Ah yes, interesting--it's eight beats but the emphases are shifted from the normal "One two THREE four".  I love the non-moving riff which starts at 0:16, he doesn't keep it up for long but I've always enjoyed it when the solo doesn't move note, everything else moves around it.  When he starts playing other notes (0:24) it reminds me of New Order--sort of (vaguely!) the same idea at the start of Everything's Gone Green (4:20)

Back to the Muse track, the four beat kicks in clear at 0:40 when the snare starts hitting the three--One two THREE four One two THREE four--

Then the singer starts up (reminds me of Bono!)--

And then a great drum flourish at 2:11--I wonder what it would sound like if they'd kept that rhythm through the song--and dropped the drums while he was singing, just used the opening keyboard riff...heh!

Towards the end the drummer starts whacking a cymbal on the first beat: CRASH and boom and WHACK and boom--

ABout 3:56 he starts doing things with his hi-hat--but there's that snare on three (I think I'm picky about snares on three!--hard to do without slowing...something....heh....I'd call that snare on three the 'commercial' aspect of the song's sound world.)

And then the drummer gets to whack out to the end!

(On a re-listen, the drumbeat before the snare starts playing reminds me of Killing Joke)

Here's an example of the way I like a four beat: Lots going on with the bass drum, syncopation, that kinda thing, and a speedy snare on the three--or maybe I just got it all wrong!

Iggy Pop - I'm Bored (2:43)--four four kicks in at 0:16

Don't fight forces, use them R. Buckminster Fuller.