Here's another obnoxiously hummable summer hit single for you:
Owen Pallett had this interesting musicological explanation for the song's success in a Slate article:
Why did it go to No. 1? Let’s start by talking about the ingenuity of the harmonic content. This song is all about suspension—not in the voice-leading 4–3 sense, but in the emotional sense, which listeners often associate with “exhilaration,” being on the road, being on a roller coaster, travel. This sense of suspension is created simply, by denying the listener any I chords. There is not a single I chord in the song. Laymen, the I chord (“one chord”) is the chord that the key is in. For example, a song is in G but there are no G-chords. Other examples of this, in hit singles: Fleetwood Mac’s “Dreams” and Stardust’s “Music Sounds Better With You”; almost-examples include Earth Wind and Fire's “In September” which has an I chord but only passing and in inversion; same with Coldplay’s “Viva La Vida.”
“Teenage Dream” begins with a guitar sounding the I chord but an instant later, when the bass comes in, the I is transformed into an IV (an IV7 chord, to be exact). The I chord will never appear again. Notice, too, how Katy’s melody begins on the tonic—tonic: the root note of the missing I chord, the same note that the key is in. She stays around the tonic, reinforces the tonic, and the vocal melody establishes the key so clearly that there is no doubt: Katy’s voice is “home”; the rest of the song is oscillating around her. Even when the tonic note would clash with the chord (as it does over the V chord, on “feel like I’m living a”) she hammers it home. Her voice is the sun and the song is in orbit around it.
The “feeling of suspension” I mentioned is an effect of this. The insistence of the tonic in the melody keeps your ears’ eyes fixed on the destination, but the song never arrives there. Weightlessness is achieved. Great work, songwriters!
The second key to this song's Enormous Chart Success has to do with the weighting of the melody lines. Perfect balance of tension and release. Each line of the verses begin straight, on the beat, but end with a syncopation: [straight:] “you think I'm pretty without any” [syncopated:] “makeup on.
As Katy moves out of introspective mode and starts using imperatives “Let’s go all the way tonight! No regrets! Just love!” she gets straight, more serious, no syncopation. Then—genius—the chorus inverts the weighting that we heard in the verse. [Syncopated:] “You make me [straight:] “feel like I’m living a …” [syncopated:] “teenage dream!” And the gooey heart of the song, the “skin tight jeans” bit, is rhythmically entirely straight, voice tumbling out of the tonic-focused cage of the verse and chorus, like long-hair from a scrunchie released.
A particular point of pleasure: The title of the song (“Teenage Dream”) is sung syncopated on the chorus, but straight on the bridge. Compare the two in your head. Do you hear that? How brilliant. The title of the song is rhythmically weighted two ways—it’s like a flank attack. Two sides of the same face. You WILL remember the name of this song.
So for him, it's all about the rhythm and the variation from root. Personally I like how she sings on ninths in the coda, but whatever.