Music in Theory: 5/4 4/4 polyrhythmic exercise

I feel like this is going to be a new series of specific posts where I just talk about music theory, different exercises and things that i've thought up that may shed light on something or somethings that musicians are either struggling with or else it's a completely new subject to them or opens a completely different door to them musically. If I can inspire my fellow musicians as much as they inspire me, then I can die happy.
so here goes.
Lesson 1 in the aptly named: Music in Theory

The 5/4 4/4 Polyrhythmic Exercise

ok so first up. what is a polyrhythm? what is a polymeter? are they related? did they go to school together? are they sleeping together?

A polyrhythm is effectively different rhythms happening in the same bar, they are simultaneous and line up, starting and finishing at the same time. a polymeter however is when different instruments play in different meters and come in and out of synchronization with eachother.

We're only going to worry about polyrhythms right now though. so the exercise will consist of 2 rhythms that will start and finish with eachother just to show how a polyrhythm works.

before we progress, hit play on this link so you can listen to the track. I'll begin to break it down in the next section.

https://soundcloud.com/craig-mccomish/a-study-in-audiosynthesis-54-and-44-exercise

Description

ok so, the first 9 bars. 9 is a bit excessive, i'm sorry.

So, for 9 bars we just have our fictional drummer, lets call him Rupert, just setting a feel with the kick and the snare at a nice, balanced and slow tempo. No hi hats, just the kick on beat 1 and the snare hitting on beat 3

For the second set of 9 bars, we have a 5/4 feel, 5 crotchet beats in a bar. But the kick and snare do not change tempo. written as 5/4, the Kick is still on beat 1, but the snare hit has now shifted to the second 8th note, or the 'And' of beat 3. The hi hats are holding the 5/4 feel and landing on beat 2,3,4 and 5.

And finally, for the last set of 9 bars, Rupert kicks things up a notch, and the Hi hats speed up to a straight 8th feel in 4/4 again.
Since we've returned to 4/4 feel. the snare has reverted itself back to beat 3. The Kick and the snare have not changed tempo since the very beginning.

Conclusion

In Keeping the same tempo, the kick and the snare have slipped in and out of a different feel. although the second set of 9 bars feel and sound like they are 5/4. they can easily be written as 4/4 with the hi hats written as quintuplets (5 crotchet notes in the space of 4). Resulting in Rupert's funky polyrhythm.

Additional Notes & How this was achieved

For musicians and producers who wish to replicate the above polyrhythm track, or anyone who is just curious how to move a metronome from a 5/4 feel to a 4/4 feel while maintaining the same kick and snare position/tempo, the breakdown of the track is as follows:

The metronome I use doesnt allow subdivisions so for 5/4 and 4/4 respectively, if i want to use an 8th note feel I need to make them 10/8 and 8/8 respectively.
Starting with the 10/8 beat, the Kick is on beat 1 and the Snare holds out until beat 6. the tempo for this is 286bpm.
in order to convert the 10/8 @ 286bpm to a 4/4 feel, you divide the tempo by it's present meter and mutiply it by the one you wish to change it to.
So, 286 /5 = 57.2
multiply that by 4 and you have 228.8, so 229bpm is the metronome mark for the 4/4 section.

I hope you found this useful and as always, Thanks for reading and let me know in the comments if there is anything you want me to cover next time.