Ingredients of a Well-Played Two Part Invention

[squinchy]

I started two part inventions two weeks ago, and I'm finding the one I'm working on right now (D minor) quite agreeable. I was wondering: What do you have to do to play a two-part invention 'well'?

My teacher said that the main voice needs to be louder and the secondary voice is detatched and softer, but that's all I know so far.

[bernhard]

I completely disagree.

The two voice inventions are motif based. They are like a musical game. part of the game is to delight on how the motifs get varied (they may be played backwards, for instance, or in double time values).

These pieces were not originally composed for performance, but rather to be played by connoisseurs who would follow the musical "trickery" either through palying it (and "feel" it phsysically), or by hearing it with the scorein front so that they could follow the motif transformation in both voices.

In fact many of the motif figurations overlap so that if you pay attention to the motif that is all you hear, but in the same prhase you also have the motif inverted and if you pay attention to the motif inverted you cannot hear the motif anymore. As a consequence, no matter how many times you hear the invention it always seem new and fresh and you want to hear it again so that you can "put your finger on it" which is of course impossible, They are designed to have this effect. there is a msucial ambiguity built into them. Bahc was a supreme master of this sort of effect and one can well imagine him with a twinkle in his eye as he played through them.

Unless of course the performer decides to accent one voice over the other, or the motifs over the inverted motif or vice-versa. And by doing so destroys the very ambiguity that is their main attraction.

Have a look at this thread where I discussed this in great detail in regards to the invention no. 1 in C. A lot that is in there can be equally applied to the invention in Dm.


https://www.pianoforum.net/smf/index.php/topic,2714.0.html

Have you ever seen the Escher picture below?



A two voice invention is the sound equivalent of this visual ambiguity.

Start accenting things and what you are doing is fixing one possibility over another and removing the wonderful ambiguity.

I hope this helps.

Best wishes,
Bernhard.

[xvimbi]

Have you ever seen the Escher picture below?

You must like Douglas Hofstadter's "Goedel, Escher, Bach".

[CC]

Bach's Inventions are what might be called "infinitely deep" music. No one can completely figure them out.  How did he do it? Not only that, it is meant to TEACH, even fairly new beginners. Not only that, it is based on motifs constructed from the simplest imaginable units.  Why?

First, on complexity.  It starts with the simplest things called parallel sets (my terminology, see link below), that are the simplest things you must be able to play if you are ever going to learn piano.  In link below, section III.20, I show how the inventions 1-15 are actually arranged in order of increasing parallel set complexity. That also explains why Bach later changed one particular parallel set from a more complex one to the simplest one in Invention #1 (because it was the 1st Invention!). It is therefore obvious that the Inventions are like super Hanons, and in fact, Hanon got most of his ideas from Bach. In the next level of complexity, the two hands become totally independent and play almost identical things, but in some kind of harmony/counterpoint. Therefore, now you have to play two independent things going in different directions AT ONCE! Once you learn to do that you notice that there is a constant conversation between the two hands, so there are not two things, but at least three things going on at the same time. In effect, this becomes something like an over-determined math problem -- there are more conditions to satisfy than variables available to satisfy them.  The pianist must therefore find some way to navigate this seemingly impossible conundrum. At even higher levels, Bach incorporates musical structures and theoretical concepts that are being debated to this day.

In addition, he has found the most important ways to develop the most common pianists weaknesses, and found note combinations that force you to practice them  (such as the 4th finger) -- you can't find any way to "cheat" and get around these difficulties. For example, he will give you something that plays easily as two triplets (eg, fingers 345,345) but the timing calls for three doublets (34,53,45), which requires much more control. Or he forces you to use two fingers to play one note -- which finger(s) do you use, and how do you play one note to satisfy the conditions of two melodies colliding? What if one melody requires loud and the other soft? what is the sum of loud plus soft?

Because Bach included so many things into such seemingly "simple" and short pieces, they can sound contrived in the beginning, and they certainly are. But because they are in reality so complex, and multi-layered, the "idea density" is extremely high. This makes them unusually difficult to play correctly and to memorize them. In fact, this is why they have not been played more than they were -- in effect, few students could conquer them adequately and often gave up. In short, the more you practice them, often, the worse they become, and there is no telling when you will suddenly black out and have no idea how to continue. And certainly, there is a certain speed at which they suddenly become monumentally difficult.  I show some methods in the link below to overcome these difficulties and hope that Bach will be played more than they have been before, because they are so fun to play and are so educational.

What is so amazing is that Bach composed these at a time when pianos as we know them today weren't even invented. Yet, he had found almost all the technical skills (such as quiet hands) that you need to play today's piano!

Of course, his music is not infinitely deep -- no human can do that.  However, there are so many layers that no one can figure them all out in real time as the music unfolds -- it might just as well be infinitely deep and the results would be the same.  It is like drowning -- if you drown in 20 ft of water, it doesn't matter if it is 20 ft or infinitely deep!

[timothy42b]

You must like Douglas Hofstadter's "Goedel, Escher, Bach".

Fantastic book.  I passed my copy on after reading, as I do with most books, but have been regretting it this time.  

[bernhard]

You must like Douglas Hofstadter's "Goedel, Escher, Bach".

In fact I read that book in the 1980s, when it first appeared. I thought it was  a superb book. At that time (I am most ashamed to admit it ) I was more interested in Godel and Escher than in Bach, however.

I really should re-read it and see what I think of it now.

Best wishes,
Bernhard.

[squinchy]

Thank you, Bernhard, xvimbi, Tim, CC, for your replies. [I'm adding Goedel, Escher, Bach to my list of books to read!]

I have a few questions regarding the motif in the Dm invention.

1. Is the motif the first two measures [Dm scale-ish] of the right hand, or the first four measure [Dm scale-ish followed by a broken Dm chord and then a broken A dim 7]? This has been confusing me, since I don't see how the broken chords are manipulations of the motif. [Are they?]

2. Does it matter if the motif is repeated, but a bit stretched interval-wise? The interval in the first and second measures (C#-Bb) is a major sixth, but later, in measures seven and eight (Bb-A), it is an augmented seventh. The intervals between the highest and lowest note in the motif keep changing, which confuses me.

3. In the section where the left hand has the long trill, where do all the accidentals come from? My teacher said that it modulated to A major, but then decided it was a mode. It doesn't really fully look like either to me-the only thing I can fathom is that they're there to create tension.

4. You shouldn't accent anything?? Wouldn't that be awfully boring and difficult to listen to--Or am I misunderstanding..

Meh. Looking at the score away from the piano is making me see all the escher-qualities of it. My brain hurts.

[Maui]

4. You shouldn't accent anything?? Wouldn't that be awfully boring and difficult to listen to--Or am I misunderstanding..

You're misunderstanding.
Let me explain: you should make the phrases to SING like an human voice. So it'll not be boring or difficult to listen because its much easier  to follow a sing-like melody instead of non-singing ones.
You need only to be careful making all the voices singing at the same time (i mean everytime), but in different ways, so you can make a beautiful music without losing the ambiguity miraculous.
Be careful to not give priority to some phrase, they should be equal important, but this doesnt mean that they should be played like an harpsichord.

I hope that helps,

Maui.

[xvimbi]

Be careful to not give priority to some phrase, they should be equal important, but this doesnt mean that they should be played like an harpsichord.

Well, in a way, they should be played as if playing on a harpsichord. This is how they got composed in the first place. If you have a digital piano, switch to the harpsichord sound and see what happens. It's amazing how much Baroque music changes and how much more important it becomes to play the ornaments correctly and have everything fit exactly.

Having said this, the piano offers a lot more possibilities than the harpsichord, and Bach would have most definitely taken his liberties with them. It would therefore be mistake not to do so now.

Getting the most out of Bach's music requires competent guidance. If there is no competent guidance, I would almost say, the time is wasted. Your teacher should be able to provide this guidance.

[bernhard]

Thank you, Bernhard, xvimbi, Tim, CC, for your replies. [I'm adding Goedel, Escher, Bach to my list of books to read!]

I have a few questions regarding the motif in the Dm invention.

I will answer 1, 2 and 3 very briefly. If you are not satisfied come back and I will try to give a longer answer during the weekend when I have a bit more time.

1. Is the motif the first two measures [Dm scale-ish] of the right hand, or the first four measure [Dm scale-ish followed by a broken Dm chord and then a broken A dim 7]? This has been confusing me, since I don't see how the broken chords are manipulations of the motif. [Are they?]

Strictly speaking you can regard the motif as the RH of bars 1- 4. However you can subdivide this motif in three distinct sections (sub motifs): the scale going up, the scale going down and the arpeggio figurations.

Personally I find that the most interesting analysis comes from considering RH bars 1 - 2 as the motif, and bars 3 - 4 as a countermotif. From there you should proceed by identifying every time the motif occurs, and all the different variations (melodic inversions, counterpoint inversions, evolutios, augmentations, fragments and retrogrades). Not every single figuration in this invention is the motif (there are far more entries of the motif in the invention in C).

2. Does it matter if the motif is repeated, but a bit stretched interval-wise? The interval in the first and second measures (C#-Bb) is a major sixth, but later, in measures seven and eight (Bb-A), it is an augmented seventh. The intervals between the highest and lowest note in the motif keep changing, which confuses me.

No it does not matter, specially when the motif is inverted. There are three possiblities: The intervals are kept exactly the same on the inversion: mirror-inversions. The intervals are kept the same numerically but not necessarily the same (e.g. major 3rd and minor 3rd): melodic inversions. Finally the intervals are not respected even in number, just in direction: contour inversions (or sometimes called imitations).

3. In the section where the left hand has the long trill, where do all the accidentals come from? My teacher said that it modulated to A major, but then decided it was a mode. It doesn't really fully look like either to me-the only thing I can fathom is that they're there to create tension.

Like many of the inventions,this one has an ABA form with the A in the tonic key and the B in the dominant key. The dominant of D minor is A minor. So the accidentals you see in that section modulates to A minor, both in its melodic (F# and G#) and harmonic form (G#).

4. You shouldn't accent anything?? Wouldn't that be awfully boring and difficult to listen to--Or am I misunderstanding..

This is a very interesting question, because it leads us to enquire on what exactly is an accent.

We tend to think as accenting a note as identical with playing that note louder. But it is not necessarily so. For instance, if you play a C repeatedly on the piano all with the same time value (length), all at exactly the same dynamics, it can be said that there is no accent. If every third C I play a bit louder I have an accent no doubt. But what if I keep playing all the Cs at exactly the same dynamics, but every third C I lengthened it (e.g., if I am playing quavers, every third C becomes a crochet). Then I would have a rhythmic accent.  What if I played every third C legato, and the others staccato? I would have an articulation accent. What if at every third C I played a D instead? I would have a melodic accent.

What I am driving at, is that it is impossible to play any piece of music without accents (unless it is a sequence of the same note repeatedly indefinitely – and even then, the mind tends to group things and imagine accents – like in a clock where we do not hear tic tic tic tic but tic toc tic toc).

Any piece of music already has enough accents in its structure. Playing the right notes at the right time (as Bach himself said) already gives plenty of accents. So you cannot play a piece without accents even if you wanted. So the real question becomes: Where are the accents in this piece? The score usually will answer this question, and Bach was particularly meticulous in his scores to notate exactly what he was after.

By the way, I am not proposing that one should play Bach without dynamics.

Here is an analogy. The chess set is quite a beautiful thing in itself. The checkered board, the little sculptured pieces. A person who knows nothing of the game of chess and comes across a chess set can still like it for its aesthetical value. If this person is a decorator, he may even plan the chess set as a centre piece of an elegant room. He may display the pieces in an aesthetically pleasing configuration and even topple some for added effect.

Now imagine a different situation. Two chess masters have been playing a difficult game. After a while they stop for lunch and leave the board with the pieces in their positions, to have lunch and play again later.

To our room decorator, if he happens to see this board, all he will see is how pretty the pieces look, but would it not be even nicer if he moved that piece here and that piece there so that the effect would be more aesthetically pleasing?

To a chess connoisseur, the board left by the two masters will have a completely different impact. He will be able to tell from a glance who is winning and who is loosing. He may be able – from looking at that frozen frame – intuit how the game started and which moves were made. He may be able to identify well known patterns (aha! A Sicilian defense!). And since he knows the rules of the game he may be able to predict up to a point the future development of the game and he may also wonder how he himself would fare in this game. He may be interested enough to stay and watch the game resume. And when it does resume, the players may move in the way he predicted, or the players may surprise and delight him with the cleverness of their moves.

Personally I try to approach Bach’s music like a game of chess, the beauty of which relies mostly in how these rules are used. There is a deep intellectual delight going on here.

That it also happens to be pretty is a secondary bonus.

The point is not its decorative/aesthetic value (“what a nice little tune”). It is not unusual to find people who play Bach like a decorator would arrange a chess set. They like to talk about “intuition” and "emotion" and so on. Personally I think they are ignorant of the rules of the game.

Best wishes,
Bernhard.