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Mathematically Pattern-Free Music

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..."

32 of 234 comments (clear)

  1. Rap music by Oswald+McWeany · · Score: 3, Funny

    That's nothing- rap musicians have been doing this for decades.

    --
    "That's the way to do it" - Punch
    1. Re:Rap music by TheNinjaroach · · Score: 2

      Almost all rap (or hip-hop) beats are still based on a traditional 4/4 rhythm. Even though the beats are intentionally placed in odd places, you can still count out a metronome's 1-2-3-4 rhythm and find that the music repeats (or makes a significant change) every 4 bars.

      --
      I went to eat some animal crackers and the box said, "Do not eat if seal is broken." I opened the box and sure enough..
    2. Re:Rap music by Pf0tzenpfritz · · Score: 2

      Funny, but even more incorrect than many will realize. The earlies known forms of vocalized music (or melodic lyrics) in ancient Europe were "chanted" poems or longer lyric works like Ovidius' "Metamorphoses". They must have been quite similar to rap music.

      --
      Oh, the beautiful gloss of greality!
  2. Already Done by Unloaded · · Score: 4, Funny

    ......"set out to do what no musician has ever tried — to make the world's ugliest piece of music"...... Already done... http://en.wikipedia.org/wiki/(You're)_Having_My_Baby

    1. Re:Already Done by jpmorgan · · Score: 2

      In all seriousness it has already been done. You can generate music based on a Thue-Morse sequence, which is repetition free: http://reglos.de/musinum/

  3. If you walk without rhythym, by amstrad · · Score: 3, Funny

    you won't attract the worm. Another piece of ugly music, Aphex Twin's Ventolin

  4. Step 2... by chinton · · Score: 4, Funny

    2. Add Vogon poetry as lyrics. 3. Profit

  5. autechre by versificator · · Score: 2

    they kinda did it before this guy (at least from a rhythmic perspective), as a protest against the Criminal Justice and Public Order Act 1994 here in the UK. http://en.wikipedia.org/wiki/Anti_EP

  6. cure but... by alphatel · · Score: 2

    Old hat. To discover the life of a musician who made randomization a career, see John Cage.

    --
    When the foot seeks the place of the head, the line is crossed. Know your place. Keep your place. Be a shoe.
    1. Re:cure but... by Smidge204 · · Score: 3, Insightful

      Except the "music" described in the video isn't random. To quote: "Random is easy. Repetition free, it turns out, is extremely difficult."

      =Smidge=

  7. Mathematics of Ramsey by Anonymous Coward · · 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

    1. Re:Mathematics of Ramsey by curril · · Score: 4, Insightful

      Yeah, theory aside, the speaker was just multiplying by 3 modulus 89 so values less than 30 will always be followed by a higher value, a pattern that was easy to hear in the music. The speaker confused a lack of repetition of distances between notes as being a total lack of pattern.

    2. Re:Mathematics of Ramsey by johanatan · · Score: 4, Interesting

      Not only that but he apparently did by hand the 'computationally impossible'. That section of his talk was truly confused.

    3. Re:Mathematics of Ramsey by gnufrog · · 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...

    4. Re:Mathematics of Ramsey by benthurston27 · · Score: 2

      One easy one to just use a different length between every consecutive note is the pattern 1,88,2,87,3,86...44,45. At first i thought you meant the length between every pairwise combination of notes but that would be impossible as if you had used 3 and 9 you could never use note 15 because the length between 15 and 9 would be the same as between 3 and 9. This pattern I'm suggesting is very regular though, so I guess maybe there is another condition beyond using a different length between consecutive notes? Also I think very repetitive music and too simple of a pattern in music is worse to listen to than what you demonstrated.

  8. They forgot that harmony is beauty too by sandytaru · · Score: 2

    There were a few overlapping notes from pedal suspension that created chords. Although they tried to make ugly pattern-free music, they just ended up making modern music.

    --
    Occasionally living proof of the Ballmer peak.
    1. Re:They forgot that harmony is beauty too by ClickOnThis · · Score: 2

      Although they tried to make ugly pattern-free music, they just ended up making modern music.

      Actually, I liked it. It was very thoughtful and complex. Beautiful. So as far as I am concerned, they failed, albeit in a very interesting way. Art is like that.

      I agree with both of you. Paradoxically, they made the piece interesting (and thus in a real sense, beautiful) by establishing a reason to listen to it.

      --
      If it weren't for deadlines, nothing would be late.
  9. Re:I can go one better by Anonymous Coward · · Score: 4, Informative

    Random != no pattern

    You might create a tune with no pattern but chances are there will be a pattern of some kind in there.

  10. Re:I can go one better by TeknoHog · · Score: 3, Interesting

    For a good time, cat $file > /dev/dsp. My favourite so far is the PS file of Shannon's information theory paper.

    --
    Escher was the first MC and Giger invented the HR department.
  11. Re:Not that random by idontgno · · Score: 3, Interesting

    Apophenia.

    Pareidolia.

    We're wired to see patterns; if there aren't any we'll make them up with no conscious effort or intent at all.

    --
    Welcome to the Panopticon. Used to be a prison, now it's your home.
  12. Random is trivial, as the TEDx Talk explained. by ClayJar · · Score: 2

    Actually, as was explained in detail in the video, random is easy. Completely devoid of repetition is vastly more difficult. This was not simply random, this was mathematically non-repetitive. Using random numbers outside of the audible range would not necessarily preclude repetition, and using random frequencies is atonal sound, not tonal non-repetitive "music" as was the intention of the piece.

    Completely random is trivial. Mathematically-sound aperiodic and repetition-free is a completely different kettle o' fish.

    Note that the composition used the 88-tone chromatic scale of the standard piano keyboard. Without that constraint, you could make a much longer atonal composition, of course, but the point of the exercise was to use discrete mathematics and music to create a tonal composition completely devoid of repetition.

  13. Wha? by aldo.gs · · Score: 2

    It would help if there were some definitions for "random" and "pattern-free" in this context. I find it annoying that he several times says that random music is not pattern-free.

    It is true that their definitions are not equivalent, but it seems that he is implying that you cannot generate "pattern-free" music using randomly played notes, and that -depending of the definition of "pattern-free" of course- seems very, very unlikely.

    Still, I can appreciate the effort to maximize information entropy, and the divulgation of discrete math.

    1. Re:Wha? by john83 · · Score: 2
      I'm note a musical guy, but I understand the maths, so I'll try to answer this.

      It would help if there were some definitions for "random" and "pattern-free" in this context. I find it annoying that he several times says that random music is not pattern-free.

      1. He never plays the same note twice. (A Costas array is a permutation) In a random piece, the same note can (and probably will) appear more than once.
      2. If he plays middle A, then middle B (consecutive notes), he'll never play consecutive notes (e.g. C_0 and D_0) again. 3. If he plays middle A, then something else, then middle B, he'll never play consecutive notes spaced by another note again. 4. If he plays middle A, then two other notes, then middle B, he'll never play consecutive notes spaced by two other notes again. 5. etc. 6. The same applies to pairs of notes two notes apart (e.g. middle A and middle C), three notes apart, etc. 7. Finally, he uses a Golomb ruler for the spacing between notes. I'm note quite sure what he did there, but possibly each spacing is unique. Can someone else explain? At any rate, a Golomb ruler defines unique gaps such that you get every possible gap between some pair of marks on it. (Think of a 4 cm ruler with 0 cm, 1 cm, 2 cm and 4 cm marked on it. You don't need a mark at 3 cm because you can get that from the gap between the 1 cm mark and the 4 cam mark.)

      It is true that their definitions are not equivalent, but it seems that he is implying that you cannot generate "pattern-free" music using randomly played notes, and that -depending of the definition of "pattern-free" of course- seems very, very unlikely.

      Can't is note quite true, but won't is more like it. Consider 3.14159265358979323 - the first 18 digits of pie. Random digits? Maybe (randomness, as you note, needs to be defined). However, look at triplets: 141, 535, 979, 323. Played as music, people will hear repetitions like that. Or at least, that seems to be the theory; I have no ear for these things to test it. Maybe you can hear them?

      --
      Strange women lying in ponds distributing swords is no basis for a system of government.
  14. Re:I can go one better by john83 · · Score: 2

    Random != no pattern

    You might create a tune with no pattern but chances are there will be a pattern of some kind in there.

    Exactly. This is why sports fans think that there's such a thing as form. Human beings are very bad at judging randomness - we actually bias towards alternating patterns, which is decidedly non-random.

    --
    Strange women lying in ponds distributing swords is no basis for a system of government.
  15. Prime numbers? by dada21 · · Score: 2

    Primes have no patterns, so why not just map sounds/beats to prime numbers?

    1. Re:Prime numbers? by gv250 · · Score: 2

      Primes have no patterns, so why not just map sounds/beats to prime numbers?

      But what will you use when you run out of primes?

    2. Re:Prime numbers? by john83 · · Score: 2
      --
      Strange women lying in ponds distributing swords is no basis for a system of government.
    3. Re:Prime numbers? by cvnautilus · · Score: 3, Interesting
  16. Re:Not that bad by cptdondo · · Score: 2

    Not only that, but if you actually sat and listened to it, it had a weird sense of incompleteness. It's like you;re looking for some pattern and not finding it.

    Not at all "bad" - it certainly elicited an emotional response from me. I wanted it to be complete, to have a pattern, and so I ended up listening to it to find one.

    I've heard worse - music that has a pattern but that's completely devoid of interest and impact. This is music that devoid of pattern and therefore draws your interest.

    I could really see this being orchestrated/arranged and be really cool.

  17. Re:More! by CurryCamel · · Score: 2

    Typical of them artists to ruin a perfectly ugly piece of music by their .... artistry. It should have been performed by a computer for proper ugliness!

  18. randomness != chance by ClickOnThis · · Score: 3, Interesting

    John Cage's music employed chance, not randomness. I posted 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.

    --
    If it weren't for deadlines, nothing would be late.
  19. "Applications" of math by OeLeWaPpErKe · · Score: 2

    Actually it's "useful" in the way mathematics stuff is always beautifully useless. You see, if you wanted to do echolocation with a piano (or any other 88-note instrument), this would be the piece that gave you maximum information on the target.

    http://en.wikipedia.org/wiki/Animal_echolocation#Acoustic_features

    Believe it or not, if you played this music often you would (after a loong time) become able to hear the differences in the room the music was played in, just by the sound.

    Bats use this to accomplish something that seems implausibly difficult, some species use it to dive through moving branches composing the upper level of a forest, in the dark (and they're blind or near-blind anyway), filled with environmental sounds and general noises, at ~ 180 km/h. When stationary they can use the tones to see through walls, and tell from the outside if anything in a room or cave is moving or not, including the rhythm of it's movement.