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Conicity

Postby Z-Tuba Dude » Wed Oct 31, 2018 7:51 am

Hey folks,

I am curious about the issue of conical design for tuba/euphonium/horn.

I know that no brass instrument is purely conical (or cylindrical, for that matter). The valve sections on most conical instruments are made up of cylindrical tubing. It is really what happens before and after the valve section, that defines these instruments as conical.

I am primarily interested in how the horn design compares to that of tuba and euphonium. It seems to me that horn is overall, a little more cylindrical that either the euphonium, or the tuba.

Can anyone with detailed knowledge on the subject, point me toward information that can enlighten me?

Thank you!
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Re: Conicity

Postby timothy42b » Wed Oct 31, 2018 11:38 am

Z-Tuba Dude wrote:I am primarily interested in how the horn design compares to that of tuba and euphonium. It seems to me that horn is overall, a little more cylindrical that either the euphonium, or the tuba.

Can anyone with detailed knowledge on the subject, point me toward information that can enlighten me?

Thank you!


Sure.

https://www.amazon.com/Fundamentals-Mus ... B008TVF9C6

Interlibrary loan is your friend, if in the US.
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Re: Conicity

Postby timothy42b » Wed Oct 31, 2018 11:39 am

PS probably want to brush up on Bessel functions.
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Re: Conicity

Postby Z-Tuba Dude » Wed Oct 31, 2018 1:34 pm

Thank you for that info.

To be clear, what I am curious about is whether anyone knows anything about the ratio of cylindrical tubing to conical tubing in horn design, compared to euphoniums and/or tubas.
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Re: Conicity

Postby iiipopes » Wed Oct 31, 2018 5:18 pm

Here's a start. It doesn't say how much of either makes a good tuba, but it does explain why cornets sound different from trumpets, along with the reasons for bell flares, etc.
https://acousticstoday.org/wp-content/u ... /Brass.pdf
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Re: Conicity

Postby UncleBeer » Wed Oct 31, 2018 6:52 pm

Z-Tuba Dude wrote:I am primarily interested in how the horn design compares to that of tuba and euphonium.


Might be helpful if you specify "french horn" if that's what you mean, since we all refer to our instruments as "horns". Do you mean french horn?
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Re: Conicity

Postby Z-Tuba Dude » Thu Nov 08, 2018 10:25 pm

Yes, I meant "French horn".

Thanks!
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Re: Conicity

Postby timothy42b » Fri Nov 09, 2018 8:37 am

Without looking up the numbers, a French horn must have a fixed conical length (after the valves and cylindrical tubing) and a variable length of cylindrical tubing.

On the Bb side with no valves, it's probably about 9 feet. F side with all valves down, what, about 16-18 feet? So, which ratio do you want?
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Re: Conicity

Postby iiipopes » Fri Nov 09, 2018 4:30 pm

timothy42b wrote:F side with all valves down, what, about 16-18 feet? So, which ratio do you want?

12 feet. Same as an F tuba.
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Re: Conicity

Postby Levaix » Fri Nov 09, 2018 6:54 pm

As a layman with no technical brass design experience, it seems abundantly obvious from even just looking at a horn that it is significantly more cylindrical than a tuba... It really only flares out at the bell.
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Re: Conicity

Postby timothy42b » Sat Nov 10, 2018 8:36 am

iiipopes wrote:
timothy42b wrote:F side with all valves down, what, about 16-18 feet? So, which ratio do you want?

12 feet. Same as an F tuba.


No, wait. Isn't the F side longer, like the F side on a trombone? So with no valves, it would be 12 feet, and each valve would add tubing. Am I not thinking of this right?

There are triple french horns, with a low F and a high F surrounding the Bb side, but a double horn only has the low.
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Re: Conicity

Postby the elephant » Sat Nov 10, 2018 8:55 am

A horn in F is a little longer than 12 feet (the skinny bore adds to the length by about six inches compared with most F tubas). The Bb side is a bit longer than 9 feet (same skinny tubing). A trombone is about nine feet and a euphonium is about three inches shorter than a peashooter straight trombone because it has fatter tubing.

A descant horn is the same length as a mellophone, which is an octave higher than a horn in F. A triple horn is a double horn with the descant side added, so the three "sides" mellophone, trombone, F tuba lengths, more or less.

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Re: Conicity

Postby iiipopes » Sat Nov 10, 2018 10:02 am

timothy42b wrote:
iiipopes wrote:
timothy42b wrote:F side with all valves down, what, about 16-18 feet? So, which ratio do you want?

12 feet. Same as an F tuba.


No, wait. Isn't the F side longer, like the F side on a trombone? So with no valves, it would be 12 feet, and each valve would add tubing. Am I not thinking of this right?

There are triple french horns, with a low F and a high F surrounding the Bb side, but a double horn only has the low.

@12 feet would be the open bugle on the F side, same as a single horn. Then add length of bugle multiplied by 2^(n/12) to get the total length of the horn with any particular valve pushed, with n=2 for first valve, n=1 for second valve, n=4 for 3rd valve.
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Re: Conicity

Postby timothy42b » Sat Nov 10, 2018 6:05 pm

iiipopes wrote:@12 feet would be the open bugle on the F side, same as a single horn. Then add length of bugle multiplied by 2^(n/12) to get the total length of the horn with any particular valve pushed, with n=2 for first valve, n=1 for second valve, n=4 for 3rd valve.


Yes, I agree. There's no reason to make a compensating horn, right? because you can adjust pitch with your hand?

And my point is that the ratio of conical to cylindrical changes every time you move a valve.
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Re: Conicity

Postby TheGoyWonder » Sun Nov 11, 2018 4:19 pm

faster expansion of tubing = more conical.
so YES, French horns are not so conical because they are long and not very fat. except near the bell.
are cornets more conical that trumpets? they'd have to be fatter somewhere. I guess they are, but I couldn't tell you where.

there's overall shape, and there's leadpipe shape. Because cornets and french horns have SKINNY leadpipe openings, they have significant expansion of tubing along their leadpipes.

So when you talk "conical vs cylindrical", it isn't all hokum, you just have to specify WHERE on the horn you are talking about.
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Re: Conicity

Postby timothy42b » Mon Nov 12, 2018 8:15 am

Well, another complication to add, bends.
To air flow, a sharp curve in a tube adds resistance. But to a sound wave, a sharp bend is the same as a widening of the tube.

So if you curl tubing more tightly, you have to allow for the widening at that point.
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Re: Conicity

Postby DonShirer » Mon Nov 12, 2018 6:51 pm

     In Art Benade's "Fundamentals of Musical Acousics" that Timothy mentioned, he notes that the French Horn bore (after the valves) approximates a Bessel Function with diameter given by d =B/(y-yo)^m. d is the diameter of the bore, y is the distance from the open end, and B and yo are "chosen to give proper diameters at the small and large ends". He says "French horn bells tend to have a value of the exponential power m in the range of 0.7 to 0.9". He includes an illustration showing how m affects the shape but I don't see a way to upload a photo here. I have a band rehearsal tonight and I'll ask the horn players if they have further info.
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