Conicity

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Z-Tuba Dude
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Conicity

Post by Z-Tuba Dude »

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

Post by timothy42b »

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" target="_blank

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

Post by timothy42b »

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

Post by Z-Tuba Dude »

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

Post by iiipopes »

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" target="_blank
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Re: Conicity

Post by UDELBR »

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

Post by Z-Tuba Dude »

Yes, I meant "French horn".

Thanks!
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Re: Conicity

Post by timothy42b »

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

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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

Post by Levaix »

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

Post by timothy42b »

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

Post by iiipopes »

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

Post by timothy42b »

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

Post by TheGoyWonder »

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

Post by timothy42b »

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

Post by DonShirer »

     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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