As every musician knows, the uncertainty principle can be applied to Fourier transforms of complex waveforms:
I will respond by admitting that (i) I am not actually a cowboy, and (ii) my opening statements are mischievous attempts to be provocative (or vice versa; I'm not really sure). I realize that Heisenberg and complex mathematical equations are not common areas of study for most musicians, but, whether you understand them or not, those equations certainly catch the eye, do they not? ;) In any event, please do not worry; there will only be one further mathematical equation in this blog, but I will explain it with disturbing clarity, or concise obfuscation, depending on my mood at the time. Or not…
One of the most important dichotomies to be found in most classical music is certainty versus uncertainty; today's blog is about the value of uncertainty, in a very general sense, within musical compositions.
Here are some examples of how this can work:
Theme; a recognizable melodic idea.
Development; use of familiar motives in unfamiliar contexts; transformation of motives in order to create new material. Some aspects of the material may be recognizable, but the listener may be unsure as to where it is going.
Transition; the beginning of a transition often sounds like a continuation or repetition of previous thematic material, but it soon becomes apparent that something different is going on, as modulation takes place, and the material is taken in a different direction, creating uncertainty.
Key/Modality/Pitch Center; a section is in a particular key, or modality, or, if non-tonal, it may be centered on a particular pitch class.
What key are we in? Development sections, transitions and retransitions, cadenzas, and even some coda sections (notably Beethoven's) all move between key areas, creating harmonic instability. Even tonicizations within more stable key areas can create some harmonic uncertainty.
Form; I recognize this form! I therefore have a pretty good sense of what is likely to happen next. If the form includes a recapitulation (and most do), then I have a very good sense of what to expect for the last section of the piece.
Form? Um... What's going on here? I don't recognize the form. Or, I thought I recognized the form, but the composer has thrown in unexpected elements (such as a coda that is longer than the development, or an unusually long transition, or a cadenza thrown into a piano sonata (as in Mozart's K.333, III), or a new theme in the development section). Is it sonata form, or rondo, or sonata rondo, or sui generis, etc.?
My musical "uncertainty principle" is this: It is at least as important to have sections that give rise to a sense of uncertainty in a composition as it is to have sections of certainty.
Fortunately, this can be represented by the following equation, which makes composing extraordinarily easy (if you're a physicist); x = quantity of uncertainty (measured in photon energy), p = mass of uncertainty (e.g., any Mass movement, such as kyrie, gloria, credo, etc.), and the h-bar is, of course, Planck's constant (I'm guessing this is a reference to Planck's faithful canine companion, Helmut):
Why? The excitement of a roller-coaster ride — not an emotional one, an actual one! — is probably related to both the ascents and descents; going up the big hill that tends to be right at the start creates a sense of Heisenbergian uncertainty (some might call it "dread"), as you wonder what lies in store for you once you reach the top (Is this thing safe? Why did I think this would be fun? Do I have a legal will?), and going down creates a sense of certainty (I am going to die! I know it for sure! Whee!), mixed with uncertainty (how much longer? Why is it so dark in here? Will I toss my cookies?). People who love these rides, I would guess, love both the uncertainty and the certainty of the experience, but especially the former. At least I do...
But a musical composition isn't a roller-coaster ride, is it?
Well, perhaps not, but I was making a rather loose analogy. A musical composition can be compared to a journey, and, if this analogy makes sense to you, then it is a wonderful example of the old saying that what matters most in life is the journey, not the destination. How much fun would life be if you knew exactly what was going to happen at every stage? How enjoyable would a musical composition be if you knew beforehand exactly what would happen at every stage?
→ Uncertainty; don't leave home without it!
What about compositions that are memorized? They are enjoyable, even when I know exactly what will happen next! Good point! But I think what may be taking place here is that even when you know exactly what notes are going to be played before they are actually played, I am not sure that you know exactly what your emotional response to those notes will be, so here again, I suspect that part of the attraction to the composition may be based on uncertainty. This too is analogous to a roller-coaster ride; even if you've been on it numerous times, you might respond slightly differently to it each ride.
I encourage you to look for opportunities within your compositions to try this idea out.
Below are links to two blog entries relating to this one, FYI:
• Two musical dichotomies: Familiar vs. Unfamiliar, and Expected vs. Unexpected
• More musical dichotomies
1. Besides those already discussed, to what other musical parameters can this certainty/uncertainty dichotomy be applied?
2. What are some of the ways in which it can be applied to the composition on which you are currently working?
3. Is this a useful way to think about music?
4. What are some other dichotomies to be found in music?
5. Can the certainty/uncertainty dichotomy be applied to other genres of music, such as popular, jazz, folk, or world?