"reprise", "beat" and such, are just larger scale splittings of the time dimension in the same way that frequency separates from time. Reprises and beats and rhythms are full of periodic patterns, just like the sound waves themselves, but at a different scale, which doesn't make the physical ear resonate anymore, but appeal to the brain's taste for sequencing. Thus a beat may have frequencies like 4 Hz and 2 Hz and 0.333 Hz in it (whatever is roughly in that range), whereas larger-scale song structures may have frequencies like 0.1 and 0.01 Hz. You could call rhythm and song structure a third dimension of music.
You won't be able to find those low frequencies like 4 Hz, unless one of your instruments contains them, like drums for example. Percussion instruments can have those low frequencies. And the result of adding up the fourier contributions from periodic sequences has an effect like a comb filter on the spectrum of the orignal instrument, which makes the peaks. If you have an instrument in a higher frequency range, you probably won't find those low e.g. 4 Hz frequencies, but you could find them in the envelope following signal of the original. but that's just nitpicking..haha I find it interesting to consider how a song structure could have more than one dimension... Consider the familiar time-points analysis. We structure events in music as a function of time. f: R (time) -> (set of possible sound events) The topology in this case is clear. It's a line, and music is a function mapping 1-D into the space of all possible sounds.
But a loop is a path. So, we start from point A, we go to point B and come back. So, if we have a measure of 8/8, we can represent it as the path in the plane which follows e^(2*pi*i*t/8) or many other paths. Still we have a clearly defined topology (btw, I'm just learning topology, so I'm feeling my way through this). A function maps points in time onto the loop. Again we have just one dimension. We can extend our loop into a sphere. or a torus or any other surface in more than two dimensions with holes in it Then, you could have an infinite variety of paths, representing different ways of looping, different periods, etc...
but still it breaks down... we can only have the paths as functions of time. So, no matter how complicated the song structure gets, you can flatten it into a single function. Any thoughts?
Some current rhythm perception research focuses on dynamical systems, which can have those long-range correlation properties. (again the action of perception is still a function of 1-D time) The dynamical system can have a non-integer dimension (a fractal), so you might be on to something to speculate additional dimensions in sound.