Golden Ratio (In)Harmonic Polyrhythm Metronome - a Bounce Metronome Pro animation

This shows the most inharmonic possible musical interval (hardest to approximate with a pure ratio) and the most polyrhythmic rhythm (in the same sense).

see: http://www.bouncemetronome.com/video-resources/harmonic-polyrhythms/approachi...
and
for more videos, http://bouncemetronome.com/video-resources/harmonic-polyrhythms/golden-ratio-...

For playlist see http://www.youtube.com/playlist?p=PL81924439B96B48C0

You can play rhythms like this endlessly, any tempo, any intervals and many other features with Bounce Metronome Pro - to find out more and get the software visit: http://bouncemetronome.com/features/pro/harmonic-polyrhythms#tab5


Although it is as inharmonic as possible it is still a pleasant interval to listen to - so far away from a pure ratio interval that you don't get the beating you get for notes that are just slightly "out of tune" from a pure ratio, so actually rather pleasant to the ear.

DETAILS

This shows a pattern generated by two beats at the golden ratio to each other. The pitches are also in the golden ratio.

This makes it the most inharmonic possible musical interval and the most polyrhythmic possible rhythm in a certain sense.

In a way it is the most polyrhythmic possible rhythm. 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 pitches are also in the golden ratio - and the interval of a golden ratio is in a certain sense the most inharmonic interval you can have - the most "out of tune" you can be in a sense - except that it is so "out of tune" it is actually rather pleasant. Pure low numbered ratios of frequencies are the so called "harmonic intervals" - intervals between low numbered frequencies in the harmonic series - which are the intervals that tend to sound most "harmonious".

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.

See:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi.html#philine

Also:
http://en.wikipedia.org/wiki/Continued_fraction#A_property_of_the_golden_rati...

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 Harmonic Fractional Polyrhythm Metronomes page:
http://www.bouncemetronome.com/metronome_fractional_harmonic.htm

Category:

Music

Tags:

• golden ratio
• pitch
• polyrhythm
• metronome
• harmony
• Fibonacci
• Windows
• PC
• Software