Just about everyone else has delved into the world of popular music, so here goes.
Harmonically, this song is about as simple as there are. The song rarely strays from I IV and V chords. What makes this song particularly interesting is the variety of rhythmic feels and patterns that they create without changing tempo or time signature.
The time signature for the song is 12/8 with a moderate tempo.
This tempo is not immediately heard however, because the solo guitar part that lays out the verse has accents on the off beats (meaning la, 2 and le) for the first two and a half bars. This makes it sound like it is in 3/4 with upbeats accented, but the second half of the third and fourth measure establish the triplet feel, and the harmonic changes are every 12 eighth notes.
The piece then takes an unexpected turn in the introduction of the chorus, with the bass and drums added in what initially sounds like three bars of fast 4/4. However, what happens is that the group accented the sixteenth notes of the 12/8 to make it sound like it is in 4/4. So these supposed three bars of 4/4 are really just one bar of 12/8.
The next bar has the feel of 12/8 again, but with the guitars just doing chords on strong beats 1 and 7 with a 1 (2) & 3 4 5 6 7 (8) & 9 10 11 12 rhythm in the drums. Then the bar that feels like 4/4 repeats, followed by the bar I discussed in the last sentence. The next bar also has the 12/8 feel, but contains sixteenth notes throughout the measure which has not yet been seen in the chorus. The downbeat measure repeats, followed by the 4/4 feel, with the chorus wrapping up with the downbeat measure.
The verse and chorus then repeat but with a drum part in the verse and the vocals beginning and do so once again with different verse lyrics.
Then the instrumental bridge stays in the 12/8 with really heavy guitars with a lot of emphasis on the quarter note triplet rhythm and then a drum solo that goes back into the chorus.
The final chorus is extended so the vocalist can hold out the tonic note and get that raspy quality that comes out when singers show anger, followed by a terminative phrase (ooh, big form and analysis word!) that is the simplest phrase of the whole phrase with the chords on each beat and the lead guitar following the singer on a melody that fits well in the feel.
The other great thing about this song is how all this rhythmic change relates to the lyrics. The chorus is
How do you own the world?
How do you own disorder?
Now, between the sacred silence
Sacred silence and sleep
Somewhere between the sacred silence and sleep
Disorder, disorder, disorder
It is fitting that a set of lyrics that focus on disorder has music that can also portray that disorder through changing rhythmic feels.