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TEDx Talks
Published: 2011-10-03
Source: https://www.youtube.com/watch?v=RENk9PK06AQ
so what makes the piece of music beautiful well mostly psychologists would argue that repetition is a key aspect of beauty the idea that we take a melody motif music we repeat it we set up the expectation for up to and then we either realize it or we break the rep and that's a key component of beauty so if repetition and patterns are key to beauty then
what would the absence of pattern sound like if he wrote a piece of music but had no repetition whatsoever in it if such interesting mathematical question is it possible to write a piece of music that has no repetition whatsoever it's not random random is easy repetition freak it turns out it's extremely difficult and the only reason that we can actually do it it's because of a
man who suck hunting for submarines turns out a guy who was trying to develop the world's perfect sonar ping solve the problem of writing pattern free music and that's what the topic of the talk is today so Armonk recall that sonar in sonar you have shipped it sends out some sound in the in the water and listens for an echo the sun goes down it echoes
back echoes down echoes back the time it takes the sound to come back to see how far away it is if it comes at a higher pitch it's because the thing is moving toward you if it comes back at a lower pitch it's because it's moving away from you okay so how would you design the perfect so our pain well V. in the nineteen sixties a
guy by the name of John Costas was working on the navy's new extremely expensive sonar system it wasn't working and it was because the pain they were using was inappropriate it wasn't paying much like the following here which is just you can think of this is as the notes and the first time so that was the sort of thing they were using a Downshire okay turns
out that's a really bad pain why because it looks like shifts of right the relationship between the first to notice the same as the second to you and so forth okay so he designed a different kind of sort of paying one that looks random these are look like a random pattern of dots but they're not if you look very carefully you may notice but in fact
the relationship between each pair of dots is distinct nothing is ever repeated the first few notes and every other pair of notes have a different relationship okay so the fact that we know about these patterns is his %HESITATION is unusual John Costas is the inventor of these patterns as two thousand six shortly before his death while he was the one that disorder engineer working for the
navy he was thinking about these patterns and he was by hand able to come up with them to size twelve twelve by twelve he couldn't go any further any thought maybe they don't exist of a size bigger than twelve so he wrote a letter to the mathematician in the middle whose young mathematician to California at the time Solomon Gollum turns out that Solomon Gollum was one
of the most gifted discrete mathematicians of our time are in John S. solomid if you could tell him the right reference to where these patterns were there was no reference nobody had ever thought about a repetition patterns restructure before so Solomon dollars spent the summer thinking about the problem and he relied on the mathematics of this gentleman here every scale why not go was a very
famous math is famous because he invented a whole branch of mathematics which bears his name called gal law field theory it's the it's the mathematics prime numbers are these also famous because of the way that he died so the story is that he stood up for the honor of a young woman he was challenged to a duel and he accepted arm and shortly before the dual
occurred he wrote down all of us mathematical ideas sent letters to all of his friends saying please please please this is twenty years ago please please please see that these things we get published eventually are he then fought a duel was shot died at age twenty the mathematics that runs your cellphones the internet that allows us to communicate better on DVDs all comes from the mind
of every skill law mathematician who died twenty years younger %HESITATION self when you talk about the legacy that you leave of course I could never even anticipated the way that his mathematics would be used thankfully his mathematics was eventually published so am I gonna realize that got mathematics was exactly the mathematics needed to solve the problem of creating a pattern free structure so he sent a
letter back to John saying turns out you can generate these patterns using prime number theory and John saw then went about and solve the problem sort of the sort of problem for the navy so what do these parents look like again well here's a pattern here this is an eighty eight by eighty eight our size cost disarray markets generated in a very simple way elementary school
mathematics is sufficient to solve to solve this problem it's generated by repeatedly multiplying by the number three one three nine twenty seven eighty one two hundred forty three when I get to a bigger that's larger than eighty nine which happens to a prime we keep taking eighty nines away until I get back below and this will eventually fill the entire grid eighty eight by eighty eight
there happened to be eighty eight notes on the piano so today we were going to have the world premiere of the four girls first pattern free piano sonata so back to the question of music so what makes music beautiful what's think about one of the most beautiful pieces ever written Beethoven's fifth symphony and the famous done %HESITATION motif that motif occurs hundreds of times in the
symphony of hundreds of times the first move it alone and also in all the other witnesses well so this repetition the setting up of repetition is so important for beauty so if we think about random music speak of just random notes here over here somehow Beethoven's fifth it's apparent pattern if we wrote completely pattern free music you would be way out on the tail affect the
end of the tale of music would be these patterns restructures this music that we so far before the stars on the on the grid far far far from random it's perfectly pattern free it turns out that musicologists are a famous composer by the name of Arnold Schoenberg thought of this in the nineteen thirties forties and fifties he his goal to composer was to write music that
would free music from total structure that we've recorded the emancipation of the dissidents he created the structures called tone rose this is a tone row there it sounds a lot like a cost issue right unfortunately he died ten years before cost to solve the problem of how you can mathematically create the structures so today we're going to hear the world premiere of the perfect paying this
is an eighty eight by eighty eight sized our cost disarray maps notes on a piano please using a structure called a golden rule for the rhythm which means that the starting time of each pair of notes as distinct as well this is mathematically almost impossible achieve computationally would be impossible to create because of the mathematics that was developed to it years ago through another mathematician recently
an engineer we are able to actually who is this or construct this using multiplication by the number three the point when you hear this music is not that it's supposed to be beautiful this is supposed to be the world's ugliest piece of music in fact it's it's music that only a mathematician could write so when you're listening to this piece of music I implore you trong
and find some repetition try and find something that you enjoy and then revel in the fact that you won't find it okay so without further ado Michael Linville the director of chamber music at the New World symphony well to perform the world premiere of the perfect thing and and and and boon and mmhm the %HESITATION
