Any meter that doesn’t maintain a feeling of two or four pulses per measure, or three in a waltz, is considered odd because it isn’t smoothly repeatable. But odd meters can redeem themselves if they organize time on their own terms and keep you satisfied.
Since rock is dance music, it’s hard to see how it could lend itself to odd meter experimentation. But there have been some experiments that unquestionably belong in a Rock Odd Meter Hall of Fame.
You probably thought right away of “Money” by Pink Floyd with its amazing 7/4.
The 7/4 of “Money’s” main riff is both shapely and vehement enough to be called a convincingly rocked seven. How, one wonders, could a meter of seven be convincing in any context, let alone in a rock song? “Money” works its magic by an extremely astute splicing together of two rhythmic figures, each of which submits happily to an abridgement. Let’s imagine the first section, the first three beats, as a four (we have to: a waltz isn’t in the cards). Notice that this four would be a lilting la-de-da sort of four; the event implied at beat 4 by what we’ve heard in 1 through 3 is, relatively, a time-killer that we’re quite happy to do without.
First section: 1 – 2 – 3 – (4)
Second section: 4 – 5 – 6 – 7 – (8)
Repeat: 1 – 2 etc.
Thus we’re ready to hear an advanced, syncopated beginning of another figure on beat 4. (Once we know the song, we have the choice of realizing here that we’re actually jump-cutting to the second figure—and choice of this kind is sweet.) The second section is a four, if we construe it as starting on beat 4, but what actually happens (the first time around, at least) is that we let it give the first section a more interesting finish as a four and then restart it on beat 5 as a second four. But now it’s again the case that if we filled out beats 5 through 8 as a predictable follow-up four, that last beat would be de trop, and again we happily drop it, feeling as though plenty has happened (quite stompingly, too) in the four beats 4 through 7. So in just one trip through 7/4 you get a righteous feeling twice of getting on with business.
In most uses of odd meter there is a feeling of jumping ahead or being held back each time the figure comes to the point of repeating, but here the irregularity has such a good rationale that we feel just a slight change of gears at beat 4 and we needn’t feel anything untoward at all at the return of beat 1. If you play the riff in your head, you can negotiate the turnaround quite smoothly, just as Roger Waters does when he plays it solo. But the Pink Floyd arrangement gets a different effect, mainly because the bass drum underlines beat 7 and beat 1 equally, boom boom, which hangs you up just enough on the flatted third at beat 7 that when you hear the tonic again on beat 1 it feels like stepping down an inch more than you expected to, oof. They toy with us.
Some 5/4 songs rock hard enough to raise the question how a five can have unsurpassed drive. I would give an honorable mention in this category to Jawbox for “Under Glass” and the Assemblers (my old band) for “Can Catch Him,” but the most ferocious 5/4 I know is Soundgarden’s “My Wave,” which also adroitly juxtaposes 5/4 and off-kilter 4/4 sections to give you, at times, a delicious dizzy turning sensation.
Here is the well-designed structure of its five:
Take – if you want a slice –
1 and 2 and 3 and 4 and 5 and 1 etc.
I III III III IV IV
This works because a sense of pressure pushes back the end we want. The pressure is generated by giving the first note, “Take,” more than its share of time, a beat and a half, and then running to catch up with a falling-dominoes series of syncopated notes on the off-beats starting with “if” on 2-and. The off-beat sequence needs to tumble all the way through 5-and to be completely discharged—especially since the chord changes layer in a further delay, the III chord not changing to the IV chord till beat 5—so that after the late climax we happily accept the fast arrival of the note starting the next measure. Try shortening it—
Take – if you – a want –
1 and 2 and 3 and 4 and 1 etc.
—and see how much better the full five-beat allotment feels, both for the rhythm and for accommodating a nice-sized verbal proposition. You’ve been sold on the five.
A challenge: how do you analyze the 11-beat section in “Stacey’s Trip” by the great lost piano trio Suddenly, Tammy! (1993)? It starts at 0:30.
 As heard in The Making of The Dark Side of the Moon (Eagle Vision, 2003). Peter Gabriel’s “Solsbury Hill” features an outstandingly smooth 7/4. Another you may not notice is “Right Hand Man” by Joan Osborne.
 There’s a Wikipedia “list of musical works in unusual time signatures.”
See also my post on two songs by Radiohead.