Saturday, February 16, 2013

Playing With Expectations (Part Two)

Here's a link to my previous post, Playing With Expectations (Part One), in case you missed it.  It's very short, and sets up today's blog entry.

Rewriting Beethoven might strike some as sacrilegious, inconceivable, or merely foolish, but this is what I will do in today's entry in order to explore how Beethoven plays with our expectations, or, put another way, the issue of predictability vs. unpredictabilityHow will my re-write sound? You can judge for yourself (there are audio clips), but here's a hint that may shock you (or not): Not as good as Beethoven's version! 

But what makes Beethoven's version better? In exploring the reasons for this, we may better understand an essential component in great compositions, and use this understanding to improve our own creative work.

Beethoven's Piano Sonata no. 21, op. 53, "Waldstein" is one of his greatest works. This is how the first movement begins:

Have a listen:

There are two basic ideas: The repeated chords, labelled a, and the short "tag" to these chords, labelled b; the b motive is varied and repeated two octaves higher.

Do you see or hear anything unexpected so far?

I know it is difficult to know what to expect when we first hear a piece, but I think most people bring at least some expectations to their listening experiences, and upon hearing just a few bars of a composition, more expectations are formed. If, for example, you have listened carefully to several classical piano sonatas, you probably have some expectations before hearing a sonata for the first time, such as:
  • You would expect that a work with the clever title of "Piano Sonata" would be (i) written for piano and (ii) a sonata. Beethoven does not let us down here; sure enough, it is for piano, and it is a sonata! How predictable! ;)
  • You could reasonably expect the conventions of 18th- and 19th-century harmony and voice-leading would be followed (since they are based on the practices of composers of that period, of which Beethoven was one), and sure enough, they are, albeit with some unexpected harmonic choices along the way (more on this below).
  • Experienced listeners, especially those who have studied musical form, might also expect that the first movement of a sonata be in "sonata" form because that is usually the case (and is the reason this musical form got its name; it is also called "first movement form"), and once again, this proves to be the case here. As with the previous point, however, Beethoven makes some creative and unexpected choices within this form.
However, this four-bar opening already does some unexpected things, such as:
  • Most piano sonatas begin with a melody in the right hand, and an accompaniment figure in the left hand, or, alternatively, with a short, attention-grabbing passage in octaves, as occurs in several sonatas by Mozart (K. 284, K. 309, K. 457, K. 570, K. 576). This sonata does neither; it opens with the repetition of a single chord for the better part of two bars (the chord changes on the last beat of bar 2), and the repetitive eighth notes continue unabatedly in the left hand until bar 11 (which you can see below). Beethoven's opening is highly unconventional in this regard.
  • You also might expect the right hand notes to be in the treble clef, because that is generally where they are found at the start of a piano sonata, but once again we find that Beethoven does not do this in the first three bars, placing the right hand in an unusually-low register.  This changes in the fourth bar, where another surprising event occurs:
  • The melody in bar 4 begins two-and-a-half octaves above the previous melody note in bar 3.  This extreme register shift is very unusual in classical piano music, and especially so just a few bars into the start of a composition.
  • You also might expect the key (C major) to be established unambiguously at the beginning, because this is what most compositions do; it is considered good compositional etiquette.:) Here again, Beethoven plays with this expectation: The chord that is repeated so frequently over the first two bars is indeed a C major chord, but the next one (at the end of bar 2) has an F sharp in it, which is not a member of a C scale. The F sharp is part of a D7 chord, which "tonicizes" the G chords in bars 3-4.  If you do not have a background in music theory, all this means is that when we hear a G chord preceded by a D7, the G chord can sound like it is the "home" key, not C.  This is not all that unusual, but it isn't a very common way to open a composition either.  
  • The "what key are we actually in?" confusion continues over the next bars as well, because Beethoven avoids a dominant-tonic (G7 to C) chord progression, and this is the progression needed to establish a key. We finally get a G7 to C progression in bar 12, but Beethoven throws in another wrinkle by making it G7 to C minor.  The attentive listener probably knows at this point that the music in C, but is it C major or C minor?
In short, Beethoven is messing with our minds.

Beethoven's continuation of the above has more expected and unexpected elements, but to help illustrate the point of this blog (and for fun), I made up a continuation that you probably will find less satisfying than Beethoven's; the questions, if you agree with this, are where does it begin to sound weaker, and what is the cause?  
Have a listen to the above (Warning: Beethoven connoisseurs  may become apoplectic):

At what point does it begin to sound less convincing?
  • Some might say bar 5, which is where it begins to differ from Beethoven's version. However, I don't think it sounds "wrong," or unconvincing there, probably because Beethoven does something almost identical to this in bar 18, and it sounds fine when he does it!  
  • My rationale behind writing the second line of music above was simple: In most compositions, the opening musical idea (i.e., theme, motive) is repeated, either exactly or varied in some way. Bars 5-8 above are a repetition of the first four bars, but transposed up a step (sequence).  So far so good.
  • In bars 9-10, I cut the first 4-bar idea in half, and this is sequenced up another step.  The tail end of the b' motive is inverted just to add a touch of the unexpected. 
  • Bars 11-12 continue this pattern; they constitute another sequence (up by one step) of the previous two bars, and once again the tail end of the b' motive is varied slightly.
So… Where's the problem, and what is the cause?
  • To my ears, bar 9 is when things begin to sound unconvincing; perhaps this is because at that point, it becomes a bit too predictable.  Bars 5-8 are a sequential repetition of the opening four bars. Hearing this, the part of my brain that recognizes patterns immediately begins to wonder if another sequential repetition will occur in bar 9, and when it does, I find it disappointing because that is exactly what I expected. Cutting the four-bar idea into two bars mitigates the predictability problem somewhat, but not enough to justify the continuation of the sequence in bars 9-10, at least for me. And doing this one more time in 11-12 just exacerbates the problem.  At this point, if I were in the audience, the composer would have lost me; I would be so unimpressed with the music that I would be unlikely to continue listening in a positive frame of mind.
  • The unusual harmonic progression — specifically the use of a B minor chord in bar 10, surrounded by F chords on either side — doesn't sound all that good either.
What about the last line of music above? Let's trash that now!
  • Bars 13-17 sound fine to me; not brilliant, just fine. I don't think we need to "trash" this line. The ascending, stepwise pattern in the bass continues using only the a part of the theme. Delaying the b portion until bar 16 seems to work, probably because because my brain is expecting it to arrive earlier, based on previous patterns. Delaying an expected event can heighten the listener's anticipation, and can be an effective way to play with expectations. But it must be done artfully; too much delay, and our interest in hearing the expected event may wane; too little, and we have not had an opportunity to build any anticipation, kind of like that old song, "How Can I Miss You When You Won't Go Away?"
  • This works its way back to the beginning of a varied return of the opening theme in the last bar above.
Let's look at and listen to what Beethoven actually wrote:

Recording of the above:

What makes Beethoven's version work better? 
  • Nothing!
  • Just kidding… Well, in LVB's version, the first four bars are given a sequential repetition in bars 5-8, but down a step, not up.  This may not seem like much of a difference, but the significance is that the listener is not expecting bar 5 to begin in Bb and then tonicize F. Why? Because this is a very unusual thing to do at the beginning of a composition in C major!  So, once again, we have something expected (a sequential repetition), along with something unexpected (the move to Bb and the tonicization of F).
  • A second advantage of continuing in this way is that it allows the bass line (the lowest note) to descend chromatically from C down to G (C-B-Bb-A-Ab-G). This allows Beethoven to explore some interesting and unexpected harmonic colours on the way from the opening C chord to the G chord in bar 11.  
  • My bass line has some patterns, but it also has a kind of meandering, aimless quality if you play it by itself; Beethoven's has a strong sense of building towards a goal, that being the arrival at the G chord in bar 13.
  • Another point of harmonic interest is that LVB's version touches on C minor as it arrives at bar 13; this too is unexpected.  
  • The continuation past bar 13, which is the beginning of the transition section, begins similarly to the opening bars, but this time there are three subtle but significant differences:
    1. Instead of repeated 8th-note chords, we get oscillating 16th notes; this produces a more unsettled effect and ramps up the intensity.
    2. The register is not the same as the opening; it is an octave higher.  Again, this produces a subtle but possibly unexpected colour change.
    3. The second phrase, which was sequentially repeated down by step the first time, is sequentially repeated up a step in bar 18.  Again, not a huge difference, but perhaps not what the listener might be expecting at that point.
  • We have only begun to scratch the surface here; many more surprises remain in this movement, including an unusually-long transition, modulating to E major for the secondary theme group (the expected key would have been G, and the expected mode of E in the key of C is E minor, not E major), modulating to Ab for the secondary theme group in the recapitulation, and the lengthy coda, which functions as a second development section.
As I wrote in my previous blog, doing unexpected things in your composition is not of itself particularly challenging, but great works seem to find an ideal balance between the expected and unexpected, and understanding this is one of the keys to growing from a "pretty good" composer to a very good one.

A good way to develop a feel for this ideal balance in the composition you are working on is to experiment – a little more predictable here, a little less-so there; then vice-versa – but just being aware of the value of playing with listener's expectations is a great way to start.


Evan Smith said...

I probably should have read part 2 before part 3. You answered most of my questions that I posed to dead-Beethoven.

What really struck me is the harmony. I'm always facinated with harmonic progressions, its one of my favorite things about music, and what you did in your re-creation was, I agree, perfectly fine. Things went where they should, and the tonicization of Am was expected but well-done. But to go to the b7 (Bb) is so... well there aren't words. I mean, it's a simple concept, just go down a tone, but I think Koska and Payne have ruined many peoples minds.

It's a great thing about musical notation software however. You can write something and then with a click, transpose it. Perhaps the return of A will sound better down a minor third, let's try *click*. Done.

Obviously, Beethoven did not have this luxury (and probably could just do that in his head anyway), but let's face it, none of us are Beethoven. So a little Finale or Sibelius help is much appreciated. To create something like the Waldstein by a slightly digital tranpositional accident would be okay with me.

Chris Morrison said...

There is something about humans that makes them enjoy stories, especially when they are unpredictable. We enjoy these stories because predictability is boring. Unpredictability introduces elements which grab your attention. Examples from other creative pursuits can easily be found. Life itself needs unpredictability or else it becomes static. In painting, the eye is drawn to the little things which seem out of synch with the rest of the piece. When listening to music, the ear is drawn automatically to discordant elements. We hear what could be considered mistakes much more easily than what could be considered perfection. The less predictable elements of a composition demand attention, to be heard, and to be considered, much more so than if you are listening to something that is predictable. This unpredictability jolts your attention and is impossible to ignore. The brain tends to fill in information based on what has just happened. When something completely different appears and takes you off track your brain latches onto it and tries to make it conform. It cannot enforce this conformity once you become aware of it. Within a piece, these become the parts that stand out and are most memorable. In the same way, the people we remember most are the ones that were unusual or strikingly different in some way (like Beethoven!).

André McEvenue said...

After reading this blog post, I wonder about how expectations differ for people with varying degrees of exposure to music. Would a group of people who all have the same exposure to music react the same way to any given composition? If so, then presumably, with enough data could a computer program be used to assist, or even compose a work that caters perfectly to an individual's level of familiarity.

To add to this point, I would like to consider how music differs from the game of chess. There are many who enjoy analyzing chess matches of the great players. One of the beauties of the game (in my opinion) is how tried and true opening sequences are manipulated and given variation to provide a twist that breaks the logic, and the other player is forced to adapt to this new situation. Presently, computers can outmatch any human being at this game, so why don't people analyze simulated computer matches with the same admiration and awe that they admire the cunning of Bobby Fischer's famous openings?

I am aware of the important differences between music and chess. Chiefly, we don't play music to best an opponent (but maybe some do), and we also don't play chess to be expressive. Despite this, I still think it could be an interesting starting point in understanding what it is in the balance of predictability and unpredictability that makes our heads turn. In chess the goal is to be as unpredictable as possible while still maintaining a line of logic that will take the winner to their goal. Does a piece of music share an element of this even though it doesn't always have a goal?

As listeners, do we have goals? And if so, are they more or less the same person to person, or do they change with exposure, and how much?

Robert Godin said...

A lot of these expectations are somewhat rooted in when they were composed. If Beethoven was a alive today and composed , say, a-tonal music would some of these methods still be used? Would shifting down a tone in a key area of the piece still hold the same effect? Probably not. Looking forward to part 3.

Josh Penney said...

This has been sort of enlightening to me. I think in my balancing of expected and unexpected I've been trying to overdo it. When I'm working with the expected it's fairly easy, so there's no need to get into it, however the unexpected. After reading this I think I try too hard to shock the ear, and in doing so create things that don't always have a great sense of unity. In reading this , Beethoven only change the quality of a sonority to throw off what we thought was coming, instead of just redirecting the whole progression perhaps, or changing the metric values. I think i composing further I can do less and achieve more with this balance.