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.