Sound and pitch of brass instruments

[don sawday]

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?

 

[don sawday]

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

 

[don sawday]

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.

 

[Chris Hillman]

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.

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?

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, https://www.physicsforums.com/misc.php?do=bbcode are some hints on how you can upload it to PF.

 

[don sawday]

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

 

[don sawday]

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"

 

[Chris Hillman]

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?

 

[don sawday]

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 I am not shooting blindly, and someond who i could bounce theories off of.

 

[don sawday]

the answer to your riddle is ,nothing, a violinist would never associate with a violist they are beneath them

 

[Chris Hillman]

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.

 

[don sawday]

it is funny, all we really do is keep trying to re-invent the wheel over and over, but a little rounder this time.

 

[don sawday]

thanks Chris .will keep up the fight

 

[Chris Hillman]

the answer to your riddle is...

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 Gentlemen, position your prenups! On the count of four!

 

[don sawday]

funny

 

[FredGarvin]

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.

 

[don sawday]

fred
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

 

[don sawday]

and think of this . there are many more guys that customize trumpets around the world than tubas. probably cause its too hard

 

[FredGarvin]

fred
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

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.

 

[Ouabache]

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.

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.
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Quote: good posts like wisdom, are never outdated

 

[sophiecentaur]

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.

 

[PhilDSP]

Based on an intuitive view of the situation you describe (OP) I'd say it's likely that the flow restriction set up some non-linearities. That means a differential equation that models a brass instrument's sound production would need to be extended to account for those non-linear effects. In other words, the lesser amount of air reaching the chamber doesn't fully excite the vibrational modes.

I think you get a similar situation in a flute, for instance, where if you blow gently it is much easier to produce a tone in the lowest octave and you can produce a wavering of pitch by changing breath pressure that you can't do in a higher octave.

 

[Bob S]

The effect you are observing is due to changes in the acoustic impedance of the tube as a function of its diameter. See

http://patarnott.com/pdf/JAS003432.pdf

See also

https://ccrma.stanford.edu/realsimple/vir_tube/vir_tube.pdf

I have calculated the same thing for impedance discontinuities in coaxial cable (electromagnetic) propagation. The distance between tube-diameter disconituities can create standing waves, which are dependent on the wavelength (frequency).

Bob S

 

[sophiecentaur]

The effect you are observing is due to changes in the acoustic impedance of the tube as a function of its diameter. See

http://patarnott.com/pdf/JAS003432.pdf

See also

https://ccrma.stanford.edu/realsimple/vir_tube/vir_tube.pdf

I have calculated the same thing for impedance discontinuities in coaxial cable (electromagnetic) propagation. The distance between tube-diameter disconituities can create standing waves, which are dependent on the wavelength (frequency).

Bob S

Discontinuities in stiffness too, in the case of a brass instrument, I am sure.

 

[Bob S]

Discontinuities in stiffness too, in the case of a brass instrument, I am sure.

This is a BAAAD discontinuity!

http://en.wikipedia.org/wiki/Dizzy_Gillespie

Bob S

 

[sophiecentaur]

It could also lower the tone!?

 

[turbo]

I have a friend who is a saxophonist and he's got an old tenor sax that is heavily darkened and patinated. He refuses to clean and polish it because he says it will ruin the tone. Maybe, maybe not, but there is no denying that the tone he gets now is killer.

 

[Ouabache]

This is a BAAAD discontinuity!

Story has it, after someone had sat on his trumpet and bent it like that, Diz liked the new tone and decided to keep it that way.

 

[bjacoby]

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.

I presume you are referring to the works of A. H. Benade. I actually worked for him for a time and he did a great deal of theoretical work on the theory of horns. The basic theory is that the horn acts like a transmission line. As such it forms a resonator with modes that are the notes. The resonant frequencies and harmonics are determined by the taper which of course implies the diameter along the length. The transmission line parameter give the characteristics of the horn. It's all quite complex. Prof. Benade told me that he could take a cheap student instrument and turn it into a medium quality instrument using his theory, but that the best instruments were all developed by trial and error and were well beyond the level of his theory. For example modeling the feedback at the mouthpieces was a particular problem.

He was an amazing guy and there was virtually no one else working in this area of Physics.

 

[Ouabache]

... 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

Is this the book to which you were referring?
Wood, Alexander and Bowsher, J. M. The Physics of Music, 6th ed. New York: Dover, 1961

(here is a short bibliography on http://www.ericweisstein.com/encyclopedias/books/MusicTheory.html" )

 

[bjacoby]

Is this the book to which you were referring?
Wood, Alexander and Bowsher, J. M. The Physics of Music, 6th ed. New York: Dover, 1961

(here is a short bibliography on http://www.ericweisstein.com/encyclopedias/books/MusicTheory.html")

Also check out: https://ccrma.stanford.edu/marl/Benade/writings/58to69.html

And also Amazon: https://www.amazon.com/s/ref=nb_sb_...ywords=A.+H.+Benade&x=0&y=0&tag=pfamazon01-20

 

[Ouabache]

Also check out...

Thanks for your links. I also had the pleasure of working alongside an internationally acclaimed scientist (EE/physics), so I can appreciate your enthusiasm for sharing Benade's insight. If you followed my 'related books' link, Benade's Fundamentals of Musical Acoustics is 3rd on the list.