So let's start out with the basic concept of polymeters. I've addressed this concept in a previous tutorial regarding creating pulses in your lead playing, so let's apply that to riffing, and learn how we can use these odd rhythmic pulses to create some interesting rhythm passages.
The reason I entitle these exercises "Even-Odd", is due to the fact that we're playing the same number of eighth notes in each grouping, but they're odd, meaning that we're forcing our own NEW meter within the original 4/4 meter.
The first exercise, entitled "Pulse of 5" begins with four notes and a rest; it then repeats until the end of bar four. We're now hearing a 5 eighth note pulse (5/8) over the natural 4/4 meter. Count the rest as one with the four open notes, as the break is what completes the 5/8 meter.
Note that we're also forcing a the meter to reset after 4 bars, hence the two eighth notes at the tail end of measure 4.
The riff that follows, Pulse of 5 (Riff Example), is the exact meter played in a riff context, and some notes tie into where the previous rests were.
"Pulse of 7" follows the same structure, except with two notes added to each shorter, odd meter. In this part, each grouping features 6 notes and a rest until it's eventual forced reset after bar 4.
"Pulse of 7 (Riff Example)" sticks strictly to the exact meter, but with some chromatic movement, slides and legato.
In "Pulse of 9"... well, you get the picture. Eight notes with a rest for the demonstration, and the riff example stays relatively close to the pulse. This time, let's have some fun with some triplet and 18th note divisions in amongst the meter.