Music in theory; a Question of Polymeters

This is the second in 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 2 in the aptly named: Music in Theory

A Question of Polymeters

ok so last time I covered a lot about polyrhythms and kind of explained what they are in a nutshell.
We decided that, 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.

Today we're going to look at how that works.

Once again, i've prepared a sample track. I'd advise clicking the link below and getting the track into your ears before we progress any further.

https://soundcloud.com/craig-mccomish/a-study-in-audiosynthesis-polymeter/s-Ti4uC

Description

Ok so, for the first section, we hear 10 bars of a 3/4 rhythm at a tempo of 150 bpm .
This is the first rhythm we need to worry about and the beats we hear are "1, 2, (and) 3" with an accent on beat 1.

Simple, straight forward. Uncomplicated.

After those 10 bars, we hear a second rhythm. the Tempo is still static, 150bpm but the meter has now extended to hold two additional beats, becoming a 5/4 meter. The beats we are hearing are "1,2,3,4,5" with an accent on beat 1 and a second accent on beat 4.

Then, we hear both these rhythms playing at the same time. This is our Polymeter.

Both meters have the same tempo and start on the same beat; their respective beat 1.
This will of course mean, that the 3/4 rhythm will hit it's beat 1 again before the 5/4 rhythm.

So the second bar of 3/4 starts on beat 4 of the 5/4 meter.

The Meter's Movement is broken down below;

As you can see from the above diagram, both meters start on the same beat on the left hand side but then drift out of synchronization.

And towards the right hand side, we can see that the two rhythms have drifted back in sync.

Conclusion

We can now differentiate between a polyrhythm and a polymeter by remembering a simple rule.

Polyrhythm = Two Rhythms of different Tempo starting and finishing together in the same bar.

Polymeter = Two Rhythms of the same Tempo, starting together and drifting in and out of sync with eachother.

So, is there a simple way to figure out how many bars it will take for the two rhythms of a polymeter to drift back in sync?
There is.
Using simple maths, it will take the above rhythm of 3/4 and 5/4 exactly 15 beats to rectify itself.

3 by 5 = 15, which also means it will take exactly 3 bars of 5/4 for the rhythm to synchronize with the adjacent 3/4 rhythm, and
It will take exactly 5 bars of 3/4 for the rhythms to synchronise.

So simply put, you multiply the two meters together to find the number beats until the rhythms meet on beat 1.

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