Fibonacci Music

 

I am a super nerd. I cannot help it. One day I was bored and decided to make some music based off of the Fibonacci sequence. What is the Fibonacci sequence? It is a sequence of numbers where each number is the sum of the previous two. It begins: 1, 1 and then works its way up from there. An example of the beginning of the Fibonacci sequence is:

1, 1, 2, 3, 5, 8, 13, 21 and then it continues on from there.

 

The problem is that this sequence increases in size and goes on indefinitely. This is not a good way to make music, not only would it be boring but it would also eventually pass the range of human hearing. That simply won’t do. What I did was apply a limit to the sequence so that it could not get higher than a certain number. So I basically made it to where the number, when going over the limit, would simply start back at 1. In effect I would divide the number by the limit and if it had no decimal then the number was 1, if there was a decimal it would round down to the nearest whole number and subtract the two to find the new number. In effect this is the Fibonacci sequence wrapped around a tube. But that was overly complicated so I sought to simplify it. I soon realized that the sequence would be the same if I cut off the excess, so that I didn’t need to divide anything. When a number becomes higher than the limit it is corrected to that number minus the limit. This produces the exact same effect as before but it is much simpler and easy to handle. It also makes it to where the sequence can be discovered in your head instead of needing a calculator. The interesting thing is that when a limit is applied to the Fibonacci sequence in this manner it produces a repeating pattern.

 

For instance the Fibonacci sequence with a limit of three is as follows:

1, 1, 2, 3, 2, 2, 1, 3 and from there it starts over.

The Fibonacci sequence always starts with two 1’s

1+1=2

1+2=3

2+3 is higher than the limit, 3, so we subtract the limit from the number to get 2.

3+2 we run into the same issue again and come out to the same answer 2.

2+2 is higher than the limit so we subtract the limit to get 1.

2+1 =3.

The next two numbers will both be 1’s and the pattern repeats.

 

Other sequences listed by their limits:

1)      1, 1 (this one I had issues with whether or not it should be just one 1 or two 1’s. The issue lay in the logic I use to determine the end of the pattern which is when there is the number 1 followed is by the limit. I decided that I should apply the same logic to all of the sequences regardless of the pattern. This is the only pattern that produces this problem).

2)      1, 1, 2 (this is the only pattern that has an odd number of total numbers before repetition… at least that I have found. I find it interesting that this 2 is also the only even prime number and cannot help but wonder if this is an actual relationship or a coincidence).

3)      1, 1, 2, 3, 2, 2, 1, 3

4)      1, 1, 2, 3, 1, 4

5)      1, 1, 2, 3, 5, 3, 3, 1, 4, 5, 4, 4, 3, 2, 5, 2, 2, 4, 1, 5

6)      1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 6, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 6

7)      1, 1, 2, 3, 5, 1, 6, 7, 6, 6, 5, 4, 2, 6, 1, 7

8)      1, 1, 2, 3, 5, 8, 5, 5, 2, 7, 1, 8

9)      1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9

10)  1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 10, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 10, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 10, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1, 10

11)  1, 1, 2, 3, 5, 8, 2, 10, 1, 11

12)  1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 12, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 12

13)  1, 1, 2, 3, 5, 8, 13, 8, 8, 3, 11, 1, 12, 13, 12, 12, 11, 10, 8, 5, 13, 5, 5, 10, 2, 12, 1, 13

14)  1, 1, 2, 3, 5, 8, 13, 7, 6, 13, 5, 4, 9, 13, 8, 7, 1, 8, 9, 3, 12, 1, 13, 14, 13, 13, 12, 11, 9, 6, 1, 7, 8, 1, 9, 10, 5, 1, 6, 7, 13, 6, 5, 11, 2, 13, 1, 14

15)  1, 1, 2, 3, 5, 8, 13, 6, 4, 10, 14, 9, 8, 2, 10, 12, 7, 4, 11, 15, 11, 11, 7, 3, 10, 13, 8, 6, 14, 5, 4, 9, 13, 7, 5, 12, 2, 14, 1, 15

16)  1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 16, 9, 9, 2, 11, 13, 8, 5, 13, 2, 15, 1, 16

17)  1, 1, 2, 3, 5, 8, 13, 4, 17, 4, 4, 8, 12, 3, 15, 1, 16, 17, 16, 16, 15, 14, 12, 9, 4, 13, 17, 13, 13, 9, 5, 14, 2, 16, 1, 17

18)  1, 1, 2, 3, 5, 8, 13, 3, 16, 1, 17, 18, 17, 17, 16, 15, 13, 10, 5, 15, 2, 17, 1, 18

19)  1, 1, 2, 3, 5, 8, 13, 2, 15, 17, 13, 11, 5, 16, 2, 18, 1, 19

20)  1, 1, 2, 3, 5, 8, 13, 1, 14, 15, 9, 4, 13, 17, 10, 7, 17, 4, 1, 5, 6, 11, 17, 8, 5, 13, 18, 11, 9, 20, 9, 9, 18, 7, 5, 12, 17, 9, 6, 15, 1, 16, 17, 13, 10, 3, 13, 16, 9, 5, 14, 19, 13, 12, 5, 17, 2, 19, 1, 20

21)  1, 1, 2, 3, 5, 8, 13, 21, 13, 13, 5, 18, 2, 20, 1, 21

22)  1, 1, 2, 3, 5, 8, 13, 21, 12, 11, 1, 12, 13, 3, 16, 19, 13, 10, 1, 11, 12, 1, 13, 14, 5, 19, 2, 21, 1, 22

23)  1, 1, 2, 3, 5, 8, 13, 21, 11, 9, 20, 6, 3, 9, 12, 21, 10, 8, 18, 3, 21, 1, 22, 23, 22, 22, 21, 20, 18, 15, 10, 2, 12, 14, 3, 17, 20, 14, 11, 2, 13, 15, 5, 20, 2, 22, 1, 23

24)  1, 1, 2, 3, 5, 8, 13, 21, 10, 7, 17, 24, 17, 17, 10, 3, 13, 16, 5, 21, 2, 23, 1, 24

25)  1, 1, 2, 3, 5, 8, 13, 21, 9, 5, 14, 19, 8, 2, 10, 12, 22, 9, 6, 15, 21, 11, 7, 18, 25, 18, 18, 11, 4, 15, 19, 9, 3, 12, 15, 2, 17, 19, 11, 5, 16, 21, 12, 8, 20, 3, 23, 1, 24, 25, 24, 24, 23, 22, 20, 17, 12, 4, 16, 20, 11, 6, 17, 23, 15, 13, 3, 16, 19, 10, 4, 14, 18, 7, 25, 7, 7, 14, 21, 10, 6, 16, 22, 13, 10, 23, 8, 6, 14, 20, 9, 4, 13, 17, 5, 22, 2, 24, 1, 25

26)  1, 1, 2, 3, 5, 8, 13, 21, 8, 3, 11, 14, 25, 13, 12, 25, 11, 10, 21, 5, 26, 5, 5, 10, 15, 25, 14, 13, 1, 14, 15, 3, 18, 21, 13, 8, 21, 3, 24, 1, 25, 26, 25, 25, 24, 23, 21, 18, 13, 5, 18, 23, 15, 12, 1, 13, 14, 1, 15, 16, 5, 21, 26, 21, 21, 16, 11, 1, 12, 13, 25, 12, 11, 23, 8, 5, 13, 18, 5, 23, 2, 25, 1, 26

27)  1, 1, 2, 3, 5, 8, 13, 21, 7, 1, 8, 9, 17, 26, 16, 15, 4, 19, 23, 15, 11, 26, 10, 9, 19, 1, 20, 21, 14, 8, 22, 3, 25, 1, 26, 27, 26, 26, 25, 24, 22, 19, 14, 6, 20, 26, 19, 18, 10, 1, 11, 12, 23, 8, 4, 12, 16, 1, 17, 18, 8, 26, 7, 6, 13, 19, 5, 24, 2, 26, 1, 27

 

 

Those are all of the patterns I used to produce the final sequence. But I did not simply go in order from one to twenty seven. That would have been boring and short. What I did was use the last one (limit 27) as the base. For each number in that pattern I put the corresponding pattern of that limit. This basically was using the pattern limit 27 to determine the order I would play each pattern. The total length of the pattern ended up being 2328 numbers before it repeated. The full sequence can be found here

 

I then applied a note to each number so that 1 = 110 Hz and 27 =1396.91Hz.

For now each note is 1/10 of a second long followed by the same amount of silence. I plan to eventually apply another Fibonacci pattern for the lengths of the notes but that would be a pain so I’ll save it for another day when I have nothing better to do.

For now the file is too large for me to upload but I can make available a horribly ‘southern engineered’ version of the music.

I made a file for each note and the made a program to compile a play list based off of the sequence.

To hear the music simply unzip the .zip and play the file fib.m3u. Make sure that you disable ‘shuffle’ or it will all be random.

The .zip file can be found here. I will try to make the full mp3 file available as soon as possible.

 

The full version of this music can be found here:

http://www.soundclick.com/bands/5/nathanielsummersmusic.htm

Download the mp3 and if you want to stream it then do not use the lo-fi version because it is severely distorted. The file is already compressed enough as it is.

 

If you have any questions feel free to email me at nthnlsmmrs@hotmail.com

I also have a website at http://ngal.fateback.com and it is full of my artwork. (No it is not based off of obscure mathematical formulae).

 

Please forgive me for using MS word to create these pages. I felt like being lazy and I don’t care what these pages look like anyway. :P