Strange Attractors

Discussion in 'Trumpet Discussion' started by Vulgano Brother, Jan 20, 2012.

  1. Vulgano Brother

    Vulgano Brother Moderator Staff Member

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    Have been trying to wrap my head around chaos theory for years, and came across an article by Douglas Hofstadter in Metamagical Themas (an anagram of Mathematical Games, which Hofstadter used in his tenure with Scientific American) on “Sparking and Slipping” that gave some insight into how the trumpet works. (I know, a horribly long sentence, which I blame on my time spent living in Germany—sorry!)

    Anyway, in talking about Strange Attractors he used the analogy of a marble in a bowl. At rest, it will be in the same place (depending on the shape of the bowl), but when disturbed, it will take time to go back to that “attractive” place. Seems to me that notching on the trumpet is related to that—the time it takes for the note to “come to rest” has implications for response and security. Weird thing is, there are trumpets that respond well but aren’t all that stable, and there are horns that are stable that don’t respond well.

    Am hoping some of the more savvy minds amongst us can shed some more insight on this. (I know that practice can counteract this—I’m not interested in fixing the problem, but rather understanding it.)

    A turbulent thing, the trumpet. Chaotic too.
     
  2. the newbie

    the newbie Pianissimo User

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    I hate mathematics with a passion. Philosophically i think its all relative. Shape of bowl, type of ball, position of the bowl and situation of the bowl etc could alter where the ball lands. Trumpet playing: hitting a high note in a phrase you are comfortable with etc, the ball will land in the usual spot. Going for something out of your comfort zone?... Who knows where that ball will land!

    Its all relative to the mind. regardless of trumpet. unless its a clanker!



    i think
     
  3. kingtrumpet

    kingtrumpet Utimate User

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    the problem with Chaos theory is that it eliminates actual scientific facts -- especially about sound. On a nanophysical level, the very act of measuring and quantifying something (ie. such as sound) empirically affects the particles or waves that produce that sound, thus altering the "actual" sound.

    in your chaos theory above whether it relates to a marble in the bowl or the sound in a trumpet --- by measuring and quantifying the sound waves --we have disturbed and disrupted such sound waves, as to make the orginal quantification of them to be inherently different than the measured.

    So instead of Chaos theory, I think to understand that everything is in a "system" that is moveable, changeable, and effects all other things in the environment.

    you should probably look up "butterfly effect" and how it is postulated that something as small as a butterfly on the other side of the world, could potentially be a causitive effect that produces a hurricane ---------then you will find that chaos theory is so complicated, that perhaps a nanophysics level of understanding may be better suited to your discussion ----------hey, I am just saying!!!!!!!!!
     
  4. rowuk

    rowuk Moderator Staff Member

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    Chaos is simply a higher form of mathematics. What appears to be random or changeable is simply beyond our comprehension.

    As far as the bowl goes, returning to a stable state (in the case of a trumpet, there are 2) is a question of efficiency of the resonant system. High efficiency starts and stops the standing wave quickly. The bowl only has one stable state - at rest, there is no resonance where the marbles travel is predictable.

    As the trumpet is a complex system, defining the resonant state is harder than just measuring it.

    Simulation of Brass Instruments

    Here is a link to producing a multiresonant bowl.....

    Optimization

    More to come when the discussion moves on a bit.
     
  5. turtlejimmy

    turtlejimmy Utimate User

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    VB,

    Chaos theory is very simple .... we can't understand it. :lol:

    Actually, I believe it's a theory that states that everything has an order to it, even though it appears totally chaotic to us. With computers, we've been able to plot, visually, what this "chaos" looks like, and came up with the Lorenz Butterfly (pattern). So, it isn't all just random, there's a plan (God's plan?).

    So, to review, THERE IS NO CHAOS. (outside of my practice sessions :-?). No, I don't want to talk about it. :-P

    But, strange attractors? Would that be like a trumpet player and a violist? Obviously, more research is needed here.


    Turtle
     
    Last edited: Jan 21, 2012
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  6. Vulgano Brother

    Vulgano Brother Moderator Staff Member

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    Frank Holton was optimizing horns back in the day, and Schilke learned from him. I had a rotary Bb converted into C go through the BIOS tests, and it was remarkably in-tune up to E above high C (except for the 1-3 and 1-2-3 combinations [duh!]) with a remarkable "Q" factor. It is a good horn. I'm just confused by the fact that a horn can be a real dog with no response or stability or have one of the two, or both. I've had horns that responded well and horns that notch well, and have come up with an eclectic collection of good instruments (along with a drawer full of mouthpieces, some of which match a particular horn really well).

    Benade stated that there are two problems for the brass instrument maker: acoustics and fluid dynamics. Helmholtz figured out most of the acoustical problems long ago, but fluid dynamics and the turbulence it involves makes things chaotic, seems to me....
     
  7. rowuk

    rowuk Moderator Staff Member

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    What do we need to adjust response? Generally a well defined starting and end point for the standing wave. The starting point involves the throat size of the mouthpiece, the reactive air chamber called the cup and the suppleness of the lip mass. The endpoint for the standing wave is in the bell for very high frequencies and in front of the bell for low frequencies. The taper of the bell determines what octave gets what acoustical length.

    Specific notes are greatly affected by the position of the waves null and maxima. In physics we learn that a tubes length determines its resonant frequency, a horn depends on the rate of taper and irregular shaped objects by volume. For higher frequencies, we have an effect that some of the maxima are in a tube, some in the horn, some in irregular places like the valve cluster and depending on the octave can even be outside of the horn. This means that the air mass is different at different parts of the wavelength and can help or hurt efficiency. I don't think that turbulence is a big factor because it only occurs in the "unnecessary" DC component of our playing.

    I have noticed that horns with bigger bells often are harder to play up high. Cutting them down did not fix the problem. It was a function of the taper. Monette for instance has a standard taper for all bells BUT on the bigger diameter ones, the last part is not a taper, rather flat. This helps to launch the low frequencies better without getting in the way of the upper register.


    More later.........
     
  8. gmonady

    gmonady Utimate User

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    This comment may be side stepping Chaos theory, but I do agree rowuk's observation. I have found my mutes, that fit perfectly well in my other horns, have a more difficult time staying in my Martin Committee. I have had to buy new mutes with more cork to make them fit. Clearly, the taper on the Committee has a unique quality that is a vital function to it's unique tone. The harmonics I have observed from a brilliant experiment conducted by Professor Eddie Brookshire on my horns clearly demonstrated that there is no detectable overtone, just a pure tone with the Committee. My Getzen Eterna Flugel and Olds Recording during this same experiment demonstrated significantly noticeable overtones (lower tones for the Eterna, higher harmonic tones for the Recording). There may be other variables (brass alloy?), but I bet the bell taper is a major contribution to this observation
     
    Last edited: Jan 22, 2012
  9. kingtrumpet

    kingtrumpet Utimate User

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    and YET, on a nanophysical level of YOUR horn -- the very act of you playing it changes the characteristics of the sound -- versus having someone else play it, they have their own characteristic of playing, style, breath, etc. which causes a disparity in sound or causes the trumpet to behave differently depending on a multitude of physical difference inherent in the players themselves. ((noting that ---perception in the sound may or may not be distinguishable by the auditory capacity of the human ear)) - however introducing a new player will introduce a new sound ------------------even in a Martin committe

    ps. as how this relates to chaos theory -- I can only mention --------DR CHAOS, must have something to do with it!!!!!!!!! ROFL ROFL ROFL
     
  10. gmonady

    gmonady Utimate User

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    I cannot agree more with your comment, but I was referring to the pure tone it creates, and I bet any person playing this horn, no matter what sound they produce, will have a pure tone. But perhaps you have reconnected my comments with the thead topic, the chaos is in the sound.
     
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