A Primer in Polyrhythms:
To understand polyrhythms you have to have a basic understanding of fractions & ratios. For a simple example I'll use 2 against 3 (which I think most people know the sound of, and is easy to play. This formula will give you the ability to work out any basic polyrhythm. You can use it with any two numbers - like 4 vs. 5, or 7 vs. 3.
First you multiply the two numbers to get the smallest amount of beats that each can divide into: in this case 2x3=6. I'll represent this as 6 "o's" - that you can think of as 1/8th notes. o o o o o o
Then you divide the 6 into two groups of three: ( o o o )( o o o ) - and three groups of two: ( o o )( o o )(o o )
If you play this, one will sound 1-2-3 1-2-3 ,and the other 1-2 1-2 1-2.
(o o o)(o o o) (o o o)(o o o)
RH 1 & or 1 2 LH 1 2 3 1 a &
(oo)(oo)(oo) (oo) (oo) (oo)
So, this makes a little melorhythm which you can hear and remember.
Each polyrhythm has it's own little melorhythm like this which you familiarize yourself with & play from each perspective (2 over 3 & 3 over 2).
Once you are able to hear and play these you realize that polyrhythms are not so much the ability to hear two separate rhythms, but the interaction of the two, thought of as one melorhythm (which describes the inter-relationship between melody and rhythm) broken up between limbs (in this case RH &LH) like this: ( together--L-R-L- ).
I recommend Gary Chaffee's "Patterns" book "Rhythm & Meter" as the best, most simple and straight forward way to learn these concepts. It will get you to a very advanced level (I wish I had that book before I got with Zappa - it would have prepared me very well!!!)
For coordination studies I recommend my 4 videos "Solo Drums" &" Melodic Drumming and the Ostinato", as well as the book "4-Way Coordination" by Dahlgren & Fine