At what level should I start working on Bachs two part inventions?

[oscarr111111]

I've been wanting to get into these in terms of playing and analyzing the theory behind them.  What kind of level should I reach before I begin them?

Also, can anyone recommend any resources on how to properly analyze a piece like this?  Perhaps something with a walk-through of the first, I want to do most of them myself.  If not can anyone suggest how I should go about it, just a list of what to look for in a piece like this ('find the subject, identify variations' etc.) would help.

I'm away from my teacher for a good while now (couple of months), so I can't get him to help me with them in my lessons.

Thanks.

[stevetrug]

https://www.pianostreet.com/smf/index.php/topic,3171.0.html
This should answer all your questions Follow Bernhard's links, excellent.
Good luck
Steve

[oscarr111111]

https://www.pianostreet.com/smf/index.php/topic,3171.0.html
This should answer all your questions Follow Bernhard's links, excellent.
Good luck
Steve

Thanks, but the links are broken .

[teresa_b]

Hi Oscar,

I can't quote you a resource, but you can look at a Bach two-part invention and start by picking out the first theme, noticing how it echoes in the other hand, etc--Find this theme everywhere it turns up in the piece, and mark it.  Then look for the 2nd theme, etc.  Look for inversions of the theme. 

If you have done a few easier Bach preludes and fugues, you should be able to begin the Inventions.  Choose one, and after you've played with it a little to see how it flows, then start working slowly, hands separately.  I suggest you memorize it HS before putting it together.  Then practice it HT. 

Have fun! 
Teresa

[pars]

Thanks, but the links are broken .

Gosh, thats a pity. Those pages should be saved somewhere please Mr Moderator whoever you may be...

Try here instead then. https://www.pianostreet.com/smf/index.php/topic,2714.msg23310.html#msg23310

It's a classic read!

Good luck

[stevetrug]

I took the time to copy and paste this brilliant post from Bernhard.
Hope this helps: I've split it into two posts, part 1....
BACH INVENSIONS LESSON PLAN

Bach’s music can be roughly divided in three categories:

1.      Voice music, which is music that will sound wonderful on the human voice. I am including here instrumental works that are clearly inspired on the human voice. When Bach writes this sort of music for the keyboard all the technical problems relating to making the instrument “sing” will appear.
2.      Dance music. Usually the problems in this kind of music relate to rhythm.
3.      Instrumental music that targets specific technical aspects of the instrument. It is easy to spot these compositions since they would not make sense if you tried to sing them (they may have effects that are impossible to accomplish with the voice, or they may have a range outside the human voice).

The inventions have examples of all three kinds (and some are mixed).

Number 1 (C major) is a very good example of “voice” music. One can easily imagine it sung by two people. So the most important considerations in playing this invention are:

1.      The ability to play legato.
2.      The ability to bring each voice clearly, which implies hand and finger independence.
3.      The ability to phrase.

Technically this is not a difficult piece but two things will make it or break it:

1.      Appropriate fingering.
2.      Hand independence and co-ordination.

Finally we have the matter of ornamentation. This piece has some light and simple ornamentation, but for a student not used to it, it may become an unsurmountable block.

Have a look here as well, where ornamentation is discussed (I will have something to say about it later on):

https://pianoforum.net/smf/index.php?topic=87.0

Another important consideration is that most of Bach’s music is motif based. Usually we tend to think of music as a nice tune with an accompaniment. But Bach (and many other composers) does not follow this model at all. He starts with a fragment of melody –in the case of this invention only 7 notes long – and simply varies it in numberless ways.

So before learning how to play this invention it is very important to observe what Bach is doing in terms of motif variations and development. If you listen to this invention on a CD (best for that purpose are Rosalyn Tureck or Glenn Gould), you will have the uncanny feeling that no matter how many times you listen to it, you never seem to quite grasp everything.

So first step: Listen to the invention on a CD, preferably played by as many different pianists as possible (I give the student a compilation with 10 different interpretations of it).

There is always something new to listen to the next time you hear it. This is because of the extremely clever way it is constructed. And that is what I first examine with a student by simply working on the score.

So here we go. First identify the motif. Once a student knows what a motif is, he usually spots the motif right away: It consist of the first seven notes: CDEFDEC.

The next step is to investigate the possible ways in which this motif can be varied and still keep its identity. To start with, it can be played in different degrees of the scale (CDEFDEC is played in C major, on the degrees I-II-III-IV-II-III-I, or if you prefer – tonic – supertonic – mediant – subdominant - supertonic – mediant – tonic) [side note: this gives me the opportunity to dive right in into scale theory with the student – by the end of the lesson s/he will know about scales, scale degrees/names and scale relationships]. We can see that in bar 2, where the motif is repeated starting on degree V (dominant) of C major: GABCABG.

So, right there on the first two bars, we have the motif making four entries: Bar 1 on the right hand, then on the left hand, and bar 2 on the right hand and then on the left hand, but also played in different degrees of C major.

Some clever students who have been doing their scale homework at this point ask: Isn’t the motif in the second bar in G major? This gives me the opportunity to introduce modes. No, it is not in G major, it is the myxolydian mode.How do we know? Because the F is natural, and there is no F natural in G major. But there is a more subtle reason. The ear automatically shifts tonal centres without you needing to know any theory. This is a very good opportunity to demonstrate this to the student, so don’t miss it! Play bar 2 (in its entirety), and then play bar 7. If you simply look ath the motif in bar 7, it looks exactly the same (indeed it is the exact same notes). But in bar 7 – unlike in bar 2 – the F# makes its appearance amongst the non-motif notes. This throws the tonal centre into G major with the consequence that in bar 2 the ear hears the G as a dominant note, while in bar 7 the ear hears it as a tonic note. This always surprise students. They cannot believe how the same note can sound completely different simply because of tonal context. It is a real eye (ear) opener. Of course this is the main device of motif variation in Western tonal music, and it is called modulation. You can go on several lessons on this one. You can talk about equal temperament, how Bach invented it, and why it is so important, for instance.

This is one of the reasons I love these inventions. They are wonderful teaching devices: they present do many problems to the student, and the solutions are always neat and open ended (they lead to more problems). If the student is willing, and the teacher does its job properly, a student may well learn all of musical theory from just working on these inventions.

So by just looking at the motif in bars 1 and 2, we have learned about two ways in which the motif can be developed: It can be stated in a different mode (different degrees of the same scale), or it can be modulated (stated in the same degrees of a different scale). It is important that these concepts are understood aurally as well as from the score. So keep playing for the student to listen to, the motifs in bar 1, bar 2 and bar 7.

On bars 3 and 4 something even more interesting happens to the motif. If you look at the first seven notes (RH) of bar 3: AGFEGFA, you can see (from the score is much clearer) that this is like a mirror image of the motif. While the motif had an ascending scale fragment (CDEF) followed by descending thirds (FDEC) [the Fs overlap], in bar 3 we have a descending scale fragment (AGFE) followed by ascending thirds (EGFA). This is called motif inversion. And in fact there are four motif inversions in bars 3 – 4: [AGFEGFA], [FEDCEDF], [DCBACBD] and [BAGF#AGB].

Now are you ready for the next one? It always blows my mind! So it should blow yours and the student’s too!

Go back to bar 3, but instead of looking at the first seven notes, skip the first three notes and look at the next seven notes: EGFAGFE. This is actually the motif backwards, also called a retrograde. There are two more retrogrades on bars 3 – 4: [CEDFEDC] and [ACBDCBA].

Have you got it? So you have four inversions and three retrogrades. But what blows my mind (and should blow yours and the student’s) is that Bach overlaps them. This means that as you play through bars 3 – 4 there will be an ambiguity on the third beat of each bar: you can hear it as the end of the retrograde or as the start of the inversion. So no matter how many times you lsten to this line, you always miss something! This is the aural equivalent of some visual illusions where you see either an old lady or a young woman depending on how you look at the picture. Or some of those Escher drawings where you have stairs that go up and down at the same time.

I cannot even begin to tell you how difficult this is in terms of composition, because most people cannot recognise (aurally) a retrograde as a motif. In fact it is so difficult that Bach only uses a retrograde in a few of his compositions (another famous instance in the “Crab” canon from the Musical Offering).

So at this point I will play for the student bars 3 and 4, but omitting the notes that make for the overlaps, that is I will play either the four inversions or the three retrogrades. Once the student can recognise by ear the inversion or the retrograde, then I will play the line (RH only) and the illusion becomes obvious: If you listen for the inversion you cannot hear the retrograde; if you listen for the retrograde you cannot hear the inversion. This overlapping/ambiguity is something that Bach is very fond of doing (another good example is the Eb major fugue in Book 2 of the WTC).

(By the way, Rachmaninoff fans out there, the 18th variation on a theme of Paganinin is a retrograde of the theme).

We are still in the first two lines of this invention and yet the student has been exposed to a wealth of knowledge from motif analysis to visual illusions (make sure you have a book of Escher’s drawings at hand to show him/her). So you can see what incredible teaching device these inventions are.

Now I will keep going through the piece identifying all  the motifs, and motif variations (invertions and retrogrades). There are 22 bars in this piece and 46 entries of the motif. I usually let the students find the remaining entries (on bars 1- 4 alone there are 11 entries).

Once they can recognise the motif entries form the score, we start actually  playing the motifs. At this point I will give the student a score where only the motifs appear, all other notes being deleted. We will practise this score until the student can play the whole piece (motifs only) perfectly. Our aims now are: correct fingering, development of the necessary movement/finger co-ordination to tackle the motif sequence, and motif recognition (as s/he plays, s/he must say what s/he is playing: motif, inversion or retrograde). S/he must be able to play the whole piece twice: one bringing out the inversions, the next bringing out the retrogrades. Finally, and this is really the most important: S/he must be able to play the piece without bringing out either inversion or retrograde, for if you do so you destroy the ambiguity.

In pieces like this, the performer must not bring out anything, since it is the listener that must experience the ambiguitiy and decide how to solve it. To bring out anything would be the equivalent of using a yellow marker to highlight some of the stairs in an Escher’s drawing. For a full enjoyment of this kind of piece, it must be played many times, with the listener educated in what to listen for, and preferably following with the score. Therefore this is not “performance” music, and will not work as such this is music for the private enjoyment of the cognoscenti. You can only and truly appreciate it if you are a nobleman with a musician in residence (the case in Bach’s time), or if you are a keyboardist (or if you are my student, he he).

But I digress. I will continue later.
Picking up the thread where I stopped.

So, in teaching invention no. 1, my first step was to identify the motif; to show how it could be varied by being inverted and being played backwards (retrograde); how it could be played in different degrees of the scale and on the same degrees of a different scale (modulation).

This was first worked out at the score (using coloured pencils to identify the several forms of the motifs), then aurally (me, playing the several motifs while the student followed them on the score), and finally by learning how to play the motifs – through  a score where every note that was not the motif had been taken away. This motific “skeleton” was then used a lot until the student could play the whole piece, motifs only.

Incidentally: the motif CDEFDEC, is repeated 46 times equally in both hands and in different spots of the keyboard. Repeat each occurrence of the motif and move to the next one smoothly and what do you have? A Hanon exercise! Therefore anyone working on this invention is already doing Hanon, without ever needing to touch the “Virtuoso Pianist”.

But I digress.

part 2 of this post to follow...

[stevetrug]

here's part 2...

Once the student can do the motif version of the score, we do the next step, which is to reintroduce all the notes that have been taken away. For the most part they consist of augmentations of fragments of the motifs (the same pitches, but with increased note values, e.g., the motif had an ascending scale fragment in semiquavers. This ascending scale fragment appears now in quavers linking the motifs).

This means learning the piece as it was originally written, but this time with hands separate. Ornaments are not introduced yet at this stage.

If the previous step (motifs only) was thoroughly mastered, this next step is achieved very fast. In fact it may take one or two weeks t master the motifs, but the whole piece with HS may take just one lesson.

We will keep working HS, repeating it many times, but each time we will be concentrating in a different aspect. For instance, looking at the intervals by which the motifs get displaced. Or observing how Bach reverse voices (counterpoint invention), or dedicating a whole lesson to pure technique (how to move, how to press the keys, etc.)

Then the third step will be to join hands. This is the most difficult step in any piece, but particularly in this kind of imitative music where the hands must be completely independent and yet totally co-ordinated. I will use every trick in the book, but if the previous stages were properly done, it should be pretty smooth sailing – but it will take time. At this stage I usually work back to front (start at the last bar and keep adding bars in front), and work in small sections again.

It takes between 20 – 40 daily 20 minutes practice sessions for someone who has never seen this kind of piece to master it. Here is the scheme I use:

10 practice sessions  (15 – 20 minutes each) to master the motif score:

     Session 1: bars 1- 2.
     Session 2 : bars 3 – 4.
     Session 3: bars 11 – 12.
     Session 4: bars 1 – 4 & 11 – 12.
     Session 5: bars 5 & 7 – 10.
     Session 6: bars 1 – 12.
     Session 7: bars 13 & 15 – 18.
     Session 8: bars 1 – 18.
     Session 9: bars 19 – 21.
Session 10: bars 1 – 21 (the whole piece).

14 practice sessions to master the piece with separate hands.

     Session 1 - bars 1 – 2 (Add first beat of bar 3.)
     Session 2 - bars 3 – 4 (Add first beat of bar 5.)
     Session 3 - bars 5 – 6 (Add first beat of bar 7.)
     Session 4 - bars 1 – 6 (Add first beat of bar 7.)
     Session 5 - bars 7 – 10 ( Add first beat of bar 11.)
     Session 6 - bars 1 – 10 (Add first beat of bar 11.)
     Session 7 - bars 11 – 12 (Add first eat of bar 13.)
     Session 8 - bars 1 – 12 (Add first eat of bar 13.)
     Session 9 – bars 13 – 14 (Add first beat of bar 15)
     Session 10 – bars 1 –14 (Add first eat of bar 15.)
     Session 11 – bars 15 – 18 (Add first eat of bar 19.)
     Session 12 – bars 1- 18 (Add first eat of bar 19.)
     Session 13 – bars 19 – 22
     Session 14 - bars 1 – 22 (the whole piece)
     
     15 practice sessions to master the piece with hands together:
     
     Session 1 - bars 19 – 22.
     Session 2 - bars 15 – 18 (Add first beat of bar 19.)
     Session 3 - bars 15 – 22.
     Session 4 - bars 13 – 14 (Add first beat of bar 15.)
     Session 5 - bars 13 – 22.
     Session 6 - bars 11 – 12 (Add first beat of bar 13.)
     Session 7 - bars 11 – 22.
     Session 8 - bars 7 – 10 (Add first beat of bar 11.)
     Session 9 – bars 7 – 22.
     Session 10 – bars 5 –6 (Add first beat of bar 7.)
     Session 11 – bars 6 – 22.
     Session 12 – bars 3- 4 (Add first beat of bar 5.)
     Session 13 – bars 3 – 22
     Session 14 – bars 1- 2 (Add first beat of bar 3.)
     Session 15 - bars 1 – 22 (the whole piece)
     
Each of these blocks of sessions must be done in order: motifs, followed by hands separate, followed by hands together. However, the sessions within each block may be treated more or less independently. For instance, you could work on sessions 1 – 2- 3 and 9 of the motif block in four different practice sessions on the same day.

What you should not do (because it is a waste of time) is to repeat session one 4 or 5 times on the same day. Do one specific practice session for 15 - 20 minutes. Then only touch it again the next day. Use the remainder of your practice time to do other pieces, or other sessions within the same block.

The scheme above is of course just a suggestion. Depending on the student you may have to break down a practice session in much smaller chunks. Or you may be able to do more than two bars in one session. The important thing is that you organise the learning of the piece, and be extremely consistent on a daily basis, so that it all adds up to something after a few weeks.

But we are not finished yet. The fourth stage is to add the ornaments. This would probably need a thread in itself, since ornament practice in Bach has been completely distorted by 19th century and early 20th century performers and editions. In fact most pre-1950’s editions that have realised ornaments for this invention have it wrong. I myself learned them all wrong in my teen years and had to relearn them all. Have a look at this thread where there is some discussion on this:

https://www.pianoforum.net/cgi-bin/yabb/YaBB.cgi?board=stud;action=display;num=1016762121

Fifth stage. At this point the student should know this piece back to front, and it is probably memorised and at performance level. I now give him/her a score where I have made an harmonic reduction of the piece, so that we can follow the harmonic progressions and modulations. I want to answer the question: Where is this piece going harmonically, and how is it getting there? This is ultimately what holds the music together and creates climaxes, moods and so on. And yet it is all on the border of consciousness. We do no pay much attention to it, and its mostly a subliminal effect (as it should be). It is similar to a movie’s soundtrack. It is there, but we are hardly aware of it (which is as it should be). And yet, the soundtrack is the single most important element for a movie to be effective. Just take the soundtrack away and you will see what I mean. It creates mood, climaxes, and it is the most important element in the suspension of “disbelief” so important for the enjoyment of a movie. Likewise, a music student must be made aware of harmonisation. Bach is particularly good for this purpose, since he was a consummate master of Harmony (his harmonisations of Lutheran chorales are still models of study in harmony classes)

Once the student has gone through theses five stages and is thoroughly conversant with them, s/he is ready to start learning the piece! (he he  ). This is the final stage , and it is here that matters of interpretation and performance will be tackled.

Best wishes,
Bernhard.