Robert Inventor

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Fibonacci Rhythm

Click on the name for the mp3 (rendered to audio with the Roland Sound Canvas).

Intro - About this type of tune - mp3s and midi clips - To find out more


These mp3s were rendered to audio with the Roland Sound Canvas. It has sounds similar to those on the wave table soundcards you get on many computers nowadays.

You can DOWNLOAD your free trial of Tune Smithy to play any of these tunes endlessly - and by varying the parameters you can make them into new tunes of your own. To find out more, see Play & Create Tunes as intricate as Snowflakes - First steps.

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What is a Fibonacci Rhythm?

A fibonacci rhythm is an interesting way to go beyond the repeating framework of ordinary bars. They are highly ordered, and almost repeat but never repeat exactly. They are also fractal.

To explore this option in Tune Smithy, try the tunes in the Fibonacci Rhythms drop list that comes with the Player or Composer task, and explore the Fibonacci Rhythm window.

To fill this out a bit more - if you listen you may hear a pattern of beats such as say L S L L S where L means a long beat and S means a short beat. If this is the first time you've come across one of these, you may keep waiting for the pattern to repeat. But it never quite does. That one continues: L S L L S L which seems promising - perhaps the bar is just L S L | L S L. But the next beat is an S. If you look at a longer section it is:

L S ~ L ~ L S ~ L S ~ L ~ L S ~ L ~ L S ~ L S ~ L ~ L S ~ L S ~ L ~ L S ~ L

The ~s there are the equivalent of the bar lines. So there are two basic "bar"s - a two beat bar consisting of L S, and a single beat L. These group together to make larger patterns. For instance, the pattern L S ~ L occurs many times, also L S ~ L ~ L S. In fact, any pattern you pick out, however long, repeats infinitely many times. But the pattern as a whole never repeats - there is no repeating bar of any length. It's what's called an "almost repeating" pattern.

In fact it's a fractal pattern - to see this group the L S together as a single longer L' beat and the single L bar as a longer S' beta. Then the fragment just shown runs:

L' S' L' L' S' L' S' L' L' S' L' L' S' L' S'

Which gives us the same pattern again, only slower.

L' S' ~ L' ~ L' S' ~ L' S' ~ L' ~ L' S' ~ L' ~ L' S' ~ L' S'

We can repeat the process in this way to get longer and longer beats. This property, together with the almost repeats, makes the rhythm in these tunes fractal.

In fact the L and S beats here correspond to the wide and narrow rhombs in a row of a Penrose tiling, so giving an interesting connection between musical rhythms and geometry. See Penrose Tilings.

The idea of this approach is originally due to David Canright - see his Fibonacci Gamelan Rhythms

Tune smithy explores many variations on this approach. One idea due to David Canright is to arrange the beats by flipping the L and S if necessary so that the L is closest to the most deeply reinforced beat (the one with most instruments playing simultaneously) - the result may sound better musically.

L S | L | S L | L | S L | L S | L | S L | L S | L | L S | L | S L | L S | L | S L | L S | L | L S | L | S L | L S

Other things you can do include setting your own beat patterns for the L and S, and exploring patterns with three beat sizes.

For the technical background, and details, see Fibonacci rhythm and tonescapes

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Mp3s and midi clips

For the midi clips, click on the red or blue notes below. Or click on the name below for the mp3 again.

bassoon prime harmonics [4 mins] beautiful 13 limit harmonic series melody [4 mins] cello tune fibonacci with two to one beat ratios [4 mins] cos one over x vibrato [4 mins] From Olympos [4 mins]
golden ratio cello tune [4 mins] golden ratio tune [4 mins] never repeating dance rhythm with flute and french horn [4 mins] non repeating bongos [4 mins] resting in the shade [4 mins]
strolling away from a dark and dangerous place [4 mins] three beats ex [4 mins] Trilobites [4 mins] two beat ex [4 mins] uo timbre experiment [4 mins]


(1 minute ) (4 minutes )

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To find out more

Most of the tunes can continue endlessly (for all practical purposes). So, in these recordings, they fade out at the end of the clip.

To find out more, see Tune Smithying.

* Note, some of these clips may not play correctly in your web player, especially if you use Quicktime - seems to be some sort of an issue to do with the exceedingly short notes in them. You may get stuck notes or notes left out altogether They play fine normally on soundcards and synths, and play fine in real time in Tune Smithy. It's mainly an issue with the quicktime embedded player.

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