A few weeks ago I came across a muscial sub-page of The On-Line Encyclopedia of Integer Sequences (or OEIS for short) which contains a number integer sequences converted to music. I thought it would be cool to write a short post about the underlying idea and generate some mathematical music:
I will directly kick off with the mathematical music I made:
Integer sequences
The music was made by converting mathematical integer sequences to sound. An integer is a whole number and a sequence is just a collection of enumerated objects which means that there is a first, second, third etc. object. So an integer sequence is a collection of enumerated integers. Sequence are usually denoted using braces and commas, for example {5,10,3} is sequence with first element 5, second element 10 and third element 3.
Sequence don't have to have to consist out of finite numbers. For example, the fibonacci sequence has infinite elements. The fibonacci sequence is also an example of a sequence where the next element in the sequence is determined by the previous elements. More specifically, a number in the sequence (after the first two numbers) is determined by the two numbers that appear before it. Not all sequences are of this type. For example, you can turn π into a sequence by turning its decimals into a sequence, so like this {3,1,4,5,9, .... }. If I would only give you the first few numbers of this sequence without telling that it is connected to π it would be difficult to guess what the next number should be.
Converting integer sequences to sound
How can you convert integer sequence to sound? Here is one way of doing it:
In the above picture I identified a number with a white key on the piano. Here 0 is the so-called middle C of the piano. From there on I just number the keys in ascending order. The problem here is that if you start numbering the piano keys you will at some point run out of keys to number so when that happens I will just return to the middle C. A normal piano has 35 keys from the middle C which means that the number 36 corresponds to the same tone as 0 which is the middle C again. That is all there is to it :)
Some interesting things to notice from the music
For two of these integer sequence you can hear something interesting happening:
- Prime numbers: You can hear the music intervals between the tones increasing over time. This is connected to the theory on so-called Prime-Gaps [1].
- Fibonacci numbers: It repeats itself. This is because of special type of periods occuring in the Fibonacci sequence which are called Pisano periods[2].
References
[1] Prime gaps. http://mathworld.wolfram.com/PrimeGaps.html
[2] Pisano periods. http://mathworld.wolfram.com/PisanoPeriod.html
All images made with inkscape. It is free! The video was made using OpenShot
Merchandise :D
There is a MathOwl shop which sells my artsy fartsy stuff. If you got some spare money head over there. You can learn about the colors of pi over here here. I also have really cheap stuff available like these stickers They are an absolute hoot.
Join #steemSTEM
#steemSTEM is a community project with the goal to promote and support Science, Technology, Engineering and Mathematics related content and activities on the STEEM blockchain. If you wish to support the #steemSTEM project you can: Contribute STEM content using the #steemstem tag | Support steemstem authors | Join our curation trail | Join our Discord community | Delegate SP to steemstem
Convenient Delegation Links:
