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)

100 comments

I don't get it. Any ping I ever heard was just one tone at an evenly paced interval. I must have missed how this is used in, or benefits radar 😛

I think tone is an even more important factor of beauty than repitition. To me the sound of this beautiful piano is still to an extent enjoyable. Compare that to violently screeching on a violin, with each repetition making your ears bleed even more.
On the other hand, isn't a beautiful round tone the result of even vibrations? (If so, their repetition theory might still be right, but I don't know that much about acoustics…)

Creating a system entirely devoted to eradicating repetition…
Its conception, its performance, its reverberation, its existence, its creation highlights a great deal of repetition. The concept is a repeated one, just a little more refined and with musical example.
Not to get bogged down tho..
I perceived a tonal centre. Very abstract but this infers repetition. I believe the identification of repetition is up to the individual – in the eye of the beholder. The tone of the pianist greatly affects the music. It was written a certain way, a way not really established, practiced or ingested on a regular or popular basis and if we also consider that: the concept of the debut – not only the debut performance but the debut witnessing – well I think one will encounter a slew of obstacles in controlling the outcome of the performance within EVERY given individual or by the performing individual.
Ultimately, 'normal' music: the division of silence with systematic melody, harmony and rhythm – to produce 'beauty' as we've called it here falls victim much less to the inconsistencies of a performer and that audiences reception of the 'kernels' of identity – how the music makes them feel, think, remember, forget. I make the point that the subtleties a player requires to express the idea of non-repetition, as a kernel are directly controlled by tone (how the pianist strikes the piano: velocity, time held, legato movement etc) and transcend the notes and the rhythmic subdivision they follow.What we've failed to recognise here is that music is inescapably repetitive because we're hitting the notes. HITTING THEM. Again and again. That in the absence of a clear melody, harmony, rhythm we are left with volume. And I think we're underestimating the power that still holds over humans in a 'musical' context.

this is nonsense – mathematicians should stick to numbers. it didn’t even occur to these people to play more than one note at a time. Dumbest Ted talk out there.

A pattern that has no pattern is a pattern with no pattern this sentence is a pattern that has a pattern with no pattern.

Anything could sound bad if played wrong. And btw… The quote "Beauty is in the eye of the beholder" can be applied to music taste. “Beauty is in the EAR of the beholder. " ✌️ peace out

Repetition is annoying like a Chinese water torture. You don't see much beauty in simple patterns in landscape. Repetition is childlike simple and unthoughtful. Predictable like the fourth corner. Like a child with a crayon. Bland music is all I hear. Classical is nothing more than over fluffed nonsense.

many times I went to free jazz improvisation sessions and I felt physically sick, at least now I know why

Oddly though some things were consistent between notes – the dynamics and articulation. All forte and marcato. If they wanted to really throw people, there should be variation there too. That would make it even uglier.

「数学的に」というフレーズがなかったら、ただ単に人を困惑させるためだけに生まれた曲のようにしか思えない作りだなw

Schoenberg was not interested in eliminating patterns (indeed tone rows provided him with the patterns he needed, if anything it was all about creating an endless variation of patterns); the emancipation of dissonance meant freeing music from the need to obey tonal hierarchies whereby dissonance had necessarily to resolve into consonance.

Para mí la música mas fea sigue siendo el reguetón o la banda, esto suena como gotas de agua de lluvia calléndo en un bosque.

What this music claims to be doing, it is not. Perhaps what this piece is attempting is perhaps impossible. The notes do not have a pattern, but the rhythm does. The only non-pattern music would be SILENCE.

The notes were very interesting. The repetition of force used on each hammer is what caused the raucous. As such, the speaker expressed that any form of repetition is key to a the creation of music. As the repetition of max volume caused expressions void of voice, throughout the piece, it seems as if the host allowed brute force to prove his point. Play any piece of music on the piano with as much force as you can muster and it will not be appreciated as written. Music is nuance, nuance is the manipulation of a structure at scalar levels.

The Prime Directive… Mother Music must be given the honor and respect that is Her due .

Rock the cosmos! Make the musicverse shake, shake, shake, rattle and roll.

Qapla'

'Nuff said.

The song sounds aggresive, but the mind finds phonetic similarities in the sound and it doesn't listen so stranger.

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