Tech/maintenance A question for the math experts

[CliveMA]

Can you also measure the distance from the hinge to the inner edge of the tonehole?

If so, you can calculate B.

Tan of the hinge angle = ratio of opposite to adjacent
B/A = b/a where "a" is distance from hinge to middle of tonehole
Therefore B = (A x b)/a

and a = (D + A)/2 where D is distance to inner edge of tonehole.

E&OE

In above calculation
A is distance from hinge to outer edge of tone hole, not diameter of tone hole.

 

[CliveMA]

Why has original post changed? Where is the reference to making an additional measurement? Please clarify?

 

[CliveMA]

Why has original post changed? Where is the reference to making an additional measurement? Please clarify?

Ignore this post as I was looking at the wrong post.

 

[AlexAdams]

Assuming that you know A. Yes, not very complicated.

With d & b known, and the distance between d & b being half of A.

But, with domed resonators, the pad is not flat as you have drawn meaning this height becomes an additional variable. If the height of the dome is known, which becomes an additional variable, then an accurate enough figure for the purpose would be straightforward to calculate.

 

[AlexAdams]

I see A is actually hinge to edge of tone hole. If you know the diameter of the tone hole then yes you could calculate.

It's also important to note that any calculation needs to incorporate the fact the the hinge point is not inline with the top of the tone hole

 

[LostCircuits]

Pretty straightforward I would say. If you know b and A and the diameter of the tone hole you take A - 1/2 diameter of the tone hole to get a right triangle and from there you can calculate any of the wanted dimensions. That's 5th grade geometry using Pythagoras equation.

 

[LostCircuits]

#Hipparion: A:B = (A-1/2e):b (with e= tonehole diameter)
or A*b = B*(A-1/2e)
B= A*b/(A-1/2e)

 

[h4yn0nnym0u5e]

...but unfortunately, if you read the OP carefully (the diagram is a bit unclear) A is already the tone hole diameter, you don't have to invent e to be that. We figured out in July that it is not possible, let alone straightforward, to calculate what was wanted from available information. Sure, if you add the right information, it becomes possible.

But @AlexAdams makes the excellent point that in reality the pivot point may not lie in the plane of the tonehole (as the diagram implies), so we might end up needing even more information than we thought in July. None of which is available, because it wasn't recorded at the time, or has since been lost.

 

[LostCircuits]

...but unfortunately, if you read the OP carefully (the diagram is a bit unclear) A is already the tone hole diameter, you don't have to invent e to be that. We figured out in July that it is not possible, let alone straightforward, to calculate what was wanted from available information. Sure, if you add the right information, it becomes possible.

But @AlexAdams makes the excellent point that in reality the pivot point may not lie in the plane of the tonehole (as the diagram implies), so we might end up needing even more information than we thought in July. None of which is available, because it wasn't recorded at the time, or has since been lost.

You are correct, I misread that in the drawing. Let me go back and look at it again....
And yes, if only the average b and the tone hole diameter are known, then the information is not sufficient. Again, my bad for misreading OP's post and diagram

 

[jbtsax]

It is interesting to see this thread revived. I can see now how the original image could be a bit confusing. I have edited it as shown below. The values A and b are known. It is known that the value b is the average of B and d which are unknown. My original question was is there any way to find the value of B, the commonly defined key height?

 

[mizmar]

if it was meself that was going find the value of B, faith, I wouldn’t start from here.

 

[kevgermany]

My original question was is there any way to find the value of B, the commonly defined key height?

In short: No.
The thread went all over the place but the bottom line is that there's not enough information.
I'd guess that the reason for calculating the mid point height is that this is what's needed to establish the overall air column length for pitch calculations.

 

[Tenor Viol]

Have to agree, without knowing the distance to the pivot point and the angle you just don't have the required information.

 

[turf3]

Well, this begs the question - why are you looking up the data? Most people would be doing so in order to determine what values to use in setting their own keys.

In that case, if the tabulated data exist for your particular instrument, then you have the distance to the pivot point - just measure the instrument sitting on your lap! Now you can convert the "average" value to "max" value, using the actual measurements of the actual instrument.

In practice, the key height variation of stack keys is strictly limited by the key linkages and the need to reduce lost motion to a minimum. So once you set a particular key height, all the others will follow from that one with only minor variation allowed. Another constraint is the design of the key feet - if we assume the original design of the saxophone was roughly correct, and if things haven't gotten too badly bent up, key feet are designed to have about 1-2 mm of cork on them. If you find yourself stacking 6 mm of cork, or having to file down the feet, you're setting the key heights wrong.

Once you get the stack key heights set correctly, the side and palm key heights are mostly going to be duplications or extrapolations from that. You'll go and tweak them individually a bit to try to match tone or intonation.

So I'm not convinced that detailed analysis of tables of key heights is really all that useful in practice, maybe as an academic exercise, or if you're a saxophone designer contemplating a radically different mechanical design.

 

[Stephen Howard]

if we assume the original design of the saxophone was roughly correct, and if things haven't gotten too badly bent up, key feet are designed to have about 1-2 mm of cork on them. If you find yourself stacking 6 mm of cork, or having to file down the feet, you're setting the key heights wrong.

Quite common to see key feet with 4+mm of buffering from new (lower stack, at least). Typically it's split between cork on the key feet and felt on the body.

 

[jbtsax]

Well, this begs the question - why are you looking up the data? Most people would be doing so in order to determine what values to use in setting their own keys.

If you go back to the initial post in this thread, my reasoning will be made clear. M. Postma has gone to great lengths to measure and record the specs of different makes and models through the years which gives us a wonderful historical record of the evolution of the design of the instrument. The key heights as he found them on each saxophone were given as the average of the opening at the front and the back of each key. I was hoping there might be a way to convert those figures to the front opening we commonly use today so we could compare with instruments we have now.

 

[turf3]

It would be easier to convert measurements for current instruments to the average opening value.

The average opening is actually the more acoustically important value and it takes the arm length out of the equation, so if you're looking to compare venting amongst instruments of various eras, comparing average values will be the way to go.

 

[jbtsax]

It would be easier to convert measurements for current instruments to the average opening value.

Kind of "reverse engineering". I hadn't though of that but it would require a tremendous amount of work.

The average opening is actually the more acoustically important value and it takes the arm length out of the equation.

Do you have any reference in acoustic literature to support this claim? The only information I have been able to find is in "acoustical aspects of woodwind instruments" by Nederveen where he cites a study by Benade that calculates the increase in a woodwind tonehole's "end correction" due to a disk hanging above a tonehole. An increase in the "end correction" lengthens a notes wavelength thereby lowering the frequency or pitch.

The attached file below shows some calculations I made using Benade's formula and the graph from Nederveen's book which supports the "rule of thumb" key opening (at the front of the key) of at least 1/3 of the diameter of the tonehole to have no effect upon the pitch.

 

[mizmar]

I was also curious. I'd'v thought the interesting thing would be the closest distance between tone hole and cap... Assuming, on the one hand, that beyond a certain distance it makes no difference; and on the other hand on open tone hole instruments half closed make holes a lot of difference.
But given that the geometry is quite constrained, d, b and B are likely strongly correlated..