Bell throat measurements

[hyperbolica]

With all of this talk about bell throats being thrown around, all we have are vague claims, and "bass" or "tenor" throats that no one has backed up. So I decided to measure the horns I have handy and start to quantify this characteristic at least for the horns I have. It may be wrong, but it's better than what we have now, which is nothing.

Here's what I did:

• I put a trombone bell on a table

• put a music stand right next to it.

• measured 7 inches (~178mm) from the bell rim to the tray of the music stand)

• put the tray of the music stand right up next to the bell throat

• placed calipers on the tray of the music stand

• measured the bell diameter at that point

I'm sure a real characterization of the bell throat would require multiple measurements, but I wanted to reduce this to a simple single number that we could use for comparison for trombone bells. 7." from the rim is kind of arbitrary, but with the horns I had, it was a point at which there was a reasonable difference between tenor and bass.

Here are some measurements for different models that are available to me:

Elkhart 88h = 1.65"
Olds Recording = 1.67"
79h = 1.63"
36B = 1.63"
Wessex supertenor = 1.95"
Kanstul 1662i = 2.07"

If other people are interested in taking measurements and adding to this list,that would be cool. Especially for common reference models of all brands in both tenor and bass persuasion. I'm also interested in the "tweener" type horns like 5b, 88hk, Bach 45, and maybe small horns with big sound (Bach NY 6, Conn 24h) or big horns with more focused sound (Duo Gravis) or big horns with woofy sound...

I know sound comes from a number of factors, I'm not here to slog through that again. I'd just like to characterize something that has been left to mystery for too long.

Already with the measurements, you can see a correlation between throat diameter and the sound of the horn, for those familiar with these models.

Please measure what you have and add it.

[elmsandr]

Can you post a picture of your measurement method? The better the instructions, the more likely they are to be repeatable.

Cheers,
Andy

[hyperbolica]

Yeah, great idea. I was actually doing that when you wrote. Takes a little time to get pictures setup.

Here's a photo of setting up a wire stand at the measured height.



And here's a photo of using the calipers against the stand tray to measure the bell. The music stand just helps you get a semi-repeatable position to measure. I understand there are going to be some tolerance and repeatability issues, but this is something that any trombone player with a set of calipers can do. And it gives us ball-park (or better-than-nothing) characteristic numbers so we can all talk about things more intelligently.




You might also be able to do this with an adjustable height trombone stand and a desk or table, or any other combination of things that allows you to measure the diameter at 7.25" up the bell from the rim.

[CharlieB]

I made a very similar set of measurements on some of my horns a few years ago.
I found the measurements to be inconclusive.
Example: Olds Recording, Shires .500, and Kanstul 1606 all measured exactly the same at a constant distance from the bell rim; but each horn sounded entirely different from the others in the group.
Other horns in the sample group had differing bell measurements, but again there was no direct correlation (Such as bigger is darker) between this one measurement and the sound of the horn.
Unfortunately, I think we're just stuck with describing bells using the inadequate set of adjectives we have:
bright, dark, open, crisp, foggy, thin, mellow, lively, dead, complex ...........

[hyperbolica]

I made a very similar set of measurements on some of my horns a few years ago.
I found the measurements to be inconclusive.........

Yeah, that's one possible outcome - that there is no correlation. All the components from the mouthpiece rim to the bell rim contribute to the sound. It might be that there's a given ratio, like the bell shape constant divided by the average radius of the tuning slide radius that gives a characteristic number.

Or maybe each horn is broken down into a multi-axis visualization like I've seen done for SEO data analysis


I don't think we're stuck with the vague mess we have now. I'm sure manufacturers have a more sophisticated way of comparing the response of musical instruments that would be useful to musicians.

In any case, I think the numbers I measured do correlate to an aspect of the sound of the respective instruments. The Kanstul is a bass, and the Wessex is a tweener. The Recording has a thicker, weightier sound, and the 88h is more lively, along with the similarly light sounding 79h. The 36b and 79h play similarly in some respects.

If you want to add more details about your study, that might be useful here.

[CharlieB]

If you want to add more details about your study, that might be useful here.

Thanks, but I am done. I disproved my hypothesis to my satisfaction with the first data set.
With sufficient research and a very large data set, you may reach more useful conclusions. It is good to have an open mind and question things. Best of luck to you in your study.

[Tremozl]

I think it might make more sense to calculate the 'volume' of the Bell Throat.
To do this, assuming the throat is increasing in size at a linear or nearly-linear rate, you'd want to know the length of the entire bell's throat and the maximum diameter it reaches, as well as the diameter where it starts, which should be (if we're using common sense) the bore size.

Bell throat is probably one of the larger factors behind how open a horn plays and how dark it sounds. And the length of this conical tubing has a large impact on the 'volume' (not the sound but the space I am referring to above) - not just the starting, ending, or even midpoint sizes

[hyperbolica]

I think it might make more sense to calculate the 'volume' of the Bell Throat....

Yes, but volume isn't readily measurable easily by regular joes. It would just be another excuse for having a theoretical/mythical comparison. The point of having a simple diameter at a given location is to have a common means to characterize a bell throat. Is it imperfect? Yes, but it's easy to obtain and gives a clear comparison.

All we have now for characterizing a bell throat is "does a bass mute fit?" That's even more flawed than the diameter measurement. I'm just trying to improve on that, while remaining practical.

[noordinaryjoe]

I think it might make more sense to calculate the 'volume' of the Bell Throat....

Yes, but volume isn't readily measurable easily by regular joes.

Fill the bell section up with water and pour it into a graduated container to measure. Fill it all the way up. Fill it to various points and throw in a little subtraction to get the volume of various parts of the bell that you want to quantify....

[Tremozl]

Yes, but volume isn't readily measurable easily by regular joes.

Fill the bell section up with water and pour it into a graduated container to measure. Fill it all the way up. Fill it to various points and throw in a little subtraction to get the volume of various parts of the bell that you want to quantify....

I'd get behind that plan wouldn't actually do it myself though haha.

[hyperbolica]

Fill the bell section up with water and pour it into a graduated container to measure. Fill it all the way up. Fill it to various points and throw in a little subtraction to get the volume of various parts of the bell that you want to quantify....

Good idea, especially if you removed the tuning slide. But it wouldn't work for TIS horns and would mischaracterize ballroom horns, with short bells.

[boneagain]

Here is a picture from a project I did a few years ago:

manybells.png

Might be from 2009 or 2010.

The measurements without "adams" in them were done by some very knowledgeable people for whom I have great respect. The measurements with "adams" were done using a reference grid and digital camera with a quite long optical zoom. I have a 9 page PDF describing the method, and PDF for printing off the grid. It involves using the GNU Image Manipulation Program (GIMP) to count pixels to get external bell measurements within a few thousandths of an inch, assuming very careful setup to avoid known sources of error.

It also involves characterizing the curve made by the bell flare. In "Fundamentals of Musical Acoustics" by A. H. Benade, section 20.5 covers "Musically Useful Shapes: The Flaring and Conical Families of Brasses." Within this section, Benade provide this equation:
D = B/(y+y0)m
which characterizes the diameter D of the bell flare at any distance y from the large end of the bell.

This equation is not easy to rearrange to solve for "m." Spreadsheets like LibreOffice Calc or programming languages make it possible to solve this by iteratively substituting different values for the other parameters until things match up. I have a worksheet for this. It is not fun to use. But given a relatively few points along a curve, it does a very nice job of providing a single, unique identifying parameter for the curve.

You will note I have not attached the either the PDFs or workbook to this post. I feel I have good reason for not doing so. If I read Benade correctly, these curves are very good at identifying the gross tonal differences between trumpets, horns, and trombones (for example.) They are not so good ON THEIR OWN for determining how a specific trombone will sound.

For example, the bright green trace for the Duo Gravis lies closer to the Stearn Fuchs than anything else. The Sandhagen 70h is MUCH further from the Stearn Fuchs. Yet I'm CERTAIN we could all hear clear differences between the Fuchs and the Duo Gravis. I'm willing to bet we would rank the Sandhagen 70h as being closer to the Fuchs than the Duo Gravis.

I pick this particular example because those two boundary shapes have tuning in the slide. This has a very significant impact on how far the taper of the bell reaches before any acoustic disturbances to the waveform. But this also introduces very significant sound modification in the mass and resonance of the main slide.

So my bottom line is this: it is easy to get all wrapped up in this one component of the system and still not get much closer to much of a sound characterization.

Most of the progress I've seen on this front is still pretty experimental. A member of "The Trombone Forum" did some remarkable work, touched on in this link: https://www.science20.com/news_articles ... st_century

You can use Dr. Braden's name to find some other interesting work. You can alse search for this paper: "Acoustic pulse reflectometry for the measurement of musical wind instruments" by David Brian Sharp.
This paper might be closer to what you are interested in: "NON-LINEAR PROPAGATION CHARACTERISTICS IN THE EVOLUTION OF BRASS MUSICAL INSTRUMENT DESIGN" by Myers, Gilbert, Pyle, and Campbell.

For me the biggest selling point of the above two papers is that they deal with the entire instrument hardware system. These help explain why adding an in-line 2nd valve can make a horn sound and feel very different. Pulse reflectometry sounds exotic (at least to me.) But keep in mind that the same basic ideas are used to allow a cell phone to measure projectile velocities. If the demand arises it is only a matter of time before "good enough" consumer apps using low cost microphones and sound sources make it possible to do this at home.

BTW: on the bell measurement: the non-adams values were taken inside the bell. My measurements were taken outside, then adjusted for the average thickness of the bell. Of course, such adjustments are fraught with error sources. For one thing, there is not law of physics that says a piece of metal being spun on a mandrel will spin EXACTLY down onto the mandrel, or at the same thickness. For another, as the bell flares out, the added diameter of, say, .020" of metal runs into some interesting trigonometry and adds more and more than .020" to the outer diameter.

Good luck with your quest quantifying tonal characterization!

[CharlieB]

Using calipers to predict a horn's personality is like using a tape measure to predict a woman's personality.

[hyperbolica]

...these curves are very good at identifying the gross tonal differences between trumpets, horns, and trombones (for example.) They are not so good ON THEIR OWN for determining how a specific trombone will sound.
...
Good luck with your quest quantifying tonal characterization!

Thanks for posting this. Interesting stuff.

Gross differences in the bell would be all I'm interested in, as we have ways of quantifying other aspects. Instruments are complex systems made of many parts. Really just looking at characterizing the bell, which it looks like your curves do just fine. They are essentially tracing the profile/shape of the bell. Looks like maybe I should be measuring at 5" rather than 7.25". Do you have any data comparing basses to tenors?

Using calipers to predict a horn's personality is like using a tape measure to predict a woman's personality.

I understand that you're kind of down on the whole idea, but sound is created by the vibrating air inside a cavity, and the size and shape of the cavity affects the sound. Dimensions affect shape. Can we predict the personality? No, but we can characterize some aspects of it.

Horns do have specs for a reason. You still have to play test an instrument to really understand how it sounds and responds, but specs get you in the ball park. We have a measure for bore, for mouthpieces, for venturi in a leadpipe, for bell flare diameter, bell thickness, why not some characterization for bell shape? All these other specs influence the sound, so does bell shape.

[boneagain]

... Do you have any data comparing basses to tenors?

Never got around to it. When I have time I may still do exactly that. I've been REALLY curious where on the curve my Bach 6 fits AND the Benge 190f.

[boneagain]

... but sound is created by the vibrating air inside a cavity, and the size and shape of the cavity affects the sound. Dimensions affect shape. Can we predict the personality? No, but we can characterize some aspects of it.

Horns do have specs for a reason. You still have to play test an instrument to really understand how it sounds and responds, but specs get you in the ball park. We have a measure for bore, for mouthpieces, for venturi in a leadpipe, for bell flare diameter, bell thickness, why not some characterization for bell shape? All these other specs influence the sound, so does bell shape.

The bell and the mouthpiece work together to overcome the fundamental behavior of a pipe closed at one end. In theory, such a tube plays only every other overtone. We get our "natural" overtone series by "compressing" these with the flare and cup shape. This makes it possible to not only reinforce all the "natural" tones in the series, but the harmonics of those tones. So, we would expect quite a lot of sound characterization from them.

I feel very grateful that the Benade worked so hard to make this stuff approachable by non-acousticians like me. I am also grateful for the incredible work by the Edinburgh guys and Alistair Braden. There are SO many ways to look at these things. But I don't think any of them are simple or likely to leave your brain any way other than tied in knots by the time you get through puzzling it out

[hyperbolica]

updated list.

Elkhart 88h = 1.65"
Olds Recording = 1.67"
79h = 1.63"
36B = 1.63"
Wessex supertenor = 1.95"
Kanstul 1662i = 2.07"
Holton tr159 = 1.69"
Olds Flugabone - 1.63"
48h = 1.62"
Yamaha 350c = 1.68"

measurement setup:

measure.jpg

[elmsandr]

Nice!

So, I did not record my measurements this weekend; they weren’t accurate enough to bother to draft. BUT I did spend some quality time with calipers on 3 Bach 45 flares. If I started the comparison at a common point near the T.S. Ferrule, about 8” farther down I had a difference of about 0.010”, or just enough to be reliably ‘different’. Then at similar points another 4” down or so, below where you are measuring here, what I would more call the middle of the throat, one of them opened up sooner, difference jumped to 0.020” and increased from there as you transition to the flare greatly there.

Back on topic a bit, I would be more interested in diameters from a known gauge line, that is; what is size and rate of change say an inch above and below 2.0”? (Or 1.75”, whatever value makes sense to compare). The rate of change is pretty important to see as well as the absolute values. Always the pain in trying to characterize the differences.

Cheers,
Andy

[ithinknot]

Back on topic a bit, I would be more interested in diameters from a known gauge line, that is; what is size and rate of change say an inch above and below 2.0”? (Or 1.75”, whatever value makes sense to compare). The rate of change is pretty important to see as well as the absolute values. Always the pain in trying to characterize the differences.

And that way you're not misled by flares made to the same pattern but spun out to different diameters. (The method above would give a 36/42 difference, for example.) Distance from the ferrule would avoid that particular trap, but still be misleading given the range of bell lengths out there. It's complicated.

[hyperbolica]

Elkhart 88h = 1.65"
Olds Recording = 1.67"
79h = 1.63"
36B = 1.63"
Wessex supertenor = 1.95"
Kanstul 1662i = 2.07"
Holton tr159 = 1.69"
Olds Flugabone - 1.63"
48h = 1.62"
Yamaha 350c = 1.68"

conn 32h - 1.56"
yamaha ysl455 - 1.60"

[hyperbolica]

I reordered the instruments by measurement, and there's a correlation that makes intuitive sense. Two measurements would be better.

Kanstul 1662i = 2.07"
Wessex supertenor = 1.95"
King 1480 = 1.81"
Holton tr159 = 1.69"
Yamaha 350c = 1.68"
Olds Recording = 1.67"
Elkhart 88h = 1.65"
79h = 1.63"
36B = 1.63"
Olds Flugabone - 1.63"
48h = 1.62"
Getzen 3508r = 1.62"
yamaha ysl455 - 1.60"
conn 32h - 1.56"