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Sound and pitch of brass instruments

  1. Dec 12, 2007 #1
    The physics of sound have been explained by many people but the relationship of practical applications are a blur.
    I am a brass instrument player and designer of bras instruments
    the relationship between bore size, taper and length are very crucial and way over most peoples head.
    so here is the question.on the latest trumpet prototype,with a bore size of .460, there was a bore size restriction in a few areas(specifically where the knuckles left the valve section) of .005-.010 of an inch. The result was pitch went flat in quite a few places. when the bore size was corrected to the correct size of .460 the pitch went in tune.
    can some one explain or is it even possible to explain in laymen terms?
  2. jcsd
  3. Dec 12, 2007 #2
    my theory is that when a tube gets smaller the wave length becomes longer some how making the pitch go down and vice versa, a bigger tube means a shorter wave length resulting in raised pitch
  4. Dec 12, 2007 #3
    i have also read articles from the 1940's written by the instrument maker Conn that said they shrunk a horn at a certain areas on a node point which lowered the fifth partial. their problem was that at that certain spot it also changed the forth partial. so their claim was that all musical instrument were compromises.
  5. Dec 12, 2007 #4

    Chris Hillman

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    Whoa, whoa, back up a bit. Have you read any books on the physics of music? For example there is a Dover reprint which might give a mathy person a clue for very simple models of the simplest brass instruments, like a valveless straight trumpet. Anything more complicated than that quickly becomes so complicated you must have recourse to numerical mathematics, I think.

    Well, never say never. I'd be very impressed if anyone can give a ten page explanation full of mathematics involving PDE theory I know! If anyone can do that we can start in on reducing it to layman's terms.

    By the way, a really nice diagram in finest CADCAM style would help here; if you have on, here are some hints on how you can upload it to PF.
    Last edited: Dec 12, 2007
  6. Dec 12, 2007 #5
    yes i know i get dizzy just looking at the first page of any of those books . i asked a physics professor at UC Irvine, who also was a violinist and she told me my questions were way over head
  7. Dec 12, 2007 #6
    its combining the art of music with the physics of science its two world that are so different from each other. what this industry does mostly is trial and error with no real answers except "i guess it sounds better"
  8. Dec 12, 2007 #7

    Chris Hillman

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    Well, some violin makers seem to play around with quite sophisticated computer models, or so I hear. If anything this is probably more complicated than a brass instrument.

    Here's an idea: demand for Christmas two dozen really fine numerical models (as in finite elements) of some really fine brass instruments made the old-fashioned trial and error way. Figure out how to evolve them using a genetic algorithm and let the magic of selection do its thing!

    Here's one for your friend the violist: what do you get when you cross a viola with a violin?
  9. Dec 12, 2007 #8
    The problem with all the math on paper is that that works "only on paper" The real world deals with so many more variables,like metal thickness,metal composition,metal hardness,how much metal the guy polishes in the buffing room, how much lacquer,silver or gold plating we put on. I mean its never ending. But i do know for a fact that all the above does matter and can change the way horns play and sound.
    Where the people in this forum will have the expertise in psychics, my tallent is with my ears which in the end game is really what it is all about.
    but it would be nice if someone could help me so im not shooting blindly, and someond who i could bounce theories off of.
  10. Dec 12, 2007 #9
    the answer to your riddle is ,nothing, a violinist would never associate with a violist they are beneath them
  11. Dec 12, 2007 #10

    Chris Hillman

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    Theoretical insight is absolutely invaluable when you can get it, but it requires a long hard fought campaign, typically starting with an idealization which is carefully refined and artfully analyzed. Eventually a combination of exact solutions to idealized equations and perturbations of same can yield the kind of understanding you seek. In the theory of brass instruments, as far as I know, this process hasn't yet advanced as far as one might wish. Still, if you haven't poked around in your local physics library, keep trying, something might turn up.
  12. Dec 12, 2007 #11
    it is funny, all we really do is keep trying to re-invent the wheel over and over, but a little rounder this time.
  13. Dec 12, 2007 #12
    thanks Chris .will keep up the fight
  14. Dec 12, 2007 #13

    Chris Hillman

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    why, a crash.

    You know, the genetic algorithm program crashed, get it? Because as any string player will tell you, the mating of a viola and a violin is music to the ears of the divorce lawyers :wink: Gentlemen, position your prenups! On the count of four!
  15. Dec 12, 2007 #14
  16. Dec 13, 2007 #15


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    As a fellow trumpet player I feel your pain. I have the book Chris mentioned and he is right. When it comes to brass instruments, there have to be a lot of assumptions made to make the math manageable. By the way, that Dover book is really fantastic. I actually used it in one of my PDE classes because it talks a lot about circular membrane vibrations for drums.

    Anyways, I have always had notions about what I think may drive these issues, but they are just theories. I have never made or tested an instrument in an engineering sense. I would bet that your localized bore restrictions effect the nodal response of the tube itself. Even though we know the sound comes out the bell, I am convinced that the vibrational response of the instrument has an effect on sound quality. It falls in place when you think of how basic changes in bore size, material and finish can effect the sound.
  17. Dec 13, 2007 #16
    no doubt these things have a huge effect on everything. some old time repair guys say that you can feel the node on the horn when it is played. so i had a tuba played righe infront of me playing a middle concert F and i just started feeling around the horn. I found a spot on one of the branches that was extra tingly and when he switched to an Eb the spot changed.
    so one of my theories that stems from the conn article is if you shrink or expand a nodal point it will change pitch.
    especially with tubas if you think about them as a giant trumpet, they have several notes out of tune, so if you could find the nodal points for the bad notes you could adjust the horn in that spot and basically dial the horn in.
    on the tuba i'm working the Eb is sharp and since i know where the Eb node is i could shrink the bore by putting in a sleeve maybe 1 inch long in that spot and lower that note.

    the questions are how many nodes all over the horn for each note
  18. Dec 13, 2007 #17
    and think of this . there are many more guys that customize trumpets around the world than tubas. probably cause its too hard
  19. Dec 14, 2007 #18


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    You don't see too many custom tuba makers out there do you? I used to date a classical tuba player.

    I would think that, despite the change in shape, the number of nodes in an instrument should be close to those predicted by a simple open pipe and standing wave theory. However, that does not address the structural situation. I wish I had the time to do some measurements and analysis. It sounds like a cool college project.
  20. Mar 10, 2010 #19


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    Your experience confirms something I noticed with my brass instrument. I recently had a trombone refurbished (removed dents, realignment, plated & refinished). It looks and feels beautiful. But when I play it, the tone seems thinner compared to another trombone (same model) that has never been refinished and which I've played for several decades. I wondered if I just needed to adjust my embouchure to achieve a fuller tone. But with your discussion, I am thinking it is an innate characteristic of this refurbished horn.
    Quote: good posts like wisdom, are never outdated
    Last edited: Mar 10, 2010
  21. Mar 10, 2010 #20


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    The treatment it was given may have work-hardened it in local spots which could change the resonances in the brass. You could try having it annealed and see whether that makes a difference. It wouldn't be in the same state as when the sections were first drawn and bent to shape, with nice symmetrical stresses in them, though. It might make it 'decidedly dull' if all the metal were to be relatively soft.

    It would be a bit like striking a match to test it - you couldn't get back to square 1.
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