Why is a trumpet/cornet out of tune? (Monette, Lawler, Schil

[ChemistryComesAlive]

The story begins with a Schilke MCII from the 60's which had slides and extenders to play in either C or Bb. When playing in Bb, I played false finger D and E because I thought they were flat, or so they sounded when playing the entire scale.

Then I bought a tuner and was shocked. When played in Bb, I learned that the 5'th partial (F, F#, G) was sharp, the D and E were OK. Another surprise was that when played in C, the fifth partial was NOT sharp.

I thought that when my Monette B993 arrived that it would fix this. However turned out to also be sharp on the 5th partial. The rest of the horn was right on (excepting of course low Db). Because the monette's tone quality is not tied to its pitch, lip skill can compensate for pitch issues, which was not the case with the schilke.

My new Lawler cornet arrived yesterday and the fifth partial was about the same as the Monette but the middle G is a bit flat.

I can understand tuning issues that involve combinations of valves, but what I cannot understand is why the open pipe tuning of these high quality horns varies from instrument to instrument, indeed, even in the same instrument (ie same lead-pipe, same bell) I thought that the sound frequencies would follow the overtone series of open pipes. Heck, you can do this with a garden hose.

I am looking for some good references and ideas. I have an advanced degree in math and am working as a researcher in a scientific environment, so I am not afraid of nasty details.

[_Don Herman]

For the real meat, dig up a good acoustics books (look for the ones with all the interesting double integrals; there are good ones that are Navy-based (think sonar)). I have a couple, but they're at home.

Quick answers:

1. Different manufacturers "tune" their horns differently. You can't get them all in tune (usually) so you pick your compromise. Other factors, e.g. small variations in diameter along the leadpipe, help "tune" the horn by introducing impedance matching elements (if you will) to help intonation. Everybody uses slightly different recipes...

2. While the trumpet behaves much as a closed-ended pipe, the flare through the tubing affects the acoustic properties and thus the simple physics-text equations don't exactly apply.

HTH - Don
_________________
Don Herman/Monument, CO
"After silence, that which best expresses the inexpressible, is music." - Aldous Huxley

[music matters]

As the trumpet works on harmonics it will never be in tune with the "new" equal temperament system that is based on frequencies and not harmonics. A G# was not the same as an Ab until equal temperament came along and made them the same frequency. On all Bb trumpets the low C# and D are sharp and the D and E above are flat which is why trumpeters have the slide for the low notes and use either lip or alternative fingering for the D and E. I would recommend looking up harmonics on the trumpet to find out more.

[Tom LeCompte]

Don is absolutely correct in that a trumpet as a closed ended pipe is an approximation, one that doesn't well match a real trumpet. A better approximation is to think of an unwound straight trumpet: it makes sense to describe it in cylindrical coponents: r, z and theta. You can have air vibrations along all three directions. Each of these has a natural frequency, but the motion is coupled, and when you have coupled oscillators, the natural frequency of the system is not necessarily the frequency of any of the components. (You can find more details in a mechanics textbook like Marion or Symon under "normal modes" - what you essentially do is write down a matrix where each row represents an oscillatory motion, and then diagonalize the matrix: the output of that process is the normal modes of oscillation) Specifically in this case, the natural frequencies of our idealized trumpet are not the same as the natural frequency of an infinitely thin tube of the same length. If the strength of the coupling between modes is frequency dependent, the overtone sequence will not exactly match the idealization of a thin pipe.

Once you start bending a trumpet, you are pretty much guaranteed that you will have a frequency (more accurately, wavelength) dependency, so the partials will be out of tune with respect to each other. By making subtle changes in the piping, trumpet designers can adjust the coupling strengths, which effect the horn's intonation and tone.

Music Matters is correct that equal tempering means that even a trumpet that has a perfect natural harmonic series will not be in tune with a piano. However, the sharpness of the low D and C# has little to do with this. What you want valves to do is to add a fixed fraction of the length of the horn, but of course, you can only add a fixed length. So when you have many valves engaged, you are adding too little length, and thus the horn is sharp. This is actually a conscious design - its because we want 3 to be an alternate fingering for 1 and 2. Older horns made 3 a little longer than 1 and 2, and then the D and C# were much closer. The price you pay is that the alternate fingering becomes flat. Different designers make the compromise in different places.


Cheers,

Tom

[ChemistryComesAlive]

Thank you for your excellent posts.

The issue of the lenghts of valve slides and their combinations is well understood and I think I tried to put it to the side in kicking off this forum. What is confusing me is the open pipe/closed pipe stuff.

The issue of equal temperament is also not really involved here also. For example, the open low G on the cornet is flatter than the other horns. I do understand that the tuner is equal temperament, but I have often looked at the numbers comparing natural harmonics and equal temperament and am certain that the variations discussed here far exceed the differences between the two systems. Here I am comparing different horns, or a single horn with different setups.

The mouthpiece is also an issue. I have another old cornet that is way too flat (pipe is too short) to play in a band when played with every mouthpiece,...until the last one, a monette prana 1-5M, which is the same "length" as the rest of them. With that mouthpiece, the too-short horn is playable. By the way, I used this mouthpiece and the trumpet version of the same mouthpiece on all experiments mentioned earlier.

I am quite confused about the open pipe/close pipe issue. There is a recent ITG journal article on this issue which I will go back and re-read.

I am inclined to do some experiments with garden hoses. This might remove some extraneous issues.

I will look up the mechanics book. Thank you.

[trumpetmike]

You might want to check out the Smith-Watkins website - some good technical stuff on there (well, I assume it's technical stuff - means nothing to me!!).
Richard Smith is also quite a fascinating guy to talk about this sort of stuff with - if you dropped him an email he may well have some more detailed answers for you, from the maker's point of view.

http://www.rsmi.u-net.com/

[_swthiel]

Don,

Can you recommend some specific references for acoustics?

Thanks,

Steve
_________________
Steve Thiel

Matthew 25:31-46

[Tom LeCompte]

There's always Rossing's book. Warning - it has Bessel functions on about page 2. That sort of sets the stage for the mathematical background he's assuming.

Cheers,

Tom

[Ebayscrounger]

Interesting posts, and great science. How does all of this relate to dents in a horn, especially in a tuning slide, which would only impact some notes? I have heard that some old time horn players intentionally dented their instruments to gime them More "character".
_________________
I once had it, but I lost it. Where did it go???

Still looking for my horn...

[_swthiel]

[Tom LeCompte]

That's the one. (I didn't know there was a second edition, though)

The book does cover a lot of interesting physics for different musical instruments. It has one chapter on brass, so I wouldn't recommend buying it unless someone is interested in other instruments. The chapter on the piano is quite interesting - it explains why stretch tuning is absolutely necessary. Much of the voodoo that "everyone knows" about brass instruments is not in the book. It's up to you whether this is a good thing or a bad thing.

Cheers,

Tom

[Lawler]

For what its worth, My findings with changing the shape of the bends in the tapered sections of a trumpet or cornet do affect the intonation as well as how much cyclindrical tubing is introduced and where it is introduced. The problem I have is the players point of reference as to what feels and sounds good to them. I can make a cornet to play well in tune on the open partials...but because of the taper that would be used for this the sound it less full and dark...so a compromise is made in the taper to darken the sound which in turn shifts some partials out of line. But most of these shifts are handeled by the player. The player makes the compromise in playability for sound. Now I would draw the line if intonation is very out. Just for a dark or great sound. Most players will get tiered of working so hard to keep the instrument in tune for this dark wonderful sound. I have a good example. A few years back when every brass player was trying to get as dark symphony sound as possible many Bass trombone players where bringing instruments in to have the leadpipes taken out and just having a receiver put in so just the mouthpiece would fit in...WOW theyed say! What a dark sound.. Students followed coming in having mouthpipes removed WOW! what a dark sound. Not one at the time said anything about the scale being as out of tune as a Chinese flute. I will tell you a few weeks later I sold more leadpipes and put back leadpipes in all my days doing this. So my point...well I do think we have reference points but playability is in the beholder.
R. Lawler

[ This Message was edited by: Lawler on 2004-06-05 10:22 ]

[Tom LeCompte]

Scrounger,

I suspect that by far the most important effect is psychological. If you think that a change in the horn will change the sound, it will. People seem to think that a psychological effect is somehow less "real" than a physical one, and I think that's nonsense - the mind is intimately involved in the creation of music, or at least it should be!

Also, changing the shape of the main tuning slide will change the resistance of the horn. That's a big change, and I'll bet it's the second most important effect.

Changing slightly the coupling between z-modes and r-modes is probably not what is making most of the difference.

Cheers,

Tom

[Mikester]

Wow...This is great!!!

Now my Master's in Mechanical Engineering and my obsession with trumpets finally come together.

I can live in peace.

Thanks everyone.

Guess, I'll be requesting a book from the library.

[FreshBrewed]

You mean the horns aren't all tuned at the factory? Man, I want my money back...........hehehe
_________________
Mike

Those who roll up their sleeves rarely lose their shirts!

Eclipse MHY Bell- Savannah Finish