In today’s MUSC 316 class, Sam and Randall presented their analyses of Joo Won Park’s Elegy. They varied in significant ways but weren’t incompatible. I want to use this opportunity to show how a mathematical model found frequently in nature illuminates and connects points Sam and Randall made today.
I may have mentioned the Golden Ratio in this class briefly when we were discussing form. If you dig maths but haven’t heard of this before: sorry, there goes your evening, along with some of your friends if you can’t stop talking about it. If you need to create a final composition project with a fixed length and have no idea for a formal structure: you’re welcome.
What It Is
You might have heard of the Rule of Thirds in visual arts, the notion that images seem to be more interesting when key foreground objects and backgrounds (like the horizon or treeline) coincide with lines dividing the image into a 3×3 grid. In nature, mathematicians have found that divisions at 62% are more natural and common than 50% or 2/3, but 62% is close to 2/3. This may explain why the Rule of Thirds is readily taken with some liberties leaning toward the center.
Here is an article by Icon Photography School with examples of the Golden Ratio in imagery, including a video by DNews which is also helpful: https://photographyicon.com/goldenratio/
Anyway, it works in time-based works as well, and Park’s Elegy is a great example. The golden ratio point (about 62% from the beginning) is about 2’ 44”, where Sam heard the “balloon of serenity” burst and return to “rough” pitch clusters; Randall described this point as being where the only sustained single pitch ends and the two-pitch clusters return. If you’re keeping track of exact pitches, you’d notice that this returning cluster is the same as the opening and closing motive, just up an octave (D–E-flat), and the melodica simply ruminates on that dyad for the rest of the piece (motivic development has concluded and waits for the other parameters to reach their closure—parameters like pitch range, loudness, and visual clarity/blur). This 62% point is a common place to find climaxes, recapitulations, or other significant moments.
It is sometimes useful to look at 62% from the ending as well, in this case about 1’ 38”. It’s around that point that Sam noted a distinct change in attitude and Randall noted that the two-pitch clash returns after the motives have change from ascending to descending. If you were keeping track of pitches, you would further notice that the music had only used a C Dorian scale so far (C minor, except with A-natural instead of A-flat). The first descending motive introduces an A-flat, which, you might argue, opens a middle section that disrupts what had been established in the opening. That A-flat “disruption” is set aright in the accompaniment with an A-natural that happens to be right about the 50% point in the piece. 50% divisions are uncommon and rarely effective, but its precision makes me wonder if it was an intentional design.
Visually, the double image fades in leading up to this point and moves around the most turbulently after the descending clash. The video returns to the single image as the melodica plays the single sustained C.
These divisions portion the piece nicely into three sections (and I can see them being divided into smaller sections too, so Randall’s slightly different 3-section model and Sam’s 5-section model are still valid): I see an opening in which a rough clashing half-step pitch cluster expands into wider, more consonant intervals (divided into ascending and descending halves, as Randall noted), a middle section that goes back to the half-step cluster and reaches its widest point at the 50% mark and then settles on a single sustained pitch (which happens to be C) (which could be two distinct smaller sections, as Sam saw it), and a closing section that ruminates on the opening D-E-flat half step cluster. You also might find that this closing section consists of four motives in the melodica: 1. the opening dyad an octave higher, 2. the opening of the middle section but upside down (descending turned into ascending, and still echoing the D–E-flat dyad), 3. a sustained C (like the end of the middle section) but thwarted at the end by becoming an ascending cluster (the first descending motive backwards?), and 4. the opening motive repeated, more closely, as Randall noted.
Taking my first section alone, the Golden Ratio point is at 1:00 where both students show the change from ascending to descending motives. Taking the last section alone, the Golden Ratio point is where the last melodica motive enters, where Randall notes the return of the opening motive and Sam notes arrival at acceptance.
So What’s the Right Answer?
This is a great example of what I mean when I say, “There are few wrong answers; mostly poorly-supported answers.” Sam and Randall presented valid and supported models that were different in significant ways. They each work well, and they each highlight different aspects of the work. Their differences don’t make them wrong; their consideredness and supporting points make them each strong.
NOTE 1: DON’T take the Golden Ratio as an absolute rule or requirement! However, do feel free to use it as an often-effective rule of thumb whenever you can’t make up your mind on the proportions among things.
NOTE 2: Yes, I did mention pitch here, because it’s important to certain readings of the piece. Notice that Sam and Randall got there quite well without referring to pitch. Talking about pitch is not off limits when it’s playing a significant role. If you were focused too much on pitch, you might get stuck on the C minor (C Dorian) modality of the piece, which isn’t a dynamic element—it’s just wallpaper, and you might miss many significant points instead. For your analysis, talk about whatever you find contributes to a model that explains how most elements within the piece work together. For your composition project, be careful that it relies on course concepts for its substance, not relying on melody, key/modality, or constant metric structure for its substance.
A couple other observations:
- Those wind and wave sounds are surprisingly harsh, but they’re kept at a striking “distance” from us. It’s not a dynamic element in the piece, but it does help set the stage for the thoughts that occurred to us during the piece by separating our emotions from physical presence so starkly.
- As I said in class, this is a good example of the subtle detail required to make a “one concept / one moment” piece successful. We might describe it as “just sad melodica sighs and waves…,” but if it didn’t have all these other details we noticed, then we would follow our statement with “…and it was dumb/worthless” instead of being able to appreciate its well-crafted focus. Keep this in mind as you conceive your final compositions: it takes many subtle details to make “simplicity” not “suck” (so to say).