An In-depth Harmonic Analysis of Bach’s Prelude in C (BWV 846)


Version: 1.0.2 (9/8/21)

Introduction

Today, I want to offer an in-depth harmonic analysis of Johann Sebastian Bach’s famous first prelude in C, BWV 846, from Book 1 of his Well-Tempered Clavier. There are many harmonic analyses available on YouTube but I would like to offer an analysis that is quite different, based on my study of Partimento and Counterpoint.

There will be no Roman Numerals, Chord Symbols, or Harmonic Function Theory (e.g. IV-V7-I, etc) used in this analysis. This analysis will instead focus on partimento, figured bass, and music schema theory.

Influences and Inspirations

This prelude uses a single texture which is a broken chord going up. We see this in early Bach and this may have been inspired by his predecessors such Johann Kuhnau or Johann Caspar Ferdinand Fischer. Scholars have noted the influence of Fischer’s Ariadne Musica on Bach’s Well-Tempered Clavier. The Ariadne is also a collection of preludes and fugues and Bach quotes several themes from Fischer in his Well-Tempered Clavier. Additionally, we see this broken chord texture in some of Fischer’s pieces such as his Prelude from his Clio suite, his Chaconne, and his Harpeggio Polymnia, all taken from his Musicalischer Parnassus. Let’s take a listen to Fischer’s Prelude from his Clio suite.

As we dive into Bach’s prelude, we will observe how much further Bach goes in his choice of chords.

Overall Structure

Before we get into a detailed bar-by-bar analysis, it may be useful to take a general overview of the piece’s structure as a whole. We begin in C major for the first 4 bars, and then the first shift begins in bar 5. The chord in bar 5, a 6 chord on C announces a passage in G major. From there, there is an extended Prinner that leads to a final cadence in G, in bar 11. You could even say this could be the end of the 1st half of the prelude and put a double bar line. And just like a galant composer, we have a Fonte in bars 12-15 going from Dm to C. Returning to C, there is a literal transposition of the material from bars 6 to 11 when we were in G to the 2nd half of the prelude in bars 14-19 when we return to C to maintain a coherent pattern, coming out of the middle of the Fonte. Now we stay in C but with several twists, He hints at F major with a Bb in bar 20 but continues to stay in C. There are some chromatic chords on F# and A♭ that target the bass note G that hint at C minor and then this leads us to a long pedal section note on G, but we are still in the key of C all the way. That’s one thing that, coming into my lessons in partimento, which fascinated me, this idea of “hinting” at new keys. Nowadays keys are considered these firm areas of tonality, but I am appreciating the fluidity of these 18th-century composers with respect to key areas. During the pedal on G, there are some interesting dissonant chords coupled with consonant chords in a sort of “tension-resolution” sequence to add tension before a Quiescenza schema to end in the final line. Now let’s really dive in and try to break this piece down bar by bar.

Bars 1-4: A Phrase in C

This piece consists of phrases, and the first phrase would be the first four bars which are in the key of C. It is an elaboration of a very simple cadential idea. You have a mild cadence of the 7th scale step rising to the 1st scale step B to C. It’s considered mild because we do not have the 5th scale step so we have a milder, softer effect. You could even omit the 2nd bar, and it would still work perfectly well, albeit now with an irregular odd number of bars, 3. Let’s listen to the piece with the 2nd bar omitted:

With Bar 2 omitted, 1 – 7 -1

It’s just the rule of the octave in C major. Now apparently he didn’t like the idea of irregularity within the number of bars, so he lengthens the first stage C but not simply by repeating the chord twice for two bars would not really work but by applying tension into the 2nd bar by keeping the same bass but by moving up the entire chord. So what do we have? He writes a dissonant 6/4/2 on the 2nd bar which makes that bar the most interesting of those 4 bars so what is interesting is that on the one hand is he creates regularity with the regard to the number of the bars but irregularity with regard to the metric organization because the strongest bar is no longer the 1st and the 3rd, but the strongest one metric-wise becomes the 2nd. And although it does feel like the piece is a whole at this point with a mild 7-1 cadence, we go further on as the top voice is E, not C. So this is the end of the first phrase in C.

Bars 5 – 11: Modulation to G

Now he uses one of the most common ways of modulation by using an elaborated version of what Professor Robert Gjerdingen calls the Prinner. You get C – B – A – G in the bass and typically between the A and the G, he puts in the D. What I’m going to do is simplify this section by omitting bars 5 and 6, 8, and then I’m going to combine bars 9 and 10 into a single bar. I’m going to also repeat the bar in bar 5, changing the top voice as well so that the phrases are clearly separated and then it makes rhythmic and harmonic sense. Let’s listen now to what would be considered a normal Prinner, to first get a sense of the basic template of the Prinner.

A “normal” Prinner with Bars 5,6 and 8 Omitted

Now let’s see what Bach does. Bach makes this Prinner stronger and more sophisticated by inserting multiple extra chords. As noted in the overview, the 6 chord on C announces G major in bar 5, and then on bar 6, we have a 6/#4/2 which is a link to the opening 6/4/2 chord in bar 2, with the F# also strengthening the passage in G. Then we have yet another 6/4/2 chord on bar 8 with a minor 2nd between B and C in the bass. So it’s very interesting that over the course of 3 lines we maintain a logic of added 6/4/2 chords and in each instance, we have 3 different types of 6/4/2 chords. In bar 2 of line 1 we have the minor chord. in bar 1 of line 3, we have the major chord but with a minor 7th, and then at the end of that line we have a major chord and a minor 2nd, so we have 3 different interval structures but the chords in themselves are all 6/4/2 chords.

So on the one hand we have a very typical beginning but highly personalized via these extra chords. Up to this point, it feels quite complete as a section so you could even put a double bar line at the end of the 4th line and a repeat sign. All you would have to do is change the final position of the chord to prevent parallel 5ths and 8ths and it would work.

Bars 12 – 15: Fonte from Dm to C

“a sequence of chords that act functionally as a circle of 5ths but use diminished chords”

Bars 12-15 is where we find Bach behaving as a galant composer and using a typical 18th-century schema known as the Fonte, which is something you might normally find after a double bar line.

What a normal Fonte would look like

Before we look at Bach’s version, it would be instructive to see what would have happened if we continued Bach’s used of 642 chords into the Fonte. [plays example of 6/4/2 Fonte bar 12: G, A, E, A, C# and bar 14: F, A, D, F, B] This would have been perfectly fine but let’s see what Bach does.

Bach’s Fonte with 6/4/3 chords

Let’s tie this example with some partimento theory. When Fenaroli teaches the Rule of the Octave descending in a minor key he gives an alternative for the 4th scale step going to the 3rd scale step. Fenaroli explains that you can alter the 2 in the 6/#4/2 chord into a b3, so instead of a 6/#4/2 chord, you get a 6/#4/3 chord [demonstrate in Dm]. When we arrive at bar 11 on a G major chord which contains a G and B, in order to announce the shift to D minor, one could introduce 2 of the important key-defining notes in D minor, apart from the F natural, they are the leading tone C# and the B on the 6th scale degree. Instead of perhaps announcing a chromatic Fonte and shifting to D major, which also contains a C#, the B in the 6/#4/3 chord changes that perception to D minor.

The 2nd half of Bach’s Fonte is interesting because of the presence of an A which should not be in the key of C major. This note is referred to as a “hermaphrodite” note because it brings a minor (modal) flavor into the 2nd half of the Fonte which is typically 1st half minor, 2nd half major. Let’s listen to what would it have sounded like if Bach chose not to use the hermaphrodite chord and instead use a 6/4/2 chord:

Now let’s listen to the original, paying special attention to the hermaphrodite note, A:

https://youtu.be/VVOIwDfbqBQ

This use of the “hermaphrodite” note was apparently a source of controversy but we see Mozart favoring the hermaphrodite variant. The resulting chord is a literal transposition from bar 12 as another 6/#4/b3 chord. And that is the Dm to C Fonte from bars 12-15, and we are back in C major.

Bars 16-19: A Transposition of Bars 8-11 in C

Now that we are back in C, what happens now? You see that he returns to the extended Prinner idea from bars 6 to 11 re-introducing the 6/4/2 chords. If we take a look back at bar 6 we see a D major chord over a C bass and that progresses to G major in bar 11. We will take that entire phrase and transpose it to the key of C. This almost-exact transposition begins at bar 14 including the hermaphrodite note. If there was no A in that chord, and a G instead, then it would have been a completely exact transposition from G to C. By repeating this progression in C, this establishes coherence. If we wanted to, we could say that the piece is actually complete at this point and that everything else from this point on is a sort of Codetta or Coda.

Bars 20-21: Codetta – Hinting at new keys (F/Cm) but staying in C

Approaching the end of a piece, the right thing to do would be to give some prominence to F major, in order to make the cadence in the main key stronger. We give the impression that we are going to F and then come back to the normal key to make the cadence more satisfying. And that is exactly what Bach does at this point, introducing the B in Bar 20 which announces a shift to F major. However, we don’t actually shift to F because of the E on the next chord in Bar 21. If we were to have gone to the key of F, that E, which would have been the leading tone, would have risen to F but is prepared to become a dissonance of a 7th on 4th scale degree of C.

Bars 22-23: How do we analyse these strange chords?

And then we come to the 2 very interesting chords in the piece. There are many, many interpretations of these chords.

These are two chromatic chords on F# and A♭ which hint at C minor because of the E♭ on the F# diminished 7th chord and the A♭ in the bass in bar 23 which are the 3rd and 6th scale degree of C minor. We do not actually change the key to C minor but again as is common in the 18th-century there are hints of modulation without actually modulating. They are targeting the dominant G bass note in bar 24.

The F# diminished 7th chord is a chromatic chord and it’s important to realize it is not a modulating chord. We have certain chords when you have an alteration in the bass, that they announce a new key but here, this F# is not announcing a new key but really is just a chromatic note between F and G. But the F# does not go immediately to G and he fools us. What he does is give both notes which have such a strong tendency towards the 5th scale step that’s the F# going to G, that’s the A going down to G so he leaps from the F# to the A to build up the tension even more and then the G even really comes in as a relief. So it’s logical that he goes to A because the distance between F# and G is the same as from A♭ and G, it’s a half-step, creating this chromatic enclosure.

Next, apart from the horizontal contrapuntal reason, is the reason of context and mode. The fact that he introduces an E on top of the F# gives the impression of a minor mode. When you have this F# diminished 7 chord, you cannot simply replace that chord within this minor impression with an equally dissonant chord in a major key, that doesn’t work. He stays within the same region, so he has to stay within the same minor, which in this case is C minor. So you have to see the chord with the F# in the bass as a chord in C minor. So the E functions as the 3rd scale step in C minor. so when you think C minor and the next chord which is a replacement for the one with the F# also has to respect C minor hence the A, which is the lowered 6th scale step in C minor. When we arrive at the chord at the start of the pedal note, we have returned back to C major. So there is a brief hint of C minor in those two bars.

Let’s talk a little bit more about the 2nd chord in this chromatic enclosure, the chord on A. It’s actually a chord that we see Bach has used for his whole life, from this prelude up until right at the end of his life with the Art of Fugue. If we take a look at the Art of the Fugue, Contrapunctus I, bar 70, we are in D minor you have a 6th scale degree Bb in the bass in the middle of the bar, and that Bb descends to the 6/4 chord on A in the next bar. So we have exactly the same situation as in the prelude and what he writes on top of the Bb is E natural, G and not E or not D but C# giving a C#dim7 chord. This is a problem for Roman Numeral analysis but you cannot put a diminished 7th chord before a dominant chord, you need to introduce a subdominant chord.

If we go back to the Prelude, the reason some people want to consider the C here as the chord tone and the B as the passing tone is that then you have your F minor subdominant chord in the key of C minor leading to the dominant chord on G, which makes sense in Roman Numerals but Bach seems to continually confound this functional perspective. In fact, for him, there were multiple options for sonorities on the 6th scale step, the diminished 7th chord just being one of them.

Bars 24-31: Pedal on G (Codetta)

The Pedal begins on the G dominant 7th chord and ends with a G dominant 7th. The chords are the same with the only difference being that the tenor voice and the soprano voice have swapped their notes. In between these two dominant 7th chords you have a bunch of free and optional chords who exist to build up the tension. The chords follow a sort of “tension” and “resolution” sequence with the first dominant chord resolving to a C major chord. Then we have a very modern sounding chord that chord symbol people would just call a G7sus4 chord and not think too much about it but it’s a very striking, almost crazy chord in the 18th-century and I’ll tell you why: normally when we have 4-3 suspension, you don’t introduce the 7th at the moment of the 4, and he does, you have the 4 and the 7, giving an extremely modern sound for the 18th century. So that resolves to the 3 in the next bar, a G dominant 7th chord, and we return to our F#dim7 chord again, and this is the same kind of idea, anticipating our pedal note G, with a resolution. Back to our crazy 4-3 suspension with the 7th on the 4th which resolves to 3 and that’s the end of our pedal.

Bars 32-35: Final Bars

Now we come to the ending of the piece, coming out of the pedal on G. At this point, we have our leading tone in C, a B note which typically should rise to C but instead Bach makes it Bb. There is a rule which says that a leading tone can be replaced chromatically by an equally strong, equally good dissonance that is the 7th and that is what Bach is doing here, making it a 7th on C. It’s interesting because some scores tell you to play diminuendo or pianissimo but that note is quite a shocking note that shoots out.

And it’s the first stage of a larger four-stage schema happening here known as the Quiescenza, where you have a pedal on C and an upper voice plays Bb in the first stage, then an A, then a B before arriving back to C in the last stage.

I want to talk about that low B in the penultimate bar, he could have easily played a C there and it would have been fine but don’t we don’t understand early enough that the B is a strong note within that chord so gives the B. This has led him to be criticized for this because of parallel octaves, he doubles the leading tone here. In a normal polyphonic setting, you would not do that but this is not a normal polyphonic setting, this is a situation where you have an unfolding out of chords over time and making the instrument sound out.

Conclusion

Well, quite a lot to say for a piece that is only 35 bars long. I found that probably the biggest takeaway from this analysis for me is not so much the labeling of the chords, but trying to see what a more simple realization would have been and contrasting Bach’s more complex realization with it.

Other Analyses of the Piece

Professor Vasili Byros (see example 6): https://www.mtosmt.org/issues/mto.15.21.3/mto.15.21.3.byros.html

Nikhil Hogan

I'm a graduate of Berklee College of Music (summa cum laude) and am the host of the Nikhil Hogan Show, a music interview podcast. I started Songbird Music Academy to promote Partimento, Italian Solfeggio, Counterpoint, Music Schema Theory, and Figured Bass.

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