Well it's not so much illogical as it is under a very different rigid set of logical rules... When I heard that song the first time I was angry, saying to myself "Music isn't supposed to sound like that!" but at the same time I have never had such an emotional reaction to music before, so I naturally kept on going down the rabbit hole.
The 12-Tone-Method (in which each of the twelve notes of the chromatic scale is used once before it is used again) makes for some very interesting music, and supplants mathematics for artistic expression, but in doing so it makes its own unique version of artistic expression that I find haunting. My first (really really really shitty) submission here is a homage to that technique.
But in the end, all forms of classical music tickles my fancy, from the precise mathematical genius of Bach, to the flowery language of Haydn, down to the emotional impact of Brahms, and then to the 'degenerate music' of Schoenberg, the avant-garde of Gyorgy Ligeti, and to the present day harmonic minimalism of Steve Reich and Phillip Glass. But that's just me rambling off names...
A great book on the history of modern music is Alex Ross' The Rest is Noise. If anyone is remotely interested in how music came to be what it is today (in the Western progressive sense), as well as the foundations of jazz, bebop, the Beatles, and more, that is the book to read.