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Hi all,

I have a Miraphone Hagen 6/4 Bb which are tuned at 443 Hz but equiped with a main tuning slide for 440 Hz.
Right now I test different mouthpieces to find which is best in tune for me, and to do this testing as good as possible I like to pull the different valve slides so they all are in tune at 440 Hz.
Any one know how much I teoretical needs to pull out each slide ?

Did you try the mouthpiece that originally comes with the Hagen, the Miraphone TU43 ? It is very deep with a huge bore, so maybe can help lowered the pitch. It is also surprisingly easy to control for the size.

If I can help any here, the way I understood the post, Erik has no real problem playing in tune. So the subject may be a little misleading.

What I think he's looking for here, is sort of like the "factory default settings", so that while he tests various mouthpieces, he's testing them against the vanilla tuba that ought to play at A=440, not against whatever adaptations he's already made to accommodate his current mouthpiece.

I salute his fastidiously scientific approach, and I hope we hear more about his findings, but I slightly doubt that the question has a known answer. The issue around the 443/440 tunings wasn't real clear to me, but I assume that it by itself doesn't give us any clue to the tuning settings, and really only someone thoroughly acquainted with an instrument exactly like it would be in any position to help. Our only hope may be that among the Germans at the factory, there are one or two with that same meticulous attention to matters like this.

Donn is correct. I'm an engineer (with a tuba built for 443 Hz, but here where I live all play at 440 Hz).
I have a main tuning slide (from factory) for 440 Hz.

I like to find which of my mouthpieces that gives best intonation.
To do this test as good as possible I like to have a 440 Hz starting point for all valves. This is the reason I like to know how much to pull.

My thinking is like this: when the engineers designed the tuba everything was optimized to give best performance at 443 Hz.

Now I adjust the tuba to 440 Hz which means I move away from the intended design. This may not be a big thing but if all valve slides are adjusted from 443 to 440 Hz I am as close I can get to the intended design.

My belief is that the sound maximum is at design Point. Next step is to try to find a mouthpiece that take me as close to this (I see it as a curve (Excel)) as possible. After that I will practise till I learn to play in tune with this set up.

I fully realise this may be an odd method but for me it is the most natural way to do it.

Erik_Sweden wrote:Now I adjust the tuba to 440 Hz which means I move away from the intended design. This may not be a big thing but if all valve slides are adjusted from 443 to 440 Hz I am as close I can get to the intended design.

Do you know where the slides would be set, for A=443? I would assume not - that there's no dead-on factory setting - but if there is, then it's a simple problem to calculate the difference for A=440. Decide what ratio the slide must have to the bugle length, and apply the 443/440 ratio to that (I'm no whiz at this, so check my reasoning that the ratio between frequencies is the same as the ratio between wavelengths.) The first part is where the thinking is needed, I'd look for a table of notes and frequencies for reference. Go ahead and use note pitches even though a tuba player would normally adjust valves slightly flatter for combinations -- the difference won't make any difference, as you're working with absurdly small values anyway.

I expect if that made any sense, you would have already worked it out, but ... maybe I'm just confused by why the A=443 thing matters here. Anyway, if you can find a mouthpiece that plays better in tune on all the "open" notes, I'm confident it will hold its advantage on valve notes as well - and if it doesn't, it will be for reasons that invalidate your premise anyway.

If you do your intonation tests at the same temperature as the factory used when tuning your tuba then the below calc will work.

To lower a tuba from A=443Hz to A=440Hz you have to add ((443/440)-1) x The Theoretical Length of that Tuba. The theoretical length because the real length is shorter due to the effect of the bell flare.

((443/440)-1) is very close to 0.682% (0.6818181818 with 18 continuing endlessly).

To lower a given valve from A=443Hz to A=440Hz you have to add 0.682% of the real length of that given valve tubing, which is the length of the visible valve tubing plus the length of one passage through the piston or the rotor. You will have to pull the slide half of the calculated length.

Maybe except for the 4th valve we are talking next to insignificant lengths, which will be really insignificant compared to incalculable effects of the turbulences created by pulling the slides.

If you can measure the exact difference in length of the 443Hz and the 440Hz main slide branches, then let us call that difference Y. And let us call the (12th root of 2) Z.

Then the 2nd slide shall be pulled by Y*(Z-1)

The 1st slide shall be pulled by Y*((Z high 2)-1)

The 3rd slide shall be pulled by Y*((Z high 3)-1)

The 4th slide shall be pulled by Y*((Z high 5)-1)

The 5th valve shall be pulled by Y*((Z high 7)-(Z high 5))

I don’t know math and tech English, but I know the mat.

Klaus

Use your ears, minimize the beats. The overtone series is not in tune with a well-tempered system, so no equation will adequately work.

lost wrote:The factory settings on my horns are ignored in place of sitting down with a tuner.

You have factory settings? Is the inner slide marked with a scratch ring or something? That's very interesting, I just didn't know there was such a thing.

windshieldbug wrote:Use your ears, minimize the beats. The overtone series is not in tune with a well-tempered system, so no equation will adequately work.

I totally agree as said with other words in my posting. Only wanted to show that if the engineering approach was preferred, then the math is absolutely doable. I use Excel.

The intervals that should be in tune with a tuner are the open octaves. Preferably also the open fifths. The rest has to be managed otherwise. My main tool for that is refingering.

Klaus

That shouldn't be confused with a factory setting, i.e. reference tuning position. An instrument that did play A=440 that way would have an obvious tuning problem.

Based on Klaus post I get following result:
For a 440 Hz main tuning slide with a extra lenght of 40 mm (20 mm pull) I get following needed slide pulls:
1st: 1.3 mm
2nd: 1.2 mm
3rd: 1.4 mm
4th: 1.6 mm

Erik_Sweden wrote:Based on Klaus post I get following result:
For a 440 Hz main tuning slide with a extra lenght of 40 mm (20 mm pull) I get following needed slide pulls:
1st: 1.3 mm
2nd: 1.2 mm
3rd: 1.4 mm
4th: 1.6 mm

Aside from the length for the 2nd valve those numbers obviously are wrong and don’t represent an understanding of the formula I set up. That formula expresses the math behind the equal temperature tuning system. High 2 means ’i 2. potens’ in my language.

With 3 spaces behin the dot the pulling lengths are:

1st: 1.189 mm
2nd: 2.449 mm
3rd: 3.784 mm
4th: 6.697 mm

The dimensions may, at least for the 1st, 3rd, and 4th valves, be checked by the equalent Pythagorean pulls, which would be 1/8, 1/5, and ⅓ respectively of the main tuning additional pull of 20mm.

Klaus

Based on Klaus post I get following result:
For a 440 Hz main tuning slide with a extra lenght of 40 mm (20 mm pull) I get following needed slide pulls:
1st: 1.3 mm
2nd: 1.2 mm
3rd: 1.4 mm
4th: 1.6 mm

Combined with:

You have factory settings? Is the inner slide marked with a scratch ring or something? That's very interesting, I just didn't know there was such a thing.

Miraphone designs their tubas so that SOME slide pull is needed on all the slides to get the horn "tuned up". The advantage of having a slide such as the easy to reach 1st valve slide out a bit for most notes, means that you can push the slide in while playing to raise the pitch of some flat notes to bring them in-tune.

Since even the artist who helped them designed that particular tuba never feels the same two days in a row and never has the exact same environmental situation to play in two days in a row, at some point a real person has to..................

ADJUST THE SLIDES A BIT AND THEN PLAY THE D**N THING TO THE BEST OF THEIR ABILITY THAT DAY.

Set your main tuning slide so that the Bb's are in tune.
Set your second slide so that "A's" are in tune or 2-3 cents flat.
Set your 1st slide so that "Eb's" are in tune. Check the "Ab's" and decide to personal taste if you want to set the slides so that you split the difference.
Set your 3rd slide so that the "Db's" played 2&3 are in tune. You'll play more Db's than Gb's.
Set the 4th slide so that the "C" below the staff is in-tune.

After you set up a 4 valve BBb tuba like I suggest above, you are ready to "man-up" and play it. Now you can compare your mouthpieces to see which gets you the most (warm fuzzy feelings, sound, good intonation, compliments, sweet smelling beath, etc.) whatever you are looking for.

There is no math formula that will bypass the fact humans can screw up anything.

You are correct Klaus. I hade my serie: 2^(1/12), 2^(1/11)... but correct is 2^(1/12), 2^(2/12)... I also had 4th as 4 semi tones but it is of course 5

You are also correct Matt. In the end it up to my playing. I was just curios about the theoretical pull

Hello Erik,
Matt's answer is the science you are seeking. Comments in this thread are in basic agreement, apart from the choice of terms used to describe it.
As for the science of pitch: You are blowing into something cooler than you are. The pitch is changing every time your breath warms the instrument (constantly).

A research scientist I know plays horn and gave me an elegant description of the temperature effect. Still, not a person says, "let's tune, who has the thermometer?". Or, "who has the ruler?"

swillafew wrote:A research scientist I know plays horn and gave me an elegant description of the temperature effect.

Since I just happened across this recently - The Effect of Temperature Changes on a Brass Instrument, thanks to Art Hovey. I'm going to assume that it's valid.

I don't think any of this really addresses the point, though. He was not looking for a way to play his tuba better in tune. He is concerned with this aspect of his mouthpiece selection, though, and while evaluating the mouthpieces he wants to return the tuba to a "vanilla" tuning that ought to play in tune under ideal conditions. That way he can recognize the ideal mouthpiece when it comes along. You don't have to agree that this is worth thinking about, but that's the idea, as I understand it.

I don't think any of this really addresses the point, though

The one who addresses the question is Matt. The question in the post is "how far should the slides be pulled to match the main slide". The answer is, start pulling and see what works. It's not an equation, it's a horn that is changing from moment to moment, the air inside not even being equal temperature from one end to the other. As musicians we function without the math.

swillafew wrote:As musicians we function without the math.

I don't think Erik intends to use math to play, either, but it applies fairly well to what he was trying to do.

Hell, everybody is overthinking this: pull the 2nd valve slide a hair. Pull the 1st valve slide two hairs or a smidgen Actually, pull it so Eb and Ab are in tune. If 3rd space C is flat, figure out how flat and have the outer tubes shortened this amount so that you can push for C and leave it out a proper amount for Eb and Ab. Pull the 3rd valve slide 3 about half what the tuning slide needs to be pulled out to tune to 440 at room temperature. the 4th valve slide is probably too short anyway and needs to be pulled a significant amount, whether 440 or 443.

On all the tubas I have played, everything has needed to be pulled, from a hair to almost the length of the adjustment, whatever pitch was being played. This is especially so on 3-valve instruments, where 3rd has to be pulled to get 2+3 in tune, or play a hair flat, so 1+3 is lippable, if the 1st can't be pulled.