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:
Certainty
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Uncertainty
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Theme; a recognizable melodic idea.
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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.
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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.
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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.
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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.?
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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
Questions:
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?
Posts
20 comments:
I agree that a good piece of music, like you said, has just the right balance of certainty vs. uncertainty and I think that that goes for any and all genres. I think that the use of certainty vs. uncertainty is going to mean the life or death for the piece I'm working on now. Where this piece is very much rooted on tonality, if not outright tonal in places I'm being very careful to make my progressions not go where one would expect but I also need to be careful not to go completely out to lunch as, sometimes, that's not quite what I'm going for with this.
Articulation and phrasing can also be a way of creating uncertainty as when something is repeated but with a totally contrasting articulation it makes for a more interesting repeat.
Very interesting blog, I'll have to take a look at the other two that you said were related.
I like roller coasters!!
I also like this blog!! Except the math, that scared me.
It really does seem that throughout the passage of time in classical music, the idea of uncertainty has become more and more common in the compositional decision making processes. Back in the day, which was a Wednesday, when da b'ys Palestrina and his posse were not faced with as much, if any, walls of uncertainty as we do today. Back then, he wrote a mass or a motet and he knew exactly the form, key areas, transitions, you name it....anything else would have been blasphemy and he would have been kicked in the head for being the devil, or something.
Now, at least to me, if we think about composing in this way, it is "wrong" and BORING (which I think is a problem, or at least a discouragement). Instead we do need to find this balance of certainty and uncertainty to create interesting music.
In my piece I am writing now for trombone quartet, I am trying to compose using different modes of limited transposition, which do have common aspects of traditional music, but there is also a great amount of unfamiliar aspects that really give the piece an uncommon sound.
I look forward to my future compositions and how I learn to find a balance between these topics.
ahhhh, good old uncertainty.
I live for the stuff, really. Whenever I choose repertoire, buy music to listen to, EAT, I almost always go for something I have never heard of or seen before. I'm really trying to go back to that sort of root in my piece for trombone quartet. So far I've been relying heavily on crunchy chords mixed with just the right amount of more simple, diatonic chords. I've also been trying to mix up the texture by using longer note durations juxtaposed with shorter, more rhythmic passages.
My problem usually comes with good development of these sort of ideas. I get bored with musical ideas easily, which is basically why I tend to listen to and write shorter music in general. I'm usually too concerned with "whats next" in terms of an entire piece, rather than a section of a piece, so I try to wrap things up and move on.
I think that finding the right balance between certainty and uncertainty is definitely important, maybe I should give those equations another look...
I definitely agree with all of these statements. I do think that composers play with our uncertainty (or at least the good ones) and only give us just enough to keep us following along.
However I feel like due to this, composition has become sort of a paradox in today's age. Mozart was able to challenge us with his forms, and we could never be sure of where his forms would take us next. Than we caught on to his tricks, and Beethoven came along and took it one step further. and than etc. etc. until now.
Most composers have used expectation makers/breakers of the past in new ways to make/break new predict-abilities. This is where the creativity of the composer comes in I believe. I think to compose interesting and enticing music, the material or mood or emotional aspect of it is very important, however the way you alter people's expectation of what's next is the most important/ hardest thing (to be original with).
Oh saturated ears..:(
While reading this blog, I was unconsciously mulling over the last piece of music that I had heard - it was Chopin's etude Opus 10, No.4. I have just recently began listening to this piece and I am going to start working on it as soon as exams finish. After reading this blog I believe I have found the reason why I enjoy it so much, and continue to listen to it. The first listening I was very certain of a tonal center and it's fast paced rhythmic quality. I was uncertain as to what would happen with the harmonic progressions because of it's speedy chord changes and also uncertain with the form. I enjoyed this ratio of certainty / uncertainty. The second time I listened to it, I enjoyed it even more because I was expecting certain climax sections, accented notes, exciting moments and waiting for them to occur. Once those moments came, I was able to notice more things about those moments and also concentrate on other aspects. Similarly, the third time I became more aware of the dynamics and articulation, the harmonic progressions became more familiar, and I was able to sense a better character of the piece. I would like to echo the "journey" statement in you blog by saying that indeed the whole process of listening more than once and eventually playing this piece will be filled with certain things and uncertain things, but the combination and progression of them both will really make this process great.
This certainty/uncertainty dichotomy can also be applied to articulation, dynamics, register of pitches (if pitches at all... 4'33), origin of sound in physical space, tonal center, rhythm, timbre, audience participation, aleatoric elements...
The composition I am currently working on will be very much dependent on this principle as I am using a couple predictable chord progressions, yet also unpredictable as I am using one voice to add non-chord tones, as well as the controlled aleatoric elements and extended techniques.
This is a useful way to think about music because as a composer I do not want to write music that is boring and predictable (I have attended too many concerts that are plainly unexciting because I was certain what would happen next).
Character juxtaposition and timbre differences (example - strings and winds) can also be dichotomies.
This certainty/uncertainty principle can be applied most easily to jazz as there is usually a definite chord structure and form to the piece, yet an improvisatory part where the audience (and generally the player until the moment of) do not know what will happen.
Uncertainty and unpredictability are very important traits for a composition to have. Without them, a composition is boring, and listeners switch off. However, without any sense of a rooted 'home' (whether it be melodic, rhythmic or otherwise), a piece can feel like a bit of a trainwreck, with nothing for a listener to hold on to. I find that sometimes to strive for too much uncertainty can cause massive confusion for both listeners and players. Music tends to imitate life, with periods of solidity and certainty contrasting with times of strife. But it's usually important to have at least one constant thing to hold on to, however small.
A few things come to mind here:
- You are hilarious.
- This concept makes SO much sense! And is not just applicable to music (or physics). Any good book will have a huge element of uncertainty - yet somehow balanced with enough certainty to hold the plot together. And some of the funniest people are those who come out with unexpected comments/looks/actions at bizarre times. And as you said, life would be rather uninteresting if we always knew what's coming up next.
- I understand the importance of this balance between certainty/uncertainty. But I find it a difficult thing to achieve. I certainly tend to favour the "certain" side when I'm writing, following what sounds/looks/feels "right". How to find ways to add some unpredictability without totally throwing things off? Or maybe it would be good to throw things off? Balance.
This was a very interesting blog post. First off, when I read the title I chose to read the blog post because the name Heisenberg reminded me of Breaking Bad (great tv show). Then when I saw the equations I got even more excited, because I'm a huge math nerd. Even though the blog was neither chemistry-teacher-turned-meth-cooker related nor math related, I was still very intrigued.
This is not something that I've ever really given any thought to before reading this post, but now that you've said it it makes a lot of sense. If you look back at the composers who are considered "great" they all played with the idea of uncertainty in their compositions. Music that is predictable gets boring fast. In fact, everything that's predictable gets boring fast. The vast majority of people like something about uncertainty. Maybe it's not something that can be articulated, but it evokes an emotional response within us that is enjoyable in some way or another. It's like watching scary movies. Why would anyone watch a scary movie? Well, probably because they like being surprised by the scary pop-up moments. Now personally, I hate scary movies. I'm much too easily scared to enjoy them. But I still love the element of surprise in music. I think when it's done well, and in a seemingly coherent manner, it can make the difference between a good piece and a great one.
I think this is something that composers should be aware of. Maybe we subconsciously are aware of it because of our theory training, but I think that experimenting with the proportions of certainty and uncertainty requires our focus on what that means in music, and ways it can be achieved. I know I'm inclined towards staying in my comfort zone, and thus sticking to certainty. But now that I think about it, all of my favorite music has more uncertainty than I write personally. I found this blog to be quite eye-opening. Thanks Dr. Ross!
I think that in relation to one piece that I'm currently working on an element of familiarity becomes present after the first few measures, and continues in the same fashion throughout the piece, and acts as a sort of groundwork to the piece - however, I have been experimenting with some elements of uncertainty. I think these "bumps in the road" of the musical line have helped to create more interest to the listener and overall make the piece better. In that regard, I began to think about how much "certainty" was in not only the musical line, but also the dynamic range, articulations and thematic materials. Once I've listened to the piece hundreds of times, it becomes very familiar to the ear no matter how much uncertainty is in the music, so I find it very important to step away and "defamiliarize" myself with the music, and after I return to it the unexpected points of interest become even more interesting. Often in my compositions, I tend to play it safe, staying away from strange rhythms and unpredictability, but I find my pieces sound much better after incorporating and element of surprise here and there, even though it might sound out of my comfort zone, but oftentimes it sounds static and lifeless - adding uncertainty creates a much more organic sound and feel to the music.
A piece consisting only of certainty may be aesthetically pleasing for a brief time, but I think the audience arrives with greater hopes than candy for their ears. Uncertainty, or perhaps more importantly, the unexpected, is the linchpin of compositional intrigue. Denial of expectations is what creates interest in a piece, drawing the listeners in with questions about where it's going, and when they will be returned to solid ground, before ultimately being rewarded when the composer comes at length to satisfy our expectations. However, I think that all uncertainty must be anchored in some way by the familiar, even if distantly. Many means can be used for this, including rhythmic, harmonic, textural, and melodic connections between new and old material. Even if the audience doesn't consciously hear the connections, these links provide the brain (which is always looking for patterns to understand the world around it) with context for sections of uncertainty, and strengthens the contrast between what we expect and what the composer gives us. Otherwise, listeners are left completely adrift, and with no discernible pattern for the brain to latch on to, the piece loses their attention, the randomness leaving them confused and unsatisfied. Therefore, I would agree that certainty and uncertainty must be balanced in a piece in order to maintain interest, but that uncertainty should typically involve familiar elements to hold the listeners' attention.
Hey Dr. Ross, I totally agree that the perfect composition has a great balance of predictability and unpredictability. As an up and coming composer (or so I like to refer to myself. I dunno, I just write notes on paper and pray it sounds good) I can find it difficult to find a happy balance between this familiarity and the unknown. I guess a big problem I have is trying to figure out if something is unpredictable but still close enough to the familiar passages that it can be considered relevant. Like, if I was writing a symphony and had this beautiful, sweeping passage in the string section then came in with cluster chords in the horns, piano, saxophones, bassoons, and didgeridoos, the audience would certainly be caught off guard, but whether or not this is a constructive part of the piece is up for debate.
I guess a question I have is how do you know if your new idea is going to be relevant enough to the previous material? Is it just intonation? Should you just use your musical sense?
The second I saw a math equation I nearly turned my back on this blog post…math is not my greatest subject and the idea of applying numbers to music is just a nightmare for me.
I really enjoy the powerful quote: “What matters most in life is the journey, not the destination.” Glad I kept reading!
The idea of music certainty vs. uncertainty is a quality that I think applies to all music genres. Maybe some genres are more predictable then others but either way your emotional response can be slightly different every time. For example, I can listen to so many different interpretations of the same piece and even that can create a new sense of unpredictability. As I am taken on this familiar musical path the multitude of different interpretations can recreate the sense of unpredictability. That’s just one of the beautiful things about music. Even if the path is familiar the journey can still be interesting and unpredictable.
I can remember in my first year at MUN discovering Stravinsky's "Rite of Spring", Holst's "The Planets", Shostakovich's 10th Symphony, Takemitsu's "Requiem for Strings". Those pieces stand out to me because at that time I hadn't heard anything like them. But what they all have in common is varying degrees of unpredictability amongst predictability. I think as composers it is very important for us to constantly have this balance in our mind as we work because sometimes I will hear ideas that are interesting on their own from fellow composers but they are sustained for far too long without any unpredictable aspects. I don't think that it's for any reason other than "unpredictability" wasn't an active part of their thinking when writing. Just by thinking of its importance, we can make it a part of our wheelhouse of creativity.
Even popular music uses predictability vs. unpredictability in this way. Some of the best popular music in my opinion is excellent at keeping you on your toes. Radiohead, The Beatles, Sufjan Stevens and Queens of the Stone Age are all great examples of this.
This being said, I don't think ALL music needs a LOT of unpredictability. Max Richter, a post-minimalist composer whom I love the works of, uses unpredictability sparingly but writes beautiful, fully formed music that does not leave me wishing I was caught off-guard more often.
Great article, Dr. Ross.
I think uncertainty and expectations play a big role in composition. The music which I find most exciting is that which shatters expectations.
There is a lot of 20th century music which relies on this breaking of expectation. In the music of Schoenberg, it would be nearly impossible to tell which note will occur next, unless the listener has an incredible ear and ability to identify rows. On top of that, serialist music is known for scattered and complex rhythmic activity, which again leads to to a suspension of expectation.
The same principle applies to the music of the minimalist pantheon. The exciting part of a lot of Philip Glass's music is when it changes. Glass suspends our expectation by repeating a motive until we, the listeners, know it very well. Then Glass changes something about the motive, and this makes for a large musical impact, because it breaks the expectations of the listener. In this case, something very predictable adds a slight amount of unpredictability for a huge musical and emotional impact.
I really enjoyed this post, because I had no idea where it was going to go with the math equations. So I guess that, in a way, this post in itself may also prove the very point it is trying to make!
As you said, this balance between certainty and uncertainty is extremely important with regards to composition. Over my last year and a half of composing, I think this is one of the most crucial lessons I have learned along the way. I have definitely noticed that the moments my peers and my professors have enjoyed most in my compositions are the points that surprised them. However, these surprises are only effective if they are surrounded by elements which are less surprising. When I write, I find myself falling into specific forms and ostinatos to unify the music. I think this is partially because I often try to write where I feel like I hear the music going in my head, and often these first ideas that always come to mind are part of a periodic structure, or flow nicely with what I have already written. I have found it important to follow this structured approach only sometimes, while consiously going against it other times. If I feel like it has been a while (a few musical decisions) since I used something other than the first thing that came to mind, I actively try to think past that first structured, logical idea and go for something that makes less logical sense. These illogical decisions can throw the listener for a loop, surpirse them, and stop them from zoning out.
Although I still don't understand a single thing about the Heisenberg principle after reading this post, I know that it definitely made the post a lot more interesting and captivating. Like with composition, a decision doesn't always have to make sense to catch the reader's/listener's attention!
I will admit, I almost didn’t read this because of the math equations at the beginning, but I’m glad I kept going. I was very uncertain (how fitting) as to how they would tie into this post. I agree that there has to be a balance of certainty/uncertainty. While uncertainty is good and keeps the piece interesting, there is also the possibility of too much uncertainty, in which the piece becomes too confusing and difficult, which will turn the listeners off.
I think the dichotomy could also be applied to the heavy metal genre. There are so many bands who do a great job of keeping the balance, and others who don't. For example, one of my favourite bands, Dynazty, has a good balance. They use unexpected key changes in a lot of their songs even though the forms they use are pretty straightforward (verse, chorus, verse, chorus, epic guitar solo, chorus, etc.) Another band I listen to, Amaranthe, also does this to a degree, although not as frequently. An example of a band who I don't think has a good balance is Dream Theater. They're a good band, and I love how complex their music is, but sometimes I feel like their songs are too convoluted and I don't enjoy them as much.
That is a pretty funny comparison. I think it makes sense to leave a lot of things as ambiguous, recent studies (at least ones that I read) support the idea that the joy of music stems from surprise as well as anticipation. I agree with music being a journey, when I used to listen to Beethoven it sounded pretty magical, I did not expect any of the resolutions and surprises, and now, when I grew to know his style so much better, ever when I hear a new piece I never heard before it is no longer a surprise. However, it does not mean I hear it every time the same way: part of the journey is in the moment and in the context in which you listen to the piece, which might sound so different at some point.
Perhaps in contrast to some other students who may be reading this post, I am fairly familiar with Heisenberg’s uncertainty principle. Having studied this principle in both chemistry and physics electives during my degree, I was curious as to how this principle could be applied to music (it created…uncertainty in my blog post commenting experience) (haha). However, after reading the post, I’m totally on board and I actually think this is a pretty great analogy for creating moments of stability and instability in composition.
In my understanding of the Heisenberg uncertainty principle, Heisenberg determined that it was impossible to know for sure both the position and speed of an electron. This is because it is impossible to know whether or not an electron is acting as a particle or as a wave at any given time (or both?? It’s out for debate. JJ Thompson won a nobel prize for discovering that an electron was a particle, and then his son later won a nobel prize for discovering that it was a wave. And nobody’s been able to prove either of them wrong. Controversial). The more we know about an electron’s position, the less we know about its speed, and vice versa. I think that this is an effective method that can be applied to composition. Perhaps during a development section, we may know the motivic material as maybe it is being presented again in fragments, but we may not know about the harmonic material as it is constantly changing and moving away from the home center. Perhaps the harmonic structure remains constant, but the melody is embellished, or a countermelody is added. Perhaps the rhythm stays the same, or perhaps it changes. There are so many elements of music that can be either changing or held constant: form, melody, harmony, rhythm, dynamics, texture, etc. etc. etc. The possibilities and combinations are endless to create uncertainty and build interest for the listener. All this to say, I think the key to achieving coherent instability is to have elements that are known and unknown, and as Heisenberg suggests, the more we know about one element, the less we can know about the other.
I have actually been thinking a lot recently about a different, but very similar dichotomy in music: tension vs. release. This idea can be found in all sorts of music; the tension of a sonata's development vs the release of its subsequent recapitulation, the tension of the variations vs the release of the theme in a Theme and Variations, a modern pop song's verse and pre-chorus vs the inevitable chorus, etc. I think tension/release often runs parallel to predictability/unpredictability, and the two often go hand in hand. Unpredictability is often a significant source of tension in music, while a noticeable shift back to the familiar both provides release and is usually accompanied by a newfound predictability. While this might not be a truly universal way of analyzing music worldwide, I do believe that most if not all great Western Music is built upon these two dichotomies.
One other musical element that can benefit from predictability/unpredictability is rhythm. A composer may choose for the areas of predictability to be made up of simple, easy-to-understand rhythmic devices that do not necessarily challenge the reader. Then, in areas of unpredictability, use far more complex rhythms to keep the listener engaged. One of my favorite examples of this is in the song "Oyasumi" by math rock band Tricot. The verses and pre-choruses are all written in the (relatively) unconventional and unpredictable 5/8 time signature, only for the chorus to kick in with a much simpler and predictable 6/8. The shift to this less intense rhythm results in an explosive release of tension and a new sense of predictability, making it an excellent and memorable musical moment for me.
Not going to lie, I saw the formulas in the first part of the post and was immediately taken back to Math 1000 from first year (*shudder*).
Jokes aside, I think it's very important for pieces to have some predictability, but not too much so that a piece becomes boring. Occasionally, you have to throw in a couple of note and/or rhythm changes to keep listeners on their toes, otherwise they will be deprived of the new and fall asleep (unless you're composing a piece that people are meant to be able to fall asleep to; in that case, maybe do keep things predictable).
This is why songs on the radio typically have bridges, since if the second chorus was simply followed by an additional verse, the song would get rather repetitive, and therefore, slightly boring.
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