Question: what's the hardest concept to teach intro music theory students?
Well, there are all sorts of advanced harmonic concepts involving intricate voice-leading, harmonic resolution, motivic development, and so forth.
But by the time you get that far, your students have already developed a strong foundation of knowledge to help them understand these more advanced topics. They're already masters at reading and writing musical notation, which enables them to organize their ideas on paper. The advantage here cannot be understated.
I would argue that one of the hardest concepts to teach is actually one of the most basic, usually covered in the very first classes of Music Theory 101. And that concept is meter -- the idea that music is organized into beats and measures, with an underlying pulse comprised of strong beats and weak beats.
Think about it: to understand meter and how we notate it, the student has to already understand a wide range of intersecting concepts: beats, measures, pulse, rhythmic division, staff lines, bar lines, beaming, and of course all of the symbols (note heads, stems, flags, dots, rests, etc). And even once all of this information is learned, terminology soon becomes complicated: "whole notes" fill a whole measure in 4/4, but not in 5/4 or 6/4. By contrast, in 2/4, it's the half note that fills the whole measure.
It's a lot to take in all at once.
But even once the basics are well-understood, there's still one aspect of meter that – in my own experience teaching university students – continues to stump students for quite some time.
And that aspect is metric pulse.
What's the difference between 2/4 and 4/4?
Aren't 3/4 and 6/8 exactly the same?
Why use 8/8, when you could just use 4/4?
For some reason, the idea that each meter has its own unique pulse – that 3/4 feels different than 6/8 because one of them is triple and the other is duple, for instance – is really hard for students to grasp.
In the spirit of helping my fellow educators teach about meter, I'd like to offer a useful example from Disney's Frozen, which might help your students to better understand metric pulse.
The song I'll discuss is actually metrically ambiguous, but this is precisely its pedagogical value. The ambiguity forces us to listen more closely than we otherwise might. It also encourages us to tackle difficult questions about what meter is and why it matters.
And finally, it's an INTRIGUING example, because it doesn't start off with musical instruments. Rather, it begins with the sound of ice saws being thrust through the frozen waters of Norway... not what you'd expect to hear in a course on music theory!
(starts around the 0:42 mark in this video)
As I've written in a previous blog post, one of Disney's hallmarks is a musical technique called "Mickey-Mousing" - the close synchronization of music, sound effects, and animation. "Frozen Heart" is a great example. As the scene opens, we see the workers thrusting their saws into the ice, and we hear the sound effects that result from this labor. There's no indication, at first, that what we're hearing is music. But when the workers start singing, the sound of the ice saws continues, becoming an important part of the music's percussion section. Are the ice saws musical instruments? Well, not necessarily, but that's exactly the point: as in so many other Disney movies, this scene blurs the boundaries between music and noise.
But I digress.
Here's an unmetered notation of the song's opening, starting with the ice saws and continuing with the melody:
I have heard this song so many times, but until this weekend, I was completely stymied by its metric pulse.
See, here's the thing: I imagined hearing each of these ice saws on the strong beats of either 2/4 or 4/4. That seems logical enough, but then the melody comes in awkwardly early, on a weak beat. The pulse feels consistently "off," accenting beats that feel like they should be weaker, while glossing over beats that seem like they should be more prominent. What gives?
And then this weekend, I was driving down Cypress Avenue on my way to our local grocery store, listening to this song, and it suddenly hit me. What if the workers aren't sawing on the strong beats, but rather on the weak beats?
What if, instead of sawing on the first beat of each measure, they actually saw on the second beat? WHAT IF THE SCORE ACTUALLY BEGINS WITH A REST? Here's what that would look like:
Bingo! Now, the melody comes in strongly on beat 1, and the pulse moving forward feels totally natural. The percussive sawing on the off-beats alternates with the singers' down-beats, creating a driving "heeve-ho" effect that befits a labor song.
In fact, this alternative notation feels so natural to me, that I can't believe I never thought of it before.
But that's the thing.
Why didn't I?
Why had I misheard this, for so long, as sawing on the downbeats, if that's so clearly not what's happening?
The answer is: the complete, total, and utter lack of musical context.
When the saws begin sawing, they don't sound like music. Each crash through the ice sounds identical. There's no alternation of strong and weak. There's no melodic contour or harmonic context to help shape an underlying pulse. How, in short, could one possibly know whether they're sawing on the downbeats or upbeats, when there aren't any contrasting sounds to tells us where downbeats and upbeats lie?
It's only once the singing comes in that we can identify a musical relationship: the sawing suddenly aligns with the melody's weak beats.
When students learn about meter, it's important for them to understand that meter doesn't work in isolation. Rather, it's a system for organizing the relationships among myriad musical elements. When all we hear is the repeated sounds of ice-saws crashing through the ice, each time with the same pitch, dynamic, and articulation, and always evenly spaced one from the next, how can meter exist? It's only once we add in the melody – with its melodic contour, rhythmic diversity, harmonic implications, and so forth – that the sound of the ice saws enters into a musical system, interacting and contrasting with other musical elements.
As a metaphor, consider that you're working on a puzzle. An enormous, 5,000-piece puzzle. You know the type. It's maddening, but so addictive. Anyway. You take a few pieces out of the box and look them over. They all look exactly the same. They are all solid black, with two innies and two outies. Now ask: which part of the picture are these? It's a ridiculous question, isn't it? Where is there a picture? Where are there parts? These are just a group of identical, solid-black pieces.
It's only once you dump out all of the rest of the pieces – all 5,000 of them – and you see that they are all different that any sense of a larger whole can come into play. Eventually, it becomes evident that these black pieces are part of one section of the puzzle, while these sparkly pink pieces are part of a different section, and these other pieces go somewhere else. It's only when contrasting elements enter into a relationship with each other that any sense of a larger whole can exist.
And that's how meter works. It organizes contrasting elements, contextualizing them in relation to each other, and showing how they all add up to a larger, meaningful whole.
The great thing about discussing "Frozen Heart" with our students is that is provokes conversation. Because it's so ambiguous, the students can be easily dissuaded from thinking they can take a single "correct answer" for granted. Instead of memorizing the single "right answer," they can actually think about the material, discussing the relative merits of each interpretation with their classmates. In the process, they dive into fundamental questions of what meter is, what it does, and how it works. It also challenges us to ask difficult questions about what music even is in the first place, which, in my experience, is GUARANTEED to spark curiosity and fill an entire class period with lively, engaging discussion.
What do you think? Would discussing this song make it easier for your students to understand meter? Let me know in the comments below!
Music theory is not about rules! It's about conventions!
And sometimes, those conventions aren't the best way to do things.
Take the opening of "Do You Want to Build a Snowman" from Frozen. The "correct" notation in 4/4, shown above, completely blurs the meter, the counterpoint, the rhythm, and even the genre. What's more, it's hard to play! (Catch that left hand Eb on the last 16th note of beat 1!)
But when we re-beam it to fit the three unequal beats of 8/8 rather than the more conventional 4 equal beats of 4/4, a whole galaxy of details springs to life.
Why does any of this matter? Well, this passage is not just dramatic but also a huge part of both setting up the film's narrative and establishing Anna's personality.
This song comes after that heart-wrenching scene where the troll king erases Anna's memory, to spare her the trauma of her near-death experience. As the scene comes to an end, a confused Anna watches as her sister completely shuns her by locking herself up in her room. The musical background fades into a soft, slow, descending melody, orchestrated very sparsely, a perfect depiction of the loss, abandonment, confusion, loneliness, etc. felt in this scene by both sisters.
And this lonely music moves immediately into a fast, upbeat tango as a now-older Anna races to her sister's door to invite her to play together. What a dramatic contrast! It highlights how playful, giddy, and carefree Anna has become, and makes the tragedy of her memory loss and abandonment all the more poignant.
Sure, you don't need to know any theory to feel this emotional contrast between one scene and the next. But music theory -- including a sensible, if unconventional, notation -- helps us understand that contrast on a much more nuanced level, which means we can also feel it in a more nuanced way. And it also makes it easier to perform!
To pass the time during my cancer treatment, I did a live stream on Twitter about the history of Disney music. Why not, right? :-)
Sam Zerin is a PhD student in musicology at New York University and a former lecturer in music theory at NYU, Brown University, and the Borough of Manhattan Community College. He also runs Social Media Music Theory (@SocialMediaMus1)