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.

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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. unpredictability. How 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.

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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.

Playing With Expectations (Part One)

One of the best ways to become better at making something is to study good examples of the thing(s) you admire in order to learn what makes them work.  If your goal is to build a better car, you could look at (by which I mean take apart!) good cars, and try to understand the function of each part as a way of learning how cars work.  If your goal is to become a better composer, you could study good compositions (by which I mean take apart!) in order to understand how they work.

In both cases, the objective of learning how things work is partly general interest (if you love something, learning more about it is its own reward), and partly self-interest (you are hoping to discover and understand aspects that you can borrow, improve, or otherwise modify in your creations).

An aspect I enjoy most about my job is that I get to analyze music on a regular basis for various courses that I teach. There are different types of musical analysis, but I think they all revolve around the fundamental question of how a composition works. Or, more generally, how does music work?

There is no single answer to this question — the reasons that any composition works are many, and different compositions work in different ways — but it seems to me that there is at least one thing common to all good music, and it is this (drum roll, please):

Good music plays with our expectations. 

(To enhance the dramatic effect of the above, play this short clip immediately!)

By "playing" with our expectations, I mean that the music sometimes does what we expect (and how does it do that?), and sometimes doesn't, and the ways in which expectations are created, fulfilled, and thwarted, constitute an essential part of the reason we are drawn to the music. Understanding how this works can be an extremely valuable skill for a composer.

It is easy to introduce unexpected elements to a composition, but this, by itself, does not produce compelling art. Really good compositions somehow set-up expectations and leave us guessing as to which will be fulfilled and which won't be, as we go along for the ride.  How do they do this?

More to follow in parts two and three.

How much theory do you have to know in order to be a composer?

This is a question that I am sometimes asked, and it came up recently in a conversation I had with Karim Al-Zand, the visiting composer for our recent (January 26-28, 2012) Newfound Music Festival.  I won't attempt to quote him from memory, but my sense of the conversation is that he felt that it was very helpful for a composer to have good music theory skills, and I happen to agree, so I thought I would explain my reasons.

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What is meant by Music Theory?

"Music theory" may refer to any of the following:

• Analysis (structural, melodic, harmonic, rhythmic, Schenkerian, set theory, phenomenological, psychoacoustic, stylistic);
• Orchestration and instrumentation;
• Under "music theory," our university also lists rudiments, aural skills (ear-training), keyboard harmony,  and jazz theory;
• Harmony and counterpoint (renaissance counterpoint, baroque counterpoint, common-practice harmony, late-romantic harmony, 20th-century techniques).

By way of comparison, "art theories" cover a variety of topics such as theories of the nature, functions, and effects of art,  mimetic theories, procedural theories (abstraction, expressionism, formalism, minimalism, naturalism, romanticism, symbolism), expressive theories, formalist theories, processional theories, aestheticism, theories of organic unity, and pragmatism.  Click this link to read more, or do a Google search of "art theory" and browse some of the results.

"Theory" has very different meanings in music and visual art!

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Breaking it down…

With the understanding that "music theory" refers to a wide variety of topics as listed above, how much theory do you have to know to be a composer?

Let's break it down by topic within the wider category of music theory:

Analysis is an attempt to understand how music works using a variety of methodologies.  Analytical skills are useful for composers on at least four levels:

1. Discovering how other composers' music works is one of the best ways to develop compositional skills.
2. Analysis of others' works can stimulate the creative process by giving you ideas of things to try in your compositions.
3. Analytical skills are essential in achieving a deeper understanding of your own music — this understanding can help you make the most out of your musical materials, and can help get you unstuck when you feel as though you've run into a compositional brick wall. and
4. It is easy to lose perspective while composing, because the experience can be so subjective.  Analysis of one's own music is one method of introducing some semblance of objectivity into the equation.

Orchestration and instrumentation:  Instrumental ranges, the ways in which different instruments change tone colour in different registers, how to write idiomatically for different instruments, extended techniques, types of bowing, how different instruments sound in combination with one another, how to create different textures — it's all stuff composers should know.

Rudiments: As the name suggests, this refers to the study of the fundamental aspects of music, such as key signatures, time signatures, scale types, chord types, and accepted notation practices. But many composition students struggle at times with incorrect notation of rests and rhythms, and illogical and/or inconsistent enharmonic spellings. It's basic, it's boring (to some), but it's essential knowledge for composers who want others to perform their music.

Aural skills are among the most important skills a composer can have. It is useful to be able to hear an unusual chord, chord progression, tune, rhythm, etc., and to be able to quickly transcribe it, which might spur a creative impulse such as using some aspect of your transcription in your next piece, or to be able to quickly transcribe your complex musical ideas. If you have an idea, either in your head or something you've worked out on your instrument, struggling to notate your idea correctly introduces frustration, which is an inspiration killer. Good aural skills are also essential when rehearsing your music; if someone plays wrong notes or rhythms, you need to be able to hear this instantly and correct the problem. Or, if the ensemble plays notes or chords that don't jibe with what you intended to write, you need to figure that out and fix the wrong notes.

Keyboard skills:  Almost every "great" composer that you learn about in music history since the piano's rise in prominence in the late baroque era was regarded as an outstanding keyboard performer.  This suggests that keyboard skills are (or at least were) extremely important and useful for composers, but are they as important nowadays? To answer that, it would be helpful to know why so many great composers were great pianists. My guess is that there were at least three reasons:

1. Historically, excellent piano skills enabled composers to perform their music for others, even if the music was not written for piano, such as chamber music or a symphony. We now have computer technology to make approximate realizations of our music, but in earlier times, the piano (or organ) was the only way to do this. 
2. Historically, excellent piano skills were a great asset in the development of composers because they enabled composers to hear realizations of their own compositions long before computer technology existed that could fulfill this role.  
3. Being a skilled pianist facilitates score study of works by other composers.  Nowadays we can listen to recordings while studying scores, but even so, you discover things by playing (or, in my case, hacking) through a score that you don't necessarily get any other way.

The fact that there are many successful composers in the world today who are not piano virtuosi illustrates that exceptional keyboard skills are no longer essential for composers, although I believe it is very useful for any composer to have keyboard competency.

Harmony and counterpoint: In order to become a skilled composer, do you really need to master Bach-style harmony and counterpoint, or renaissance counterpoint, or late-romantic harmony, or many 20th-century techniques? Some people may tell you that John Cage and Iannis Xenakis didn't know any of this stuff, and they became two of the most important composers of the 20th century!

But how true is it that "they didn't know any of this stuff?" Wikipedia tells us that Cage had piano lessons as a boy, although he was apparently more interested in sight-reading than developing virtuoso technique – but lots of sight-reading is great training for a composer! He studied for two years with Arnold Schoenberg (who Cage apparently "worshipped"), and also with Henry Cowell. However, Cage claimed to struggle with harmony:

After I had been studying with him for two years, Schoenberg said, "In order to write music, you must have a feeling for harmony." I explained to him that I had no feeling for harmony. He then said that I would always encounter an obstacle, that it would be as though I came to a wall through which I could not pass. I said, "In that case I will devote my life to beating my head against that wall." (Pritchett, James. 1993. The Music of John Cage. Cambridge University Press; p. 260)

Wikipedia tells us that most of Cage's compositions from the 1930s are "highly chromatic and betray Cage's interest in counterpoint." The importance of structure was stressed to him by at least one of his mentors (Richard Buhlig). Cage drew upon an impressive variety of extra-musical influences, including art, architecture, Zen Buddhism, philosophy, and mathematical formulae. He may not have developed the deep mastery of traditional (i.e., "common-practice period") harmony and counterpoint that we associate with most other composers, but he did have some training in these areas with some pretty impressive composer-teachers!

Iannis Xenakis studied architecture and engineering at the National Technical University of Athens, and was subsequently employed at Le Corbusier's architectural studio in Paris, working on a number of projects, perhaps most famously the Philips Pavilion at the Brussels World's Fair in 1958, completed by Xenakis alone, from a basic sketch by Le Corbusier (Hoffmann, Peter. "Iannis Xenakis", Grove Music Online, ed. L. Macy).

Phillips Pavillion, Brussels World's Fair (1958), 
bearing an uncanny resemblance to a nun's fancy cornette and habit (below):

Coincidence?

But he also had musical training, having studied notation and solfège as a boy, and having sung works by Palestrina, Mozart, and other composers in his school's choir. [One of the best ways to learn renaissance counterpoint, by the way, is sing Palestrina, so this in itself represents a kind of training.]  While working for Le Corbusier, Xenakis also studied harmony, counterpoint, and composition with a variety of teachers. However, when he asked Messiaen if he should continue his studies in harmony and counterpoint, Messiaen famously recommended against it, something he apparently did with no other student.

I understood straight away that he was not someone like the others. [...] He is of superior intelligence. [...] I did something horrible which I should do with no other student, for I think one should study harmony and counterpoint. But this was a man so much out of the ordinary that I said... No, you are almost thirty, you have the good fortune of being Greek, of being an architect and having studied special mathematics. Take advantage of these things. Do them in your music. (Matossian, Nouritza. 1986. Xenakis. London: Kahn and Averill; p. 48)

Both Cage and Xenakis had training in harmony and counterpoint, although it was arguably less rigorous than the training received by most composers of classical music, even in the 20th-century.

The fact is that so many composers were well-trained in harmony and counterpoint, even among the avant-garde of the 20th-century, might suggest that these are probably still important skills to master for any composer.

But was this cause or effect? Did skills learned as students in harmony and counterpoint contribute to composers' later "greatness," or were "great" composers such good musicians, even when they were students, that they naturally did well in these subjects, whether or not they applied this knowledge to their mature compositions? We can't know for sure of course, but my hunch is that, for most composers, the harmony and counterpoint learned as students probably informed the development of their mature style, and made them better musicians.

If you studied harmony and counterpoint and did not do well, I do not suggest that your future development as a composer is irrevocably compromised, however.

For one thing, you can go back and study this stuff again. I did poorly on most of my Royal Conservatory of Music (Toronto) theory exams until I began my studies in composition, mainly because the material didn't seem relevant to me, and I had no background in classical music. When I began studying with Dr. Samuel Dolin, he told me that "harmony and counterpoint are relevant, but you won't know why until you become good at them." Since he had trained so many good composers before me, I figured he knew what he was talking about, and I dedicated myself to becoming more skillful in these areas.

For another, the fact that at least a few composers without extensive training in harmony and counterpoint went on to do very well for themselves would suggest that this training may not be as vital as was once considered to be the case (and probably still is in music schools and conservatories).

I nevertheless believe in the importance and value of becoming highly skilled in harmony (part-writing and analysis) and counterpoint because subsequent experiences as a composer have convinced me that Dr. Dolin's advice was 100% right. And for that I remain forever in his debt.

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Conclusion

How much theory do you have to know in order to be a composer?

• Think of the many aspects of music theory as a toolkit; the more tools (skills) you have, the better equipped you are to be a composer.
• It helps to know a lot!