Tech/maintenance A question for the math experts

[jbtsax]

Marten Postma has complied and posted a great amount of data accumulated over many years concerning saxophones he has taken measurements of. The portion of his work that pertains to this post is located here: M. Postma Saxophones Go to "measurements", "holes, keys"

There is a lot of useful and interesting data compiled by the author, but for some unknown reason he chose to list key heights as the average of the distance from the top of the tonehole to the pad measured at both the front and back of the key. Repair techs always refer to key heights or key openings at the front of the key where the opening is the widest. This is where I could use some help. I have created the following illustration to clarify the issue. M. Postma has measured the distance from the top of the tonehole to the pad at locations (B) and (d) and then averaged them to find (b). In the data the value of "A" -- the tonehole diameter and "b" the average of the openings are known.

My question then: Is there a way mathematically to find the value of "B" with the known values of "A" and "b". Thanks

 

[Pete Thomas]

Is there a prize?

BTW thanks for buying the CD, or is there another Talcott in Springville with exceptionally good taste?

 

[h4yn0nnym0u5e]

No, sorry.

A is no help, all you know is B > b > d and b=(B+d)/2. And d is non-zero, because the pivot is where it is...

Cheers

Jonathan

 

[jbtsax]

Is there a prize?

BTW thanks for buying the CD, or is there another Talcott in Springville with exceptionally good taste?

Another chance not to win an iphone? 😉

Yes. My wife who had the good taste to marry me. 🙂

 

[BigMartin]

A and b aren't sufficient information, as @h4yn0nnym0u5e saidb, because they convey no information about the angle of the pad compred to the tonehole. I expect you coulod work it out if the knew the length of the key arm (ie ie how far is the pad form the pivot point.

 

[Pete Thomas]

I expect you coulod work it out if the knew the length of the key arm (ie ie how far is the pad form the pivot point.

It's a pad!!! There was me thinking it was a wheelie bin lid 🙂

Apologies to @h4yn0nnym0u5e and BigMartin who are actually being helpful!

 

[Pete Effamy]

Marten Postma has complied and posted a great amount of data accumulated over many years concerning saxophones he has taken measurements of. The portion of his work that pertains to this post is located here: M. Postma Saxophones Go to "measurements", "holes, keys"

There is a lot of useful and interesting data compiled by the author, but for some unknown reason he chose to list key heights as the average of the distance from the top of the tonehole to the pad measured at both the front and back of the key. Repair techs always refer to key heights or key openings at the front of the key where the opening is the widest. This is where I could use some help. I have created the following illustration to clarify the issue. M. Postma has measured the distance from the top of the tonehole to the pad at locations (B) and (d) and then averaged them to find (b). In the data the value of "A" -- the tonehole diameter and "b" the average of the openings are known.

My question then: Is there a way mathematically to find the value of "B" with the known values of "A" and "b". Thanks

View attachment 15054

My contribution only extends as far as - it’s wonderfully drawn..

 

[Jeanette]

It's a pad!!! There was me thinking it was a wheelie bin lid 🙂

Not sure they have wheelie bins in USA, trash cans I believe 🙂

Jx

 

[jbtsax]

A and b aren't sufficient information, as @h4yn0nnym0u5e saidb, because they convey no information about the angle of the pad compred to the tonehole. I expect you coulod work it out if the knew the length of the key arm (ie ie how far is the pad form the pivot point.

Thanks BigMartin. I was afraid of that. I can measure the distance of the "hinge" to the outer edge of the tonehole of the Mark VI I currently have on my bench and on a "parts" YAS-23 on the shelf. Perhaps this might provide enough "data" to sort of extrapolate the figures for other makes and models, at least enough to come close to the "B" measurements.

 

[Tenor Viol]

Bizarrely @jbtsax I was watching a maths video on a very similar subject the other evening... (I lead an exciting life...) and without knowing the angle or the length of the other side you are kind of stuffed. For this sort of problem you need 3 pieces of information, the length of the two sides and the included angle... or what you have plus both angles

 

[saxyjt]

The obvious formula to use would be A² + B² = C²

But you'd have to know C.

Very nice drawing though! 😉

 

[Colin the Bear]

Two old arabs...selling old horses...came away hurriedly...that's all I got. 😉

 

[CliveMA]

I can measure the distance of the "hinge" to the outer edge of the tonehole

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

 

[h4yn0nnym0u5e]

Can you also measure...

@jbtsax's original question was to do with working from the known / published data. The trouble is that the published information is insufficient, and relates to a large number of different instruments. Measuring a couple of examples (Mk VI and YAS-23), as he says, may allow exact result for those (within build variations), and reasonably good extrapolations for others.

Another approach might be simply to email Mr Postma and ask if he could also publish the extra measurements he must have made at the time...

 

[Morph]

As all the others have said I believe the answer is no...at least I currently can't see a way!

For right angle triangles there are generally two approach to find unknown angles and sides:

1) Pythagoras' theorem: If you have two known sides
2) Trigonometry: if you have one known side and one known angle.

So you need two bits of information about the triangle.

Another fact which may be useful is that the smaller right angle triangle (with "b" as the side), is mathematically similar (i.e. A scaled down version of) to the bigger right angle triangle (with "B" as the side)

 

[CliveMA]

@jbtsax's original question was to do with working from the known / published data. The trouble is that the published information is insufficient, and relates to a large number of different instruments. Measuring a couple of examples (Mk VI and YAS-23), as he says, may allow exact result for those (within build variations), and reasonably good extrapolations for others.

Another approach might be simply to email Mr Postma and ask if he could also publish the extra measurements he must have made at the time...

No, @jbtsax was not only working with the published data, he was also making an adfitional measurement A. If he makes one more measurement to the inner edge of the tonehole he can calculate what he needs using basic trigonometry as I showed above.

 

[CliveMA]

2) Trigonometry: if you have one known side and one known angle

My answer above uses trigonometry. Tan is the ratio of the opposite side over the adjacent side. It is what makes the two triangles mathematically related without requiring the angle which is harder to measure with accuracy.

 

[h4yn0nnym0u5e]

Marten Postma has complied and posted a great amount of data accumulated over many years concerning saxophones he has taken measurements of. ... [he] has measured the distance from the top of the tonehole to the pad at locations (B) and (d) and then averaged them to find (b). In the data the value of "A" -- the tonehole diameter and "b" the average of the openings are known.
....
My question then: Is there a way mathematically to find the value of "B" with the known values of "A" and "b". Thanks
View attachment 15054

We are all agreed there's insufficient data given to compute B...

No, @jbtsax was not only working with the published data, he was also making an adfitional measurement A. If he makes one more measurement to the inner edge of the tonehole he can calculate what he needs using basic trigonometry as I showed above.

...which he can only do for the two instruments he mentions having to hand, not the full range measured by Marten Postma (link provided in the original post: a total of 44). As you rightly state, one additional measurement from the pivot point to (either) tonehole edge will suffice to do the calculation, either using trigonometry or similar triangles. As highlighted above, A is known from the published data, but as it's the tonehole diameter it doesn't help. It's not totally clear from the diagram what A is measuring, but it is from the text: I note you've taken it to be the distance from the pivot to the outer edge of the tonehole, but it doesn't matter - still not enough data!

I'm not familiar enough with the variations in sax construction to know if cup arms tend to have a length that's related to the corresponding tonehole diameter - it's certainly not the case for the palm keys - but I'm assuming here that @jbtsax would like something better than an estimate, and for more than two instruments, if at all possible.

Cheers

Jonathan

 

[jbtsax]

Another approach might be simply to email Mr Postma and ask if he could also publish the extra measurements he must have made at the time...

I had the opportunity to ask Marten if he kept all of his original measurements in a discussion on SOTW. Unfortunately he said he did not.

 

[h4yn0nnym0u5e]

I had the opportunity to ask Marten if he kept all of his original measurements in a discussion on SOTW. Unfortunately he said he did not.

Pity... guess that's a lesson to us all - never ever discard the raw data!