Golden Ratio and Other Non Repeating Polyrhythms
Golden ratio polyrhythm
This rhythm is intimatedly connected with the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 ( where each number is the sum of the previous two, e.g. 3 + 5 = 8, 5 + 8 = 13 and so on).
So for instance the beats almost coincide at 5 in one part and 8 in the other, even closer at 8 and 13 and so on. Works like that because the ratios 8/5, 13/8, 21/13 etc are closer and closer approximations to the golden ratio
Who is this page for?
Anyone interested in unusual rhythms or microtonal pitches - and the golden ratio - composers, mathematicians, or just for fun.
What are they?
These are rhythms with polyrhythmic measure beats - or polymeters that are neither beat nor measure preserving. In Bounce Metronome with the next release I just call them "polytempi", since the measure beats and the beats can also be thought of as just steady beats at different tempi.
Anyway whatever you call them, what you have is a steady pattern of beats with no whole number of beats in the measure. The golden ratio one is particularly interesting since it is as far as you can get from any pure ratio type approximation - so in a certain mathematical sense is "as polyrhythmic as you can possibly get".
Although as time goes on you get beats closer and closer together, they never exactly coincide with mathematical precision, and the rhythm as a whole never repeats exactly.
Pitched Inharmonic Polyrhythms
For the pitched versions of this type of rhythm, see Golden Ratio Inharmonic Polyrhythms
It's fun to play along with one of these rhythms, just playing your music with one of the beats, while the others go on in the background of your playing. Probably a good exercise to help develop steady sense of rhythm, and independence.
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 Π : 4 feature.