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Golden Ratio φ : 4 Polyrhythm - with Bounce Metronome Pro to help you keep time

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Published on May 19, 2011

This shows the most polyrhythmic rhythm (hardest to approximate using ratios) - or you could call it a polytempo if you prefer.

You can play rhythms like this endlessly, any tempo, any intervals and many other features with Bounce Metronome Pro - see http://www.bouncemetronome.com/metron...

DETAILS

This shows a pattern generated by two beats at the golden ratio to each other.

This makes it the most polyrhythmic possible rhythm in a certain sense.

First of all, the two rhythms never coincide exactly after the first beat - but any irrational number like PI or E would do that. What is special about this polyrhythm is that the ratio of the two rhythms is hardest to approximate with a pure ratio.

A human player couldn't play this polyrhythm without assistance from a computer because it continues endlessly without ever repeating the exact same pattern of clicks. In fact there's a connection betwen this rhythm and the aperiodic Penrose tilings as well.

The golden ratio is one of the numbers which is hardest to approximate with a pure ratio. The numbers which get closest to it with small number quotients are ratios of successive Fibonacc numbers.

So this means, that after e.g. 8 beats of the blue ball in this video, and 5 beats of the red ball the notes will come closer together than for any earlier beat. Same happens again after 13 and 8, and so on.

If you want to play a golden ratio polyrhythm without a video or click track to keep you in time, then 8 : 5 is a reasonable approximation. After that. 13 : 8 will get you pretty close, then 21 : 13 and 34 : 21 (if you can manage those) get you even closer.

See:
http://www.maths.surrey.ac.uk/hosted-...

Also:
http://en.wikipedia.org/wiki/Continue......

Bounce Metronome Pro can play this and various other Harmonic Fractional Polyrhythms based on PI, E, or whatever other intervals you like.

To find out more visit its Fractional Polyrhythm Metronomes page:
http://www.bouncemetronome.com/metron...


see http://bouncemetronome.com - this is one of many rhythms you can play with this versatile metronome.

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