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Valve Circuit Lengths

Postby Mike-ICR » Wed Jul 22, 2009 10:32 am

I don't know if it exists, but I'm looking for a mathematical equation/book/online resource/chart that can help me determine valve circuit lengths for various bore sizes and keys. I've used the rubber hose method so far but it's just not practical in the long run. I've also taken many measurements from other horns over the years but there are a lot of holes and gray areas in the research. Is there such a thing? Is it all guess work?
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Re: Valve Circuit Lengths

Postby Dan Schultz » Wed Jul 22, 2009 11:07 am

Mike-ICR wrote:I don't know if it exists, but I'm looking for a mathematical equation/book/online resource/chart that can help me determine valve circuit lengths for various bore sizes and keys. I've used the rubber hose method so far but it's just not practical in the long run. I've also taken many measurements from other horns over the years but there are a lot of holes and gray areas in the research. Is there such a thing? Is it all guess work?


Bore size has little to do with the pitch that results from a certain length of tubing.

On an old computer that crashed last last year... I had a program that would give you the tube length for any frequency (or note) that you desired. I think I got the program from someone here on TubeNet. It's gotta be somewhere on the Web. I'll root around a bit. Maybe the 'donor' will pop up.
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Re: Valve Circuit Lengths

Postby The Big Ben » Wed Jul 22, 2009 11:18 am

Art Hovey has the Excel template which computes those lengths:

http://galvanizedjazz.com/tuba.html
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Re: Valve Circuit Lengths

Postby Mike-ICR » Wed Jul 22, 2009 2:41 pm

Thanks, guys. These sound like good starting points. Art's page is very interesting.

Dan; are you saying, for example, that the length of the 1st valve circuit on a BBb tuba with a .750" bore is the same (or close to it) as one with a .687" bore? I'm not sure I understand.

For example: Let's say I want to build a Bb bass trumpet using a trumpet valve section. I can find the parts and build it to play in Bb but how do I determine the slide lengths? Obviously the original trumpet slides won't work, and I can't imagine that a 1st valve circuit measurement from another tenor voiced instrument would tell me the new length because the bore would be around .60" smaller. I know how to calculate slide length when I already have an existing slide to start with. I mean, I could calculate the lengths and add a 1st, 2nd, and 4th slide to a horn that already has a 3rd (or a measurement for one).
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Re: Valve Circuit Lengths

Postby Tuba Guy » Wed Jul 22, 2009 2:59 pm

Ok...I would suggest a graphing calculator (or freeware, if they have it)
The equation I use is
Y=N/(2^x/12)
N is the original legnth of the tubing
X is the number of semitones higher that you want to go
I wrote a program for the calc to get it to that point where you just enter "original legnth=" and "number of semitones raised" (though my calculator is packed up somewhere)
I wanted to get it to the point where you put in the key of the horn and the key you want it in, and it does it for you, but...well, school was over by that point...and we were working in 3d, so i actually needed to pay attention.
For figuring out the valve legnths, x would be -1 for the 2nd valve (i'm pretty sure...check these numbers to make sure they seem logical), -2 for the 1st valve, -3 for the 3rd valve, and -5 for the 4th valve
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Re: Valve Circuit Lengths

Postby Dan Schultz » Wed Jul 22, 2009 10:10 pm

Mike-ICR wrote:Thanks, guys. These sound like good starting points. Art's page is very interesting.

Dan; are you saying, for example, that the length of the 1st valve circuit on a BBb tuba with a .750" bore is the same (or close to it) as one with a .687" bore? I'm not sure I understand.

For example: Let's say I want to build a Bb bass trumpet using a trumpet valve section. I can find the parts and build it to play in Bb but how do I determine the slide lengths? Obviously the original trumpet slides won't work, and I can't imagine that a 1st valve circuit measurement from another tenor voiced instrument would tell me the new length because the bore would be around .60" smaller. I know how to calculate slide length when I already have an existing slide to start with. I mean, I could calculate the lengths and add a 1st, 2nd, and 4th slide to a horn that already has a 3rd (or a measurement for one).


I don't think the bore size makes much difference. the length of the 1st valve circuit with a .750" bore should be the same as one with a .687" bore.

For that bass trumpet in Bb.... it should be pitched the same as a baritone in Bb. All of the tubing lengths will be twice the length of a trumpet. Trumpet = approx. 4.5 feet of open bugle. Baritone or trombone = Approx. 9 feet of open bugle. BBb tuba = approx. 18 feet of open bugle. The valve circuits can be determined by using ratios of those dimensions.

I've seen a program that will give you the open pipe for any given frequency but I can seem to find it again. I had it on an old computer. That program worked fine for determining straight tubing. Those calculations go out the window for conical sections and bells. The 'hose method' you are using is about a scientific as you can get. You can always start long and trim it until you get the desired pitch. I approach brass the same way. Leave it a little long. Trim the valve circuit until you get what you want... and then trim a little more to cover yourself to keep from being flat due to weather conditions. Basically.... the very best 'scientific' approach is called prototyping. Computers and calculators are great but they aren't the whole answer.

This may be some useful information:

BBb Tuba 18 ft. open pipe
CC Tuba 16 ft. open pipe
F Tuba 12 ft. open pipe
Eb Tuba 13.5 ft. open pipe
Bb Euph/Tenor Trombone - 9 ft. open pipe
Bb trumpet/cornet - 4.5 ft. open pipe

Tuba tuning circuit lengths:
Valve tubing lengths:
F
1st valve = 18"
2nd valve = 8"
3rd valve = 27"
4th valve = 48"

Eb
1st valve = 20"
2nd valve = 9 1/2"
3rd valve = 29 1/2"
4th valve = 52"

CC
1st valve = 23.7"
2nd valve = 11.257"
3rd valve = 34.957"
4th valve = 61.62"

BBb
1st valve = 26.66"
2nd valve = 12.66"
3rd valve = 39.32"
4th valve = 69.32"
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Re: Valve Circuit Lengths

Postby sloan » Wed Jul 22, 2009 11:01 pm

Exercise: measure a *real*, *existing* tuba that plays in reasonably good tune with itself. Measure all of the valve-slide tube lengths. Use the formula provided above to determine the length of the bugle. Measure the length of the bugle.

Questions:

a) are the valve-slide tube lengths *consistent* with each other (that is, do they predict the same length
for the bugle?
b) does the predicted length of the bugle come anywhere near matching your computed value?
c) do you have a hacksaw handy?
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Re: Valve Circuit Lengths

Postby Dan Schultz » Wed Jul 22, 2009 11:58 pm

Searching for the calculator I mentioned earlier... I found this:

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/opecol.html

I found it interesting that when I plugged the number 58 into the F2 slot on the template... the result is just about 18'.... the length of a BBb tuba open bugle. 58hz is the frequency of the BBb below the bass clef staff. The table is metric. You'll have to do you own conversions... 1 meter = 39.37"
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Re: Valve Circuit Lengths

Postby sloan » Thu Jul 23, 2009 9:52 am

TubaTinker wrote: Computers and calculators are great but they aren't the whole answer.


They aren't the whole answer because the models we use (and hence the questions we ask of the computers and calculators) are gross approximations. As long as you realize that the calculations based on an approximate model will only give approximate answers (and are prepared to tweak during prototyping) then all is well. The difficulties start when someone is given the calculation and *believes* it...to 5 decimal places.

For example - several people have cited: "CC = 16 ft bugle". Well, guess what? A CC tuba does not have a "CC bugle"! But, "16ft" is more correct than "100ft", or "10ft". What you *can* do is (for example) measure the 2nd valve tubing and figure out how long the open bugle *would be* IF your simple model were correct. Whether you can then use that information to correctly calculate the lengths of the other valve tubing is an interesting question - to answer that question I recommend measurement rather than calculation. Perhaps someone will take up my suggestion (the "Exercise" in a previous post) and post the results?

I know it's difficult, and tedious - but it's instructive to actually *measure* a working example. Of a tuba, not an organ pipe.

but...have faith - the day is in sight when computer power will be adequate to work with a *much* more complicated model of brass instruments. It will require a fundamental change in the models used (to the point where people will not be able to do anything useful on the back of an envelope, alas) - but it will be worth it.
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Re: Valve Circuit Lengths

Postby iiipopes » Thu Jul 23, 2009 9:57 am

#@!! I saw this thread yesterday, but I had to go and got beat to posting the [2^(n/12) X B] - B formula for computing "theoretical" circuit lengths.

Now here's the fun part: the valves have displacement. That must be factored in. We also pull, and sometimes push, for certain notes. That has to be factored in.

Depending on the throat and bell of the tuba, sometimes it's @ 18 feet, other times, 220 inches is closer. The rule of thumb used by Rusk and others was to cut 24 inches off the bugle to turn a BBb into a C. Think about it: that would be the theoretical length of the 1st valve circuit on a CC tuba, and you can go from there.
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Re: Valve Circuit Lengths

Postby Dan Schultz » Thu Jul 23, 2009 10:04 am

sloan wrote:
TubaTinker wrote: Computers and calculators are great but they aren't the whole answer.


They aren't the whole answer because the models we use (and hence the questions we ask of the computers and calculators) are gross approximations. ..... but...have faith - the day is in sight when computer power will be adequate to work with a *much* more complicated model of brass instruments. ....


Generating musical instruments completely from solid computer models is a lofty goal. It's true that software has come a long way in the field of acoustics. However... I don't think it will ever replace the need for prototyping. Simply measuring a tuba and attempting to reproduce it... no matter how accurately... does not fly, either. The Chinese (who are VERY good at copying just about anything) have already taught us that simply copying a horn doesn't work very well.
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Re: Valve Circuit Lengths

Postby Mike-ICR » Thu Jul 23, 2009 10:45 am

TubaTinker wrote:For that bass trumpet in Bb.... it should be pitched the same as a baritone in Bb. All of the tubing lengths will be twice the length of a trumpet. Trumpet = approx. 4.5 feet of open bugle. Baritone or trombone = Approx. 9 feet of open bugle. BBb tuba = approx. 18 feet of open bugle. The valve circuits can be determined by using ratios of those dimensions.

This may be some useful information:

BBb Tuba 18 ft. open pipe
CC Tuba 16 ft. open pipe
F Tuba 12 ft. open pipe
Eb Tuba 13.5 ft. open pipe
Bb Euph/Tenor Trombone - 9 ft. open pipe
Bb trumpet/cornet - 4.5 ft. open pipe

Tuba tuning circuit lengths:
Valve tubing lengths:
F
1st valve = 18"
2nd valve = 8"
3rd valve = 27"
4th valve = 48"

Eb
1st valve = 20"
2nd valve = 9 1/2"
3rd valve = 29 1/2"
4th valve = 52"

CC
1st valve = 23.7"
2nd valve = 11.257"
3rd valve = 34.957"
4th valve = 61.62"

BBb
1st valve = 26.66"
2nd valve = 12.66"
3rd valve = 39.32"
4th valve = 69.32"


TubaTinker wrote:Searching for the calculator I mentioned earlier... I found this:

http://hyperphysics.phy-astr.gsu.edu/hb ... pecol.html

I found it interesting that when I plugged the number 58 into the F2 slot on the template... the result is just about 18'.... the length of a BBb tuba open bugle. 58hz is the frequency of the BBb below the bass clef staff. The table is metric. You'll have to do you own conversions... 1 meter = 39.37"


Things are starting to make much more sense now. Especially the trumpet to bass trumpet concept. The side by side comparison of bugle length to valve circuit length is also a tremendous eye opener. Thanks a lot for getting the ball rolling!

I realize there is no replacement for prototyping. The trouble is that I rarely build the same horn or even use the same parts more than a few times. I know that I could never eliminate all of the guess work. It's a matter of getting 'close enough' from the start in order to save time overall.
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Re: Valve Circuit Lengths

Postby sloan » Thu Jul 23, 2009 11:20 am

TubaTinker wrote:
sloan wrote:
TubaTinker wrote: Computers and calculators are great but they aren't the whole answer.


They aren't the whole answer because the models we use (and hence the questions we ask of the computers and calculators) are gross approximations. ..... but...have faith - the day is in sight when computer power will be adequate to work with a *much* more complicated model of brass instruments. ....


Generating musical instruments completely from solid computer models is a lofty goal. It's true that software has come a long way in the field of acoustics. However... I don't think it will ever replace the need for prototyping. Simply measuring a tuba and attempting to reproduce it... no matter how accurately... does not fly, either. The Chinese (who are VERY good at copying just about anything) have already taught us that simply copying a horn doesn't work very well.


The trick, of course, is knowing what to copy.

And how to tweak.

I wouldn't be so sure about the "loftiness" of the goal. As always - the capability is already there. The main question is the cost. Over the past 50 years, most of the big winners in computer technology have gotten there by guessing high (compared to the competition) about what will be possible in the near future.

Measuring is clearly not sufficient - but it's a damn sight closer than a very simplified formula based on a high-school physics model of reality. In both cases, you *must* understand that the first step only gets you into the right ballpark.

Of course, I agree that "measuring" the bugle is a hopeless idea. There are two major problems with it: first, it's not clear what to measure, and second, it's not clear what to do with the answer once you have it.

Nevertheless, I recommend that anyone interested in this topic actually try to do the measurements I gave AT LEAST ONCE. And then think about the results.

I do NOT recommend cutting and bending based on these measurements (unless you are prepared for considerable tweaking, with a good set of ears handy).

Nor do I think that future computer modeling will remove the need for tweaking. What I do believe is that modeling can minimize the defects FOR WHICH WE HAVE NO GOOD MODEL FOR TWEAKING. Think about the things the player can do to change tuning and sound. Now think about the things a repairman can tweak by taking things apart and putting the same parts back together. There are still issues that are "cast in brass" by the shape of the parts. THOSE are the issues that I think can be minimized by detailed computer modeling. In the past, these issues have been (slowly) attacked by prototyping. Computer modeling has the potential to make faster progress in the prototyping stage. It won't reduce the need for careful assembly, or properly setting the default settings for the valve slides, or the need to push and pull (depending on your standards).
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Re: Valve Circuit Lengths

Postby bloke » Thu Jul 23, 2009 11:33 am

The first tuba (that I know of) that was designed on a computer was the Phillips model Holton (yawn).

As I've made a few tubas out of other tubas, when I'm in the middle of such a process (before undoing, moving, or cutting anything), I find myself starring at that part of the instrument often (literally) for hours. When I'm building a tuba out of reclaimed parts (etc.), until my "mind's eye" has a complete "picture" of what I'm about to do (often, in my mind, pictured accurately down to 1/100 of an inch, and - when actually fabricated - down to 1-2/1000's of an inch), I don't do it.

I guess that's much of the reason why I procrastinate so much when it comes to starting on one of these projects (as I have several waiting to be done that should prove to be successful ventures) and why I flatly refuse to take on such projects for customers...I just don't care to do any less than my best on such projects and - typically - my "best" involves around 250 or more hours of work.
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Re: Valve Circuit Lengths

Postby windshieldbug » Thu Jul 23, 2009 5:50 pm

Measuring only gets you in the ballpark. To somebody's solution to the physical problems.

We know that 3 valves don't cut it when you start adding valve lengths together.
Compensating systems aren't perfect, either.

And then there's the physics of overtones. A few of which aren't in tune.
And then there's the matter of temperament. Well-tempered, pure, "stretch", etc. etc.

Basic brass acoustical modeling isn't a walk in the park even if you DO have the computational power... :shock:
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Re: Valve Circuit Lengths

Postby GPT » Thu Jul 23, 2009 6:13 pm

windshieldbug wrote:And then there's the physics of overtones. A few of which aren't in tune.
And then there's the matter of temperament. Well-tempered, pure, "stretch", etc. etc.

Basic brass acoustical modeling isn't a walk in the park even if you DO have the computational power... :shock:


That depends on your definition of `in tune'. It seems to me that most tubists like to have every partial equal-temperamentally tuned, which is why just or pure intonation is so hard. If everyone preferred to have their fifth harmonic a little bit flat, their seventh harmonic a great deal flat etc., pure intonation WOULD be a walk in the park. But I digress. :tuba:
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