# The world’s ugliest music | Scott Rickard | TEDxMIA

So what makes a piece of music beautiful? Well, most musicologists would argue that repetition is a key aspect of beauty, the idea that we take a melody,

a motif, a musical idea, we repeat it, we set up

the expectation for repetition, and then we either realize it

or we break the repetition. And that’s a key component of beauty. So if repetition and patterns

are key to beauty, then what would the absence

of patterns sound like, if we wrote a piece of music

that had no repetition whatsoever in it? That’s actually an 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-free, it turns

out, is extremely difficult, and the only reason

that we can actually do it is because of a man

who was hunting for submarines. It turns out, a guy who was trying

to develop the world’s perfect sonar ping solved the problem of writing

pattern-free music. And that’s what the topic

of the talk is today. So, recall that in sonar, you have a ship that sends

out some sound in the water, and it listens for it — an echo. The sound goes down, it echoes

back, it goes down, echoes back. The time it takes the sound to come back

tells you 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 moving away from you. So how would you design

a perfect sonar ping? Well, in the 1960s, a guy

by the name of John Costas was working on the Navy’s extremely

expensive sonar system. It wasn’t working, because the ping

they were using was inappropriate. It was a ping much

like the following here. You can think of this as the notes

and this is time. (Piano notes play high to low) So that was the sonar ping

they were using, a down chirp. It turns out that’s a really bad ping. Why? Because it looks

like shifts of itself. The relationship between the first

two notes is the same as the second two, and so forth. So he designed a different

kind of sonar ping, one that looks random. These look like a random pattern

of dots, but they’re not. If you look very carefully, you may notice that, in fact,

the relationship between each pair of dots is distinct. Nothing is ever repeated. The first two notes

and every other pair of notes have a different relationship. So the fact that we know

about these patterns is unusual. John Costas is the inventor

of these patterns. This is a picture from 2006,

shortly before his death. He was the sonar engineer

working for the Navy. He was thinking about these patterns, and he was, by hand, able to come

up with them to size 12 — 12 by 12. He couldn’t go any further

and thought maybe they don’t exist in any size bigger than 12. So he wrote a letter

to the mathematician in the middle, a young mathematician in California

at the time, Solomon Golomb. It turns out that Solomon Golomb was one of the most gifted discrete

mathematicians of our time. John asked Solomon if he could tell him

the right reference to where these patterns were. There was no reference. Nobody had ever thought

about a repetition, a pattern-free structure before. So, Solomon Golomb spent the summer

thinking about the problem. And he relied on the mathematics

of this gentleman here, Évariste Galois. Now, Galois is a very

famous mathematician. He’s famous because he invented

a whole branch of mathematics which bears his name,

called Galois field theory. It’s the mathematics of prime numbers. He’s also famous

because of the way that he died. The story is that he stood up

for the honor of a young woman. He was challenged to a duel,

and he accepted. And shortly before the duel occurred, he wrote down all

of his mathematical ideas, sent letters to all of his friends,

saying “Please, please” — this was 200 years ago — “Please, please, see that these things

get published eventually.” He then fought the duel,

was shot and died at age 20. The mathematics that runs

your cell phones, the internet, that allows us to communicate, DVDs, all comes from the mind

of Évariste Galois, a mathematician who died 20 years young. When you talk about

the legacy that you leave … Of course, he couldn’t have

even anticipated the way that his mathematics

would be used. Thankfully, his mathematics

was eventually published. Solomon Golomb realized that that was

exactly the mathematics needed to solve the problem of creating

a pattern-free structure. So he sent a letter back to John saying, “It turns out you can generate

these patterns using prime number theory.” And John went about and solved

the sonar problem for the Navy. So what do these patterns look like again? Here’s a pattern here. This is an 88-by-88-sized Costas array. It’s generated in a very simple way. Elementary school mathematics

is sufficient to solve this problem. It’s generated by repeatedly

multiplying by the number three: 1, 3, 9, 27, 81, 243 … When I get to a number that’s larger

than 89 which happens to be prime, I keep taking 89s away

until I get back below. And this will eventually fill

the entire grid, 88 by 88. There happen to be 88 notes on the piano. So today, we are going to have

the world premiere of the world’s first

pattern-free piano sonata. So, back to the question of music: What makes music beautiful? Let’s think about one of the most

beautiful pieces ever written, Beethoven’s Fifth Symphony

and the famous “da na na na!” motif. That motif occurs hundreds

of times in the symphony — hundreds of times

in the first movement alone and also in all the other

movements as well. So the setting up of this repetition

is so important for beauty. If we think about random music

as being just random notes here, and over here, somehow, Beethoven’s Fifth

in some kind of pattern, if we wrote completely pattern-free music, it would be way out on the tail. In fact, the end of the tail of music

would be these pattern-free structures. This music that we saw before,

those stars on the grid, is far, far, far from random. It’s perfectly pattern-free. It turns out that musicologists — a famous composer by the name

of Arnold Schoenberg — thought of this in the 1930s,

’40s and ’50s. His goal as a composer was to write music that would free music

from tonal structure. He called it the “emancipation

of the dissonance.” He created these structures

called “tone rows.” This is a tone row there. It sounds a lot like a Costas array. Unfortunately, he died 10 years

before Costas solved the problem of how you can mathematically

create these structures. Today, we’re going to hear the world

premiere of the perfect ping. This is an 88-by-88-sized Costas array, mapped to notes on the piano, played using a structure called

a Golomb ruler for the rhythm, which means the starting

time of each pair of notes is distinct as well. This is mathematically almost impossible. Actually, computationally,

it would be impossible to create. Because of the mathematics

that was developed 200 years ago, through another mathematician

recently and an engineer, we were able to actually compose

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 music

that only a mathematician could write. (Laughter) When you’re listening to this

piece of music, I implore you: try and find some repetition. Try and find something that you enjoy, and then revel in the fact

that you won’t find it. (Laughter) So without further ado, Michael Linville, the [Dean] of Chamber Music

at the New World Symphony, will perform the world premiere

of the perfect ping. (Music) (Music ends) (Scott Rickard, off-screen) Thank you. (Applause)

This piece would actually go good with a confused, deranged, psycho killer trying to find his next victim.

It kind of sounded like horror music at times.

masterpiece or masterpiss?

Reggaeton music

re-pe-ti-tion le-git-i-mi-zes