What If It's Just This?
I don't quite remember the website where I found Owl City's music, but I do know that wherever it was I downloaded "Hello Seattle" for free: at the time I was a cheapskate high school student in love with music and averse to piracy.
For many years I was a customer of iTunes alternative eMusic, who at the start of that time, charged a flat fee of "one download credit" per song, regardless of how long it was. From that point of view, post-rock behemoth Godspeed You! Black Emperor's 4-track double album Lift Your Skinny Fists Like Antennas To Heaven was a bargain, and the fact that it turned out I loved the music too was sort of a happy accident.
Owl City achieved a surprise breakout hit with "Fireflies" a couple years later, after I had already, on the strength of "Hello Seattle," become a big fan of his self-released EP Of June and album Maybe I'm Dreaming. Maybe it's the contrarian hipster in me, but it's really those two albums I return to most often still, although I can appreciate the higher production value of his major label work.
The six songs on Of June, for the most part, are structured more like poems or elaborate jokes than pop songs. For example, to a first approximation, none of the songs has a chorus, exactly. Instead like a joke, all of the songs build to a punch line. Structurally, this bit usually functions more like a bridge in the song. However, although some of his major label work is more deliberately punny, the songs on Of June sound pretty earnest.
"Hello Seattle" has the most lyrical repetition, with those two words starting each of the first six stanzas of the song. A rerecord, with added major label oomph, appears on the same album as "Fireflies", and there is a fun dance remix in the iTunes bonus tracks. I'm not a good DJ, but I think it has some good layering potential, particularly since the first 2 minutes of the remix have no drums and seem eminently scratchable. The lyrical construction of the songs also lends itself to this sort of treatment: even without more of the trappings of dance music, the songs on Of June tend to have instrumental hooks that feed your desire as a listener for a chorus. In that sense, it's a very 2017 EP, particularly for having been released in 2008.
Anyway, early Owl City has some fantastic drum programming. I've been sitting down bit by bit to figure out some of it. My favorite track on the EP is "Designer Skyline," which is absolutely chock full of good arpeggios. Initially I was a little surprised to discover that the song is exactly 120BPM, the default tempo of Ableton Live. I was even more surprised to find that the second kick drum of the song, which is syncopated, was one 32nd note off of the beat.
The reason this is surprising is that it's generally quite difficult to do something very complicated with rhythm and have it sound natural and catchy. Syncopated kick drums are pretty common, especially in hip hop influenced drum programming, but 32nd notes are significantly beyond the pale.
After a bit more figuring, I noticed on a whim that if I changed the time signature to 3/4, the intro properly took up 4 bars. But listening to the song, it is in 4 and not 3. After a couple minutes as the math meme lady, I figured it was time to multiply by 4/3.

And indeed, "Designer Skyline" is in 4/4 time at 160BPM, which is 4/3 of 120. The second kick in the drum pattern falls on the "and" of the second beat (meaning it is delayed one eighth note).
In other words, sometimes the thing that is fancy and complex is your framework of understanding and not the thing itself. It's really sexy for things to be fancy and complex.
Tomorrow, I'm attending a reading group that's going to discuss some notes on the intersection of topology and digital sound. Skimming through, the sexy soundbites abound. The "duality" between sampling and aliasing, for example, is first analogized to a covering map from the real line (absolute frequencies) to the circle (perceptual or aliased frequencies). Later it is claimed that this duality is merely a manifestation of a much deeper duality, namely the Pontryagin duality of locally compact, abelian topological groups. I was skimming so it's quite likely that I missed it, but this claim seemed not to be followed up on.
If you check that Wikipedia link, you'll see that there is some truth to the statement: in a certain sense, the Pontryagin duality operation is a generalization of the Fourier transform, which is central to our current understanding of digital audio.
But also, it might be less deep and complex than that too, right? A connection between the flat torus (aka the way the edges of the screen work in a game of Pac Man) and a framework for understanding perceptual audio position in a room with rectangular walls might just be that in both situations, the "angle of incidence equals angle of reflection" law is wrung out for all its worth. Worse still, the notes appear to miss that it's not quite the flat torus which has the desired behavior, but the billiards table orbifold.
Sitting at the intersection of technical capacity in math and music I'm often told that there are such exciting connections that could be made between each, but I'm still not sure what exactly they are. Most of what I read from the music side of things gets a lot of juice out of mathematical ideas that are not deep at all. The "Euclidean rhythms" paper is a good example of this. There's an interesting phenomenon happening there, certainly, and also the concept is a bit embarrassing mathematically. Like, yes, if you want to space some number of hits evenly across another number of beats, what you're doing is absolutely connected with Euclid's algorithm for the greatest common divisor. What explanatory power does this have for the profusion of instantiations of this among folk rhythms globally? Not much beyond what was already said, probably.
Conversely, most deep mathematics is not particularly applicable to music because musicality isn't one of the parameters of the field. I've had some fun building little visualizations or sonifications of some mathematical concepts near to my research, particularly just faithful renderings of those aspects closest to dynamical systems. Maybe that's the connection: music about math and vice versa. But I'm not sure there's a deep theoretical insight here. Similarly to the way the notes read; I find myself thinking that if there really were a deep connection this close to the surface, this is not how I would be finding out about it.
To finish by bringing back in Owl City, I was wondering what it felt like in 2008 to have put out this EP, Of June, and Maybe I'm Dreaming. I love these works of art to bits, and I've never really interacted with Adam Young personally about them, or at all. Certainly some needles moved on account of these songs, given that Owl City's next album came out on Universal Republic. I don't know any of the story of how those songs went from Adam's MySpace page to landing a record deal. I also don't really know the prehistory of these songs. I've read Adam talking about more or less living at home in rural Minnesota, working at a warehouse, and making music in his free time. It's a nice story, but doesn't explain where his taste in synthesizers or drum kits came from, for example.
When I put out a song, I can check in on how it's doing more or less daily. That kind of engagement tracking was possible in 2008, too, of course, but tended to stop more or less at the point of sale. From Adam's perspective, I provided some fraction of the retail price for the sale of these albums, and until I started using Apple Music to stream them, I might have never listened to them again for all he would have been able to tell.
My next music project, if it's a smash hit for me, will probably have an impact as big or smaller than Of June. To paraphrase Cardi B, if I did Of June numbers, I would pop champagne, but if Cardi did my numbers she would jump out a plane. There was probably no Of June tour, although there may have been a small amount of merch. I like to think—and I have examples of this in my music library—I would love the early Owl City albums even if the artist project fizzled out after their release. To me as a listener, that's success. I guess I'm curious to find out more of what it feels like as an artist.