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.