The conductor of my high school band was surprised at the increasing ease with which his students could navigate rhythmic complexity -- especially surprised, because the ease with which they could count it off was steadily diminishing. When confronted with complex rhythms, we'd have difficulty saying the appropriate numbers and ands, but when asked to clap them (or play them) did so without mistakes.
Here are two hypothetical measures as we were supposed to see them, with xs denoting notes:
1 2 3 4
x xx xx
1 2 3 4
xx xx xx
Counted out, this would be, "1 2-and and-4 1-and and-3 4-and".
But it's much easier if you see it thusly:
x xx xx xx xx xx
(Shift the phase of the 123 as you see fit.)
A 3/4 time signature is embedded within the 4/4 and that's what you concentrate on. Easy to clap. Hard to count because we weren't allowed to do it this way.
I had noticed a similar generation gap at a violin lesson years before. My teacher, a member of the Ann Arbor Symphony Orchestra, had a sheet of music from The Rite of Spring out when I arrived and was having trouble with it. "The rhythm just seems so random," she explained.
It was all the same note, and it looked like this (I'll put consecutive measures on consecutive lines):
In other words (well, in words, period), there was a note on the first and fourth beat of the first measure, on the third beat of the second measure, etc.
She played through part of it, slowly and carefully, and I heard immediately that it wasn't random at all, though I didn't correct her. I thought I must have been mistaken -- how could I, a 7th-grade violin beginner, catch something that eluded a professional musician? Here's how I saw the same beat (read it like a 4 lines of prose with very wide margins, not like 4 lines of poetry; numbers in bold are notes, unbolded are rests)
Stravinsky hadn't bothered to change the time signature, but he was using polyrhythms, laying patterns of 3 over the 4/4 of the piece. He'd done so only a few years after Scott Joplin had composed The Entertainer, which at the time was attacked (along with all other ragtime) by the establisment for being "syncopation gone mad". Of course, it wasn't syncopation the way Beethoven used it, as a once-in-awhile exercise in surprise; it was syncopated because like modern hip hop-listening high-schoolers, Joplin understood polyrhythms and filled his music with them.
During the main melody, the left hand does this:
1 2 3 4 1 2 3 4
(I haven't looked at it, but I suspect in the sheet music it's actually 1 and 2 and 3 and 4 and, at half-time compared to what I have here. That's irrelevent for our purposes, though.)
And the right hand, the melody, does this:
1-and and-3 4-and and-4-and-1-and-2-and and-4 1
xx xx xx xxxxxxx xx x
(That last 123 may be stretching a bit, but I think it's there.)
Line them up and you get
1 2 3 4 1 2 3 4 1 2 3 4 1
ddec ec ec cddecde bd c
(The letters are notes -- italics denote sharpness, so D# would be d.)
Not syncopation gone mad, but a pattern of three that rises and submerges within a pattern of four. (There are patterns within the melody, too, but I'm getting tired of graphing stuff. Also worth noting is that though I've portrayed the song in C for convenience, I'm not sure what its actual key is -- /msg me if you know.)
The history of modern art is mostly the history of groups coming together for the first time ever, of the practices that had devolped in isolation for 5,000 years suddenly mixing into each other. Music is certainly no exception: in America, the descendents of slaves retained a surprising number of the artistic idioms that their ancestors had spent centuries creating in Africa -- in particular, a rhythmic richness (of which polyrhythms comprise only a small part) that equaled the melodic richness of Europe. The Entertainer is an early example of this cultural melding; today's music (yes, even pop) displays a sophistication of rhythmic expression at least as thoughrough.
I've only taken one class in music theory, a pretty basic one as part of a larger Humanities course in 12th grade, and nothing in this writup was touched on. Certainly none of it surfaced in the four years of high school band I had (not even in Jazz Band); the band director, though talented, considered all new music "crap" and hip hop not music at all; and some of the choir director's comments ("put the melody on top, where you can hear it") made him seem like he'd fallen out of a wormhole terminating in 1957.
Most listeners can apppreciate most modern music -- otherwise most modern music would be something else -- and for them this node may be mostly superfluous (especially among teenagers and 20-somethings; over the decades, as cultures have mixed more and more, polyrhythms have percolated more and more into the charts), but a surprising number of smart, educated, musical people think that Kylie Minogue (for example) is shite. Similar divides exist between rock and jazz, between punk and disco -- really, between any style and any other, at least to an extent; idioms of one genre are misinterpreted by listeners of another (I'm going to kill myself if I hear another reference to a "melencholy jazz solo").