I've been toying around with making musical patterns from the Fibonnacci numbers, and looked on YouTube to see what people have done with this. I found the following video, which I do not find very convincing:
https://www.youtube.com/watch?v=IGJeGOw8TzQ
The reason I think it's unconvincing is that he's playing the digits of the Fibonacci numbers:
1, 1, 2, 3, 5, 8, 1, 3, 2, 1, 3, 4, 5, 5...
...and to me these digits sound more or less random. But I was wondering: is this true in some sense?
I know random is not quite the right word... I remember reading about whether pi is a normal number, and I guess I'm asking something along those lines.
The paper The Fibonacci Sequence is Normal Base 10 by Benfield and Manes shows that in the sequence $11235813213455\dots$, every $k$-digit block occurs equally often in the long run. So if one played the digits of sufficiently large Fibonacci numbers on the piano, it would be essentially equivalent to playing random notes.
If we begin with the first few Fibonacci numbers, there will still be discernible patterns: knowing the first digit of one Fibonacci number lets you make a good guess at the first digit of the next Fibonacci number, and early on that's a good prediction of what happens 3-4 notes later. I'm unconvinced that those slight correlations will make meaningful musical sense, however.