Step # 1 - Odd Time SignaturesBefore we can construct all those fancy polymeters we're just itching to play, we have to understand why these particular prog "tropes" are so popular. There is no official way to refer to "crazy wonky time signature awesomeness." If I may attempt to sum up every term I've heard: People have said "odd," "unusual," "asymmetric," "irregular," and "complex." The words "meter" and "time signature" are also apparently interchangeable, as far as most people are concerned. For more generalized study of time signatures, head over to the Wikipedia article on Time Signatures. For our purposes, we're looking at very specific, prog-focused odd meter. Common odd time signatures used in prog include 3/4, 5/4, 7/8, 9/8, 11/8, so on and so forth. Understanding these numbers is, in actuality, extraordinarily simple. For example: 3/4 - Three-four means "three-fourths," or "three quarters." Three quarter-notes. Therefore, following our understanding of notation, there are 6 eighth-notes. 12 sixteenth-notes. Essentially, 3/4 is like chopping off one quarter note, four sixteenth notes, etc. 5/4 - If 3/4 removes a quarter note, 5/4 adds one. Very intuitive. 7/8 - Seven-eighths. "7 eighth-notes." 14 sixteenth-notes. 3.5 quarter-notes. Think of this like chopping off two of your last four sixteenth notes. 9/8 - 9/8 is to 7/8 as 5/4 is to 3/4. You're replacing subtraction with addition. Instead of chopping off two of the last four sixteenth notes, you're adding two sixteenth notes, or one eighth note, onto the end of your 4/4 measure. Using this formula, you can understand literally any time signature you decide to mess around with. Fire up your Tuxguitar, and start experimenting with the altered rhythms of your riffs, interspersed among 4/4 or other time signatures. Try to really feel the effect that cutting or elongating your riffs has. A good starting point, if you're really not sure where to begin, could be to take the fourth measure of a repeating 4/4 riff and switch it to 5/4, elongating it by one degree.
Step # 2 - PolymetersPolymeters, put simply, consist of taking these time signatures we've come to understand, and having one instrument play them while another (or several others) plays in standard 4/4, providing a contrast. The instruments playing in an odd meter seems to resolve at different points during the course of the 4/4 groove underneath it. For instance, a riff in 5/4 played over 4/4 drums, would seem to restart one quarter note (four sixteenth notes) after the drums' restarting point, continuously, until it eventually resolves naturally, or you choose to force a resolution. Forced resolution, as a quick side note, is essentially crunching a polymeter back down into 4/4 at the end. Essentially, halfway through the fourth measure, regardless of where your polymeter currently is, you alter the riff in some way (rests, flourishes, whatever works) and then begin it again when the drums start fresh in the next measure. For some additional information, and plenty of audio examples, take a look at these video lessons. The first is polymeters, the second is odd time signatures.