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Math Music

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..."
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Mathematically Pattern-Free Music

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  • Rap music (Score:3, Funny)

    by Oswald McWeany ( 2428506 ) on Friday November 04, 2011 @04:39PM (#37951978)

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

    • 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.
    • 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.
  • by Unloaded ( 716598 ) on Friday November 04, 2011 @04:42PM (#37952020)
    ......"set out to do what no musician has ever tried — to make the world's ugliest piece of music"...... Already done...'re)_Having_My_Baby []
  • by amstrad ( 60839 ) on Friday November 04, 2011 @04:43PM (#37952034)
    you won't attract the worm. Another piece of ugly music, Aphex Twin's Ventolin []
  • Step 2... (Score:5, Funny)

    by chinton ( 151403 ) <{moc.liamg} {ta} {todhsals-100notnihc}> on Friday November 04, 2011 @04:44PM (#37952044) Journal
    2. Add Vogon poetry as lyrics. 3. Profit
  • The consensus was that "Friday" already held that title.

  • 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. []
  • by alphatel ( 1450715 ) * on Friday November 04, 2011 @04:49PM (#37952130)
    Old hat. To discover the life of a musician who made randomization a career, see John Cage [].
    • I prefer the more recent Nick Didkovsky, the father of JMSL []

    • Re:cure but... (Score:4, Insightful)

      by Smidge204 ( 605297 ) on Friday November 04, 2011 @05:27PM (#37952574) Journal

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


    • by PCM2 ( 4486 )

      John Cage is interesting, but he created music that was random. That's not what this is.

    • randomness != chance (Score:4, Interesting)

      by ClickOnThis ( 137803 ) on Friday November 04, 2011 @05:31PM (#37952616) Journal

      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.

  • by Anonymous Coward on Friday November 04, 2011 @04:49PM (#37952134)

    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.

    • You missed the "there is some number N" and "sufficiently large complete graph" - the implication is that, for a long enough musical piece, some repetition can be found. But you need to figure out the appropriate value of N for a given class of musical compositions, before you can claim that a particular piece can not be pattern free.
    • by curril ( 42335 ) on Friday November 04, 2011 @05:57PM (#37952866)

      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.

      • by john83 ( 923470 )
        Well spotted (by which I mean, mod parent up!). He could have used a larger primitive root of 89, like 30, and that wouldn't have occurred.
      • by johanatan ( 1159309 ) on Friday November 04, 2011 @06:42PM (#37953214)
        Not only that but he apparently did by hand the 'computationally impossible'. That section of his talk was truly confused.
        • by gnufrog ( 19906 ) on Friday November 04, 2011 @08:15PM (#37953838) Homepage

          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...

    • by john83 ( 923470 )
      Interestingly, if you try to generate more than 88 notes by the method Rickard described, they start to repeat periodically.
  • Krzysztof Penderecki's Threnody to the Victims of Hiroshima [] is the most horrible "music" I've ever heard. (Intentionally so - Penderecki made it as dissonant and a-tonal and possible)

    Don't believe me? Listen to it here []

  • by sandytaru ( 1158959 ) on Friday November 04, 2011 @04:51PM (#37952154) Journal
    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.
    • by rmstar ( 114746 )

      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.

      • Absolutely. I'd listen to it on purpose. What is ugly to some is beautiful to others. I think part of what makes that still beautiful is that the individual notes from a good piano that is apparently in tune as far as I can tell, are distant enough in time to allow me to forget the previous note's relationship to it.

        If you really want to make ugly music, use notes generated by different poorly tuned instruments in disrepair and speed it up.

      • 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.

  • This kills off any kabbalist's notion of the importance of numbers as such. Now music have no pattern, too.

  • Something must be wrong with me, because I loved this piece immensely and would really like more. Hearing it again and thus repeating it seems to destroy the beauty of it.

    • by john83 ( 923470 )
      There are additional possible solutions. They used an 88x88 Costas array for the notes, and a length 88 Golomb ruler for the intervals. I'm not sure how many Golomb rulers there are of that size, but there are more Costas arrays of that size - at least as many as there are primitive roots of 89.
    • Nothing wrong with you at all.

      Music evolved as a tool for learning. Rhythmic behaviour around the campfire teaching others how to hunt and all that.

      Anything which our brain perceives as innovative in comparison to what we know is considered a new concept, and learning new concepts gives us pleasure (knowing more concepts is a survival trait).

      So you get pleasure not from the repetition of patterns in Beethoven's Fifth, but from the interplay and differences. The pattern is set up initially, and then it's how

    • 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!
  • 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
    • by john83 ( 923470 )
      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

      • by john83 ( 923470 )
        Please note that "note a musical guy" was not intended as a pun, but was in fact my brain on too little sleep.
  • That music isn't ugly. It does happen to be optimally dissonant, but ugly and dissonance are not the same thing. Related - but not same thing.

    If you want some truly ugly music I recommend you get to YouTube and check out The Residents. They work hard to bring you the ugly.

    Here is an example. [] It is the Residents covering the Rolling Stones Satisfaction. FAR more ugly than this mathematical oddity. You'll note that it is fairly repetitive and still PLENTY ugly.

  • by dada21 ( 163177 ) <> on Friday November 04, 2011 @05:16PM (#37952466) Homepage Journal

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

    • by gv250 ( 897841 )

      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?

    • by john83 ( 923470 )
      No patterns []?
    • Re: (Score:3, Interesting)

      by cvnautilus ( 1793340 )
      Also Ulam Spiral []
    • PI also has no pattern [], why didn't they choose it?

      Your post is a good example of a bad argument, or a good question. At some point he says something like "A piano happens to have 88 keys", as if it were an afterthought.

      The point here was to find something that was completely pattern free, but can also be represented by some sort of musical instrument. Mathematically proven pattern free, not just apparently pattern free. So you would have to use primes mod 88. No one has proven that primes mod 88 is pat

  • It's so cute when the kids think they've discovered something nobody's tried before (eyeballs roll up in head). Welcome to the 20th century!

  • Bastard Noise: The Analysis of Self-Destruction is the worst voluntary atonal arrhythmic non-patterned music ever.
    If you don't consider suicide during a listening session, you are deaf!

  • So if I understand this correctly, since 3 and 88 are relatively prime, then every number in the closed field F88 is a multiple of 3, and if you keep multiplying by 3, you'll eventually hit each number.

    But that's a pattern, isn't it?

    • by john83 ( 923470 )
      It is, but not of the kind they were looking to avoid. There are Costas arrays without that pattern, but they're not known for sizes over 28 x 28. They're called 'sporadic' arrays [], and they're actually the most common type for small sizes (there are infinitely many generated by field theory, but that's not a fair comparison as we can't find large sporadic arrays).
  • So...this guy is trying to recreate white noise, then? I'm pretty sure there's an app for that...

    • by john83 ( 923470 )
      No, white noise is random, which wouldn't have the same properties as this. For a start, it would have the same key more than once.
  • ... just leave the cover on the piano keyboard open when the cat is out patrolling.

  • It is, after all, still better than most of what is sold as "music" these days.

    Now get off my lawn...
  • ...and put on some Rush. :-)

  • To the under 25s: This is what kids will be listening to when you're middle-aged. Enjoy. :)

  • I shudder at the thought of what happens when the noisegrind [] community discovers this research.

  • Whenever some hardcore relativists speaks about all music being equally good, I just get them to load a random exe file into a sample editor and play it back. The result is usually the most horrendous piece of crap you can imagine, that squeals and grates like a ZX spectrum on acid. I'm serious, it's not pure white noise, it really sounds horrible.

  • Meh! Any fourth grade beginning strings class does this. Mind you, the intent may be different, but the results are pretty much the same.
  • It's only repetition-free if you can hear the intervals accurately, so that a jump from (say) a low A to an F-sharp five octaves up really sounds completely different to you from a jump from a low A to an E. I can't hear long jumps that accurately. By picking notes out of the 88-key keyboard, they get music in which the note-to-note interval jumps are much larger than they are in a traditional tune or theme. Those jumps are so large--and so divorced from any total center--that I, at least, don't hear them a

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