1 Analysis of Bach Invention no.3 in D major: Introduction: J.S Bach’s two-part inventions is a collection that serves numerous purposes to performers and composers alike. The composition alone is so regimented that it teaches the basic concepts of composition without becoming too repetitive or boring. I will explore this concept more fully later in the essay, however it is important to note that Bach did not create these inventions solely to aid other composers but hoped they would benefit keyboard players as well. ‘Upright Instruction wherein the lovers of the clavier, and especially those desirous of learning, are shown a clear way not alone (1) to learn to play clearly in two voices but also, after further progress, (2) to deal correctly and well with three
obbligato parts; furthermore, at the same
time not alone to have good inventions [ideas] but to develop the same well, and above all, to arrive at a singing style in playing and at the same time to acquire a strong foretaste to composition. Produced by Joh: Seb: Bach Capellmeister to His Serene Highness Anno Christi 1723, the Prince of Anhalt-Cöthen’1 Above is a transcription of the foreword given by Bach to accompany his two and three part inventions. From this we can begin to understand the purpose Bach wished for these collections. In his opinion, by playing his inventions the performer would be able to improve many areas of their technical ability on a keyboard instrument and would thus facilitate the performer when moving on to more demanding pieces such as fugues where the performer needs to portray each voice as a separate line yet also treating them musically. In this essay I will be looking at Bach’s invention no.3 in D major from a purely compositional direction. I have provided a full copy of this invention on page 14.
1 Leisinger (2008, pIV)
2 Why do the two parts of the invention work well together? When looking at the relationship between the two voices of the D major invention, it is easier to break the piece down into smaller sections. Initially I will focus on the first 12 bars ending with the perfect cadence in A major on the first beat of this bar. For the entirety of this essay I will consider the first two semiquavers in the upper part as an anacrusis into bar 1. In order to see the way in which the two parts harmonically fit together I have included a copy of this extract below with all the harmonic intervals shown.
Fig 1: Bars 1-12
From this diagram it is possible to see that Bach’s composition uses very functional harmony and tonality with certain dissonances between the parts treated in the correct way. Even though the invention is incredibly measured and regimented it is in no way boring. There are many aspects of this opening section that demonstrate different techniques, many of which can easily be detected from the surface of the music without taking the treatment of intervals into account. The most apparent technique Bach has included, not only within this section but throughout the whole piece, is repetition. There is repetition between parts and within the piece as a whole. At first I shall address the use of repetition between the parts which can first be seen in bars 1-4. The opening 2 bar motif with added anacrusis in the right hand is repeated exactly in the left hand as it enters.
Fig 2: Bars 1-4
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Fig 3: Bars 5-8
The passing of this first motif between the two voices helps to establish the key of D major. The repetition within the piece then continues in the following 4 bars however in a slightly different way. The new repetition which can be seen above in bars 5-8 uses both parts together with bars 7 and 8 being an exact imitation of bars 5 and 6. During these 4 bars there is a dominant pedal heard in the lower part which supports the modulation into the dominant key, A major. This pedal on the A also highlights the only difference that can possibly be seen within this section because at some point within these four bars the dominant pedal evolves into a tonic pedal in A major as G#’s are introduced in the melody. Because of the repetition it is not clear exactly when this change occurs. It is important to note that when discussing the piece in an analytical way the written ornamentation is not integral to the composition. Ornamentation was often provided by the performer to decorate the melody or on occasions the bass line. This decoration would always fit perfectly with the tonality of the piece, however it would never alter the harmonic line. Bach has himself added ornamentation to this invention such as an appoggiatura on the second beat of bar 4 in the right hand. This appoggiatura bridges the gap of a third in the upper part by placing a passing note in the middle. Although passing notes are often encouraged in counterpoint and other Baroque compositions, in this instance the placement and resulting harmony between the two voices creates problems.
Fig 4: Bars 3-4
When looking at the upper voice alone, the B seems to be a good choice of passing note as the melody rises back to the C# again immediately after the A, however when adding the lower part, the B creates 3 consecutive 4ths in the piece. 4ths are considered a dissonance and must always be treated in the correct way, so it is strange for Bach to imply using 3 of them in a row. In order to try and rectify this, Bach has paid more attention to the approach and exit of this
4 and the use of contrary motion with the parts helps to create independence in the two voices so that the consecutive 4ths do not stand out. When continuing to look at Bar 3, it is possible to identify another moment in which the harmony at first does not seem to be conventional. On the second semi-quaver of this bar, the lower part plays an E, however the dissonance does not resolve by step. At first I thought that perhaps the B in the right hand could be seen as a passing note instead of the E in the lower part, however this does not explain why the 4th is not resolved correctly. The lower part has compound melodies present which can explain the purpose of the E in two different ways.
Fig 5: Bars 3-4
Fig 6: Bars 3-4
In the first instance the compound melody can be seen as implying the chord of E minor on the second beat with D major chords on beats one and two. This is supported with B in the right hand giving us the 5 th of E minor. Although this adds more interesting harmony to the piece which has been solely in D major until this point I find it strange that the chord on the second degree of the scale is the first other that the tonic to be used. Because of this I believe the second explanation is more apt for both this bar and bar 1. I have placed the E and G together on the second semi-quaver beat in order to portray these as lower and upper mordents to the F. This allows us to continue thinking of bar 1 and 3 as entirely D major. It does not matter that there is a B present in the upper part of bar 3 because this can be explained as an accented consecutive passing note with the C#. This makes the upper part more conjunct allowing for it to flow and not feel too disjointed. In the above example I found an alternative explanation to the idea of compound melody, however in some cases compound melody is the most appropriate idea. A moment such as this in the section stated is bars 5-8, however this is revisited in the same way in bars 47-50.
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Fig 7: Bars 4750
At this point there is compound melody within the lower part underneath an inverted tonic pedal. The harmony mainly stays on the chord of D major however the second beat of each bar alternates between the sub-dominant and supertonic. The descending triads in bars 48 and 50 allow us to stay anchored in the key of D major as it descends towards the tonic. Although I have mainly focused on the first section of this piece, each technique can be applied to many places as the material evolves and is used throughout in different ways. The two parts relate to each other harmonically throughout as well as rhythmically with the quaver beat remaining the same throughout. Although the parts work well together it is also possible to see that each part is often independent and could stand alone. This shows the complexity of the composition and counterpoint used.
6 Task 2: How does Bach use the two parts of the invention to imply harmonic and tonal content? In order to look at the harmonic and tonal content within the piece I will focus mainly on bars 25-38. I have already shown that in the first section the piece establishes itself in D major, however over the duration of 12 bars we modulate into the dominant key (A major). The section I will be looking at includes a circle of 5ths which can help to alter the harmonic and tonal intent within a piece. Below is the section with the relevant chords of each bar written.
Fig 8: Bars 25-38
The circle of 5ths starts with each new chord sounding over two bars, however in bar 32 the chord progression introduces a new key in each bar. In the same bar both the surface and implied harmony can be seen to be different. In my opinion we reach A major in this bar and the following bars can all be seen as chords within this key. The G# diminished chord has many similar properties to that of E major being an E7 chord without the root and is therefore a predominant chord wishing to take us into A major, not C# minor. This is shown in the diagram above with the use of roman numerals which are completely separate to the note names above them. Another way in which the tonality can be seen after this point is as a continuation of the circle of 5ths which can continue until the perfect cadence into A major at bar 38. I believe the idea we land and stay in A major at bar 33 is the most convincing, however it is interesting to consider why the implied harmony and lack of anchored tonality is
7 included. Bach may have done this as the circle of 5ths maintains a sense of journey within the piece, showing that the tonality is travelling toward one particular point, in this case the cadence at bar 38. The continuation of the chord progression also accentuates this cadence more seeming to give the arrival into A major more definition. Not only does the implication of this continued chord progression accent the cadence into bar 38 but the anticipation used as a rhythmic device accents the arrival into the new key. Within this section the harmonic material is offset between the two parts with each new phrase entering a semi-quaver after the other hand. This can be seen in 26 where the upper part arrives in E minor on the first beat of the bar; however the lower part doesn’t arrive in E minor until the third beat. This continues until bar 32 when finally, the parts come together and the harmony moves in the same places from then on. I think this is another indication that Bach means us to primarily think of the following bars in the key of A major because it is here that the parts come together and the previous ideas that were part of the circle of 5ths change. It is at this point we can definitely say the harmonic offset is resolved and also that the pedal notes and suspensions finish, indicating once more the end of one sections and the beginning of another.
Fig 9: Bars 27-30
Above, is the first interrupted suspension within this section. Normally a suspension would resolve either immediately or after perhaps one or two beats. However, in this section the resolution does not occur until 2 bars later. In the second bar above there is a dissonance created on the first beat of the bar with the G# against the A, but as the lower part holds this A, the right hand eventually resolves to an F# and a D major chord two bars later providing a 7-6 suspension. This occurs again two bars later in bar 32 with the F# against the G#, however the interrupted resolution lasts for only 2 semi-quavers again implying the change within this bar. The way in which the resolutions of these suspensions are allowed to be so delayed is because of the pedal notes every 2 bars in alternating parts. When these pedal notes are present in the upper hand, the pedal is a median pedal placed on the 3 rd of the key chord within the chord
8 progression, although in bars 28 and 29, there is a tonic pedal placed on the root of the chord. This section overall implies 2 separate harmonic and tonal ideas, however this is once again not the only part within the piece to do this. I go back to the first section where we encountered the dominant pedal on A in bars 5-8. At first this seemed a straight forward pedal however it then evolved within those 4 bars into a tonic pedal in A major, modulating both parts into the dominant key through the use of this single pedal at octaves.
9 Task 3: How does Bach manipulate the basic materials of the invention to create an extended piece of music? Bach’s two-part inventions all span two or less A4 pages allowing the performer to place the music at the piano without having to worry about page turning although as you look through the pieces it is easy to recognise many recurring themes and motifs. Bach has changed these motifs throughout the piece so that the material seems familiar to the listener or performer yet not boring. I will try to prove that there is no single bar within this invention that cannot be linked to somewhere else within the piece. The invention opens with the main motif in bar 1 which can be seen throughout, occasionally with slight changes. I have chosen to view the two semi-quavers that act as the anacrusis to the entire piece as part of the initial motif, however Bach has often omitted these when recycling the motif.
Fig 10: Bars 1-4
The initial motif recurs immediately in the second bar which has many properties of a retrograde inversion of the first full bar. The shape of the melody seems to imply that this is true, however the last two semi-quavers are not true to an exact retrograde inversion which means these two notes should be G->F# instead of F#->D. This may be to fit harmonically with the entry in the lower part but it also helps to establish the key of D major through the first 4 bars. The entry of the lower part is an exact imitation of the upper part which again helps to anchor the tonality of the piece and also helps the two parts relate and communicate with each other instead of starting as completely separate lines. With the entrance of the left hand in the 3 rd bar is the introduction of a new way in which the initial motif can be seen, with the addition of a second line of quavers moving in a conjunct motion. Below I have included an example of this bar along with examples of other bars that correspond with it through the piece.
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Fig 11: Bars 3,9,10,39,40, 45,51,52
In these examples, it does not matter whether the melodic line appears in the upper or lower part as it always makes sense harmonically. This is because the technique that has been used is inverted counterpoint at the 12 th. In all of these cases the quaver movement remains fixed with the semi-quavers rotating around this at the 12th so that all the intervals make sense with the dissonances still being treated correctly. This new point of interest still incorporates the initial motif, however there are a few bars where no version of the motif can be seen. These are mainly at cadential points as seen below at bars 11-13.
Fig 12: Bars 11-13
In my opinion the reason there is no part of the motif in bars such as 11 before cadences is to signify that these bars have important harmonic and tonal implication within the piece as it is at these points where we know we have arrived in certain keys. It looks as though the motif is not present in bar 12 and then subsequently bars 14, 16 and 18, however I believe the scalic motions in the melodic line can be explained as an extension to the semi-quaver anacrusis into bar 1. At these points the motif therefore becomes 2 bars instead of 1. This explanation can also be applied to the scalic motion in bars later in the piece such as bars 24, 26, 28, and 30. In bar 32 there could be dispute as to whether the motif is present however I believe it is. As you can see below, although the intervals are not exactly the same, the overall melodic shape is the same as the main motif and therefore could be considered a development of the first bar. Manipulation of the intervals used in the main motif are used in a couple of other sections in the invention, however the most noticeable would be in bars 5-8 and 47-51.
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Fig 13: Bar 32
Fig 14: Bars 5-8, 47-50
The melodic line in bars 5-8 and 47-50 are the same although they appear in the opposite parts. Each bar has the initial motif present, however the intervals between the first 4 bars have been changed in two ways. Firstly the intervals between the 1st and 2nd and then the 3rd and 4th semi-quavers have been changed from a second to a third. This in itself is a form of expansion within the motif, however in the second and fourth bars of these sections the compound melody descends rather than first ascending then descending. This adds variety to the four bars which otherwise could have become too monotonous but also allows the melody to travel towards a certain point that could have harmonic or tonal importance. We know this is true in these sections as we need this driving force to give the pedal note pupose. So far, I have looked at smaller sections of recycled and repeated material however it is also used on a much larger scale. Bars 43-54 for example, are a repetition of the initial section of the piece explored in task 1. One main difference between the two sections however, is that bars 43-54 remain in the tonic key without modulating into the dominant. Returning once more to bars 5-8 and 47-50 it is easy to notice another difference between the two parts. This new difference is the inversion of parts. In bars 47-50, there is an inverted pedal in the upper part which remains tonic throughout the four bars and although the melodic line is then put in the lower part, the relationship between the two lines
12 remains the same. The intervals between the parts are therefore an exact inversion. Because the pedal in bar 47-50 is allowed to remain tonic throughout we have a clearer idea of the harmonic intent of the pedal D. I believe at this point, it is solely to anchor us once more into D major as we approach the conclusion of the piece. Another example of repetition in a larger sense within the piece can be seen in bars 12-18. Here is again a circle of fifths travelling towards the relative minor however it is possible to note similarities between this section and bars 25-32. Bars 12-18 use techniques such as the interrupted suspensions however at this point the resolutions occurs after just one bar implying that not only are the suspensions in bars 25-32 extended but the way in which the circle fifths has been used is also.
Fig 15: Bars 12-24
Above, we can see in bars 12-18 the offset harmony within the section as each hand has moments of harmonic interest at different points until you firmly arrive at the relative minor (B minor) in bar 19. However once more, it is perhaps possible to argue that the circle of 5ths can continue until the perfect cadence into B minor in bars 23 and 24. A recurring theme at cadences through the piece is the inclusion of anticipation in the melodic line and it can be seen as an indication to the audience that we will arrive in a new key. In all occasions apart from one, this is the case as each
13 defined cadence is a perfect cadence establishing the new key. However in bars 54-55 there is an interrupted cadence of V-VI in the key of D major. The final cadence does not occur for another 6 bars. Bach may have used this interrupted cadence as an indication that we are approaching the final perfect cadence of the piece, however there is still time to reuse some material that has not been recycled within its own right.
Fig 16: Bars 53-59
The last 6 bars takes material from 2 different places in the piece and are linked together with a suspension which resolves in bar 56, again after one bar. Bars 54 and 55 are taken from bar 13 where the suspension on the G is introduced on the third quaver of bar 54. However, as already stated, this is not resolved until bar 56 where the material is taken from bar 35. Bar 56 to the end is similar to bar 3538 beat 1, however the end of the piece has transposed the original material down a major 5th back into the tonic key of D major so that the final perfect cadence allows the piece to start and finish in the same key. In conclusion, the material used in Bach’s invention no. 3 in D major is recycled and reused throughout although it is never used in the same way or within the same context. This has allowed Bach to compose an interesting piece that follows Baroque harmony incorporating aspects of counterpoint. The reuse of material has enabled Bach to explore the tonic key fully allowing the performer to gain a more thorough understanding of the harmony and modulations from both a practical and compositional perspective.
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Fig 16: Invention No.3
16 Task 4: Creative Assignment: After looking at Bach’s invention no.3 in depth we were given the task of creating our own composition that used some of the techniques we’d seen in the invention. We decided to compose another invention that would also be in D major but that would perhaps explore other ideas that would not have been considered in the Baroque era. Initially we composed another two part invention from which it was easy to decipher the main themes.
Fig 17: main motif
Above is the main motif that is present throughout the composition and is passed between the instruments. After finalising the invention in two parts it was time to score the invention for six instruments; two flutes; two soprano saxophones; tenor horn; piano. We transcribed the piano score exactly for the 5 wind instruments however no piano part was written out as this would be improvised. We attempted to pass the motif in all its forms to each instrument, occasionally adding in a third voice, for example at bar 5 for 4 bars.
Fig 18: Bars 58
17 After this we had the basic outline of our invention, however when practising we kept adding more ideas, such as a repeat of the first section before the modulation into Bb major. In this repeat we tried to add some modern twists to our composition with the piano providing more complex chords with added 9ths and 13ths. There was also an improvised aspect to this new section where each performer would use the score merely as an outline, adding more complex harmonies where they could. An example of this would be in the circle of 5ths where the melodic line was occasionally played a 3 rd higher or 6th lower depending on the harmonic intent. One problem that arose in the transition into the Bb major section was the presence of a false relation between the Tenor Horn and Piano. For the four bars previous to the key change the piano played a pedal G major harmony, however just before the modulation there was a concert Bb in the tenor horn. There were many attempts to rectify this but we all decided that we liked the sound of the false relation and it was subsequently kept and included in the performance. I have included a copy of the score that was used as an outline to the performance and the basis of our composition.
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Fig 19: Creative Assignment
List of Sources: Leisinger, Jonas (2008) J.S Bach Zweistimmige Inventionen Urtext Edition (Schott/Universal Edition: Austria) IMSLP Music Library: Online resource [accessed 21/3/11 and 7/5/11]
List of Illustrations: Figure 1: Bach Invention No.3 BWV 774, bars 1-12 Figure 2: Bach Invention No.3 BWV 774, bars 1-4 Figure 3: Bach Invention No.3 BWV 774, bars 5-8 Figure 4: Bach Invention No.3 BWV 774, bars 3-4 Figure 5: Own interpretation (1) of Bach Invention No.3 BWV 774, bars 3-4 Figure 6: Own interpretation (2) of Bach Invention No.3 BWV 774, bars 3-4 Figure 7: Own interpretation (1) of Bach Invention No.3 BWV 774, bars 47-51 Figure 8: Bach Invention No.3 BWV 774, bars 25-38 Figure 9: Bach Invention No.3 BWV 774, bars 27-30 Figure 10: Bach Invention No.3 BWV 774, bars 1-4 Figure 11: Bach Invention No.3 BWV 774, bars 3, 9, 10, 39, 40, 45, 51, 52 Figure 12: Bach Invention No.3 BWV 774, bars 11-13
23 Figure 13: Bach Invention No.3 BWV 774, bar 32 Figure 14: Bach Invention No.3 BWV 774, bars 5-8, 47-51 Figure 15: Bach Invention No.3 BWV 774, bars 12-24 Figure 16: Bach Invention No.3 BWV 774, (full) – IMSPL Music Library Figure 17: Bloomfield, Firth, Gibson, Peck, Putney, Musk, Creative Composition, main motif Figure 18: Bloomfield, Firth, Gibson, Peck, Putney, Musk, Creative Composition, bars 5-8 Figure 19: Bloomfield, Firth, Gibson, Peck, Putney, Musk, Creative Composition, (full)
