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Fibonacci Sequence and Sound

Page history last edited by Dani 14 years, 9 months ago

Home >  Mathcasts Library > Creative Side of Mathematics > Fibonacci Sequences and Sound

 

Fibonacci Sequences and Sound – by Dani Novak and Linda Stojanovska

 

Mathcast Movie and PowerPoint Presentation

 

Suppose you have two sounds:

·         A ”one beat” sound “ta”.

·         A “two beat” sound “tata”.

Suppose your measure has 1 beat. There is 1 combination.

·         You can only put 1 “ta” in each measure.

Suppose your measure has 2 beats. There are 2 combinations.

·         You can put 2 “ta” in each measure  or

·         You can put 1 “tata” in each measure.

Suppose your measure has 3 beats.  There are 3 combinations.

·         You can put 3 “ta”  or

·         You can put 1 “ta” and  1 “tata”.

·         You can put 1 “tata” and  1 “ta”.

Not too interesting so far. But …

Suppose your measure has 4 beats.  There are 5 combinations  (see table below).

Suppose your measure has 5 beats.  There are 8 combinations  (see table below).

 

Here is a table with this information in it.

·         The ”one beat” sound “ta” is denoted by a 1.

·         A “two beat” sound “tata” is denoted by a 2.

 

   

Measure

Measure

Measure

Measure

Measure

Number of Beats in Measure

1

1

        

1

        

1

        

1

        

1

        

2

1

1

      

1

1

      

1

1

      

1

1

      

1

1

      

2

        

2

        

2

        

2

        

2

        

3

1

1

1

    

1

1

1

    

1

1

1

    

1

1

1

    

1

1

1

    

1

2

      

1

2

      

1

2

      

1

2

      

1

2

      

2

1

      

2

1

      

2

1

      

2

1

      

2

1

      

4

1

1

1

1

  

1

1

1

1

  

1

1

1

1

  

1

1

1

1

  

1

1

1

1

  

1

1

2

    

1

1

2

    

1

1

2

    

1

1

2

    

1

1

2

    

1

2

1

    

1

2

1

    

1

2

1

    

1

2

1

    

1

2

1

    

2

1

1

    

2

1

1

    

2

1

1

    

2

1

1

    

2

1

1

    

2

2

      

2

2

      

2

2

      

2

2

      

2

2

      

5

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

  

1

1

1

2

  

1

1

1

2

  

1

1

1

2

  

1

1

1

2

  

1

1

2

1

  

1

1

2

1

  

1

1

2

1

  

1

1

2

1

  

1

1

2

1

  

1

2

1

1

  

1

2

1

1

  

1

2

1

1

  

1

2

1

1

  

1

2

1

1

  

2

1

1

1

  

2

1

1

1

  

2

1

1

1

  

2

1

1

1

  

2

1

1

1

  

1

2

2

    

1

2

2

    

1

2

2

    

1

2

2

    

1

2

2

    

2

1

2

    

2

1

2

    

2

1

2

    

2

1

2

    

2

1

2

    

2

2

1

    

2

2

1

    

2

2

1

    

2

2

1

    

2

2

1

    

 

The number of combinations is the Fibonacci sequence.  Say what?

 

The first two members of the Fibonacci sequence are 1 and 2.

After that, the rule is that each member is the sum of the previous 2 members.

So we have: 1, 2 and then 1 + 2 = 3  

Now we have: 1, 2, 3 and then 2+3 = 5

Now we have: 1, 2, 3, 5 and then 3+5 =8

    And so on.  

 

So the Fibonacci sequence is: 1, 2, 3, 5, 8, 13, 21, …

 

We showed you the combination for a 1, 2, 3, 4, and 5 beat measures.

      See if you can find the 13 combinations for a 6 beat measure!

-----------------------------------------------

The Fibonacci Sequence was discovered in India thousands of years before it came to the west.  From the Fibonacci sequence we can find a magical number called the Golden Mean. It has many connections with geometry.

 

For example: The ratio of the diagonal of any regular pentagon to its side is the Golden Mean.

  

Here we saw a connection between the Fibonacci Sequence and Sound.

 

 Mathematics is magical – it connects everything!

 

 

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