Mathematically Pattern-Free Music 234
gary.flake writes "'Scott Rickard set out to do what no musician has ever tried — to make the world's ugliest piece of music [video]. At TEDxMIA, he discusses the math and science behind creating a piece of music devoid of any pattern.' He used mathematics of Évariste Galois (who was born 200 years ago) to create pattern-free sonar pings which he mapped to notes on a piano, and then played them using the non-rhythm of a Golomb Ruler. Now, why didn't I think of that..."
Mathematics of Ramsey (Score:4, Interesting)
Well, I use the mathematics of Frank Plumpton Ramsey and Bartel Leendert van der Waerden (who were born about 100 years ago) to call bullshit on this claim: There is no sequence of anything (including musical notes) which is pattern free.
cf.
http://en.wikipedia.org/wiki/Van_der_Waerden%27s_theorem
http://en.wikipedia.org/wiki/Ramsey%27s_theorem
Re:I can go one better (Score:4, Interesting)
Re:Not that random (Score:4, Interesting)
Apophenia. [wikipedia.org]
Pareidolia. [wikipedia.org]
We're wired to see patterns; if there aren't any we'll make them up with no conscious effort or intent at all.
randomness != chance (Score:4, Interesting)
John Cage's music employed chance, not randomness. I posted [slashdot.org] about him back in 2007 (search for my username, my post is near the top.)
Xenakis would be a better example of a composer who used randomness in a truly stochastic sense. However, he used it in a very deliberate and purposeful way, to shape only some elements of a composition, not the entire work. In contrast, Cage used chance as a way of abdicating control, although (like Xenakis' use of randomess) he employed it for only some elements of a work.
Re:Prime numbers? (Score:3, Interesting)
Re:Mathematics of Ramsey (Score:4, Interesting)
Re:Mathematics of Ramsey (Score:4, Interesting)
True. Apologies. What I was trying to say was that it's really hard to, via brute force search, find large Costas arrays. In fact, we've only just been able to enumerate all 29-by-29 sized Costas arrays (took nearly 400 years of CPU time). To find all 30-by-30's will take 5 times longer; Each time we increase the size of the array by one, it takes about 5x longer to enumerate the space (don't know why that's the case). So, needless to say, we're going to have to wait a while to find even a single array of size 88-by-88 by brute force search. But, thanks to Galois+Golomb+Costas, we can just multiple by 3, 87 times, and find one. So we can construct what is very difficult to find via brute force search. To use 'computation' to mean 'brute force search' was a poor choice. My bad...