Who is this page for?

Anyone interested in polyrhythms and the harmonic series - composers, mathematicians, or just for fun.

What are they?

In these harmonic polyrhythms, the pitches are related to each other in the same way as the rhythms. Here 4/3 (Brian Ferneyhough's notation) means four "third notes" to a measure so the beats are all a bit longer than the beats of 4/4. So both rhythms have four beats to a measure, but the 4/3 measure is longer than the 4/4 measure.

As a result the measures are also played polyrhythmically.

Play all these videos one after another

More about how these rhythms work

Take 3/4  3/5  2/4  7/5 as an example.

The way to understand this is to compare it with polyrhythms like 7:4. Since you usually notate polyrhythms using quarter notes for all the rhythms, then that notation is short for 7/4 : 4/4 - where the 7/4 has 7 beats for every 2 beats of the 2/4.

Then 7/5 since it uses fifth notes instead of quarter notes, goes 5/4 times faster than a 7/4, which if you work it out meanbs it has 35 beats for every 8 beats of the 2/4

Similarly the 7/5 has 35 beats for every 12 beats of the 3/4 - and it has 7 beats for every 3 beats of the 3/5. So, at 35 beats of the 7/5, they all come together - which happens just after 29 seconds into the movie.

There I'm using the convention that in a polyrhythm such as 7 : 3 or 3 : 2 with the measure sizes the same then you use quarter notes to notate all the polyrhythms. So then you have to interpret 7/5 and 3/5 etc as in the video.

Another alternative notation (more awkward for these rhythms)

Another possible alternative is to use a fixed size of quarter note for all the rhythms, e.g. four "quarter notes" to a measure and so notate e.g. 5 : 3 using fifth notes and third note.

If you do that then you have to interpret the normal 7:4 polyrhythm notation as 7/7 : 4/4. So then since the 7/5 in the video is beating 35 beats every 4 measures, so you would notate it using 4/35th notes. The time signature then would be 7 / (4/35).

I think you can understand why I don't use that notation, it gets rather awkward for these types of rhythms though it might have its place for some rhythms.

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. To find out more see Harmonic Polyrhythms.