his genius to make it D-F♯-A.

So, as the third development section begins, we hear once again that we are — albeit temporarily — in a key other than the home key of the fugue. This time, that temporary key is D minor — despite the F♯. That will change when the G: V - I cadence arrives.


Unlike every one of the cadences I have discussed to this point, G: V - I does not end a section of the fugue. Instead, it is found in the middle of the third development section.

On the "THREE" beat in the 19th measure, which begins in the key of D minor as a result of the dm:V - i cadence just analyzed, we hear (as just mentioned) a note that ordinarily does not belong here: F♯. F♯ is not part of the D minor scale. It is, however, part of the G Major scale. Perhaps its presence here foretells that D minor's time as the reigning temporary key will end quickly, and a V - I cadence initiating G Major as the new temporary key of the piece can be expected soon.

Indeed, a G: V - I cadence is completed (as the timeline indicates) in the middle of measure 21. On the "THREE" beat of that measure, the notes that are heard are G (bass and tenor), D (a held-over note in the alto voice), and B (in the soprano). G-B-D is the I triad in G Major. (Notice that since the soprano voice is playing D and not G, this is an imperfect authentic cadence.)

Given that this event concludes a G: V - I cadence, albeit imperfect, one would expect to find among the immediately preceding notes an explicit V triad of the key of G Major, D-F♯-A, stacked up nicely as a single chord. And so we do. On the "TWO" beat of the same (21st) measure, we have F♯ in the bass, A in the tenor, and D in the alto. (The soprano voice is playing a C, but never mind.)

In the space of just two of the four principal beats of a four-beat measure, a G: V - I imperfect authentic cadence has occurred, and we are now out of the brief temporary key of D minor and into a new temporary key, G Major.

Notice that, although this is technically an authentic cadence, it does not feel like one. There is no sense of conclusion or finality. No sense that a point of articulation has been reached, where one section of the music gives way to the next. At most, we feel like the cadence is just there to limn the change of key from D minor (with a key signature of 1 flat) to G major (1 sharp), en route to quickly settling back into the original key of the fugue, C Major (no flats or sharps). And, in fact, that is exactly what is going on.

So, not surprisingly, the temporary key of G Major will itself hold sway but briefly, until the C: V - I cadence discussed earlier has been completed at the beginning of measure 24.

If you look again at the way that cadence transpires, you will see that G — the "destination" note of G Major — is sounded both in the V chord and then in the I chord of the C: V - I cadence. In the tenor voice, it is even sounded as a single, sustained note that is held over from one chord to the next. The "destination" note of the key that is on its way out (G Major) turns out to be also the "pivot" note by means of which the successor key (C Major) is ushered in.

Clever fellow, that Bach! He is always building harmonic order (chord progressions) out of supposedly "free" melodies (voices) by using such devices as pivot notes and faux Picardy thirds. That is, after all, the essence of the art of the fugue.

WTC I: Fugue No. 1 in C Major, Part II

In WTC I: Fugue No. 1 in C Major, Part I I began a discussion of the fugue portion of Bach's Prelude and Fugue in C Major from Book I of his Well-Tempered Clavier. Now I'd like to continue the discussion by talking about the cadences Bach uses.

You will get the most out of the discussion if you open this web page in a separate browser window or tab. It contains a Macromedia presentation of the fugue as played by David Korevaar and as analyzed by him and by music scholar Timothy Smith. The presentation includes the score in musical notation, measure by measure, and also a timeline giving an overview of the score.

Running along the bottom of the timeline are occasional cryptic symbols. For instance, at the very beginning — underneath the very first appearance of the subject of the fugue, as shown by a gold bar — is C:. It means that what immediately follows (which is the entirety of the fugue) is in the key of C Major.

Centered under the end of the 6th measure, meaning that it spans the bar line between that measure and the next, seventh, measure, we can see C: V - I⁶. The symbols following the colon specify a "cadence": a particular kind of chord change from a setup chord (here, "V") to a resolving chord (here, "I⁶").

See below for more on what a cadence is, in general. Note, moreover, that Wikipedia has this article on the subject of cadences. Also, see this lesson on cadences at Gary Ewer's Easy Music Theory web site.

As it is used here, this particular C: V - I⁶ cadence means (among other things) that the music you are hearing is confirmed as being in the key of C Major.

That is, the musical scale Bach is using at this point in his fugue has the note C as its keynote. A chord progression from the V ("five") chord of the C Major key to the I ("one") chord of the same key — here, the specific resolving chord is actually the I⁶ or "one six" chord — tells the ear that the "destination" note or tonal center which the music revolves around and resolves to at is C.


The V chord in C Major is made of the three notes G, B, and D. The I chord in C Major is, normally, C, E, and G. But for the I⁶ chord, the sixth degree of the C Major scale, A, is added to make C-E-G-A.

As I say, moving from V to I (whether or not the latter is a "six" chord) is a good way to highlight what key the music is in. Bach does this highlighting trick at the exact transition from the "exposition" section of the fugue to the fugue's first "development" section in order to highlight the fugue's key of C Major!

One reason for doing this is that, in measures prior to measure six, Bach uses an alternate key, that of G Major, for two of the four voices. The music is written in such a way that some ears will hear an abrupt key change from C Major to G Major starting in measure two, though other ears will not. Accordingly, when Bach switches gears with the intention of launching into the first development section of the fugue, he uses a cadence that will tell all ears, "C Major is really the official key!"

Another function of the C: V - I⁶ cadence at this point is to signal the end of the opening section of the fugue — the exposition — and the beginning of a new section, the first development section.


Specifically, Bach arranges for the notes G, B, and D to sound together, as if they were written as a single chord, on beat "FOUR" — the fourth non-"and" beat — of measure six. (You count the eight beats of each measure of this fugue "ONE-and-TWO-and-THREE-and-FOUR-and." Normally, "ONE," "TWO," etc. are the emphasized beats. Here, the "and" beats are the more prominent.)

G, B, and D are the notes of the V chord in C Major: the G major triad. In this sequence, the V chord in the sixth measure "resolves to" the I chord of the same key — C Major — appearing in the seventh measure.

The I chord in C Major, to repeat the above, is made up of the notes C, E, and G. The first notes to sound in measure seven are E (in the bass voice) and G (in the tenor and alto voices). The G in the alto voice is actually the continuation an earlier G note that is being held over from the previous measure's G major triad: G, B, and D. It serves as a pivot tone between the two chords of the cadence.

That G-B-D triad sounds on the FOUR beat of measure six, with G in the bass, D, in the tenor, G again in the alto, and B in the soprano. The G in the bass is also held over from an earlier G note in measure 6 ... très complex, no?

Getting back to measure seven, the soprano voice is silent at the outset of the measure, and there is as yet — as of the "ONE-and" beats — no sign of the C note. The fact that the supposed I⁶ chord at this point lacks both the C note and the A note weakens the cadence to the point of being just barely perceptible.

But now the initially silent soprano voice begins calmly to restate the subject of the fugue ... starting on C! At that same instant, the alto voice falls silent, and the bass voice plays C as the first (and also the third) of four sixteenth notes. (Unfortunately, as the score is presented, the notes of the various voices do not line up under one another precisely as they ought.)

Then, all through the remainder of measure seven, we hear in the soprano voice the notes E, G, and A (to make a quasi-arpeggio of the I⁶ chord) played with greater prominence than any of the other notes the voice also plays. Along with the C which leads off the the subject, E, G, and A are the four notes of the I⁶ chord in C Major! They are actually heard on the "and" beats, which makes them stand out to the ear.

It further helps that they are in the soprano voice. That voice, along with the bass, is one of the two "outer" voices in a four-voice fugue. As such, the soprano and bass voices are easier for the ear to follow than either of the two "inner" — tenor and alto — voices.


All that notwithstanding, the actual C: V - I⁶ cadence at this juncture officially ends on the "ONE" beat of measure seven with just the notes E (bass), G (tenor), and G again (alto) being heard. The V chord on the "FOUR" beat of measure six was, from bass to soprano, G-D-G-B. That makes it a root-position chord — i.e., it is not "inverted." It has its tonic note, G, in its lowest voice.

But the subsequent I chord does not have the tonic note, C, in root position in the bass voice. Nor does it repeat the tonic in the highest voice, the soprano ... which, on this beat, is silent. In fact, the tonic is not heard at all in this chord on the "ONE" beat.

For all these reasons, the I chord cannot here be considered as constituting the finish of what is known as a "perfect authentic cadence" from V to I. Instead, it wraps up what is merely an "imperfect authentic cadence." If a perfect authentic cadence (PAC) is analogous to a period in a musical utterance, an imperfect authentic cadence (IAC) is like a comma. And this particular IAC is like a very faint comma, indeed.


The sequence from V to I⁶ is, as I have been saying, an example of a "cadence," a musical term which derives from the Latin word cadentia, for "falling." Whether or not the I chord is a sixth (as it is in this case, with the A note eventually being added to to the C major triad of C, E, and G), the progression from V to I, however weak it may be, is nonetheless called an "authentic" cadence. This is so because it starts on the V chord (in the key of C Major, the notes of the V-chord are G, B, and D) and "falls" to the I chord: C (whose appearance is delayed), E, and G. The fact that this cadence is imperfect does not make it any less an authentic cadence, from the point of view of music theory.

The direction of movement is "falling" for the simple reason that the root note of the V chord, G, is higher in scale degree (with respect to the C Major scale, the scale which embodies the key of the music at this juncture) than the root note of the I⁶ chord, C. G represents the fifth degree of that scale, while C represents the first degree.

An authentic cadence is typically considered one of the most musically conclusive ways to finish a section of a piece and assert what key the music is in. It is as if the ear hears the cadence and says to itself, "Ah! We are definitely in the key of C Major, as this particular section comes to an end!"

Musical devices such as cadences that are used to tell the ear when a section or musical phrase has come to an end are sometimes referred to as "articulations."

Later on, Bach will use authentic cadences not to reaffirm the original key of the piece, as here, but to show how it has (temporarily) been changed. Many but not all of these cadences will end sections of the fugue. Some, however, will occur in the middle of a section and will constitute the endings of phrases rather than sections. Even so, all these cadences can be considered to be articulations.


Near the outset of the second development section of the C Major Fugue, Bach changes the key to A minor. The timeline shows the cadence which confirms this "modulation" — as a key change in the middle of a piece is usually called — as am:V - i. Here, "am" signifies the new key of A minor (the letters are in lower case for a minor key). The chord progression which introduces the new key is V to i in that new key. (This time, the i chord — shown with a lowercase "i" because it is a minor chord — is not a sixth. That fact is of no great importance here.)

The V chord in A minor consists of the notes E, G♯, and B. The fact that the "V" is uppercase signifies that the "default" triad (three-note chord) based on the root note E, when E is taken as the fifth degree of the A minor scale, is not being used here. Why not? The default fifth-degree triad of the minor key whose keynote is A is made up of these three notes: E, G (without the ♯), and B. It is a minor triad, where E, G# (with a ♯), and B constitute a major triad.

A major triad, not a minor one, is typically needed to initiate a cadence. To get a major chord to act as the triad based on the fifth degree of a minor key — specifically, the key that uses A as its "destination" note or tonal center — Bach has to raise the note G to G♯. G is not a part of the A minor scale, but G♯ is. Specifically, G♯ is the so-called "leading note" of A minor; it pulls the ear toward the keynote, A.

Since G is not given a sharp sign in the key signature at the beginning of this fugue's score, it has to be given one expressly in the measures leading up to an including the actual cadence. In musical notation, expressly given within-measure sharps or flats are called "accidentals."

So in measure 11, on beat "FOUR," in the soprano voice we suddenly hear (possibly consciously, possibly subliminally) a heretofore unexpected note: G♯!

The actual completion of the V - i cadence which this entry of G♯ foretells will not happen until the start of measure 14. Meanwhile, every time a note that would ordinarily be played as G is indicated in the score, it is sharpened to G♯. (Confusing the issue is the fact that — some, but not all — F's are also being sharpened, to F♯. In G Major, F's are sharpened to F♯ ... and at times some of the voices in this passage are in G Major.)

By the time we get to the "TWO" beat in measure 13, Bach is ready to give us, as an initiation of his actual V - i cadence, a full statement of the V major chord in the key of A minor: notes E (tenor), G♯ (alto), and B (soprano).

The bass voice is already playing a quarter note, D, which is not in this V triad; Bach is using not just the V triad but the V7 or "five seven" — the so-called "dominant seventh" chord. That's fine: a V7 chord can lead off a cadence, in place of V.

Then, on the "and" following beat "THREE" in measure 13, voilà! The notes E (bass), A (tenor), and C (soprano) sound, with the alto voice falling silent. These notes form — yes! — the i chord of the key of A minor.

However, this succession of chords is just a preliminary hint of the actual am:V - i cadence that is about to transpire. This preliminary am:V - i cadence, though an technically authentic one, is imperfect. It ends up on a triad that is inverted from the canonical root-position A-C-E i chord. Moreover, the soprano voice is sounding C, not the root note A.

The actual am:V - i cadence begins on the "FOUR" beat of measure 13, where we see "tr" (for trill) printed above the notes B (soprano) and E (bass). These are two of the three notes of the V chord in the key of A minor, E-G♯-B. A split second later, the missing G♯ sounds in the tenor voice. Then, hot on the heels of that, we hear the new keynote, A, as a sixteenth note in the soprano voice, leading to ...

... that very same new keynote, A, being immediately confirmed by being sounded, in those same three voices, on the "ONE" beat of measure 14. This impresses the ear as the actual conclusion of a perfect authentic cadence — even though only the tonic note of the i chord, A, is actually heard at this point. And Bach's second development section has officially begun!


There are more cadences yet to come in this fugue. I will discuss them in the next post in my "Bach's WTC" series.

WTC I: Fugue No. 1 in C Major, Part I

In Bach's Well-Tempered Clavier I hailed this WTC web site as a fine introduction to Bach and his music. Now I'd like to look a little further into what it says about one of the Bach pieces, the Prelude and Fugue in C Major, from WTC Book I.

In what follows, you will be well advised to have this Macromedia movie at that site open in another browser window or tab.

I find the problem with even as clear and straightforward a presentation as the one given by Timothy Smith and David Korevaar in their Macromedia movie is that they assume their visitor is a serious student who has a more thorough knowledge of musical terms and concepts than this particular visitor actually does. Their measure-by-measure timeline for the fugue portion of the C Major Prelude and Fugue is an invaluable aid ... but it presents the casual visitor with terms and symbols that may be unfamiliar. I'd like to have a go at filling in some of the blanks.


The timeline shows the 27 measures of the fugue as dotted-outline blocks, representing measures. Each measure is split into (up to) four musical "voices" per measure. Each voice in a fugue is a melody. It is a coherent series of notes played on (in this case) the piano to the accompaniment of ... well, of the other three melodies. Notes of the four voices often coincide in time — they are struck together, at the same instant — but often they arrive at different moments in time.

Having different melodic lines unfurling at the same time is the essence of counterpoint. Contrapuntal music is said to be "polyphonic": many-voiced. As the quasi-independent voices make their individual statements, their juxtapositions and overlappings yield an ad hoc harmony, as if chords were being played instead of four individual melodies at once.


Bach sets up the situation for this to occur by choosing a snippet of melody, called a "subject," which is played all by itself at the beginning of the fugue. Specifically in this particular fugue, the subject is the first 14 notes to be heard. (On the musical staff of the score in the Macromedia movie these look like 15 notes, not 14, because two of the score notes are joined by a "tie" — which means they are played as one long note.)

These 14 notes take us all the way through the first measure of the music and well into the second. It may seem confusing at first, this idea that a musical motif such as the subject of a fugue need not coincide with some full number of measures. But there it is — it usually doesn't.

The subject is then picked up by the second voice to enter the proceedings, which is higher in pitch than the first voice. This happens partway through the second measure.

Meanwhile, the first voice goes right on to play something other than the subject — something which complements the second voice's (higher) rendering of the original subject. In fact, the first voice plays the first two sixteenth notes of that complementary stretch of music — called "free counterpoint" — even before the second voice comes into picture. That's one reason why there is an eighth rest shown at the outset of the second voice's part in the score. (As a matter of fact, there is also an eighth rest at the very beginning of the score, preceding the first statement of the subject. You could even consider the prefixed eighth rest to be part of the subject.)

Bach's subject (again, preceded by an eighth rest) enters the fugue for the third time in the fourth measure, in yet another voice. This voice is lower than the first two. We can consider the first voice to be the "alto" voice, if we wish, and the second voice to be the "soprano," because it is higher in pitch. That makes the third voice the "tenor" voice, and the fourth and lowest voice (which will take up the subject in measure five) the "bass."


The echoing of the subject in a second voice — in this case, in the soprano voice — is what fugue aficionados call an "answer." Here in this fugue, the answer is raised from the original key of the piece, C Major, to another key: G Major. The note G is the fifth degree of the C Major scale; it is referred to as the "dominant," to the note C's "tonic," in that scale.

Because the keynote G of the answer is not the same as that of the original subject, which is C, this is a "tonal" answer. A tonal answer will usually be transposed into the dominant key — e.g., into G Major when the original key is C Major.

In some fugues, the answer is in the same key as the subject, and such an answer is referred to as "real" rather than tonal.

One of the ways you can tell by looking at the score that the answer is in G and not C — when the key is a major key, it is not necessary to keep qualifying its name by adding "Major" every time — is by noticing that, during this passage of the music, the note F often receives a sharp sign ("♯").

F♯ is the seventh degree of the major scale with G as its tonic. The seventh degree of any major scale is just one semitone below the octave of the tonic note. When F♯ is played in the right context, the ear wants it to resolve to G a single half-tone up. That's why the seventh degree of a scale is called a "leading note": it leads to the tonic.

Here, F♯ first shows up in the alto voice which accompanies the soprano's answer to the subject it has just finished stating. Between the alto's statement of the subject and the first F♯ we hear are a pattern of sixteenth notes, and then an eighth note, that serve to break the news gently to the ear that the key is changing. This is what musicologists call a "modulation."


A modulation is a series of notes by means of which a key change is established. In the case of a fugue, a short passage used to modulate the key is also called a "bridge." A bridge in a fugue often employs a note pattern very much like one that is part of the subject itself. Here, the bridge note pattern is four sixteenth notes, with the first and third at the same pitch. The second is one degree of the scale higher than those two. And the fourth is one scale degree lower than them.

When originally heard at the tail end of the subject, this quick "bop-bip-bop-bup" starts on the pitch G, to form G-A-G-F. Then, in the bridge, these four pitches are lowered to E-F-E-D, and then again to C-D-C-B. Next comes an eighth note on A to complete the downward progression, and a leap to that first F♯, another eighth note, acting as leading note. Finally, the tonic note of the new key — G — is sounded at some length, as two tied notes, a quarter and an eighth.

Meanwhile, the answer is being stated by the soprano voice in the same key of G. Once that has been done, the soprano voice goes on to play several groups of four sixteenth notes per group. These groups are much like the similar sixteenth-note groups in the bridge that were just discussed ... except that "bop-bip-bop-bup" becomes "bop-bup-bop-bip," with the second note in the group being lower than the others.

These sixteenth-note groups lead (again, via a leading note on F♯) to G, thereby confirming it as the tonic note or keynote for this passage of the music.

All the while, however, we hear the subject being restated, this time by the tenor voice. This is done in the key of G major, as had been the answer by the alto. One easy way to tell what key the subject is in is to look at its first note — in this case, it is G on the bass clef.

So, what is the alto voice doing while all this is going on? It's undercutting the otherwise agreed-upon key of G by playing free counterpoint that conspicuously features F notes that have not been sharpened to F♯!

Three notes after the first F-natural it plays, a descent from that note to C — the original tonic note of the fugue — has been completed. More filigree follows, in both the alto and soprano voices, that modulates the tonality of the music "officially" from G back to C — as emphasized by a comparatively "huge" half note on C in the soprano voice in bar 6.

A good thing, that, because the bass voice has already entered the proceedings, in bar 5, by making its own answer to the tenor's subject restatement which arrived in bar 4. It's in the home key of the fugue: C.


We have just heard, in the space of just the first six bars or measures, four statements of the fugue's subject — or, if you like, two statements, each followed by an answer — one each in each of the four voices of the fugue. We have also heard a plethora of bridge material and filigree which not only complements the subjects/answers, it also helps the composer to modulate the key from C to G and then back to C.

By the time the bass voice gets done stating its version of the subject, in C, we have just begun the seventh measure of the fugue. The seventh measure is the start of the first of three "development" sections; the first six measures were the fugue's "exposition."

Notice how the very last notes of the exposition bleed into the first measure of the first development. Fugues do not section as neatly as, say, a tangerine.

In the development section, we hear different voices again initiating the subject, but now in such a way that the statements of the subject by the different voices often overlap one another. The soprano voice leads it off near the outset of measure seven. Later in the same measure, the tenor voice follows suit. Altogether from measure seven through measure 13 the subject will appear, in the four voices, six times.

When a voice is reprising the subject in some form or other, it is shown on the timeline as a rectangle in a gold color, usually spanning measures. When not reprising the subject, the same voice may be playing complementary material, or it may be silent. When silent, the timeline shows it as space without a dotted outline. When it is playing material other than the subject, the voice is shown, measure for measure, as space with a dotted outline. The dotted outlines represent measures, not musical content, but when a voice is silent during all or part of a measure, there is no dotted outline.


The second development section begins with measure 14. For five measures, the voices will play almost nothing but the subject of the fugue. This is done. as already mentioned, in staggered, overlapping manner. Bach is proving that the subject can overlap itself in various ways to pleasing effect. Sometimes the relative pitches and pitch intervals of the subject are altered slightly to make this a possibility.

At one point in measures 15 and 16, Bach has the soprano voice begin the subject ... and then, before finishing it, begin it again!

The stacking up of multiple versions of the subject in staggered, overlapping, and capriciously altered versions is called "stretto," from an Italian word meaning "narrow." I think it may be akin to the English word "strata." At any rate, in stretto, multiple voices' statements of the subject are squeezed into a single stretch of time.


Measures 19 through 23 constitute yet another development section, the third. In this section there are five occurrences of the subject, in whole or in part. Measure 23, the final one of the section, is the only measure up to that point in the fugue in which none of the voices is stating any portion of the subject. It lets the ear know that something big is about to happen.

That something big is the final section of the fugue, the "coda." It occupies measures 24 through 27. In it just two of the voices, the tenor and the alto, reprise the subject, slightly offset in time and with changed pitch intervals. The soprano voice plays its own complementary little filigree, and the bass voice plays a "pedal": a single, sustained note that lasts all the way through the coda.

Next, in Part II of this series of posts, I'll talk about the cadences Bach uses. A cadence, for purposes of analyzing a Bach fugue like this one, is a juxtaposition of two chords that suggests a feeling of conclusion. In the timeline, where you see notations like C: V - I⁶, you are being alerted to a cadence.