As an example to show how these work, 4/3 (Brian Ferneyhough's Notation) has four beats to a measure, but the beats are third notes instead of quarter notes - so it has three beats for every four beats of 4/4. So the four beats of 4/3 span a measure a third longer than 4/4.

So though the beats come together after each measure of the 4/4 (say) the measure beats only coincide after several measures of the 4/4. If you play them fast enough then the measure beats themselves also beat out a polyrhythm.

Who are these rhythms for?

They are of special interest for Djent, and Math Metal or Death Metal, and likely to be of interest to composers generally looking for new rhythm ideas to explore. It's particularly a "must have" feature of Bounce Metronome for Djent.

You can play all these rhythms in Bounce Metronome Pro, the software used to make these videos

Playlist of them all

About the time signatures such as 4/3 - Polymeters notationIf time signatures such as 4/3 are new to you, it may help to read the wikipedia article about them here:Irrational Meters So in 4/3 you have four beats each a third of a whole tone. While in 4/4 each beat is a quarter of a whole tone. When you play them together then you get two rhythms both in 4/4 time, but one is played faster than the other, by just the right amount so that three beats of the 4/3 are played for every 4 beats of the 4/4.  Variation on Brian Ferneyhough's notation - Polyrhythms notaiton

Sometimes you are more intersted in how the measures are related to each other. So for instance in a rhythm like 6/8 : 6/7 : 6/9 : 6/10 then I wanted the measures to play an 8:7:9:10 polyrhythm.

The more usual polyrhythms such as 3 : 5 are often shown in music notation with quarter note symbols for both parts, i.e. as 3/4 : 5/4, with the understanding that the measures are the same size and the quarter notes adjusted to make the notes fit the measure. This saves the need to write lots of triplet and quintuplet signs etc. So, the upper number shows how many beats there are to the measure. Then you can use the lower number to show how the measures are related. How the polyrhythms variant notation works for more complex rhythms like 3/4 : 5/7If you follow the implications through then e.g in 3/4 : 5/7 the entire measure of the 5/7 is 4/7th of the size of an entire measure of 3/4.  This ensures that when played fast then 3/4 : 5/7 sounds like a 4 : 7 polyrhythm with each beat of the 4/4 divided into 3 and each beat of the 7/4 divided into 5. In this notation, the different parts in the rhythm use different sizes of whole tone, which makes it harder to see how the beats relate to each other. However you can immediately see how the measures relate to each other. This is just what you want when you are most interested in how the measures relate to each other. Comparision with Polymeters notation

In polymeters, then all the rhythms have the same pulse. So the quarter notes are the same size in all the rhythms.

So for instance in 4/4 : 3/4 as a polymeter then a measure of 3/4 is three quarters of the size of a measure of 4/4.

In Brian Ferneyhough's notation, you could express the same rhythm as 4/3 : 3/4. That's because, interpreted as a polyrhythm, the 4/3 has three beats in the same time as the three beats of the 3/4.

This is great when you are most interested in how the beats relate to each other. 

How the two notations relate to each other in detail

This is a bit tricky to calculate, so in practise you will probably just leave it to Bounce to work it out and choose whichever notation is most useful for the rhythms you want to make.

However for those who want to know, I'll work through the example of 3/4 : 5/7 3/4 : 5/7 in Polyrhythm notation converted to Polymeter notationIf you follow the implications through of this idea then e.g in 3/4 : 5/7 the entire measure of the 5/7 is a 4/7th of an entire measure of 5/4. In 5/4 : 3/4, then the 5/4 and 3/4 would have the same size of measure in this polyrhythm notation. So  when you change the 5/4 to 5/7 is also 4/7 of an enitre measure of 3/4. To convert 3/4 : 5/7 in this notation to  the Polymeters notation, you have to figure out how many beats of the 5/7 fit into the whole tone for the 3/4 part. So - first the whole tone is 4/3 of the measure of 3/4. Then each measure of 5/7 has 5 beats, but that's just 4/7 of a measure of the 3/4 part, so one measure of the 3/4 part has 5 * (7/4) beats. So finally the whole tone of the 3/4 part has 5 * (7/4) * 4/3=5 * 7 / 3 beats in it. I.e. 35/3 beats So in the Polymeters notation it would be5 /(35/3) : 3/4As you see it is quite tricky to express these rhythms in Polymeters notation. Also you can't immediately read out from the notation that the measures are polyrhythmic in the ratio of 4 : 7. That's why it was necessary to develop a second notation in order to make it easy to express these rhythms in Bounce Metronome Pro. Use these videos as a resource

You can use any of these videos as a resource for your own website or wikis, or make more of them yourself - see Add videos like these to your own site

Play these rhythms and animations at any tempo with Bounce Metronome

You can use Bounce Metronome Pro to practise these and many more rhythms at any tempo, including changing tempo. 

For these rhythms see the Polyrhythms like 4/4 : 4/3 feature.