Golden Ratio Inharmonic Polyrhythms

Golden ratio polyrhythm with golden ratio pitch interval

Notice how the beats nearly coincide when they reach successive Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,

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?

You could call these polytempi or polyrhythms or polymetrics. Anyway what you have is a pattern of steady beats for each rhythm, as with the usual polyrhythms- but you no longer have a whole number of beats to the measure.

Also, for the ones on these pages, the whole pattern never repeats exactly either (at least not to mathematical precision).

This page is for the golden ratio rhythm which is especially interesting. It is "As polyrhythmic as you can possibly be" in a well defined sense. (For more about this see the start of the page Approaching the Golden Ratio with the Fibonacci Sequence).

Also uses the golden ratio for the musical interval which is as far from "in tune" as you can get - so far away it is actually a pleasant musical interval to listen to, a slightly sharp major sixth.

The musical interval is a minor sixth a sixth tone sharp, E.g. the interval from C to Ab a sixth tone sharp. It is between the just intonation ratios 8/5 and 5/3.

Golden Ratio

Golden ratio polyrhythm with golden ratio pitch interval

Golden ratio, its square and its cube all played at once

Golden ratio counting in 2s and its square counting in 3s

Golden ratio, with its square and its cube counting in 3s and 5s.

Harmonic Polyrhythm for time signatures: 4/4 with 4/golden ratio

Mathematically, what happens with all these rhythms is that the number of beats per measure isn't a whole number, isn't a finite decimal, and isn't even a fraction in any form. Mathematicians call numbers like that "irrational" - which in maths jargon just means - "not a fraction".

Play all these videos one after another (also the Fibonacci sequence videos)

Practise Tips

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. See Harmonic Polyrhythms (Π : 4 tab)