Bach’s Invention 1: A Step-by-step Analysis

In today’s lesson we’re looking at Bach’s Invention no. 1 in C major, the first out of a collection of 15 written the composer wrote in 1720. We’ll be looking at the full piece: the subject, the motifs, the rhythm, the harmony and the structure. There is so much to learn in this short piece!

The reason that this piece is so fascinating is that Bach breaks down his subject into 3 tiny parts and uses only them to build his piece. In just over a minute and a half, he gives us a masterclass in motivic development and musical structure.

Before we get started watch this scrolling sheet music video. Listen to the piece (just over a minute long) and follow along the notes. 

The Subject

Upon listening to Bach’s Invention No. 1, many students often comment that it is “like a conversation”. Of course, this is true of many of Bach’s great contrapuntal works because that’s the nature of counterpoint: 2 or more melodies (also known as voices, parts or lines) of equal importance sounded together.

But for us today the most interesting and most important question is: What’s the subject of the conversation? The subject is clearly this melody that takes up one whole bar plus a sixteenth note.

Subject of Bach's Invention no 1 in C major (BWV 772)
Subject of Bach’s Invention no 1 in C major (BWV 772)

What is amazing about it, though, is that Bach breaks it down into three motifs and builds his piece using only them.

Now if you’re wondering how we can know that there are three motifs and not two, four or anything else, it is precisely because of how the music unfolds. We don’t usually know which group of notes are going to be the motifs before we listen to how the composer develops the piece.

The motifs are those small units of music that reappear over and over again in a variety of ways as if taking different shapes and sizes. At the same time, motifs remain familiar enough so that we as listeners can recognize them instantly.


The Motifs

In this analysis we will label the three motifs simply as motif a, motif b and motif c:

Subject of Bach's Invention no 1 - with motifs color coded
Subject of Bach’s Invention no 1 – with motifs color coded

Notice how every motif consists of four notes but has a unique shape. This is significant because no matter how Bach repeats, transposes, lengthens, shortens and inverts his motifs, they remain familiar to us.

Motif a is what we can call a scale fragment. It consists of 4 notes moving in steps:

Motif 'a' (from Bach Invention no 1)
Motif ‘a’ from Bach’s Invention no. 1

Motif b consists of an ascending second followed by a third in the opposite direction and finishing with a leap. This motif is unique because it’s the only one with skips.

Motif 'b' from Bach Invention no 1
Motif ‘b’ from Bach’s Invention no 1

Motif c is a swing: a swaying between a principle note (in this case the note C) and its neighbour (the note B). The motif then finishes on an ascending step.

Motif 'c' from Bach's Invention no. 1
Motif ‘c’ from Bach’s Invention no. 1

Now let’s have a look at how the piece unfolds through the subject and its motifs.

In bars 1 and 2, we get the whole subject twice allowing us to become familiar with it. In bar 2 we already get a slight change as the subject is transposed up a fifth (it started on C the first time, and now it’s on G). This is already a development even though it’s one of the simplest:

Subject from Bach's Invention no 1, transposed
Subject from Bach’s Invention no 1, original and then transposed.

At the same time as we are introduced to the subject, the subject itself is shortened (with the last 3 notes left out) and played an octave lower in the bass. This is known as imitation:

Imitation in Bach's Invention no. 1
Imitation and transposition in Bach’s Invention no. 1

It’s at this point that the subject is broken down further where we can recognize 3 distinct four-note motifs.

We’ve already seen that in the very first two bars, the subject is shortened in the bass clef.

This shortened version of the subject is inverted (meaning that it’s upside down):

Inversion of the subject in Bach's Invention no 1
Inversion of the subject in Bach’s Invention no. 1

 And repeated by sequence down a third through bars 3 and 4:

Sequence of inverted subject in Bach's Invention no 1
Sequence of the inverted subject in Bach’s Invention no 1

In the meantime, the scale fragment we know as motif a goes through these transformations in the bass part:

  1. The rhythm is doubled from eighth notes to quarter notes (a technique known as Rhythmic Augmentation)
  2. It is then transposed down a third
  3. And then extended from 4 notes to 7 (and always moving by steps only)
Transformations of motif 'a' in Bach's Invention no. 1
Transformations of motif ‘a’ in Bach’s Invention no. 1

Bars 5 and 6 bring the first phrase to a close through the same devices. This time, it’s motif b that is now developed by sequence in thirds (repeating up a third every time, in this case the motif begins on the note G, then B and then D).

Sequence on motif 'b' in Bach's Invention no. 1
Sequence of motif ‘b’ in Bach’s Invention no. 1

The next phrase begins as a transposition of the first phrase. The subject appears in full again but this time the bass part plays it first and the top part does the imitating.

Beginning of the second phrase in Bach Invention no. 1
Beginning of the second phrase in Bach Invention no. 1

At this point, the invention continues to evolve in this manner with the three motifs and their transformations put in place like a puzzle. In the meantime it is all held together brilliantly through the harmony so that’s what we’ll discuss next.  


Harmonic Analysis

As we’ve just said, the subject and its motifs are guided by an underlying harmonic progression. Overall, the structure of the piece is in three parts:

  • Section A: in the key of C major: bars 1 to 6
  • Section B: starts in G major and ends in A minor: bars 8 to 14
  • Section C: brief visits to several related keys and a return to C major: bars 15 to 22.

Despite being just 22 bars long, we still get a great example of tonal music at work. Section A establishes the tonic. Section B moves away from the tonic and towards the dominant. Section C begins in the relative minor of the original key, and then goes through some other related keys briefly before returning to the tonic.

The key scheme is deceptively simple going through a number of closely related keys:

C major -> G major -> D minor -> A minor -> D minor -> C major -> F major – C major


Motivic Development

In this part of the lesson, we’re going through the 3 motifs separately to see how each one is treated, transformed and used.

Let’s begin with motif a. After we get the original version in bar 1, the motif reappears:

  • Repeated,
  • Transposed (repeated starting from a different note),
  • Inverted (what goes up, goes down),
  • Expanded rhythmically (the note values are lengthened) and
  • Extended (from 4 notes that move by step to 6 or more notes that move by step).
  • Any of these transformations can occur together. For example, an inversion can be transposed and a repetition can be inverted (so the possibilities are quite endless!)

Here are these transformations with examples numbered by bars. The unnecessary parts in the diagrams are blacked out.

The Original: bar 1

Motif 'a' (from Bach Invention no 1)
Motif ‘a’ (from Bach Invention no 1)

Displaced by an octave: bar 1

Motif 'a' an octave lower in Bach's Invention no. 1
Motif ‘a’ an octave lower in Bach’s Invention no. 1

Bar 2

Motif 'a' transposed in Bach's Invention no. 1
Motif ‘a’ transposed in Bach’s Invention no. 1

Inverted and transposed: bar 3

Motif 'a' inverted and transposed in Bach's Invention no. 1
Motif ‘a’ inverted and transposed in Bach’s Invention no. 1

Bars 9 – 10

Motif 'a' transposed some more in Bach's Invention no. 1
Motif ‘a’ transposed some more in Bach’s Invention no. 1

Rhythmic Augmentation (meaning that the durations are made longer, in this case they are doubled): bar 3

Rhythmic augmentation of motif 'a' in Bach's Invention no. 1
Rhythmic augmentation of motif ‘a’ in Bach’s Invention no. 1

Transposition of the rhythmic augmentation: bar 3

Transposition and rhythmic augmentation of motif 'a' in Bach's Invention no. 1
Transposition and rhythmic augmentation of motif ‘a’ in Bach’s Invention no. 1

Bar 11

More transposition and rhythmic augmentation of motif 'a' in Bach's Invention no. 1
More transposition and rhythmic augmentation of motif ‘a’ in Bach’s Invention no. 1

Inversion of the rhythmic augmentation: Bar 19

Inversion of the rhythmic augmentation of motif 'a' in Bach's Invention no. 1
Inversion of the rhythmic augmentation of motif ‘a’ in Bach’s Invention no. 1

Extending of the scale fragment to more than 4 notes: Bars 5 – 6

Extending the scale fragment
Extending the scale fragment

Bar 12

Extending the scale fragment
Extending the scale fragment

Motif b

Let’s move on to motif b.

Like motif a, this one is also very often repeated, transposed, inverted and expanded but it also undergoes a unique transformation: its final interval can vary. In other words, the distance between the last 2 notes can change. 

Here’s the original from bar 2:

Original motif 'b' in Bach's Invention no. 1
Original motif ‘b’ in Bach’s Invention no. 1

Transposition: Bars 1 – 2

Transposition of motif 'b' in Bach's Invention no. 1
Transposition of motif ‘b’ in Bach’s Invention no. 1

Change of Last Interval

In bar 1, it appears as a perfect fifth. In bars 2 to 3 (shown below) it becomes a fourth:

Change of last interval of motif 'b' in Bach's Invention no. 1
Change of last interval of motif ‘b’ in Bach’s Invention no. 1

Here in bar 13 it is an ascending octave:

Another change of last interval of motif 'b' in Bach's Invention no. 1
Another change of last interval of motif ‘b’ in Bach’s Invention no. 1

And in bar 14 it is a diminished fifth with a change in direction too:

Yet another change of last interval of motif 'b' in Bach's Invention no. 1
Yet another change of last interval of motif ‘b’ in Bach’s Invention no. 1

But by far, the most common final interval of motif b is that of a second. Here it is in bars 8 to 9:

The most common last interval of motif 'b' in Bach's Invention no. 1
The most common last interval of motif ‘b’ in Bach’s Invention no. 1

And this version of it very often appears in inversion:

Motif 'b' in inversion from Bach's Invention no. 1
Motif ‘b’ in inversion from Bach’s Invention no. 1

Developed by Sequence – Bars 5 to 6:

Motif 'b' developed by sequence from Bach's Invention no. 1
Motif ‘b’ developed by sequence from Bach’s Invention no. 1

And bars 13 to 14:

Motif 'b' developed by more sequences from Bach's Invention no. 1
Motif ‘b’ developed by more sequences from Bach’s Invention no. 1

It also undergoes rhythmic augmentation just like motif a before. This is in bar 9:

Rhythmic augmentation of motif 'b' from Bach's Invention no. 1
Rhythmic augmentation of motif ‘b’ from Bach’s Invention no. 1

Another interesting transformation is when the last note is prolonged. This gives space to the ‘conversation’ between the two voices as from bar 15:

Last note of motif 'b' extended
Last note of motif ‘b’ extended

Motif c

Finally, we have motif c. This one plays a lesser role compared to the other two. It is obviously very important when the subject is played in full, and there are other hints throughout the piece, but the only clear reappearance of it is in retrograde at bar 20:

Motif c in retrograde from Bach's Invention no. 1
Motif c in retrograde from Bach’s Invention no. 1


Rhythm

So far we’ve looked at the subject, the motifs and the harmony. But we cannot ignore the rhythm, as it is just as important as everything else.

Most importantly, observe how the motifs themselves always begin on a weak part of the bar. Because of this they overlap and connect over the bar lines (or over the strong beats) and this continually drives the music forward.

In the diagram below, the top part of the invention is shown against the constant quarter beat of 4/4 meter. Notice how none of the motifs begin on a strong beat. Instead, they’re always a little ahead.

As we’ll see, this feature of the rhythm creates a kind of musical tension that is only released at the end of the phrases, where the melody begins and finishes on the strong beats.

Here are bars 1 to 4:

The rhythm of Bach's Invention no. 1
The rhythm of Bach’s Invention no. 1

When a cadence is due at the end of a phrase, Bach changes the rhythm slightly so that the music conforms to the pulse. At these cadence points, the motifs are abandoned for a very short while and what we get instead are melodies and rhythms that begin and end on the beat.

This releases the tension we mentioned earlier – the tension produced by the motifs always being slightly ahead of the pulse. And as Bach intended, releasing the tension creates the sense that the phrase is coming to its end.

The arrows in the diagram below show where the cadential material begins.

Cadential material in Bach's Invention no. 1
Cadential material in Bach’s Invention no. 1

Of course, although the cadential material doesn’t originate from any of the motifs, it always belongs to the right harmony.


Conclusion

Every aspect we’ve looked at: motifs, rhythm and harmony all work together at the same time to hold the whole structure together. This is why the piece is admired so much by composers – it’s a mini masterpiece and a gem of musical architecture.

If you’ve enjoyed this analysis, then you’ll love this one too. In this analysis we look at how Beethoven composes the entire 1st movement of his 6th symphony out of a simple 4-bar theme!

Would you like to see more musical analysis at the School of Composition? Leave your suggestions below and I’ll do my best to get to them!